Calculations of High-Temperature Jet Flow Using Hybrid Reynolds-Average Navier-Stokes Formulations
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.; Elmiligui, Alaa; Giriamaji, Sharath S.
2008-01-01
Two multiscale-type turbulence models are implemented in the PAB3D solver. The models are based on modifying the Reynolds-averaged Navier Stokes equations. The first scheme is a hybrid Reynolds-averaged- Navier Stokes/large-eddy-simulation model using the two-equation k(epsilon) model with a Reynolds-averaged-Navier Stokes/large-eddy-simulation transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier Stokes model in which the unresolved kinetic energy parameter f(sub k) is allowed to vary as a function of grid spacing and the turbulence length scale. This parameter is estimated based on a novel two-stage procedure to efficiently estimate the level of scale resolution possible for a given flow on a given grid for partially averaged Navier Stokes. It has been found that the prescribed scale resolution can play a major role in obtaining accurate flow solutions. The parameter f(sub k) varies between zero and one and is equal to one in the viscous sublayer and when the Reynolds-averaged Navier Stokes turbulent viscosity becomes smaller than the large-eddy-simulation viscosity. The formulation, usage methodology, and validation examples are presented to demonstrate the enhancement of PAB3D's time-accurate turbulence modeling capabilities. The accurate simulations of flow and turbulent quantities will provide a valuable tool for accurate jet noise predictions. Solutions from these models are compared with Reynolds-averaged Navier Stokes results and experimental data for high-temperature jet flows. The current results show promise for the capability of hybrid Reynolds-averaged Navier Stokes and large eddy simulation and partially averaged Navier Stokes in simulating such flow phenomena.
Reynolds-Averaged Navier-Stokes Simulation of a 2D Circulation Control Wind Tunnel Experiment
NASA Technical Reports Server (NTRS)
Allan, Brian G.; Jones, Greg; Lin, John C.
2011-01-01
Numerical simulations are performed using a Reynolds-averaged Navier-Stokes (RANS) flow solver for a circulation control airfoil. 2D and 3D simulation results are compared to a circulation control wind tunnel test conducted at the NASA Langley Basic Aerodynamics Research Tunnel (BART). The RANS simulations are compared to a low blowing case with a jet momentum coefficient, C(sub u), of 0:047 and a higher blowing case of 0.115. Three dimensional simulations of the model and tunnel walls show wall effects on the lift and airfoil surface pressures. These wall effects include a 4% decrease of the midspan sectional lift for the C(sub u) 0.115 blowing condition. Simulations comparing the performance of the Spalart Allmaras (SA) and Shear Stress Transport (SST) turbulence models are also made, showing the SST model compares best to the experimental data. A Rotational/Curvature Correction (RCC) to the turbulence model is also evaluated demonstrating an improvement in the CFD predictions.
NASA Technical Reports Server (NTRS)
Vatsa, Veer N.; Turkel, Eli
2006-01-01
We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for the simulation of a synthetic jet created by a single diaphragm piezoelectric actuator in quiescent air. This configuration was designated as Case 1 for the CFDVAL2004 workshop held at Williamsburg, Virginia, in March 2004. Time-averaged and instantaneous data for this case were obtained at NASA Langley Research Center, using multiple measurement techniques. Computational results for this case using one-equation Spalart-Allmaras and two-equation Menter's turbulence models are presented along with the experimental data. The effect of grid refinement, preconditioning and time-step variation are also examined in this paper.
Reynolds-Averaged Navier-Stokes Analysis of Zero Efflux Flow Control over a Hump Model
NASA Technical Reports Server (NTRS)
Rumsey, Christopher L.
2006-01-01
The unsteady flow over a hump model with zero efflux oscillatory flow control is modeled computationally using the unsteady Reynolds-averaged Navier-Stokes equations. Three different turbulence models produce similar results, and do a reasonably good job predicting the general character of the unsteady surface pressure coefficients during the forced cycle. However, the turbulent shear stresses are underpredicted in magnitude inside the separation bubble, and the computed results predict too large a (mean) separation bubble compared with experiment. These missed predictions are consistent with earlier steady-state results using no-flow-control and steady suction, from a 2004 CFD validation workshop for synthetic jets.
Reynolds-averaged Navier-Stokes based ice accretion for aircraft wings
NASA Astrophysics Data System (ADS)
Lashkajani, Kazem Hasanzadeh
This thesis addresses one of the current issues in flight safety towards increasing icing simulation capabilities for prediction of complex 2D and 3D glaze ice shapes over aircraft surfaces. During the 1980's and 1990's, the field of aero-icing was established to support design and certification of aircraft flying in icing conditions. The multidisciplinary technologies used in such codes were: aerodynamics (panel method), droplet trajectory calculations (Lagrangian framework), thermodynamic module (Messinger model) and geometry module (ice accretion). These are embedded in a quasi-steady module to simulate the time-dependent ice accretion process (multi-step procedure). The objectives of the present research are to upgrade the aerodynamic module from Laplace to Reynolds-Average Navier-Stokes equations solver. The advantages are many. First, the physical model allows accounting for viscous effects in the aerodynamic module. Second, the solution of the aero-icing module directly provides the means for characterizing the aerodynamic effects of icing, such as loss of lift and increased drag. Third, the use of a finite volume approach to solving the Partial Differential Equations allows rigorous mesh and time convergence analysis. Finally, the approaches developed in 2D can be easily transposed to 3D problems. The research was performed in three major steps, each providing insights into the overall numerical approaches. The most important realization comes from the need to develop specific mesh generation algorithms to ensure feasible solutions in very complex multi-step aero-icing calculations. The contributions are presented in chronological order of their realization. First, a new framework for RANS based two-dimensional ice accretion code, CANICE2D-NS, is developed. A multi-block RANS code from U. of Liverpool (named PMB) is providing the aerodynamic field using the Spalart-Allmaras turbulence model. The ICEM-CFD commercial tool is used for the iced airfoil
A three dimensional multigrid Reynolds-averaged Navier-Stokes solver for unstructured meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1994-01-01
A three-dimensional unstructured mesh Reynolds averaged Navier-Stokes solver is described. Turbulence is simulated using a single field-equation model. Computational overheads are minimized through the use of a single edge-based data-structure, and efficient multigrid solution technique, and the use of multi-tasking on shared memory multi-processors. The accuracy and efficiency of the code are evaluated by computing two-dimensional flows in three dimensions and comparing with results from a previously validated two-dimensional code which employs the same solution algorithm. The feasibility of computing three-dimensional flows on grids of several million points in less than two hours of wall clock time is demonstrated.
NASA Technical Reports Server (NTRS)
Vatsa, Veer N.; Turkel, Eli L.
2004-01-01
We report research experience in applying an Unsteady Reynolds-Averaged Navier-Stokes (URANS) solver for the prediction of time-dependent flows in the presence of an active flow control device. The configuration under consideration is a synthetic jet created by a single diaphragm piezoelectric actuator in quiescent air. Time-averaged and instantaneous data for this case were obtained at Langley Research Center, using multiple measurement techniques. Computational results for this case using one-equation Spalart-Allmaras and two-equation Menter s turbulence models are presented here along with comparisons with the experimental data. The effect of grid refinement, preconditioning and time-step variation are also examined.
NASA Technical Reports Server (NTRS)
Bui, Trong T.
1993-01-01
New turbulence modeling options recently implemented for the 3D version of Proteus, a Reynolds-averaged compressible Navier-Stokes code, are described. The implemented turbulence models include: the Baldwin-Lomax algebraic model, the Baldwin-Barth one-equation model, the Chien k-epsilon model, and the Launder-Sharma k-epsilon model. Features of this turbulence modeling package include: well documented and easy to use turbulence modeling options, uniform integration of turbulence models from different classes, automatic initialization of turbulence variables for calculations using one- or two-equation turbulence models, multiple solid boundaries treatment, and fully vectorized L-U solver for one- and two-equation models. Good agreements are obtained between the computational results and experimental data. Sensitivity of the compressible turbulent solutions with the method of y(+) computation, the turbulent length scale correction, and some compressibility corrections are examined in detail. Test cases show that the highly optimized one- and two-equation turbulence models can be used in routine 3D Navier-Stokes computations with no significant increase in CPU time as compared with the Baldwin-Lomax algebraic model.
NASA Technical Reports Server (NTRS)
Bui, Trong T.
1993-01-01
New turbulence modeling options recently implemented for the 3-D version of Proteus, a Reynolds-averaged compressible Navier-Stokes code, are described. The implemented turbulence models include: the Baldwin-Lomax algebraic model, the Baldwin-Barth one-equation model, the Chien k-epsilon model, and the Launder-Sharma k-epsilon model. Features of this turbulence modeling package include: well documented and easy to use turbulence modeling options, uniform integration of turbulence models from different classes, automatic initialization of turbulence variables for calculations using one- or two-equation turbulence models, multiple solid boundaries treatment, and fully vectorized L-U solver for one- and two-equation models. Validation test cases include the incompressible and compressible flat plate turbulent boundary layers, turbulent developing S-duct flow, and glancing shock wave/turbulent boundary layer interaction. Good agreement is obtained between the computational results and experimental data. Sensitivity of the compressible turbulent solutions with the method of y(sup +) computation, the turbulent length scale correction, and some compressibility corrections are examined in detail. The test cases show that the highly optimized one-and two-equation turbulence models can be used in routine 3-D Navier-Stokes computations with no significant increase in CPU time as compared with the Baldwin-Lomax algebraic model.
Reynolds-Averaged Navier-Stokes Solutions to Flat Plate Film Cooling Scenarios
NASA Technical Reports Server (NTRS)
Johnson, Perry L.; Shyam, Vikram; Hah, Chunill
2011-01-01
The predictions of several Reynolds-Averaged Navier-Stokes solutions for a baseline film cooling geometry are analyzed and compared with experimental data. The Fluent finite volume code was used to perform the computations with the realizable k-epsilon turbulence model. The film hole was angled at 35 to the crossflow with a Reynolds number of 17,400. Multiple length-to-diameter ratios (1.75 and 3.5) as well as momentum flux ratios (0.125 and 0.5) were simulated with various domains, boundary conditions, and grid refinements. The coolant to mainstream density ratio was maintained at 2.0 for all scenarios. Computational domain and boundary condition variations show the ability to reduce the computational cost as compared to previous studies. A number of grid refinement and coarsening variations are compared for further insights into the reduction of computational cost. Liberal refinement in the near hole region is valuable, especially for higher momentum jets that tend to lift-off and create a recirculating flow. A lack of proper refinement in the near hole region can severely diminish the accuracy of the solution, even in the far region. The effects of momentum ratio and hole length-to-diameter ratio are also discussed.
Towards Exploratory Aerodynamic Design using the Reynolds-Averaged Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Koo, David Tai Shun
The aerodynamic optimization framework Jetstream is applied to problems involving lift-constrained drag minimization using the Reynolds-averaged Navier-Stokes equations. A parallel Newton-Krylov algorithm is used to solve the governing equations on multiblock structured meshes; gradients are computed using the discrete-adjoint method. Geometry parameterization and mesh movement are integrated using B-spline control volumes. Drag minimization studies from past works are revisited and strategies are devised to improve optimization convergence. These strategies include linear constraints for geometric feasibility, robust flow solver parameters, and meshing with an O-O topology. The single-point and multi-point optimization of the NASA Common Research Model (CRM) wing geometry is presented. A rectangular NACA0012 wing is optimized with planform design variables, enabling significant changes in span, sweep, taper, and airfoil section. To demonstrate Jetstream's flexibility, a wing based on the B737-900 is optimized with nonplanar winglets, split-tip, and wingtip fence configurations. Finally, the box-wing optimization in subsonic flow is revisited.
Ling, Julia; Templeton, Jeremy Alan
2015-08-04
Reynolds Averaged Navier Stokes (RANS) models are widely used in industry to predict fluid flows, despite their acknowledged deficiencies. Not only do RANS models often produce inaccurate flow predictions, but there are very limited diagnostics available to assess RANS accuracy for a given flow configuration. If experimental or higher fidelity simulation results are not available for RANS validation, there is no reliable method to evaluate RANS accuracy. This paper explores the potential of utilizing machine learning algorithms to identify regions of high RANS uncertainty. Three different machine learning algorithms were evaluated: support vector machines, Adaboost decision trees, and random forests.more » The algorithms were trained on a database of canonical flow configurations for which validated direct numerical simulation or large eddy simulation results were available, and were used to classify RANS results on a point-by-point basis as having either high or low uncertainty, based on the breakdown of specific RANS modeling assumptions. Classifiers were developed for three different basic RANS eddy viscosity model assumptions: the isotropy of the eddy viscosity, the linearity of the Boussinesq hypothesis, and the non-negativity of the eddy viscosity. It is shown that these classifiers are able to generalize to flows substantially different from those on which they were trained. As a result, feature selection techniques, model evaluation, and extrapolation detection are discussed in the context of turbulence modeling applications.« less
Ling, Julia; Templeton, Jeremy Alan
2015-08-04
Reynolds Averaged Navier Stokes (RANS) models are widely used in industry to predict fluid flows, despite their acknowledged deficiencies. Not only do RANS models often produce inaccurate flow predictions, but there are very limited diagnostics available to assess RANS accuracy for a given flow configuration. If experimental or higher fidelity simulation results are not available for RANS validation, there is no reliable method to evaluate RANS accuracy. This paper explores the potential of utilizing machine learning algorithms to identify regions of high RANS uncertainty. Three different machine learning algorithms were evaluated: support vector machines, Adaboost decision trees, and random forests. The algorithms were trained on a database of canonical flow configurations for which validated direct numerical simulation or large eddy simulation results were available, and were used to classify RANS results on a point-by-point basis as having either high or low uncertainty, based on the breakdown of specific RANS modeling assumptions. Classifiers were developed for three different basic RANS eddy viscosity model assumptions: the isotropy of the eddy viscosity, the linearity of the Boussinesq hypothesis, and the non-negativity of the eddy viscosity. It is shown that these classifiers are able to generalize to flows substantially different from those on which they were trained. As a result, feature selection techniques, model evaluation, and extrapolation detection are discussed in the context of turbulence modeling applications.
A Parallel Newton-Krylov-Schur Algorithm for the Reynolds-Averaged Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Osusky, Michal
be readily extended to high order, in combination with the Newton-Krylov-Schur iterative method to produce a powerful parallel algorithm for the numerical solution of the Reynolds-averaged Navier-Stokes equations. The algorithm can efficiently solve the flow over a range of clean geometries, making it suitable for use at the core of an optimization algorithm.
Large Eddy/Reynolds-Averaged Navier-Stokes Simulations of CUBRC Base Heating Experiments
NASA Technical Reports Server (NTRS)
Salazar, Giovanni; Edwards, Jack R.; Amar, Adam J.
2012-01-01
ven with great advances in computational techniques and computing power during recent decades, the modeling of unsteady separated flows, such as those encountered in the wake of a re-entry vehicle, continues to be one of the most challenging problems in CFD. Of most interest to the aerothermodynamics community is accurately predicting transient heating loads on the base of a blunt body, which would result in reduced uncertainties and safety margins when designing a re-entry vehicle. However, the prediction of heat transfer can vary widely depending on the turbulence model employed. Therefore, selecting a turbulence model which realistically captures as much of the flow physics as possible will result in improved results. Reynolds Averaged Navier Stokes (RANS) models have become increasingly popular due to their good performance with attached flows, and the relatively quick turnaround time to obtain results. However, RANS methods cannot accurately simulate unsteady separated wake flows, and running direct numerical simulation (DNS) on such complex flows is currently too computationally expensive. Large Eddy Simulation (LES) techniques allow for the computation of the large eddies, which contain most of the Reynolds stress, while modeling the smaller (subgrid) eddies. This results in models which are more computationally expensive than RANS methods, but not as prohibitive as DNS. By complimenting an LES approach with a RANS model, a hybrid LES/RANS method resolves the larger turbulent scales away from surfaces with LES, and switches to a RANS model inside boundary layers. As pointed out by Bertin et al., this type of hybrid approach has shown a lot of promise for predicting turbulent flows, but work is needed to verify that these models work well in hypersonic flows. The very limited amounts of flight and experimental data available presents an additional challenge for researchers. Recently, a joint study by NASA and CUBRC has focused on collecting heat transfer data
NASA Technical Reports Server (NTRS)
Mehta, Unmeel; Lomax, Harvard
1981-01-01
During the past five years, numerous pioneering archival publications have appeared that have presented computer solutions of the mass-weighted, time-averaged Navier-Stokes equations for transonic problems pertinent to the aircraft industry. These solutions have been pathfinders of developments that could evolve into a major new technological capability, namely the computational Navier-Stokes technology, for the aircraft industry. So far these simulations have demonstrated that computational techniques, and computer capabilities have advanced to the point where it is possible to solve forms of the Navier-Stokes equations for transonic research problems. At present there are two major shortcomings of the technology: limited computer speed and memory, and difficulties in turbulence modelling and in computation of complex three-dimensional geometries. These limitations and difficulties are the pacing items of the continuing developments, although the one item that will most likely turn out to be the most crucial to the progress of this technology is turbulence modelling. The objective of this presentation is to discuss the state of the art of this technology and suggest possible future areas of research. We now discuss some of the flow conditions for which the Navier-Stokes equations appear to be required. On an airfoil there are four different types of interaction of a shock wave with a boundary layer: (1) shock-boundary-layer interaction with no separation, (2) shock-induced turbulent separation with immediate reattachment (we refer to this as a shock-induced separation bubble), (3) shock-induced turbulent separation without reattachment, and (4) shock-induced separation bubble with trailing edge separation.
NASA Technical Reports Server (NTRS)
Cappelli, Daniele; Mansour, Nagi N.
2012-01-01
Separation can be seen in most aerodynamic flows, but accurate prediction of separated flows is still a challenging problem for computational fluid dynamics (CFD) tools. The behavior of several Reynolds Averaged Navier-Stokes (RANS) models in predicting the separated ow over a wall-mounted hump is studied. The strengths and weaknesses of the most popular RANS models (Spalart-Allmaras, k-epsilon, k-omega, k-omega-SST) are evaluated using the open source software OpenFOAM. The hump ow modeled in this work has been documented in the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control. Only the baseline case is treated; the slot flow control cases are not considered in this paper. Particular attention is given to predicting the size of the recirculation bubble, the position of the reattachment point, and the velocity profiles downstream of the hump.
Large-Eddy / Reynolds-Averaged Navier-Stokes Simulations of a Dual-Mode Scramjet Combustor
NASA Technical Reports Server (NTRS)
Fulton, Jesse A.; Edwards, Jack R.; Hassan, Hassan A.; Rockwell, Robert; Goyne, Christopher; McDaniel, James; Smith, Chad; Cutler, Andrew; Johansen, Craig; Danehy, Paul M.; Kouchi, Toshinori
2012-01-01
Numerical simulations of reacting and non-reacting flows within a scramjet combustor configuration experimentally mapped at the University of Virginia s Scramjet Combustion Facility (operating with Configuration A ) are described in this paper. Reynolds-Averaged Navier-Stokes (RANS) and hybrid Large Eddy Simulation / Reynolds-Averaged Navier-Stokes (LES / RANS) methods are utilized, with the intent of comparing essentially blind predictions with results from non-intrusive flow-field measurement methods including coherent anti-Stokes Raman spectroscopy (CARS), hydroxyl radical planar laser-induced fluorescence (OH-PLIF), stereoscopic particle image velocimetry (SPIV), wavelength modulation spectroscopy (WMS), and focusing Schlieren. NC State's REACTMB solver was used both for RANS and LES / RANS, along with a 9-species, 19- reaction H2-air kinetics mechanism by Jachimowski. Inviscid fluxes were evaluated using Edwards LDFSS flux-splitting scheme, and the Menter BSL turbulence model was utilized in both full-domain RANS simulations and as the unsteady RANS portion of the LES / RANS closure. Simulations were executed and compared with experiment at two equivalence ratios, PHI = 0.17 and PHI = 0.34. Results show that the PHI = 0.17 flame is hotter near the injector while the PHI = 0.34 flame is displaced further downstream in the combustor, though it is still anchored to the injector. Reactant mixing was predicted to be much better at the lower equivalence ratio. The LES / RANS model appears to predict lower overall heat release compared to RANS (at least for PHI = 0.17), and its capability to capture the direct effects of larger turbulent eddies leads to much better predictions of reactant mixing and combustion in the flame stabilization region downstream of the fuel injector. Numerical results from the LES/RANS model also show very good agreement with OH-PLIF and SPIV measurements. An un-damped long-wave oscillation of the pre-combustion shock train, which caused
F-16XL Hybrid Reynolds-Averaged Navier-Stokes/Large Eddy Simulation on Unstructured Grids
NASA Technical Reports Server (NTRS)
Park, Michael A.; Abdol-Hamid, Khaled S.; Elmiligui, Alaa
2015-01-01
This study continues the Cranked Arrow Wing Aerodynamics Program, International (CAWAPI) investigation with the FUN3D and USM3D flow solvers. CAWAPI was established to study the F-16XL, because it provides a unique opportunity to fuse fight test, wind tunnel test, and simulation to understand the aerodynamic features of swept wings. The high-lift performance of the cranked-arrow wing planform is critical for recent and past supersonic transport design concepts. Simulations of the low speed high angle of attack Flight Condition 25 are compared: Detached Eddy Simulation (DES), Modi ed Delayed Detached Eddy Simulation (MDDES), and the Spalart-Allmaras (SA) RANS model. Iso- surfaces of Q criterion show the development of coherent primary and secondary vortices on the upper surface of the wing that spiral, burst, and commingle. SA produces higher pressure peaks nearer to the leading-edge of the wing than flight test measurements. Mean DES and MDDES pressures better predict the flight test measurements, especially on the outer wing section. Vorticies and vortex-vortex interaction impact unsteady surface pressures. USM3D showed many sharp tones in volume points spectra near the wing apex with low broadband noise and FUN3D showed more broadband noise with weaker tones. Spectra of the volume points near the outer wing leading-edge was primarily broadband for both codes. Without unsteady flight measurements, the flight pressure environment can not be used to validate the simulations containing tonal or broadband spectra. Mean forces and moment are very similar between FUN3D models and between USM3D models. Spectra of the unsteady forces and moment are broadband with a few sharp peaks for USM3D.
NASA Technical Reports Server (NTRS)
Rumsey, Christopher L.; Greenblatt, David
2007-01-01
This is an expanded version of a limited-length paper that appeared at the 5th International Symposium on Turbulence and Shear Flow Phenomena by the same authors. A computational study was performed for steady and oscillatory flow control over a hump model with flow separation to assess how well the steady and unsteady Reynolds-averaged Navier-Stokes equations predict trends due to Reynolds number, control magnitude, and control frequency. As demonstrated in earlier studies, the hump model case is useful because it clearly demonstrates a failing in all known turbulence models: they under-predict the turbulent shear stress in the separated region and consequently reattachment occurs too far downstream. In spite of this known failing, three different turbulence models were employed to determine if trends can be captured even though absolute levels are not. Overall the three turbulence models showed very similar trends as experiment for steady suction, but only agreed qualitatively with some of the trends for oscillatory control.
NASA Astrophysics Data System (ADS)
Boles, John A.
Hybrid Large Eddy Simulation/Reynolds-Averaged Navier-Stokes (LES/RANS) simulations of several high-speed flows are presented in this work. The solver blends a Menter BSL two-equation model for the RANS part of the closure with a Smagorisnky sub-grid model for the LES component. The solver uses a flow-dependent blending function based on wall distance and a modeled form of the Taylor micro-scale to transition from RANS to LES. Turbulent fluctuations are initiated and are sustained in the inflow region using a recycling/rescaling technique. A new multi-wall recycling/rescaling technique is described and tested. A spanwise-shifting method is introduced that is intended to alleviate unphysical streamwise streaks of high- and low-momentum fluid that appear in the time-averaged solution due to the recycling procedure. Simulations of sonic injection of air, helium and ethylene into a Mach 2 crossflow of air are performed. Also, simulations of Mach 5 flow in a subscale inlet/isolator configuration with and without back-pressuring are performed. Finally, a Mach 3.9 flow through a square duct is used as an initial test case for the new multi-wall recycling and rescaling method as well as a multi-wall shifting procedure. A discussion of the methods, implementation and results of these simulations is included.
NASA Astrophysics Data System (ADS)
Rhee, Bong
The accurate and efficient prediction of hydrodynamic forces and moments on a maneuvering submarine has been achieved by investigating the flow physics involving the interaction of the vortical flow shed from the sail and the cross-flow boundary layer of the hull. In this investigation, a Reynolds-Averaged Navier-Stokes (RANS) computer code is used to simulate the most important physical effects related to maneuvering. It is applied to a generic axisymmetric body with the relatively simple case of the flow around an unappended hull at an angle of attack. After the code is validated for this simple case, it is validated for the case of a submarine with various appendages attached to the hull moving at an angle of drift. All six components of predicted forces and moments for various drift angles are compared with experimental data. Calculated pressure coefficients along the azimuthal angle are compared with experimental data and discussed to show the effect of the sail and the stern appendages. To understand the main flow features for a submarine in a straight flight, the RANS code is applied to simulate SUBOFF axisymmetric body at zero angle of attack in a straight-line basin. Pressure coefficient, skin friction coefficient, mean velocity components and the Reynolds shear stresses are compared with experimental data and discussed. The physical aspects of the interaction between the vortical flow shed by the sail and the cross-flow boundary layer on the hull are explained in greater detail. The understanding of this interaction is very important to characterize accurately the hydrodynamic behavior of a maneuvering submarine.
NASA Astrophysics Data System (ADS)
Schoenawa, Stefan; Hartmann, Ralf
2014-04-01
In this article we consider the development of Discontinuous Galerkin (DG) methods for the numerical approximation of the Reynolds-averaged Navier-Stokes (RANS) equations with the shear-stress transport (SST) model by Menter. This turbulence model is based on a blending of the Wilcox k-ω model used near the wall and the k-ɛ model used in the rest of the domain where the blending functions depend on the distance to the nearest wall. For the computation of the distance of each quadrature point in the domain to the nearest of the curved, piecewise polynomial wall boundaries, we propose a stabilized continuous finite element (FE) discretization of the eikonal equation. Furthermore, we propose a new wall boundary condition for the dissipation rate ω based on the projection of the analytic near-wall behavior of ω onto the discrete ansatz space of the DG discretization. Finally, we introduce an artificial viscosity to the discretization of the turbulence kinetic energy (k-)equation to suppress oscillations of k near the underresolved boundary layer edge. The wall distance computation based on the continuous FE discretization of the eikonal equation is demonstrated for an internal and three external/aerodynamic flow geometries including a three-element high-lift configuration. The DG discretization of the RANS equations with the SST model is demonstrated for turbulent flows past a flat plate and the RAE2822 airfoil (Cases 9 and 10). The results are compared to the underlying k-ω model and experimental data.
NASA Astrophysics Data System (ADS)
Hillewaere, J.; Dooms, D.; Van Quekelberghe, B.; Degroote, J.; Vierendeels, J.; De Roeck, G.; Lombaert, G.; Degrande, G.
2012-04-01
During a storm in October 2002, wind induced ovalling vibrations were observed on several empty silos of a closely spaced group (pitch-to-diameter ratio of 1.05) consisting of 8 by 5 silos in the port of Antwerp (Belgium). Numerical simulations of the turbulent wind flow are performed to clarify the occurrence of the observed ovalling vibrations near the lee side corner of the group by studying the dynamic wind pressures on the silo surfaces and linking to the dynamic properties of the silo structures. As the orientation of the group largely affects the pressure distribution around the cylinders of the group, the influence of the angle of incidence of the wind flow on these ovalling vibrations is examined while other parameters, such as spacing ratio and Reynolds number are unchanged. To achieve results within a reasonable computation time, 2D unsteady Reynolds averaged Navier-Stokes (URANS) equations using Menter's shear stress transport turbulence model were performed. In order to elucidate the influence of the applied turbulence model and to qualitatively validate the spatial and temporal discretization of the 2D highly turbulent post-critical (Re=1.24×107) flow simulations for the silo group, single cylinder simulations were used. The geometric resemblance of the group arrangement with rectangular cylinders on the one hand and of the interstitial spaces with tube arrays (e.g. heat exchangers) on the other hand is used to qualitatively compare the observed flow phenomena. The simulations show that the silo group can be treated neither as a tube array nor as a solid bluff body. Subsequent linking of dynamic wind pressures to dynamic properties of the silo structures reveals strong narrow band frequency peaks in the turbulent pressure coefficient spectra of the silos near the lee side corners of the group that match the structural natural frequencies of the third and fourth ovalling mode shape of the silos. This match indicates a forced, resonant response which
NASA Astrophysics Data System (ADS)
Gorlé, C.; Iaccarino, G.
2013-05-01
Reynolds-averaged Navier-Stokes (RANS) simulations are a practical approach for solving complex multi-physics turbulent flows, but the underlying assumptions of the turbulence models introduce errors and uncertainties in the simulation outcome. The flow in scramjet combustors is an example of such a complex flow and the accurate characterization of safety and operability limits of these engines using RANS simulations requires an assessment of the model uncertainty. The objective of this paper is to present a framework for the epistemic uncertainty quantification of turbulence and mixing models in RANS simulations. The capabilities of the methodology will be demonstrated by performing simulations of the mixing of an underexpanded jet in a supersonic cross flow, which involves many flow features observed in scramjet engines. The fundamental sources of uncertainty in the RANS simulations are the models used for the Reynolds stresses in the momentum equations and the turbulent scalar fluxes in the scalar transport equations. The methodology consists in directly perturbing the modeled quantities in the equations, thereby establishing a method that is completely independent of the initial model form to overcome the limitations of traditional sensitivity studies. The perturbations are defined in terms of the decomposed Reynolds stress tensor, i.e., the tensor magnitude and the eigenvalues and eigenvectors of the normalized anisotropy tensor. The turbulent scalar fluxes are perturbed by using the perturbed Reynolds stresses in a generalized gradient diffusion model formulation and by changing the model constant. The perturbations were parameterized based on a comparison between the Reynolds stresses obtained from a baseline RANS simulation and those obtained from a large-eddy simulation database. Subsequently an optimization problem was solved, varying the parameters in the perturbation functions to maximize a quantity of interest that quantifies the downstream mixing. The
3-D adaptive grid Navier-Stokes rocket plume calculations
NASA Astrophysics Data System (ADS)
Holcomb, J. Eric
1991-01-01
Three-dimensional adaptive-grid full Navier-Stokes calculations performed for the base region and plume of the Minuteman first stage and a simplified version of the Titan first stage are used to demonstrate the applicability of the Navier-Stokes flow solver, EAGLE adaptive grid generator, and k-epsilon turbulence model to rocket plume flowfields. The calculations include realistic exhaust gas thermodynamic properties, with frozen chemistry.
An exact solution of the 3-D Navier-Stokes equation
NASA Astrophysics Data System (ADS)
Muriel, A.
2011-01-01
We continue our work (A. Muriel and M. Dresden, Physica D 101, 299, 1997) to calculate the time evolution of the one-particle distribution function. An improved operator formalism, heretofore unused, is applied for spatially uniform initial data. We then choose a Gaussian pair potential between particles. With these two conditions, the velocity fields, energy and pressure are calculated exactly. All stipulations of the Clay Mathematics Institute for proposed solutions of the 3-D Navier-Stokes Equation [ http://www.claymath.org/millennium/Navier-Stokes_Equations/navierstokes.pdf] are satisfied by our time evolution equation. We then substitute our results for the velocity fields into the 3-D Navier-Stokes Equation and calculate the pressure. The results from our time evolution equation and the prescribed pressure from the Navier-Stokes Equation constitute an exact solution to the Navier-Stokes Equation. No turbulence is obtained from the solution.
Implementation of algebraic stress models in a general 3-D Navier-Stokes method (PAB3D)
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.
1995-01-01
A three-dimensional multiblock Navier-Stokes code, PAB3D, which was developed for propulsion integration and general aerodynamic analysis, has been used extensively by NASA Langley and other organizations to perform both internal (exhaust) and external flow analysis of complex aircraft configurations. This code was designed to solve the simplified Reynolds Averaged Navier-Stokes equations. A two-equation k-epsilon turbulence model has been used with considerable success, especially for attached flows. Accurate predicting of transonic shock wave location and pressure recovery in separated flow regions has been more difficult. Two algebraic Reynolds stress models (ASM) have been recently implemented in the code that greatly improved the code's ability to predict these difficult flow conditions. Good agreement with Direct Numerical Simulation (DNS) for a subsonic flat plate was achieved with ASM's developed by Shih, Zhu, and Lumley and Gatski and Speziale. Good predictions were also achieved at subsonic and transonic Mach numbers for shock location and trailing edge boattail pressure recovery on a single-engine afterbody/nozzle model.
Mihaescu, Mihai; Murugappan, Shanmugam; Kalra, Maninder; Khosla, Sid; Gutmark, Ephraim
2008-07-19
Computational fluid dynamics techniques employing primarily steady Reynolds-Averaged Navier-Stokes (RANS) methodology have been recently used to characterize the transitional/turbulent flow field in human airways. The use of RANS implies that flow phenomena are averaged over time, the flow dynamics not being captured. Further, RANS uses two-equation turbulence models that are not adequate for predicting anisotropic flows, flows with high streamline curvature, or flows where separation occurs. A more accurate approach for such flow situations that occur in the human airway is Large Eddy Simulation (LES). The paper considers flow modeling in a pharyngeal airway model reconstructed from cross-sectional magnetic resonance scans of a patient with obstructive sleep apnea. The airway model is characterized by a maximum narrowing at the site of retropalatal pharynx. Two flow-modeling strategies are employed: steady RANS and the LES approach. In the RANS modeling framework both k-epsilon and k-omega turbulence models are used. The paper discusses the differences between the airflow characteristics obtained from the RANS and LES calculations. The largest discrepancies were found in the axial velocity distributions downstream of the minimum cross-sectional area. This region is characterized by flow separation and large radial velocity gradients across the developed shear layers. The largest difference in static pressure distributions on the airway walls was found between the LES and the k-epsilon data at the site of maximum narrowing in the retropalatal pharynx.
NASA Astrophysics Data System (ADS)
Schilling, Oleg
2014-11-01
Recent progress on the development and validation of a new K- ɛ multicomponent Reynolds-averaged Navier-Stokes model is discussed. The model includes mixture molecular dissipation and diffusion terms, molecular and turbulent enthalpy diffusion terms, and models for pressure-dilatation and dilatation dissipation. The model has successfully been applied to a set of ten reshocked Richtmyer-Meshkov mixing experiments, and more recently to experiments with larger Mach numbers and various Atwood numbers. An extension of the model to include a modeled density variance transport equation is described. The three-equation model is applied to various Rayleigh-Taylor mixing cases with complex accelerations. The evolution of various turbulence statistics, fields, and turbulent transport equation budgets are compared among these cases to elucidate differences in the turbulence production, dissipation and diffusion mechanisms. It is also shown that the mechanical turbulence timescale is poorly correlated with the molecular mixing timescale determined by the time-evolution of the molecular mixing parameter. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
NASA Astrophysics Data System (ADS)
Xiao, Heng; Wu, Jinlong; Wang, Jianxun; Sun, Rui; Roy, Christopher J.
2015-11-01
For many practical flows, the turbulence models are the most important source of uncertainty in Reynolds-Averaged Navier-Stokes (RANS) predictions. In this work, we develop an open-box, physics-informed Bayesian framework for quantifying the model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to incorporate the prior information with available observation data in a Bayesian framework to posterior distributions of the Reynolds stresses and other quantities of interest. Two representative cases, the flow over periodic hills and the flow in a square duct, are used to evaluate the performance of the proposed framework. Simulation results suggest that the obtained posterior mean has significantly better agreement with the benchmark data compared to the baseline simulation, even with very sparse observations. At most locations, the posterior distribution adequately represents the model-form uncertainties.
NASA Astrophysics Data System (ADS)
Schilling, Oleg
2016-11-01
Two-, three- and four-equation, single-velocity, multicomponent Reynolds-averaged Navier-Stokes (RANS) models, based on the turbulent kinetic energy dissipation rate or lengthscale, are used to simulate At = 0 . 5 Rayleigh-Taylor turbulent mixing with constant and complex accelerations. The constant acceleration case is inspired by the Cabot and Cook (2006) DNS, and the complex acceleration cases are inspired by the unstable/stable and unstable/neutral cases simulated using DNS (Livescu, Wei & Petersen 2011) and the unstable/stable/unstable case simulated using ILES (Ramaprabhu, Karkhanis & Lawrie 2013). The four-equation models couple equations for the mass flux a and negative density-specific volume correlation b to the K- ɛ or K- L equations, while the three-equation models use a two-fluid algebraic closure for b. The lengthscale-based models are also applied with no buoyancy production in the L equation to explore the consequences of neglecting this term. Predicted mixing widths, turbulence statistics, fields, and turbulent transport equation budgets are compared among these models to identify similarities and differences in the turbulence production, dissipation and diffusion physics represented by the closures used in these models. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
NASA Astrophysics Data System (ADS)
Schilling, Oleg; Finn, Thomas
2013-11-01
A multicomponent, four-equation Reynolds-averaged Navier-Stokes model based on the K- ɛ model and coupled to density variance and density variance dissipation rate equations is used to simulate Rayleigh-Taylor turbulent mixing experiments previously performed in a gas channel facility at Texas A&M University at Atwood numbers 0 . 04 and 0 . 6 [A. Banerjee et al., J. Fluid Mech. 659, 127 (2010)]. The model was previously used to simulate a large set of Richtmyer-Meshkov instability experiments, and is implemented in a weighted essentially nonoscillatory code. Model predictions of the Rayleigh-Taylor mixing layer width growth, volume fraction, mixing layer parameters, molecular mixing parameter, density-velocity correlation, and turbulent kinetic energy are compared to experimental data. The sensitivity of the predicted quantities to variations in the principal model coefficients and initial conditions is discussed. This work was performed under the auspices of the U.S. Department of Energy by LLNL under Contract DE-AC52-07NA27344, and by Texas A&M University under the Department of Energy National Nuclear Security Administration research grant DE-FG52-09NA29462.
NASA Astrophysics Data System (ADS)
Moran-Lopez, Tiberius; Schilling, Oleg
2014-11-01
Reshocked Richtmyer-Meshkov turbulent mixing for various gas pairs and large shock Mach numbers is simulated using a third-order weighted essentially nonoscillatory (WENO) implementation of a new K- ɛ multicomponent Reynolds-averaged Navier-Stokes model. Experiments previously performed at the University of Provence with gas pairs CO2 /He, CO2 /Ar, and CO2 /Kr (with At = - 0 . 73 , - 0 . 05 , and 0 . 3 , respectively) and incident shock Mach numbers Ma = 2 . 4 , 3 . 1 , 3 . 7 , 4 . 2 , and 4 . 5 are considered. The evolution of the mixing layer widths is shown to be in good agreement with the experimental data. Budgets of the turbulent transport equations are used to elucidate the mechanisms contributing to turbulent mixing in large Mach number reshocked Richtmyer-Meshkov instability. These results are contrasted with those from previous modeling of smaller Mach number experiments to identify the physical effects which require accurate modeling, including mean and turbulent enthalpy diffusion, pressure-dilatation, and dilatation dissipation. This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Navier-Stokes Neutral and Plasma Fluid Modelling in 3D
Riemann, J; Borchardt, M; Schneider, R; Mutzke, A; Rognlien, T; Umansky, M
2004-05-17
The 3D finite volume transport code BoRiS is applied to a system of coupled plasma and neutral fluid equations in a slab. Demonstrating easy implementation of new equations, a new parallel BoRiS version is tested on three different models for the neutral fluid - diffusive, parallel Navier-Stokes and full Navier-Stokes - and the results are compared to each other. Typical effects like density enhancement by ionization of recycled neutrals in front of a target plate can be seen and differences are linked to the neutral models in use.
Turbomachinery Heat Transfer and Loss Modeling for 3D Navier-Stokes Codes
NASA Technical Reports Server (NTRS)
DeWitt, Kenneth; Ameri, Ali
2005-01-01
This report's contents focus on making use of NASA Glenn on-site computational facilities,to develop, validate, and apply models for use in advanced 3D Navier-Stokes Computational Fluid Dynamics (CFD) codes to enhance the capability to compute heat transfer and losses in turbomachiney.
On the Dynamic Programming Approach for the 3D Navier-Stokes Equations
Manca, Luigi
2008-06-15
The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed.
NASA Astrophysics Data System (ADS)
Spotts, Nathan
As modern trends in commercial aircraft design move toward high-bypass-ratio fan systems of increasing diameter with shorter, nonaxisymmetric nacelle geometries, inlet distortion is becoming common in all operating regimes. The distortion may induce aerodynamic instabilities within the fan system, leading to catastrophic damage to fan blades, should the surge margin be exceeded. Even in the absence of system instability, the heterogeneity of the flow affects aerodynamic performance significantly. Therefore, an understanding of fan-distortion interaction is critical to aircraft engine system design. This thesis research elucidates the complex fluid dynamics and fan-distortion interaction by means of computational fluid dynamics (CFD) modeling of a complete engine fan system; including rotor, stator, spinner, nacelle and nozzle; under conditions typical of those encountered by commercial aircraft. The CFD simulations, based on a Reynolds-averaged Navier-Stokes (RANS) approach, were unsteady, three-dimensional, and of a full-annulus geometry. A thorough, systematic validation has been performed for configurations from a single passage of a rotor to a full-annulus system by comparing the predicted flow characteristics and aerodynamic performance to those found in literature. The original contributions of this research include the integration of a complete engine fan system, based on the NASA rotor 67 transonic stage and representative of the propulsion systems in commercial aircraft, and a benchmark case for unsteady RANS simulations of distorted flow in such a geometry under realistic operating conditions. This study is unique in that the complex flow dynamics, resulting from fan-distortion interaction, were illustrated in a practical geometry under realistic operating conditions. For example, the compressive stage is shown to influence upstream static pressure distributions and thus suppress separation of flow on the nacelle. Knowledge of such flow physics is
NASA Astrophysics Data System (ADS)
Xiao, H.; Wu, J.-L.; Wang, J.-X.; Sun, R.; Roy, C. J.
2016-11-01
Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has
NASA Astrophysics Data System (ADS)
Chaouat, Bruno; Schiestel, Roland
2012-08-01
The basis of the partially integrated transport modeling (PITM) method was introduced by Schiestel and Dejoan ["Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations," Theor. Comput. Fluid Dyn. 18, 443 (2005)], 10.1007/s00162-004-0155-z and Chaouat and Schiestel ["A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows," Phys. Fluids 17, 065106 (2005)], 10.1063/1.1928607. This method provides a continuous approach for hybrid RANS-LES (Reynolds averaged Navier-Stokes equations-large eddy simulations) simulations with seamless coupling between RANS and LES regions. The main ingredient of the method is the new dissipation-rate equation that can be applied as a subfilter scale turbulence model. Then, it becomes easy to convert almost any usual RANS transport model into a subfilter scale model. In particular, the method can be applied to two equation models and to stress transport models as well. In the derivation of the method, the partial integration technique allows to keep a link between the spectral space and the physical space of the resulting model. The physical turbulent processes involving the production, dissipation, and flux transfer of the turbulent energy are introduced in the equations. The present work, after recalling the main building steps of the PITM method, brings further insight into the physical interpretation of the method, its underlying hypotheses and its internal acting mechanisms. In particular, the finiteness of the coefficients used in the dissipation-rate equation is discussed in detail from a theoretical point of view. Then, we consider the analytical example of self-similar turbulent flow for analyzing the dissipation-rate equation. From an analytical solution obtained by Taylor series expansions taking into account the Kovasznay hypothesis for evaluating the transfer term, we compute the functional coefficients c
NASA Technical Reports Server (NTRS)
Brown, James L.
2014-01-01
Examined is sensitivity of separation extent, wall pressure and heating to variation of primary input flow parameters, such as Mach and Reynolds numbers and shock strength, for 2D and Axisymmetric Hypersonic Shock Wave Turbulent Boundary Layer interactions obtained by Navier-Stokes methods using the SST turbulence model. Baseline parametric sensitivity response is provided in part by comparison with vetted experiments, and in part through updated correlations based on free interaction theory concepts. A recent database compilation of hypersonic 2D shock-wave/turbulent boundary layer experiments extensively used in a prior related uncertainty analysis provides the foundation for this updated correlation approach, as well as for more conventional validation. The primary CFD method for this work is DPLR, one of NASA's real-gas aerothermodynamic production RANS codes. Comparisons are also made with CFL3D, one of NASA's mature perfect-gas RANS codes. Deficiencies in predicted separation response of RANS/SST solutions to parametric variations of test conditions are summarized, along with recommendations as to future turbulence approach.
On a particular solution to the 3D Navier-Stokes equations for liquids with cavitation
NASA Astrophysics Data System (ADS)
Rabinowitch, Alexander S.
2016-08-01
The 3D Navier-Stokes equations for incompressible viscous liquids are examined. In the axially symmetric case, they are represented in the form of three nonlinear partial differential equations. These equations are studied and their particular solution is found. In it, the velocity components are sinusoidal in the direction of their axis of symmetry. As to the pressure, it can reach a sufficiently small value at which the phenomenon of cavitation takes place in a liquid. The found solution describes some flows of viscous liquids outside vapor-filled regions in them.
Free boundary value problem to 3D spherically symmetric compressible Navier-Stokes-Poisson equations
NASA Astrophysics Data System (ADS)
Kong, Huihui; Li, Hai-Liang
2017-02-01
In the paper, we consider the free boundary value problem to 3D spherically symmetric compressible isentropic Navier-Stokes-Poisson equations for self-gravitating gaseous stars with γ -law pressure density function for 6/5 <γ ≤ 4/3. For stress-free boundary condition and zero flow density continuously across the free boundary, the global existence of spherically symmetric weak solutions is shown, and the regularity and long time behavior of global solution are investigated for spherically symmetric initial data with the total mass smaller than a critical mass.
On the Critical One Component Regularity for 3-D Navier-Stokes System: General Case
NASA Astrophysics Data System (ADS)
Chemin, Jean-Yves; Zhang, Ping; Zhang, Zhifei
2017-02-01
Let us consider initial data {v_0} for the homogeneous incompressible 3D Navier-Stokes equation with vorticity belonging to {L^{3/2}\\cap L^2} . We prove that if the solution associated with {v_0} blows up at a finite time {T^star} , then for any p in {]4,∞[} , and any unit vector e of R^3, the L p norm in time with value in dot{H}^{1/2 + 2/p} of {(v|e)_{R^3}} blows up at {T^star}.
Statistical properties of the 3-D poor man's Navier--Stokes equation
NASA Astrophysics Data System (ADS)
McDonough, J. M.
2007-11-01
The poor man's Navier--Stokes (PMNS) equation is an efficiently-evaluated discrete dynamical system (DDS) derived directly from the Navier--Stokes (N.--S.) equations via a Galerkin procedure. The 2-D version of this DDS was introduced by McDonough and Huang, Int. J. Numer. Meth. Fluids (2004), where it was thoroughly analyzed for values of bifurcation parameters that might be associated with isotropic turbulence. Yang et al., AIAA J. (2003), demonstrated that the PMNS equation could be employed to accurately fit experimental data. These results suggest possible use of the PMNS equation as part of a subgrid-scale (SGS) model for LES formulated to capture effects of interactions between turbulence and other physics on unresolved scales. Here, we consider statistical properties of the 3-D PMNS equation to ascertain whether they are sufficiently close to those of physical N.--S. flows to warrant development of such models. In particular, we will present auto and cross correlation of velocity components, probability density functions, flatness and skewness of velocity derivatives, and scaling of longitudinal velocity structure functions of orders two, three, four and six. It will be demonstrated that PMNS equation statistics are generally in accord with those of the full N.--S. equations, and as a consequence this DDS could lead to very efficient LES SGS models able to replicate small-scale turbulence interactions with other physics.
Least-squares finite element solution of 3D incompressible Navier-Stokes problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.
1992-01-01
Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.
Turbine Internal and Film Cooling Modeling For 3D Navier-Stokes Codes
NASA Technical Reports Server (NTRS)
DeWitt, Kenneth; Garg Vijay; Ameri, Ali
2005-01-01
The aim of this research project is to make use of NASA Glenn on-site computational facilities in order to develop, validate and apply aerodynamic, heat transfer, and turbine cooling models for use in advanced 3D Navier-Stokes Computational Fluid Dynamics (CFD) codes such as the Glenn-" code. Specific areas of effort include: Application of the Glenn-HT code to specific configurations made available under Turbine Based Combined Cycle (TBCC), and Ultra Efficient Engine Technology (UEET) projects. Validating the use of a multi-block code for the time accurate computation of the detailed flow and heat transfer of cooled turbine airfoils. The goal of the current research is to improve the predictive ability of the Glenn-HT code. This will enable one to design more efficient turbine components for both aviation and power generation. The models will be tested against specific configurations provided by NASA Glenn.
A least-squares finite element method for 3D incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.
1993-01-01
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.
Numerical simulation of jet aerodynamics using the three-dimensional Navier-Stokes code PAB3D
NASA Technical Reports Server (NTRS)
Pao, S. Paul; Abdol-Hamid, Khaled S.
1996-01-01
This report presents a unified method for subsonic and supersonic jet analysis using the three-dimensional Navier-Stokes code PAB3D. The Navier-Stokes code was used to obtain solutions for axisymmetric jets with on-design operating conditions at Mach numbers ranging from 0.6 to 3.0, supersonic jets containing weak shocks and Mach disks, and supersonic jets with nonaxisymmetric nozzle exit geometries. This report discusses computational methods, code implementation, computed results, and comparisons with available experimental data. Very good agreement is shown between the numerical solutions and available experimental data over a wide range of operating conditions. The Navier-Stokes method using the standard Jones-Launder two-equation kappa-epsilon turbulence model can accurately predict jet flow, and such predictions are made without any modification to the published constants for the turbulence model.
NASA Astrophysics Data System (ADS)
Rabinowitch, Alexander S.
2015-09-01
A special class of axially symmetric nonstationary flows of incompressible viscous fluids is examined. For it, the 3D Navier-Stokes equations are reduced to a nonlinear partial differential equation of the third order and a linear partial differential equation of the second order. These equations are studied and their particular analytical solutions are found. The obtained particular solution to the Navier-Stokes equations could be used to describe some types of turbulent flows of viscous fluids in the case of high Reynolds numbers.
NASA Astrophysics Data System (ADS)
Bond, Ryan Bomar
A new concept for the low speed propulsion mode in rocket based combined cycle (RBCC) engines has been developed as part of the NASA GTX program. This concept, called the independent ramjet stream (IRS) cycle, is a variation of the traditional ejector ramjet (ER) design and involves the injection of hydrogen fuel directly into the air stream, where it is ignited by the rocket plume. Experiments and computational fluid dynamics (CFD) are currently being used to evaluate the feasibility of the new design. In this work, a Navier-Stokes code valid for general reactive flows is applied to the model engine under cold flow, ejector ramjet, and IRS cycle operation. Pressure distributions corresponding to cold-flow and ejector ramjet operation are compared with experimental data. The engine response under independent ramjet stream cycle operation is examined for different reaction models and grid sizes. The engine response to variations in fuel injection is also examined. Mode transition simulations are also analyzed both with and without a nitrogen purge of the rocket. The solutions exhibit a high sensitivity to both grid resolution and reaction mechanism, but they do indicate that thermal throat ramjet operation is possible through the injection and burning of additional fuel into the air stream. The solutions also indicate that variations in fuel injection location can affect the position of the thermal throat. The numerical simulations predicted successful mode transition both with and without a nitrogen purge of the rocket; however, the reliability of the mode transition results cannot be established without experimental data to validate the reaction mechanism.
Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes
NASA Technical Reports Server (NTRS)
Marx, Yves P.
1990-01-01
An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.
Universal Bounds for the Littlewood-Paley First-Order Moments of the 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Otto, Felix; Ramos, Fabio
2010-12-01
We derive upper bounds for the infinite-time and space average of the L 1-norm of the Littlewood-Paley decomposition of weak solutions of the 3 D periodic Navier-Stokes equations. The result suggests that the Kolmogorov characteristic velocity scaling, {mathbf{U}_kappa˜ɛ^{1/3} kappa^{-1/3}} , holds as an upper bound for a region of wavenumbers near the dissipative cutoff.
Conservative multizonal interface algorithm for the 3-D Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Klopfer, G. H.; Molvik, G. A.
1991-01-01
A conservative zonal interface algorithm using features of both structured and unstructured mesh CFD technology is presented. The flow solver within each of the zones is based on structured mesh CFD technology. The interface algorithm was implemented into two three-dimensional Navier-Stokes finite volume codes and was found to yield good results.
The 3D Navier-Stokes analysis of a Mach 2.68 bifurcated rectangular mixed-compression inlet
NASA Technical Reports Server (NTRS)
Mizukami, M.; Saunders, J. D.
1995-01-01
The supersonic diffuser of a Mach 2.68 bifurcated, rectangular, mixed-compression inlet was analyzed using a three-dimensional (3D) Navier-Stokes flow solver. A two-equation turbulence model, and a porous bleed model based on unchoked bleed hole discharge coefficients were used. Comparisons were made with experimental data, inviscid theory, and two-dimensional Navier-Stokes analyses. The main objective was to gain insight into the inlet fluid dynamics. Examination of the computational results along with the experimental data suggest that the cowl shock-sidewall boundary layer interaction near the leading edge caused a substantial separation in the wind tunnel inlet model. As a result, the inlet performance may have been compromised by increased spillage and higher bleed mass flow requirements. The internal flow contained substantial waves that were not in the original inviscid design. 3D effects were fairly minor for this inlet at on-design conditions. Navier-Stokes analysis appears to be an useful tool for gaining insight into the inlet fluid dynamics. It provides a higher fidelity simulation of the flowfield than the original inviscid design, by taking into account boundary layers, porous bleed, and their interactions with shock waves.
NASA Technical Reports Server (NTRS)
Marvriplis, D. J.; Venkatakrishnan, V.
1995-01-01
An agglomeration multigrid strategy is developed and implemented for the solution of three-dimensional steady viscous flows. The method enables convergence acceleration with minimal additional memory overheads, and is completely automated, in that it can deal with grids of arbitrary construction. The multigrid technique is validated by comparing the delivered convergence rates with those obtained by a previously developed overset-mesh multigrid approach, and by demonstrating grid independent convergence rates for aerodynamic problems on very large grids. Prospects for further increases in multigrid efficiency for high-Reynolds number viscous flows on highly stretched meshes are discussed.
Frequency Localized Regularity Criteria for the 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Bradshaw, Z.; Grujić, Z.
2017-04-01
Two regularity criteria are established to highlight which Littlewood-Paley frequencies play an essential role in possible singularity formation in a Leray-Hopf weak solution to the Navier-Stokes equations in three spatial dimensions. One of these is a frequency localized refinement of known Ladyzhenskaya-Prodi-Serrin-type regularity criteria restricted to a finite window of frequencies, the lower bound of which diverges to {+∞} as t approaches an initial singular time.
An integral equation approach to smooth 3D Navier-Stokes solution
NASA Astrophysics Data System (ADS)
Costin, O.; Luo, G.; Tanveer, S.
2008-12-01
We summarize a recently developed integral equation (IE) approach to tackling the long-time existence problem for smooth solution v(x, t) to the 3D Navier-Stokes (NS) equation in the context of a periodic box problem with smooth time independent forcing and initial condition v0. Using an inverse-Laplace transform of {\\skew5\\hat v} (k, t) - {\\skew5\\hat v}_0 in 1/t, we arrive at an IE for {\\skew5\\hat U} (k, p) , where p is inverse-Laplace dual to 1/t and k is the Fourier variable dual to x. The advantage of this formulation is that the solution {\\skew5\\hat U} to the IE is known to exist a priori for p \\in \\mathbb{R}^+ and the solution is integrable and exponentially bounded at ∞. Global existence of NS solution in this formulation is reduced to an asymptotics question. If \\parallel\\!{\\skew5\\hat U} (\\cdot, p)\\!\\parallel_{{l^{1} (\\mathbb{Z}^3)}} has subexponential bounds as p→∞, then global existence to NS follows. Moreover, if f=0, then the converse is also true in the following sense: if NS has global solution, then there exists n>=1 for which the inverse-Laplace transform of {\\skew5\\hat v} (k, t) - {\\skew5\\hat v}_0 in 1/tn necessarily decays as q→∞, where q is the inverse-Laplace dual to 1/tn. We also present refined estimates of the exponential growth when the solution {\\skew5\\hat U} is known on a finite interval [0, p0]. We also show that for analytic v[0] and f, with finitely many nonzero Fourier-coefficients, the series for {\\skew5\\hat U} (k, p) in powers of p has a radius of convergence independent of initial condition and forcing; indeed the radius gets bigger for smaller viscosity. We also show that the IE can be solved numerically with controlled errors. Preliminary numerical calculations for Kida (1985 J. Phys. Soc. Japan 54 2132) initial conditions, though far from being optimized, and performed on a modest interval in the accelerated variable q show decay in q.
NASA Astrophysics Data System (ADS)
Zhai, Xiaoping; Yin, Zhaoyang
2017-02-01
The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier-Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work by Abidi, Gui and Zhang (2012) [2], and (2013) [3] to a lower regularity index about the initial velocity. The key to that improvement is a new a priori estimate for an elliptic equation with nonconstant coefficients in Besov spaces which have the same degree as L2 in R3. Finally, we also generalize our well-posedness result to the inhomogeneous incompressible MHD equations.
Computational results for flows over 2-D ramp and 3-D obstacle with an upwind Navier-Stokes solver
NASA Technical Reports Server (NTRS)
Venkatapathy, Ethiraj
1990-01-01
An implicit, finite-difference, upwind, full Navier-Stokes solver was applied to supersonic/hypersonic flows over two-dimensional ramps and three-dimensional obstacle. Some of the computed results are presented. The numerical scheme used in the study is an implicit, spacially second order accurate, upwind, LU-ADI scheme based on Roe's approximate Reimann solver with MUSCL differencing of Van Leer. An algebraic grid generation scheme based on generalized interpolation scheme was used in generating the grids for the various 2-D and 3-D problems.
Computational results for 2-D and 3-D ramp flows with an upwind Navier-Stokes solver
NASA Technical Reports Server (NTRS)
Venkatapathy, Ethiraj
1991-01-01
An implicit, finite-difference, upwind, full Navier-Stokes solver was applied to supersonic/hypersonic flows over two-dimensional ramps and three-dimensional obstacle. Some of the computed results are presented. The numerical scheme used in the study is an implicit, spatially second order accurate, upwind, LU-ADI scheme based on Roe's approximate Reimann solver with MUSCL differencing of Van Leer. An algebraic grid generation scheme based on generalized interpolation scheme was used in generating the grids for the various 2-D and 3-D problems.
NASA Astrophysics Data System (ADS)
Yu, Haibo; Zhao, Junning
2017-01-01
In this paper, we study the global existence for classical solutions to the 3D isentropic compressible Navier-Stokes equations in a cuboid domain. Compared to the Cauchy problem studied in Hoff (1995 J. Differ. Equ. 120 215-54), Hoff (2005 J. Math. Fluid Mech. 7 315-38), Huang et al (2012 Commun. Pure Appl. Math. 65 549-85), some new thoughts are applied to obtain upper bounds for density. Precisely, through piecewise estimation and some time-depending a priori estimates, we establish time-uniform upper bounds for density under the assumption that the initial energy is small. The initial vacuum is allowed.
On the Global Regularity of a Helical-Decimated Version of the 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Biferale, Luca; Titi, Edriss S.
2013-06-01
We study the global regularity, for all time and all initial data in H 1/2, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution of Navier-Stokes (NS) equations into the subspace where helicity (the L 2-scalar product of velocity and vorticity) is sign-definite. The presence of a second (beside energy) sign-definite inviscid conserved quadratic quantity, which is equivalent to the H 1/2-Sobolev norm, allows us to demonstrate global existence and uniqueness, of space-periodic solutions, together with continuity with respect to the initial conditions, for this decimated 3D model. This is achieved thanks to the establishment of two new estimates, for this 3D model, which show that the H 1/2 and the time average of the square of the H 3/2 norms of the velocity field remain finite. Such two additional bounds are known, in the spirit of the work of H. Fujita and T. Kato (Arch. Ration. Mech. Anal. 16:269-315, 1964; Rend. Semin. Mat. Univ. Padova 32:243-260, 1962), to be sufficient for showing well-posedness for the 3D NS equations. Furthermore, they are directly linked to the helicity evolution for the dNS model, and therefore with a clear physical meaning and consequences.
The 3-D Euler and Navier-Stokes calculations for aircraft components
NASA Technical Reports Server (NTRS)
Vatsa, Veer N.; Wedan, Bruce W.; Turkel, Eli
1989-01-01
An explicit multistage Runge-Kutta type of time-stepping scheme is used for solving transonic flow past a transport type wing/fuselage configuration. Solutions for both Euler and Navier-Stokes equations are obtained for quantitative assessment of boundary layer interaction effects. The viscous solutions are obtained on both a medium resolution grid of approximately 270,000 points and a find grid of 460,000 points to assess the effects of grid density on the solution. Computed pressure distributions are compared with the experimental data.
3-D Navier-Stokes Analysis of Blade Root Aerodynamics for a Tiltrotor Aircraft In Cruise
NASA Technical Reports Server (NTRS)
Romander, Ethan
2006-01-01
The blade root area of a tiltrotor aircraft's rotor is constrained by a great many factors, not the least of which is aerodynamic performance in cruise. For this study, Navier-Stokes CFD techniques are used to study the aerodynamic performance in cruise of a rotor design as a function of airfoil thickness along the blade and spinner shape. Reducing airfoil thickness along the entire blade will be shown to have the greatest effect followed by smaller but still significant improvements achieved by reducing the thickness of root airfoils only. Furthermore, altering the shape of the spinner will be illustrated as a tool to tune the aerodynamic performance very near the blade root.
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
NASA Astrophysics Data System (ADS)
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-02-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
NASA Astrophysics Data System (ADS)
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-04-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
On the Helicity in 3D-Periodic Navier-Stokes Equations II: The Statistical Case
NASA Astrophysics Data System (ADS)
Foias, Ciprian; Hoang, Luan; Nicolaenko, Basil
2009-09-01
We study the asymptotic behavior of the statistical solutions to the Navier-Stokes equations using the normalization map [9]. It is then applied to the study of mean energy, mean dissipation rate of energy, and mean helicity of the spatial periodic flows driven by potential body forces. The statistical distribution of the asymptotic Beltrami flows are also investigated. We connect our mathematical analysis with the empirical theory of decaying turbulence. With appropriate mathematically defined ensemble averages, the Kolmogorov universal features are shown to be transient in time. We provide an estimate for the time interval in which those features may still be present. Our collaborator and friend Basil Nicolaenko passed away in September of 2007, after this work was completed. Honoring his contribution and friendship, we dedicate this article to him.
Implementation of wall boundary conditions for transpiration in F3D thin-layer Navier-Stokes code
NASA Technical Reports Server (NTRS)
Kandula, M.; Martin, F. W., Jr.
1991-01-01
Numerical boundary conditions for mass injection/suction at the wall are incorporated in the thin-layer Navier-Stokes code, F3D. The accuracy of the boundary conditions and the code is assessed by a detailed comparison of the predictions of velocity distributions and skin-friction coefficients with exact similarity solutions for laminar flow over a flat plate with variable blowing/suction, and measurements for turbulent flow past a flat plate with uniform blowing. In laminar flow, F3D predictions for friction coefficient compare well with exact similarity solution with and without suction, but produces large errors at moderate-to-large values of blowing. A slight Mach number dependence of skin-friction coefficient due to blowing in turbulent flow is computed by F3D code. Predicted surface pressures for turbulent flow past an airfoil with mass injection are in qualitative agreement with measurements for a flat plate.
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Ibraheem, S. O.
1993-01-01
The convergence characteristics of various approximate factorizations for the 3D Euler and Navier-Stokes equations are examined using the von-Neumann stability analysis method. Three upwind-difference based factorizations and several central-difference based factorizations are considered for the Euler equations. In the upwind factorizations both the flux-vector splitting methods of Steger and Warming and van Leer are considered. Analysis of the Navier-Stokes equations is performed only on the Beam and Warming central-difference scheme. The range of CFL numbers over which each factorization is stable is presented for one-, two-, and three-dimensional flow. Also presented for each factorization is the CFL number at which the maximum eigenvalue is minimized, for all Fourier components, as well as for the high frequency range only. The latter is useful for predicting the effectiveness of multigrid procedures with these schemes as smoothers. Further, local mode analysis is performed to test the suitability of using a uniform flow field in the stability analysis. Some inconsistencies in the results from previous analyses are resolved.
NASA Astrophysics Data System (ADS)
Horrillo, J.; Wood, A.; Kim, G.-B.; Parambath, A.
2013-12-01
A simplified three-dimensional Navier-Stokes (3-D NS) model for two fluids, water and landslide material (mudslide) is presented and validated with standard laboratory experiments. Dubbed TSUNAMI3D (Tsunami Solution Using Navier-Stokes Algorithm with Multiple Interfaces) is applied to a 3-D full-scale landslide scenario in the Gulf of Mexico (GOM), i.e., the East-Breaks underwater landslide. The simplified 3-D NS model is conceived to be computationally efficient for tsunami calculations. The simplification is derived from the large aspect ratio of the tsunami waves (wavelength/wave-height) and the selected computational grid that has a smaller aspect ratio. This allows us to assume a horizontal fluid surface in each individual cell containing the interface (air-water, air-mudslide, and water-mudslide). The tracking of fluid interfaces is based on the Volume of Fluid method and the surfaces are obtained by integrating the fluxes of each individual fluid cell along the water column. In the momentum equation, the pressure term is split into two components, hydrostatic and nonhydrostatic. The internal friction is solved in a simplified manner by adjusting the viscosity coefficient. Despite the simplification to get an efficient solution, the numerical results agree fairly well with standard landslide laboratory experiments required by the National Tsunami Hazard Mitigation Program for tsunami model validation. The numerical effect caused by using a sharp versus a diffusive water-mudslide interface for a full-scale landslide-tsunami scenario is also investigated. Observations from this experiment indicated that choosing a sharp or diffusive interface seems to have no remarkable effect at early stages of the tsunami wave propagation. Last, a large scale 3-D numerical simulation is carried out for the ancient GOM's East-Breaks landslide by using the simplified model to calculate the early stages of the tsunami wave propagation.
Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver
NASA Technical Reports Server (NTRS)
Kim, S.-W.
1991-01-01
A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.
Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Birken, Philipp; Gassner, Gregor; Haas, Mark; Munz, Claus-Dieter
2013-05-01
We compare different block preconditioners in the context of parallel time adaptive higher order implicit time integration using Jacobian-free Newton-Krylov (JFNK) solvers for discontinuous Galerkin (DG) discretizations of the three dimensional time dependent Navier-Stokes equations. A special emphasis of this work is the performance for a relative high number of processors, i.e. with a low number of elements on the processor. For high order DG discretizations, a particular problem that needs to be addressed is the size of the blocks in the Jacobian. Thus, we propose a new class of preconditioners that exploits the hierarchy of modal basis functions and introduces a flexible order of the off-diagonal Jacobian blocks. While the standard preconditioners 'block Jacobi' (no off-blocks) and full symmetric Gauss-Seidel (full off-blocks) are included as special cases, the reduction of the off-block order results in the new scheme ROBO-SGS. This allows us to investigate the impact of the preconditioner's sparsity pattern with respect to the computational performance. Since the number of iterations is not well suited to judge the efficiency of a preconditioner, we additionally consider CPU time for the comparisons. We found that both block Jacobi and ROBO-SGS have good overall performance and good strong parallel scaling behavior.
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.
1990-01-01
The development and applications of multiblock/multizone and adaptive grid methodologies for solving the three-dimensional simplified Navier-Stokes equations are described. Adaptive grid and multiblock/multizone approaches are introduced and applied to external and internal flow problems. These new implementations increase the capabilities and flexibility of the PAB3D code in solving flow problems associated with complex geometry.
A lattice-Boltzmann scheme of the Navier-Stokes equations on a 3D cuboid lattice
NASA Astrophysics Data System (ADS)
Min, Haoda; Peng, Cheng; Wang, Lian-Ping
2015-11-01
The standard lattice-Boltzmann method (LBM) for fluid flow simulation is based on a square (in 2D) or cubic (in 3D) lattice grids. Recently, two new lattice Boltzmann schemes have been developed on a 2D rectangular grid using the MRT (multiple-relaxation-time) collision model, by adding a free parameter in the definition of moments or by extending the equilibrium moments. Here we developed a lattice Boltzmann model on 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions. We designed our MRT-LBM model by matching the moment equations from the Chapman-Enskog expansion with the Navier-Stokes equations. The model guarantees correct hydrodynamics. A second-order term is added to the equilibrium moments in order to restore the isotropy of viscosity on a cuboid lattice. The form and the coefficients of the extended equilibrium moments are determined through an inverse design process. An additional benefit of the model is that the viscosity can be adjusted independent of the stress-moment relaxation parameter, thus improving the numerical stability of the model. The resulting cuboid MRT-LBM model is then validated through benchmark simulations using laminar channel flow, turbulent channel flow, and the 3D Taylor-Green vortex flow.
NASA Astrophysics Data System (ADS)
Berselli, Luigi C.; Spirito, Stefano
2017-03-01
In this paper we consider the Navier-Stokes equations supplemented with either the Dirichlet or vorticity-based Navier slip boundary conditions. We prove that weak solutions obtained as limits of solutions of the Navier-Stokes-Voigt model satisfy the local energy inequality, and we also prove certain regularity results for the pressure. Moreover, in the periodic setting we prove that if the parameters are chosen in an appropriate way, then we can construct suitable weak solutions through a Fourier-Galerkin finite-dimensional approximation in the space variables.
NASA Astrophysics Data System (ADS)
Wu, Guochun
2017-01-01
In this paper, we investigate the global existence and uniqueness of strong solutions to the initial boundary value problem for the 3D compressible Navier-Stokes equations without heat conductivity in a bounded domain with slip boundary. The global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in H2 (Ω). Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.
NASA Astrophysics Data System (ADS)
Ge, Liang; Sotiropoulos, Fotis
2007-08-01
A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow
NASA Astrophysics Data System (ADS)
Razafison, Ulrich
We consider the three-dimensional exterior problem for stationary Navier-Stokes equations. We prove, under assumptions of smallness of the data, existence and uniqueness of solutions. By setting the problem in weighted spaces where the weights reflect the anisotropic decay properties of the fundamental solution of Oseen, we show the better decay of the solutions outside the wake region. Moreover, the solutions we obtained have a finite Dirichlet integral and under additional assumptions on the weights they are also PR-solutions in the sense of Finn [R. Finn, On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems, Arch. Ration. Mech. Anal. 19 (1965) 363-406]. The study relies on an L-theory for 1
On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Ibraheem, S. O.; Demuren, A. O.
1994-01-01
A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.; Lakshmanan, B.; Carlson, John R.
1995-01-01
A three-dimensional Navier-Stokes solver was used to determine how accurately computations can predict local and average skin friction coefficients for attached and separated flows for simple experimental geometries. Algebraic and transport equation closures were used to model turbulence. To simulate anisotropic turbulence, the standard two-equation turbulence model was modified by adding nonlinear terms. The effects of both grid density and the turbulence model on the computed flow fields were also investigated and compared with available experimental data for subsonic and supersonic free-stream conditions.
NASA Astrophysics Data System (ADS)
Choi, D.; Knight, C. J.
1991-06-01
A method to generate H and O-H grid systems for 3D gas turbine geometries has been developed. It is a simple procedure which solves a set of elliptic equations starting from an initial grid system generated algebraically. This grid generation procedure is for 3D Navier-Stokes analysis based on the scalar or diagonalized form of approximate factorization. The grids generated by this procedure have been applied to 3D heat transfer calculations and compared with experimental results. Detailed comparisons are given for both H and O-H grid topologies, considering the Low Aspect Ratio Turbine (LART) and using a two-equation turbulence model with viscous sublayer resolution.
NASA Astrophysics Data System (ADS)
Cheskidov, A.; Shvydkoy, R.
2014-06-01
Motivated by Kolmogorov's theory of turbulence we present a unified approach to the regularity problems for the 3D Navier-Stokes and Euler equations. We introduce a dissipation wavenumber that separates low modes where the Euler dynamics is predominant from the high modes where the viscous forces take over. Then using an indifferent to the viscosity technique we obtain a new regularity criterion which is weaker than every Ladyzhenskaya-Prodi-Serrin condition in the viscous case, and reduces to the Beale-Kato-Majda criterion in the inviscid case. In the viscous case we prove that Leray-Hopf solutions are regular provided , which improves our previous condition. We also show that for all Leray-Hopf solutions. Finally, we prove that Leray-Hopf solutions are regular when the time-averaged spatial intermittency is small, i.e., close to Kolmogorov's regime.
NASA Technical Reports Server (NTRS)
Lee-Rausch, Elizabeth M.; Hammond, Dana P.; Nielsen, Eric J.; Pirzadeh, S. Z.; Rumsey, Christopher L.
2010-01-01
FUN3D Navier-Stokes solutions were computed for the 4th AIAA Drag Prediction Workshop grid convergence study, downwash study, and Reynolds number study on a set of node-based mixed-element grids. All of the baseline tetrahedral grids were generated with the VGRID (developmental) advancing-layer and advancing-front grid generation software package following the gridding guidelines developed for the workshop. With maximum grid sizes exceeding 100 million nodes, the grid convergence study was particularly challenging for the node-based unstructured grid generators and flow solvers. At the time of the workshop, the super-fine grid with 105 million nodes and 600 million elements was the largest grid known to have been generated using VGRID. FUN3D Version 11.0 has a completely new pre- and post-processing paradigm that has been incorporated directly into the solver and functions entirely in a parallel, distributed memory environment. This feature allowed for practical pre-processing and solution times on the largest unstructured-grid size requested for the workshop. For the constant-lift grid convergence case, the convergence of total drag is approximately second-order on the finest three grids. The variation in total drag between the finest two grids is only 2 counts. At the finest grid levels, only small variations in wing and tail pressure distributions are seen with grid refinement. Similarly, a small wing side-of-body separation also shows little variation at the finest grid levels. Overall, the FUN3D results compare well with the structured-grid code CFL3D. The FUN3D downwash study and Reynolds number study results compare well with the range of results shown in the workshop presentations.
NASA Technical Reports Server (NTRS)
Kwak, D.
1994-01-01
INS3D computes steady-state solutions to the incompressible Navier-Stokes equations. The INS3D approach utilizes pseudo-compressibility combined with an approximate factorization scheme. This computational fluid dynamics (CFD) code has been verified on problems such as flow through a channel, flow over a backwardfacing step and flow over a circular cylinder. Three dimensional cases include flow over an ogive cylinder, flow through a rectangular duct, wind tunnel inlet flow, cylinder-wall juncture flow and flow through multiple posts mounted between two plates. INS3D uses a pseudo-compressibility approach in which a time derivative of pressure is added to the continuity equation, which together with the momentum equations form a set of four equations with pressure and velocity as the dependent variables. The equations' coordinates are transformed for general three dimensional applications. The equations are advanced in time by the implicit, non-iterative, approximately-factored, finite-difference scheme of Beam and Warming. The numerical stability of the scheme depends on the use of higher-order smoothing terms to damp out higher-frequency oscillations caused by second-order central differencing. The artificial compressibility introduces pressure (sound) waves of finite speed (whereas the speed of sound would be infinite in an incompressible fluid). As the solution converges, these pressure waves die out, causing the derivation of pressure with respect to time to approach zero. Thus, continuity is satisfied for the incompressible fluid in the steady state. Computational efficiency is achieved using a diagonal algorithm. A block tri-diagonal option is also available. When a steady-state solution is reached, the modified continuity equation will satisfy the divergence-free velocity field condition. INS3D is capable of handling several different types of boundaries encountered in numerical simulations, including solid-surface, inflow and outflow, and far
NASA Technical Reports Server (NTRS)
Biyabani, S. R.
1994-01-01
INS3D computes steady-state solutions to the incompressible Navier-Stokes equations. The INS3D approach utilizes pseudo-compressibility combined with an approximate factorization scheme. This computational fluid dynamics (CFD) code has been verified on problems such as flow through a channel, flow over a backwardfacing step and flow over a circular cylinder. Three dimensional cases include flow over an ogive cylinder, flow through a rectangular duct, wind tunnel inlet flow, cylinder-wall juncture flow and flow through multiple posts mounted between two plates. INS3D uses a pseudo-compressibility approach in which a time derivative of pressure is added to the continuity equation, which together with the momentum equations form a set of four equations with pressure and velocity as the dependent variables. The equations' coordinates are transformed for general three dimensional applications. The equations are advanced in time by the implicit, non-iterative, approximately-factored, finite-difference scheme of Beam and Warming. The numerical stability of the scheme depends on the use of higher-order smoothing terms to damp out higher-frequency oscillations caused by second-order central differencing. The artificial compressibility introduces pressure (sound) waves of finite speed (whereas the speed of sound would be infinite in an incompressible fluid). As the solution converges, these pressure waves die out, causing the derivation of pressure with respect to time to approach zero. Thus, continuity is satisfied for the incompressible fluid in the steady state. Computational efficiency is achieved using a diagonal algorithm. A block tri-diagonal option is also available. When a steady-state solution is reached, the modified continuity equation will satisfy the divergence-free velocity field condition. INS3D is capable of handling several different types of boundaries encountered in numerical simulations, including solid-surface, inflow and outflow, and far
NASA Astrophysics Data System (ADS)
Wolkov, A. V.
2010-03-01
The Galerkin method with discontinuous basis functions is adapted for solving the Euler and Navier-Stokes equations on unstructured hexahedral grids. A hybrid multigrid algorithm involving the finite element and grid stages is used as an iterative solution method. Numerical results of calculating the sphere inviscid flow, viscous flow in a bent pipe, and turbulent flow past a wing are presented. The numerical results and the computational cost are compared with those obtained using the finite volume method.
Stochastic nonhomogeneous incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Cutland, Nigel J.; Enright, Brendan
We construct solutions for 2- and 3-D stochastic nonhomogeneous incompressible Navier-Stokes equations with general multiplicative noise. These equations model the velocity of a mixture of incompressible fluids of varying density, influenced by random external forces that involve feedback; that is, multiplicative noise. Weak solutions for the corresponding deterministic equations were first found by Kazhikhov [A.V. Kazhikhov, Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid, Soviet Phys. Dokl. 19 (6) (1974) 331-332; English translation of the paper in: Dokl. Akad. Nauk SSSR 216 (6) (1974) 1240-1243]. A stochastic version with additive noise was solved by Yashima [H.F. Yashima, Equations de Navier-Stokes stochastiques non homogènes et applications, Thesis, Scuola Normale Superiore, Pisa, 1992]. The methods here extend the Loeb space techniques used to obtain the first general solutions of the stochastic Navier-Stokes equations with multiplicative noise in the homogeneous case [M. Capiński, N.J. Cutland, Stochastic Navier-Stokes equations, Applicandae Math. 25 (1991) 59-85]. The solutions display more regularity in the 2D case. The methods also give a simpler proof of the basic existence result of Kazhikhov.
NASA Technical Reports Server (NTRS)
Vatsa, Veer N.; Singer, Bart A.
2003-01-01
We evaluate the applicability of a production computational fluid dynamics code for conducting detached eddy simulation for unsteady flows. A second-order accurate Navier-Stokes code developed at NASA Langley Research Center, known as TLNS3D, is used for these simulations. We focus our attention on high Reynolds number flow (Re = 5 x 10(sup 4) - 1.4 x 10(sup 5)) past a circular cylinder to simulate flows with large-scale separations. We consider two types of flow situations: one in which the flow at the separation point is laminar, and the other in which the flow is already turbulent when it detaches from the surface of the cylinder. Solutions are presented for two- and three-dimensional calculations using both the unsteady Reynolds-averaged Navier-Stokes paradigm and the detached eddy simulation treatment. All calculations use the standard Spalart-Allmaras turbulence model as the base model.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Vatsa, Veer N.; Atkins, Harold L.
2005-01-01
We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for unstructured grids to unsteady flows on moving and stationary grids. Example problems considered are relevant to active flow control and stability and control. Computational results are presented using the Spalart-Allmaras turbulence model and are compared to experimental data. The effect of grid and time-step refinement are examined.
Navier-Stokes analysis of blunt trailing edge airfoils
NASA Technical Reports Server (NTRS)
Stanaway, Sharon; Mccroskey, W. J.; Kroo, Ilan
1992-01-01
The flow around blunt trailing edge airfoils was studied by solving the Reynolds-averaged Navier-Stokes equations. The solution procedure combines a grid around the airfoil with a second grid for the wake so that the time advancement over the domain is fully implicit. This is not only very efficient for the algorithm but also allows implicit solutions of a one equation turbulence model appropriate for both boundary layers and wakes. An algebraic and two one-equation turbulence models are tested for a blunt RAE 2822 airfoil section and detailed comparisons with experimental data are presented in the trailing edge region.
A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations
NASA Technical Reports Server (NTRS)
Guruswamy, Guru P.; Lee, Henry
2014-01-01
The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no
Numerical solutions of the complete Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Hassan, H. A.
1988-01-01
The physical phenomena within supersonic flows that sustain chemical reactions are investigated. An earlier study to develop accurate physical models for supersonic reacting flowfields focused on 2-D laminar shear layers. The objective is to examine the mixing and subsequent combustion within turbulent reacting shear layers. To conduct this study, a computer program has been written to solve the axisymmetric Reynolds averaged Navier-Stokes equations. The numerical method uses a cell-centered finite volume approach and a Runge Kutta time stepping scheme. The Reynolds averaged equations are closed using the eddy viscosity concept. Several zero-equation models have been tested by making calculations for an H2-air nonreacting coaxial jet flow. Comparisons made with experimental data show that Cohen's eddy viscosity model provides best agreement. The finite rate chemistry model used in the study of 2-D laminar shear layers is incorporated into the computer program and data is compared from a recent experiment performed at NASA Langley.
Navier Stokes Theorem in Hydrology
NASA Astrophysics Data System (ADS)
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
NASA Technical Reports Server (NTRS)
Anderson, B. H.; Reddy, D. R.; Kapoor, K.
1993-01-01
A three-dimensional implicit Full Navier-Stokes (FNS) analysis and a 3D Reduced Navier-Stokes (RNS) initial value space marching solution technique has been applied to a class of separate flow problems within a diffusing S-duct configuration characterized as vortex-liftoff. Both Full Navier-Stokes and Reduced Navier-Stokes solution techniques were able to capture the overall flow physics of vortex lift-off, however more consideration must be given to the development of turbulence models for the prediction of the locations of separation and reattachment. This accounts for some of the discrepancies in the prediction of the relevant inlet distortion descriptors, particularly circumferential distortion. The 3D RNS solution technique adequately described the topological structure of flow separation associated with vortex lift-off.
NASA Technical Reports Server (NTRS)
Chang, Ing; Hunter, Louis G.
1995-01-01
Advanced airbreathing propulsion systems used in Mach 4-6 mission scenarios, usually consist of a single integrated turboramjet or as in this study, a turbojet housed in an upper bay with a separate ramjet housed in a lower bay. As the engines transition from turbojet to ramjet, there is an operational envelope where both engines operate simultaneously. One nozzle concept under consideration has a common nozzle, where the plumes from the turbojet and ramjet interact with one another as they expand to ambient conditions. In this paper, the two plumes interact at the end of a common 2-D cowl, when they both reach an approximate Mach 3.0 condition and then jointly expand to Mach 3.6 at the common nozzle exit plane. At this condition, the turbojet engine operated at a higher NPR than the ramjet, where the turbojet overpowers the ramjet plume, deflecting it approximately 12 degrees downward and in turn the turbojet plume is deflected 6 degrees upward. In the process, shocks were formed at the deflections and a shear layer formed at the confluence of the two jets. This particular case was experimentally tested and the data used to compare with the PARC3D code with k-kl two equation turbulence model. The 2-D and 3-D centerline CFD solutions are in good agreement, but as the CFD solutions approach the outer sidewall, a slight variance occurs. The outer wall boundary layers are thin and do not present much of an interaction, however, where the confluence interaction shocks interact with the thin boundary layer on the outer wall, strong vortices run down each shock causing substantial disturbances in the boundary layer. These disturbances amplify somewhat as they propagate downstream axially from the confluence point. The nozzle coefficient (CFG) is reduced 1/2 percent as a result of this sidewall interaction, from 0.9850 to 0.9807. This three-dimensional reduction is in better agreement with the experimental value of 0.9790.
NASA Astrophysics Data System (ADS)
DeJong, Andrew
Numerical models of fluid-structure interaction have grown in importance due to increasing interest in environmental energy harvesting, airfoil-gust interactions, and bio-inspired formation flying. Powered by increasingly powerful parallel computers, such models seek to explain the fundamental physics behind the complex, unsteady fluid-structure phenomena. To this end, a high-fidelity computational model based on the high-order spectral difference method on 3D unstructured, dynamic meshes has been developed. The spectral difference method constructs continuous solution fields within each element with a Riemann solver to compute the inviscid fluxes at the element interfaces and an averaging mechanism to compute the viscous fluxes. This method has shown promise in the past as a highly accurate, yet sufficiently fast method for solving unsteady viscous compressible flows. The solver is monolithically coupled to the equations of motion of an elastically mounted 3-degree of freedom rigid bluff body undergoing flow-induced lift, drag, and torque. The mesh is deformed using 4 methods: an analytic function, Laplace equation, biharmonic equation, and a bi-elliptic equation with variable diffusivity. This single system of equations -- fluid and structure -- is advanced through time using a 5-stage, 4th-order Runge-Kutta scheme. Message Passing Interface is used to run the coupled system in parallel on up to 240 processors. The solver is validated against previously published numerical and experimental data for an elastically mounted cylinder. The effect of adding an upstream body and inducing wake galloping is observed.
Partially-Averaged Navier Stokes Model for Turbulence: Implementation and Validation
NASA Technical Reports Server (NTRS)
Girimaji, Sharath S.; Abdol-Hamid, Khaled S.
2005-01-01
Partially-averaged Navier Stokes (PANS) is a suite of turbulence closure models of various modeled-to-resolved scale ratios ranging from Reynolds-averaged Navier Stokes (RANS) to Navier-Stokes (direct numerical simulations). The objective of PANS, like hybrid models, is to resolve large scale structures at reasonable computational expense. The modeled-to-resolved scale ratio or the level of physical resolution in PANS is quantified by two parameters: the unresolved-to-total ratios of kinetic energy (f(sub k)) and dissipation (f(sub epsilon)). The unresolved-scale stress is modeled with the Boussinesq approximation and modeled transport equations are solved for the unresolved kinetic energy and dissipation. In this paper, we first present a brief discussion of the PANS philosophy followed by a description of the implementation procedure and finally perform preliminary evaluation in benchmark problems.
Stochastic 2-D Navier-Stokes Equation
Menaldi, J.L. Sritharan, S.S.
2002-10-01
In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution.
Transonic airfoil and wing design using Navier-Stokes codes
NASA Technical Reports Server (NTRS)
Yu, N. J.; Campbell, R. L.
1992-01-01
An iterative design method has been implemented into 2D and 3D Navier-Stokes codes for the design of airfoils or wings with given target pressure distributions. The method begins with the analysis of an initial geometry, and obtains the analysis pressure distributions of that geometry. The differences between analysis pressures and target pressures are used to drive geometry changes through the use of a streamline curvature method. This paper describes the procedure that makes the iterative design method work for Navier-Stokes codes. Examples of 2D airfoil design, and 3D wing design are included. It is demonstrated that the method is highly effective for airfoil or wing design at flow conditions where no substantial separation occurs. Problems encountered in the airfoil design with shock induced flow separations are discussed.
NASA Astrophysics Data System (ADS)
Kim, Bong-Sik
Three dimensional (3D) Navier-Stokes-alpha equations are considered for uniformly rotating geophysical fluid flows (large Coriolis parameter f = 2O). The Navier-Stokes-alpha equations are a nonlinear dispersive regularization of usual Navier-Stokes equations obtained by Lagrangian averaging. The focus is on the existence and global regularity of solutions of the 3D rotating Navier-Stokes-alpha equations and the uniform convergence of these solutions to those of the original 3D rotating Navier-Stokes equations for large Coriolis parameters f as alpha → 0. Methods are based on fast singular oscillating limits and results are obtained for periodic boundary conditions for all domain aspect ratios, including the case of three wave resonances which yields nonlinear "2½-dimensional" limit resonant equations for f → 0. The existence and global regularity of solutions of limit resonant equations is established, uniformly in alpha. Bootstrapping from global regularity of the limit equations, the existence of a regular solution of the full 3D rotating Navier-Stokes-alpha equations for large f for an infinite time is established. Then, the uniform convergence of a regular solution of the 3D rotating Navier-Stokes-alpha equations (alpha ≠ 0) to the one of the original 3D rotating NavierStokes equations (alpha = 0) for f large but fixed as alpha → 0 follows; this implies "shadowing" of trajectories of the limit dynamical systems by those of the perturbed alpha-dynamical systems. All the estimates are uniform in alpha, in contrast with previous estimates in the literature which blow up as alpha → 0. Finally, the existence of global attractors as well as exponential attractors is established for large f and the estimates are uniform in alpha.
NASA Technical Reports Server (NTRS)
Anderson, B. H.; Reddy, D. R.; Kapoor, K.
1993-01-01
A three-dimensional implicit Full Navier-Stokes (FNS) analysis and a 3D Reduced Navier Stokes (RNS) initial value space marching solution technique has been applied to a class of separated flow problems within a diffusing S-duct configuration characterized by vortex-liftoff. Both the FNS and the RNS solution technique were able to capture the overall flow physics of vortex lift-off, and gave remarkably similar results which agreed reasonably well with the experimental measured averaged performance parameters of engine face total pressure recovery and distortion. However, the Full Navier-Stokes and Reduced Navier-Stokes also consistently predicted separation further downstream in the M2129 inlet S-duct than was indicated by experimental data, thus compensating errors were present in the two Navier-Stokes analyses. The difficulties encountered in the Navier-Stokes separations analyses of the M2129 inlet S-duct center primarily on turbulence model issues, and these focused on two distinct but different phenomena, namely, (1) characterization of low skin friction adverse pressure gradient flows, and (2) description of the near wall behavior of flows characterized by vortex lift-off.
NASA Technical Reports Server (NTRS)
Rumsey, Christopher L.
2009-01-01
In current practice, it is often difficult to draw firm conclusions about turbulence model accuracy when performing multi-code CFD studies ostensibly using the same model because of inconsistencies in model formulation or implementation in different codes. This paper describes an effort to improve the consistency, verification, and validation of turbulence models within the aerospace community through a website database of verification and validation cases. Some of the variants of two widely-used turbulence models are described, and two independent computer codes (one structured and one unstructured) are used in conjunction with two specific versions of these models to demonstrate consistency with grid refinement for several representative problems. Naming conventions, implementation consistency, and thorough grid resolution studies are key factors necessary for success.
Large-eddy simulation/Reynolds-averaged Navier-Stokes hybrid schemes for high speed flows
NASA Astrophysics Data System (ADS)
Xiao, Xudong
Three LES/RANS hybrid schemes have been proposed for the prediction of high speed separated flows. Each method couples the k-zeta (Enstrophy) BANS model with an LES subgrid scale one-equation model by using a blending function that is coordinate system independent. Two of these functions are based on turbulence dissipation length scale and grid size, while the third one has no explicit dependence on the grid. To implement the LES/RANS hybrid schemes, a new rescaling-reintroducing method is used to generate time-dependent turbulent inflow conditions. The hybrid schemes have been tested on a Mach 2.88 flow over 25 degree compression-expansion ramp and a Mach 2.79 flow over 20 degree compression ramp. A special computation procedure has been designed to prevent the separation zone from expanding upstream to the recycle-plane. The code is parallelized using Message Passing Interface (MPI) and is optimized for running on IBM-SP3 parallel machine. The scheme was validated first for a flat plate. It was shown that the blending function has to be monotonic to prevent the RANS region from appearing in the LES region. In the 25 deg ramp case, the hybrid schemes provided better agreement with experiment in the recovery region. Grid refinement studies demonstrated the importance of using a grid independent blend function and further improvement with experiment in the recovery region. In the 20 deg ramp case, with a relatively finer grid, the hybrid scheme characterized by grid independent blending function well predicted the flow field in both the separation region and the recovery region. Therefore, with "appropriately" fine grid, current hybrid schemes are promising for the simulation of shock wave/boundary layer interaction problems.
CFL3D User's Manual (Version 5.0)
NASA Technical Reports Server (NTRS)
Krist, Sherrie L.; Biedron, Robert T.; Rumsey, Christopher L.
1998-01-01
This document is the User's Manual for the CFL3D computer code, a thin-layer Reynolds-averaged Navier-Stokes flow solver for structured multiple-zone grids. Descriptions of the code's input parameters, non-dimensionalizations, file formats, boundary conditions, and equations are included. Sample 2-D and 3-D test cases are also described, and many helpful hints for using the code are provided.
Aerodynamics of thrust vectoring by Navier-Stokes solutions
NASA Technical Reports Server (NTRS)
Tseng, Jing-Biau; Lan, C. Edward
1991-01-01
Induced aerodynamics from thrust vectoring are investigated by a computational fluid dynamic method. A thin-layer Reynolds-averaged Navier-Stokes code with multiblock capability is used. Jet properties are specified on the nozzle exit plane to simulate the jet momentum. Results for a rectangular jet in a cross flow are compared with data to verify the code. Further verification of the calculation is made by comparing the numerical results with transonic data for a wing-body combination. Additional calculations were performed to elucidate the following thrust vectoring effects: the thrust vectoring effect on shock and expansion waves, induced effects on nearby surfaces, and the thrust vectoring effect on the leading edge vortex.
Navier-Stokes computations of cavity aeroacoustics with suppression devices
NASA Technical Reports Server (NTRS)
Baysal, Oktay; Yen, Guan-Wei; Fouladi, Kamran
1992-01-01
Effectiveness of two devices to suppress the cavity acoustics was computationally investigated. Two dimensional, computational simulations were performed for the transonic, turbulent flows past a cavity, which was first equipped with a rear face ramp and then with a spoiler. The Reynolds-averaged, unsteady, compressible, full Navier-Stokes equations were solved time accurately by a second-order accurate, implicit, upwind, finite-volume method. The effect of turbulence was included through a Baldwin-Lomax model with modifications for the multiple-wall effects and for the highly vortical flow with a shear layer. The results included instantaneous and time-averaged flow properties, and time-series analyses of the pressure inside the cavity, which compared favorably with the available experimental data. These results were also contrasted with the computed aeroacoustics of the same cavity (length-to-depth ratio of 4.5), but without a device, to demonstrate the suppression effectiveness.
About the Regularized Navier Stokes Equations
NASA Astrophysics Data System (ADS)
Cannone, Marco; Karch, Grzegorz
2005-03-01
The first goal of this paper is to study the large time behavior of solutions to the Cauchy problem for the 3-dimensional incompressible Navier Stokes system. The Marcinkiewicz space L3,∞ is used to prove some asymptotic stability results for solutions with infinite energy. Next, this approach is applied to the analysis of two classical “regularized” Navier Stokes systems. The first one was introduced by J. Leray and consists in “mollifying” the nonlinearity. The second one was proposed by J.-L. Lions, who added the artificial hyper-viscosity (-Δ)ℓ/ 2, ℓ > 2 to the model. It is shown in the present paper that, in the whole space, solutions to those modified models converge as t → ∞ toward solutions of the original Navier Stokes system.
Navier-Stokes Simulation of Several High-Lift Reference H Configurations
NASA Technical Reports Server (NTRS)
Lessard, Wendy B.
1999-01-01
The subsonic flow field was numerically simulated around several High Speed Research Reference H configurations at various pitch and yaw angles. A sequence of structured-viscous grids were generated; the first grid modeled the wing-body high-lift geometry, and the second grid incorporated the nacelles and the horizontal tail. The third grid modeled the full-span geometry for sideslip calculations, and was obtained by mirroring a coarser version of the second grid. The CFL3D code, a Reynolds averaged, thin-layer Navier-Stokes flow solver for structural grids, was used for the flow solver and modeled the free-air Reference H high-lift configuration at wind tunnel conditions of Mach number 0.24 and Reynolds number of 1.4 x 10(exp 5) per in. Pitch sweeps were performed at angles of attack from 6 deg to 15 deg. Sideslip angle sweeps at 0 deg <= Beta <= +18 deg were performed at an angle of attack of 8 deg. The lateral and longitudinal performance characteristics were well predicted and very good force and moment comparisons were obtained. A very complex multiple vortical system develops at the higher angles of attack, and detailed postprocessing of the solutions provided a comprehensive three-dimensional understanding of the flow which helps to correlate and interpret the wind tunnel data.
Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Swanson, Roy C., Jr.; Turkel, Eli; Rossow, C.-C.
2007-01-01
The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.
The computation of flow past an oblique wing using the thin-layer Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Mehta, Unmeel
1986-01-01
Essential aspects are presented for computing flow past an oblique wing with the thin-layer Navier-Stokes equations. A new method is developed for generating a grid system around a realistic wing. This method utilizes a series of conformal transformations. The thin-shear-layer approximation and an algebraic eddy-viscosity turbulence model are used to simplify the Reynolds-averaged Navier-Stokes equations. An implicit, factored numerical scheme and the concept of pencil data structure are utilized. For the first time, some flow fields caused by the oblique wing in a supersonic free stream are discussed, emphasizing the separated vortex flows associated with such a wing.
Properties of the Residual Stress of the Temporally Filtered Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Pruett, C. D.; Gatski, T. B.; Grosch, C. E.; Thacker, W. D.
2002-01-01
The development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, is of current interest. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. Causal time-domain filters, parameterized by a temporal filter width 0 less than Delta less than infinity, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Delta. The behavior of the residual stress in the limits of both vanishing and in infinite filter widths is examined. It is shown analytically that, in the limit Delta to 0, the residual stress vanishes, in which case the Navier-Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Delta to infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and a priori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted.
Relaxation Method for Navier-Stokes Equation
NASA Astrophysics Data System (ADS)
de Oliveira, P. M. C.
2012-04-01
The motivation for this work was a simple experiment [P. M. C. de Oliveira, S. Moss de Oliveira, F. A. Pereira and J. C. Sartorelli, preprint (2010), arXiv:1005.4086], where a little polystyrene ball is released falling in air. The interesting observation is a speed breaking. After an initial nearly linear time-dependence, the ball speed reaches a maximum value. After this, the speed finally decreases until its final, limit value. The provided explanation is related to the so-called von Kármán street of vortices successively formed behind the falling ball. After completely formed, the whole street extends for some hundred diameters. However, before a certain transient time needed to reach this steady-state, the street is shorter and the drag force is relatively reduced. Thus, at the beginning of the fall, a small and light ball may reach a speed superior to the sustainable steady-state value. Besides the real experiment, the numerical simulation of a related theoretical problem is also performed. A cylinder (instead of a 3D ball, thus reducing the effective dimension to 2) is positioned at rest inside a wind tunnel initially switched off. Suddenly, at t = 0 it is switched on with a constant and uniform wind velocity ěc{V} far from the cylinder and perpendicular to it. This is the first boundary condition. The second is the cylinder surface, where the wind velocity is null. In between these two boundaries, the velocity field is determined by solving the Navier-Stokes equation, as a function of time. For that, the initial condition is taken as the known Stokes laminar limit V → 0, since initially the tunnel is switched off. The numerical method adopted in this task is the object of the current text.
Navier-Stokes analysis of cold scramjet-afterbody flows
NASA Technical Reports Server (NTRS)
Baysal, Oktay; Engelund, Walter C.; Eleshaky, Mohamed E.
1989-01-01
The progress of two efforts in coding solutions of Navier-Stokes equations is summarized. The first effort concerns a 3-D space marching parabolized Navier-Stokes (PNS) code being modified to compute the supersonic mixing flow through an internal/external expansion nozzle with multicomponent gases. The 3-D PNS equations, coupled with a set of species continuity equations, are solved using an implicit finite difference scheme. The completed work is summarized and includes code modifications for four chemical species, computing the flow upstream of the upper cowl for a theoretical air mixture, developing an initial plane solution for the inner nozzle region, and computing the flow inside the nozzle for both a N2/O2 mixture and a Freon-12/Ar mixture, and plotting density-pressure contours for the inner nozzle region. The second effort concerns a full Navier-Stokes code. The species continuity equations account for the diffusion of multiple gases. This 3-D explicit afterbody code has the ability to use high order numerical integration schemes such as the 4th order MacCormack, and the Gottlieb-MacCormack schemes. Changes to the work are listed and include, but are not limited to: (1) internal/external flow capability; (2) new treatments of the cowl wall boundary conditions and relaxed computations around the cowl region and cowl tip; (3) the entering of the thermodynamic and transport properties of Freon-12, Ar, O, and N; (4) modification to the Baldwin-Lomax turbulence model to account for turbulent eddies generated by cowl walls inside and external to the nozzle; and (5) adopting a relaxation formula to account for the turbulence in the mixing shear layer.
Navier-Stokes analysis of radial turbine rotor performance
NASA Technical Reports Server (NTRS)
Larosiliere, L. M.
1993-01-01
An analysis of flow through a radial turbine rotor using the three-dimensional, thin-layer Navier-Stokes code RVC3D is described. The rotor is a solid version of an air-cooled metallic radial turbine having thick trailing edges, shroud clearance, and scalloped-backface clearance. Results are presented at the nominal operating condition using both a zero-clearance model and a model simulating the effects of the shroud and scalloped-backface clearance flows. A comparison with the available test data is made and details of the internal flow physics are discussed, allowing a better understanding of the complex flow distribution within the rotor.
Transonic Navier-Stokes solutions of three-dimensional afterbody flows
NASA Technical Reports Server (NTRS)
Compton, William B., III; Thomas, James L.; Abeyounis, William K.; Mason, Mary L.
1989-01-01
The performance of a three-dimensional Navier-Stokes solution technique in predicting the transonic flow past a nonaxisymmetric nozzle was investigated. The investigation was conducted at free-stream Mach numbers ranging from 0.60 to 0.94 and an angle of attack of 0 degrees. The numerical solution procedure employs the three-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations written in strong conservation form, a thin layer assumption, and the Baldwin-Lomax turbulence model. The equations are solved by using the finite-volume principle in conjunction with an approximately factored upwind-biased numerical algorithm. In the numerical procedure, the jet exhaust is represented by a solid sting. Wind-tunnel data with the jet exhaust simulated by high pressure air were also obtained to compare with the numerical calculations.
Navier-Stokes calculations on multi-element airfoils using a chimera-based solver
NASA Technical Reports Server (NTRS)
Jasper, Donald W.; Agrawal, Shreekant; Robinson, Brian A.
1993-01-01
A study of Navier-Stokes calculations of flows about multielement airfoils using a chimera grid approach is presented. The chimera approach utilizes structured, overlapped grids which allow great flexibility of grid arrangement and simplifies grid generation. Calculations are made for two-, three-, and four-element airfoils, and modeling of the effect of gap distance between elements is demonstrated for a two element case. Solutions are obtained using the thin-layer form of the Reynolds averaged Navier-Stokes equations with turbulence closure provided by the Baldwin-Lomax algebraic model or the Baldwin-Barth one equation model. The Baldwin-Barth turbulence model is shown to provide better agreement with experimental data and to dramatically improve convergence rates for some cases. Recently developed, improved farfield boundary conditions are incorporated into the solver for greater efficiency. Computed results show good comparison with experimental data which include aerodynamic forces, surface pressures, and boundary layer velocity profiles.
A fully vectorized numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Patel, N.
1983-01-01
A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.
Navier-Stokes simulation of transonic wing flow fields using a zonal grid approach
NASA Technical Reports Server (NTRS)
Chaderjian, Neal M.
1988-01-01
The transonic Navier-Stokes code was used to simulate flow fields about isolated wings for workshop wind-tunnel and free-air cases using the thin-layer Reynolds-averaged Navier-Stokes equations. An implicit finite-difference scheme based on a diagonal version of the Beam-Warming algorithm was used to integrate the governing equations. A zonal grid approach was used to allow efficient grid refinement near the wing surface. The flow field was sensitive to the turbulent transition model, and flow unsteadiness was observed for a wind-tunnel case but not for the corresponding free-air case. The specification of experimental pressure at the wind-tunnel exit plane is the primary reason for the difference of these two numerical solutions.
Automatic differentiation and Navier-Stokes.
Bischof, C.; Hovland, P.; Mohammadi, B.
1997-12-17
We describe the use of automatic differentiation (AD) to enhance a compressible Navier-Stokes model. With the solver, AD is used to accelerate convergence by more than an order of magnitude. Outside the solver, AD is used to compute the derivatives needed for optimization. We emphasize the potential for performance gains if the programmer does not treat AD as a black box, but instead utilizes high-level knowledge about the nature of the application.
Hybrid solution of the averaged Navier-Stokes equations for turbulent flow
NASA Astrophysics Data System (ADS)
Lima, J. A.; Perez-Guerrero, J. S.; Cotta, R. M.
The Generalized Integral Transform Technique (GITT) is utilized in the hybrid numerical-analytical solution of the Reynolds averaged Navier-Stokes equations, for developing turbulent flow inside a parallel-plates channel. An algebraic turbulence model is employed in modelling the turbulent diffusivity. The automatic global error control feature inherent to this approach, permits the determination of fully converged reference results for the validation of purely numerical methods. Therefore, numerical results for different values of Reynolds number are obtained, both for illustrating the convergence characteristics of the integral transform approach, and for critical comparisons with previously reported results through different models and numerical schemes.
Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Anderson, W. Kyle
1998-01-01
A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.
Iterative solvers for Navier-Stokes equations: Experiments with turbulence model
Page, M.; Garon, A.
1994-12-31
In the framework of developing software for the prediction of flows in hydraulic turbine components, Reynolds averaged Navier-Stokes equations coupled with {kappa}-{omega} two-equation turbulence model are discretized by finite element method. Since the resulting matrices are large, sparse and nonsymmetric, strategies based on CG-type iterative methods must be devised. A segregated solution strategy decouples the momentum equation, the {kappa} transport equation and the {omega} transport equation. These sets of equations must be solved while satisfying constraint equations. Experiments with orthogonal projection method are presented for the imposition of essential boundary conditions in a weak sense.
A poor man's compressible Navier--Stokes equation
NASA Astrophysics Data System (ADS)
McDonough, J. M.; Strodtbeck, J. P.
2008-11-01
We outline derivation of a ``poor man's compressible Navier--Stokes'' (PMCNS) equation, a discrete dynamical system (DDS) extending analyses of McDonough and Huang (Int. J. Numer. Meth. Fluids 44, 545, 2004) for the 2-D incompressible Navier--Stokes (N.--S.) equation to the 3-D compressible counterpart, and we indicate a method for computing bifurcation parameters of the DDS directly from those of the original differential equations, along with known physical parameters such as transport properties. We briefly provide a mathematical characterization of the PMCNS equation, in particular noting an approximate relationship to micro-local analysis of a pseudo-differential operator of the compressible N.--S. equation. We then investigate time series, power spectra and bifurcation diagrams of this DDS for various combinations of bifurcation parameters, including those most closely corresponding to homogeneous, isotropic turbulence; and we present comparisons of PMCNS calculations with extant experimental and DNS compressible flow data. We conclude by discussing application of this discrete dynamical system to construction of subgrid-scale models for LES of compressible flows within a synthetic-velocity/multi-scale framework.
Incompressible Navier-Stokes and parabolized Navier-Stokes formulations and computational techniques
NASA Technical Reports Server (NTRS)
Rubin, S. G.
1984-01-01
The differential formulations and computational techniques currently used for the incompressible Navier-Stokes (NS) and parabolic Navier-Stokes (PNS) equations are reviewed. In particular, attention is given to problems associated with the choice of difference equations, the method of solution and the choice of algorithm, the coupling of dependent variables and discretized equations, the application of boundary conditions, and grid generation. A new composite velocity NS and PNS formulation in (u,v,p) variables is presented, and the applicability of a 'forward' difference global pressure iteration for the (u,v,p) PNS system is demonstrated.
Navier-Stokes simulations of unsteady transonic flow phenomena
NASA Technical Reports Server (NTRS)
Atwood, C. A.
1992-01-01
Numerical simulations of two classes of unsteady flows are obtained via the Navier-Stokes equations: a blast-wave/target interaction problem class and a transonic cavity flow problem class. The method developed for the viscous blast-wave/target interaction problem assumes a laminar, perfect gas implemented in a structured finite-volume framework. The approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the blast-waves with stationary targets. The inviscid flux is evaluated using either of two upwind techniques, while the full viscous terms are computed by central differencing. Comparisons of unsteady numerical, analytical, and experimental results are made in two- and three-dimensions for Couette flows, a starting shock-tunnel, and a shock-tube blockage study. The results show accurate wave speed resolution and nonoscillatory discontinuity capturing of the predominantly inviscid flows. Viscous effects were increasingly significant at large post-interaction times. While the blast-wave/target interaction problem benefits from high-resolution methods applied to the Euler terms, the transonic cavity flow problem requires the use of an efficient scheme implemented in a geometrically flexible overset mesh environment. Hence, the Reynolds averaged Navier-Stokes equations implemented in a diagonal form are applied to the cavity flow class of problems. Comparisons between numerical and experimental results are made in two-dimensions for free shear layers and both rectangular and quieted cavities, and in three-dimensions for Stratospheric Observatory For Infrared Astronomy (SOFIA) geometries. The acoustic behavior of the rectangular and three-dimensional cavity flows compare well with experiment in terms of frequency, magnitude, and quieting trends. However, there is a more rapid decrease in computed acoustic energy with frequency than observed experimentally owing to numerical
On the use of a three-dimensional Navier-Stokes solver for rocket engine pump impeller design
NASA Technical Reports Server (NTRS)
Chen, Wei-Chung; Prueger, George H.; Chan, Daniel C.; Eastland, Anthony H.
1992-01-01
A 3D Reynolds-averaged Navier-Stokes Solver and a Fast Grid Generator (FGG), developed specially for centrifugal impeller design, were incorporated into the pump impeller design process. The impeller performance from the CFD analysis was compared to one-dimensional prediction. Both analyses showed good agreement of the impeller hydraulic efficiency, 94.5 percent, but with an 8 percent discrepancy of Euler head prediction. The impeller blade angle, discharge hub to shroud width, axial length and blade stacking were systematically changed to achieve an optimum impeller design. Impeller overall efficiency, loss distribution, hub-to-tip flow angle distortion and blade-to-blade flow angle change are among those criteria used to evaluate impeller performance. Two grid sizes, one with 10 K grid points and one with 80 K grid points were used to evaluate grid dependency issues. The effects of grid resolution on the accuracy and turnaround time are discussed. In conclusion, it is demonstrated that CFD can be effectively used for design and optimization of rocket engine pump components.
Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Schwab, John R.; Bui, Trong T.
1993-01-01
A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.
NASA Technical Reports Server (NTRS)
Jones, Kenneth M.; Biedron, Robert T.; Whitlock, Mark
1995-01-01
A computational study was performed to determine the predictive capability of a Reynolds averaged Navier-Stokes code (CFL3D) for two-dimensional and three-dimensional multielement high-lift systems. Three configurations were analyzed: a three-element airfoil, a wing with a full span flap and a wing with a partial span flap. In order to accurately model these complex geometries, two different multizonal structured grid techniques were employed. For the airfoil and full span wing configurations, a chimera or overset grid technique was used. The results of the airfoil analysis illustrated that although the absolute values of lift were somewhat in error, the code was able to predict reasonably well the variation with Reynolds number and flap position. The full span flap analysis demonstrated good agreement with experimental surface pressure data over the wing and flap. Multiblock patched grids were used to model the partial span flap wing. A modification to an existing patched- grid algorithm was required to analyze the configuration as modeled. Comparisons with experimental data were very good, indicating the applicability of the patched-grid technique to analyses of these complex geometries.
Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Schwab, John R.; Bui, Trong T.
1993-01-01
A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.
Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Schwab, John R.; Bui, Trong T.
1993-01-01
A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.
The Proteus Navier-Stokes code
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Bui, Trong T.; Cavicchi, Richard H.; Conley, Julianne M.; Molls, Frank B.; Schwab, John R.
1992-01-01
An effort is currently underway at NASA Lewis to develop two- and three-dimensional Navier-Stokes codes, called Proteus, for aerospace propulsion applications. The emphasis in the development of Proteus is not algorithm development or research on numerical methods, but rather the development of the code itself. The objective is to develop codes that are user-oriented, easily-modified, and well-documented. Well-proven, state-of-the-art solution algorithms are being used. Code readability, documentation (both internal and external), and validation are being emphasized. This paper is a status report on the Proteus development effort. The analysis and solution procedure are described briefly, and the various features in the code are summarized. The results from some of the validation cases that have been run are presented for both the two- and three-dimensional codes.
NASA Technical Reports Server (NTRS)
Kiris, Cetin
1995-01-01
Development of an incompressible Navier-Stokes solution procedure was performed for the analysis of a liquid rocket engine pump components and for the mechanical heart assist devices. The solution procedure for the propulsion systems is applicable to incompressible Navier-Stokes flows in a steadily rotating frame of reference for any general complex configurations. The computer codes were tested on different complex configurations such as liquid rocket engine inducer and impellers. As a spin-off technology from the turbopump component simulations, the flow analysis for an axial heart pump was conducted. The baseline Left Ventricular Assist Device (LVAD) design was improved by adding an inducer geometry by adapting from the liquid rocket engine pump. The time-accurate mode of the incompressible Navier-Stokes code was validated with flapping foil experiment by using different domain decomposition methods. In the flapping foil experiment, two upstream NACA 0025 foils perform high-frequency synchronized motion and generate unsteady flow conditions for a downstream larger stationary foil. Fairly good agreement was obtained between unsteady experimental data and numerical results from two different moving boundary procedures. Incompressible Navier-Stokes code (INS3D) has been extended for heat transfer applications. The temperature equation was written for both forced and natural convection phenomena. Flow in a square duct case was used for the validation of the code in both natural and forced convection.
Multigrid calculations of 3-D turbulent viscous flows
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.
1989-01-01
Convergence properties of a multigrid algorithm, developed to calculate compressible viscous flows, are analyzed by a vector sequence eigenvalue estimate. The full 3-D Reynolds-averaged Navier-Stokes equations are integrated by an implicit multigrid scheme while a k-epsilon turbulence model is solved, uncoupled from the flow equations. Estimates of the eigenvalue structure for both single and multigrid calculations are compared in an attempt to analyze the process as well as the results of the multigrid technique. The flow through an annular turbine is used to illustrate the scheme's ability to calculate complex 3-D flows.
2008-09-01
triangulation, one can show that |Eh(vh)| ≤ ∑ e∈Eh n ∑ j=1 [ ceh −1/2 κe (‖ǫj‖0,κe + hκe |ǫj|1,κe) ‖JvhK‖0,e ] . Thus, |Eh(vh)| ≤ ∑ e∈Eh n ∑ j=1 [ ceh ...1/2 κe ( ‖ǫj‖21,κe )1/2 ‖JvhK‖0,e ] , ≤ ∑ e∈Eh n ∑ j=1 ceh −1/2 κe ∑ κ∈Th ‖ǫj‖21,κ 1/2 ‖JvhK‖0,e , ≤ C n ∑ j=1 ∑ κ∈Th
2014-09-06
train formation and reactant mixing in a model Chemical Oxygen Iodine Laser (COIL) unit. The configuration consists of a converging-diverging nozzle, a...appear to influence the mixing process in the lasing cavity significantly. 15. SUBJECT TERMS Large-eddy simulation, chemical oxygen iodine lasers...model Chemical Oxygen Iodine Laser (COIL) unit. The configuration consists of a converging-diverging nozzle, a lasing cavity, and a diffuser. The
Laskowski, Gregory Michael
2005-12-01
Flows with strong curvature present a challenge for turbulence models, specifically eddy viscosity type models which assume isotropy and a linear and instantaneous equilibrium relation between stress and strain. Results obtained from three different codes and two different linear eddy viscosity turbulence models are compared to a DNS simulation in order to gain some perspective on the turbulence modeling capability of SIERRA/Fuego. The Fuego v2f results are superior to the more common two-layer k-e model results obtained with both a commercial and research code in terms of the concave near wall behavior predictions. However, near the convex wall, including the separated region, little improvement is gained using the v2f model and in general the turbulent kinetic energy prediction is fair at best.
Chaos Synchronization in Navier-Stokes Turbulence
NASA Astrophysics Data System (ADS)
Lalescu, Cristian; Meneveau, Charles; Eyink, Gregory
2013-03-01
Chaos synchronization (CS) has been studied for some time now (Pecora & Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al 2002). CS in general is said to be present in coupled dynamical systems when a specific property of each system has the same time evolution for all, even though the evolution itself is chaotic. The Navier-Stokes (NS) equations describe the velocity for a wide range of fluids, and their solutions are usually called turbulent if fluctuation amplitudes decrease as a power of their wavenumber. There have been some studies of CS for continuous systems (Kocarev et al 1997), but CS for NS turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. Our DNS results show that high-wavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. The motivation for our work is to study deeply sub-Kolmogorov scales in fully developed turbulence (Schumacher 2007), which we found to be recoverable even at very high Reynolds number from simulations with moderate resolutions. This work is supported by the National Science Foundation's CDI-II program, project CMMI-0941530
Chaos Synchronization in Navier-Stokes Turbulence
NASA Astrophysics Data System (ADS)
Lalescu, Cristian C.; Meneveau, Charles; Eyink, Gregory L.
2012-11-01
Chaos synchronization (CS) has been studied for some time now (Pecora & Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al. 2002). CS in general is said to be present in a pair of coupled dynamical systems when a specific property of each system has the same time evolution for both, even though the evolution itself is chaotic. There have been some studies of CS for systems with an infinite number of degrees of freedom (Kocarev et al. 1997), but CS for Navier-Stokes (NS) turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. We present DNS results which show that high-wavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. We compare our results with related ideas of ``approximate inertial manifolds.'' The motivation for our work is to study deeply sub-Kolmogorov scales in fully developed turbulence (Schumacher 2007), which we show are recoverable even at very high Reynolds number from simulations that only resolve down to about the Kolmogorov scale. This work is supported by the National Science Foundation's CDI-II program, project CMMI-0941530.
Inverse Design of Nacelles Using Multi-Block Navier Stokes Codes
NASA Technical Reports Server (NTRS)
Naik, D. A.; Krist, S. E.; Campbell, R. L.; Vatsa, V. N.; Buning, P. G.; Gea, L. M.
1995-01-01
The objective of this work is to reshape a nacelle to achieve a specified nacelle pressure distribution. The nacelle may be either isolated or installed on an airplane. There are no restrictions on the attitude (toe, incidence, and roll) and position of the nacelle. The design algorithm is coupled to two different multi-block 3-D Navier Stokes flow solvers. The coupling between design and analysis is automated to the point where the design proceeds with minimal user input.
Compressible Navier-Stokes Equations with Revised Maxwell's Law
NASA Astrophysics Data System (ADS)
Hu, Yuxi; Racke, Reinhard
2017-03-01
We investigate the compressible Navier-Stokes equations where the constitutive law for the stress tensor given by Maxwell's law is revised to a system of relaxation equations for two parts of the tensor. The global well-posedness is proved as well as the compatibility with the classical compressible Navier-Stokes system in the sense that, for vanishing relaxation parameters, the solutions to the Maxwell system are shown to converge to solutions of the classical system.
Navier-Stokes computations for circulation controlled airfoils
NASA Technical Reports Server (NTRS)
Pulliam, T. H.; Jesperen, D. C.; Barth, T. J.
1986-01-01
Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.
Analysis of regularized Navier-Stokes equations. I, II
NASA Technical Reports Server (NTRS)
Ou, Yuh-Roung; Sritharan, S. S.
1991-01-01
A regularized form of the conventional Navier-Stokes equations is analyzed. The global existence and uniqueness are established for two classes of generalized solutions. It is shown that the solution of this regularized system converges to the solution of the conventional Navier-Stokes equations for low Reynolds numbers. Particular attention is given to the structure of attractors characterizing the solutions. Both local and global invariant manifolds are found, and the regularity properties of these manifolds are analyzed.
Navier-Stokes simulations of WECS airfoil flowfields
Homicz, G.F.
1994-06-01
Sandia National Laboratories has initiated an effort to apply Computational Fluid Dynamics (CFD) to the study of WECS aerodynamics. Preliminary calculations are presented for the flow past a SAND 0018/50 airfoil. The flow solver used is F3D, an implicitly, finite-difference code which solves the Thin-Layer Navier-airfoil. The flow solver used is F3D, an implicit, finite-difference code which solves the Thin-Layer Navier-Stokes equations. 2D steady-state calculations are presented at various angles of attack, {alpha}. Sectional lift and drag coefficient, as well as surface pressure distributions, are compared with wind tunnel data, and exhibit reasonable agreement at low to moderate angles of attack. At high {alpha}, where the airfoil is stalled, a converged solution to the steady-state equations could not be obtained. The flowfield continued to change with successive iterations, which is consistent with the fact that the actual flow is inherently transient, and requires the solution of the full unsteady form of the equations.
The Proteus Navier-Stokes code. [two and three dimensional computational fluid dynamics
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Schwab, John R.
1992-01-01
An effort is currently underway at NASA Lewis to develop two and three dimensional Navier-Stokes codes, called Proteus, for aerospace propulsion applications. Proteus solves the Reynolds-averaged, unsteady, compressible Navier-Stokes equations in strong conservation law form. Turbulence is modeled using a Baldwin-Lomax based algebraic eddy viscosity model. In addition, options are available to solve thin layer or Euler equations, and to eliminate the energy equation by assuming constant stagnation enthalpy. An extensive series of validation cases have been run, primarily using the two dimensional planar/axisymmetric version of the code. Several flows were computed that have exact solution such as: fully developed channel and pipe flow; Couette flow with and without pressure gradients; unsteady Couette flow formation; flow near a suddenly accelerated flat plate; flow between concentric rotating cylinders; and flow near a rotating disk. The two dimensional version of the Proteus code has been released, and the three dimensional code is scheduled for release in late 1991.
A unified multigrid solver for the Navier-Stokes equations on mixed element meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Venkatakrishnan, V.
1995-01-01
A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.
NASA Astrophysics Data System (ADS)
Luo, Dahai; Yan, Chao; Wang, Xiaoyong
2015-02-01
Separation commonly exists in the flows around flight vehicles and also in the internal combustor flows. Simulation of high-speed turbulent-separated flows using a reliable computational design tool is crucial for the development of supersonic and hypersonic vehicles. In this paper, we present the computational results of supersonic base and ramped-cavity flows at high Reynolds numbers using the partially averaged Navier-Stokes (PANS) method. The current PANS models are based on the Menter SST turbulence model and also the Wilcox k-ω model. Results from PANS simulations are compared in detail with the available experimental data. The effect of the resolution control parameter fk (the ratio of unresolved-to-total kinetic energy) relevant to the PANS method is investigated. More turbulent flow structures are resolved as expected with decreasing fk, but it does not mean better results can be obtained. Spatially varying and dynamically updated fk in PANS simulations has been performed. Results from variable fk PANS simulations show good agreement with the experiment and great improvement when compared to Reynolds averaged Navier-Stokes (RANS) computation and constant fk PANS simulations.
Singularity of Navier-Stokes Equations Leading to Turbulent Transition
NASA Astrophysics Data System (ADS)
Dou, Hua-Shu; Fluid Mechanics Research Team
2014-11-01
As is well known, there is discontinuity during the transition from laminar flow to turbulence in the time-averaged Navier-Stokes equations. In other words, singularity may implicitly exist in the Navier-Stokes equations. Transition of a laminar flow to turbulence must be implemented via the singularity. However, how the singularity of Navier-Stokes equations is related to the turbulent transition is not understood. In this study, the singularity possibly hidden in the Navier-Stokes equation is exactly derived by mathematical treatment. Then, it is found that for pressure driven flows, the singularity of Navier-Stokes equations corresponds to the inflection point on the velocity profile. Since the rate of amplification to a disturbance at the inflection point is infinite, the laminar flow is able to involve into turbulence at this point firstly at a sufficient high Reynolds number. This is the reason why turbulent spot is formed at the location of inflection point. It is further demonstrated that the existence of the singularity in the time-averaged Navier-Stokes equations is the necessary and sufficient condition for the turbulent transition in pressure driven flows. These results agrees well with the findings from the recent proposed energy gradient method. Professor in Fluid Mechanics; AIAA Associate Fellow.
Navier-Stokes simulation of the supersonic combustion flowfield in a ram accelerator
NASA Technical Reports Server (NTRS)
Yungster, Shaye
1991-01-01
A computational study of the ram accelerator, a ramjet-in-tube device for accelerating projectiles to ultrahigh velocities, is presented. The analysis is performed using a fully implicit TVD scheme that efficiently solves the Reynolds-averaged Navier-Stokes equations and the species continuity equations associated with a finite rate combustion model. The present results indicate that viscous effects are of primary importance in all the cases studied, shock-induced combustion always started in the boundary layer. The effects of Mach number, mixture composition, pressure and tubulence are investigated for various configurations. Two types of combustion processes, one stable and the other unstable, were observed depending on the inflow conditions. The possibility of stabilizing the detonation wave by means of a backward facing step is also investigated. Two numerical techniques were tested: vector extrapolation, to accelerate convergence, and a diagonal formulation that eliminates the expense of inverting large block matrices which arise in chemically reacting flows.
Navier-Stokes analysis of a delta wing in static and dynamic roll
NASA Technical Reports Server (NTRS)
Chaderjian, N.; Schiff, L.
1995-01-01
The three-dimensional, Reynolds-averaged, Navier-Stokes equations are used to numerically simulate non-steady high-incidence vortical flow about a 65 degree sweep delta wing under static roll and forced periodic roll motions. These computations have been previously reported in the literature, where emphasis was placed on validating the computational results with nonsteady experimental surface pressures, forces and moments. The emphasis of this research is to revisit these earlier computations and use nonsteady numerical flow visualization to analyze the nonlinear surface flow and vortex breakdown dynamics. Most notable are the periodic formation of surface-flow separation lines, and the periodic formation of vortex breakdown near the delta wing trailing edge.
Parallel performance investigations of an unstructured mesh Navier-Stokes solver
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
2000-01-01
A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense of additional memory usage. The solver is cache efficient and fully vectorizable, and is parallelized using a two-level hybrid MPI-OpenMP implementation suitable for shared and/or distributed memory architectures, as well as clusters of shared memory machines. Convergence and scalability results are illustrated for various high-lift cases.
Control-volume based Navier-Stokes equation solver valid at all flow velocities
NASA Technical Reports Server (NTRS)
Kim, S.-W.
1989-01-01
A control-volume based finite difference method to solve the Reynolds averaged Navier-Stokes equations is presented. A pressure correction equation valid at all flow velocities and a pressure staggered grid layout are used in the method. Example problems presented herein include: a developing laminar channel flow, developing laminar pipe flow, a lid-driven square cavity flow, a laminar flow through a 90-degree bent channel, a laminar polar cavity flow, and a turbulent supersonic flow over a compression ramp. A k-epsilon turbulence model supplemented with a near-wall turbulence model was used to solve the turbulent flow. It is shown that the method yields accurate computational results even when highly skewed, unequally spaced, curved grids are used. It is also shown that the method is strongly convergent for high Reynolds number flows.
An Evaluation of Parameters Influencing Jet Mixing Using the WIND Navier-stokes Code
NASA Technical Reports Server (NTRS)
Dembowski, Mary Ann; Georgiadis, Nicholas J.
2002-01-01
The WIND code, a Reynolds-averaged Navier-Stokes solver used for a variety of aerospace flow simulations, was investigated for a Mach 2 nozzle at a series of nozzle stagnation temperatures. Comparisons of WIND calculations are made to experimental measurements of axial velocity, Mach number, and stagnation temperature along the jet centerline. The primary objective was to investigate the capabilities of the two-equation turbulence models available in WIND, version 4.0, for the analysis of heated supersonic nozzle flows. The models examined were the Menter Shear Stress Transport (SST) model and the Chien k-epsilon model, with and without the compressibility correction due to Sarkar. It was observed that all of the turbulence models investigated produced solutions that did not agree well with the experimental measurements. The effects of freestream Mach number and turbulent Prandtl number specifications were also investigated.
Prediction of viscous ship roll damping by unsteady Navier-Stokes techniques
Korpus, R.A.; Falzarano, J.M.
1996-12-31
This paper describes a numerical technique for analyzing the viscous unsteady flow around oscillating ship hulls. The technique is based on a general Reynolds-Averaged Navier-Stokes (RANS) capability, and is intended to generate viscous roll moment data for the incorporation of real-flow effects into potential flow ship motions programs. The approach utilizes the Finite Analytic technique for discretizing the unsteady RANS equations, and a variety of advanced turbulence models for closure. The calculations presented herein focus on viscous and vortical effects without free-surface, and utilize {kappa}{epsilon} turbulence modeling. Series variations are presented to study the effects of frequency, amplitude, Reynolds number, and the presence of bilge keels. Moment component breakdown studies are performed in each case to isolate the effects of viscosity, vorticity, and potential flow pressures.
Three-Dimensional Navier-Stokes Calculations Using the Modified Space-Time CESE Method
NASA Technical Reports Server (NTRS)
Chang, Chau-lyan
2007-01-01
The space-time conservation element solution element (CESE) method is modified to address the robustness issues of high-aspect-ratio, viscous, near-wall meshes. In this new approach, the dependent variable gradients are evaluated using element edges and the corresponding neighboring solution elements while keeping the original flux integration procedure intact. As such, the excellent flux conservation property is retained and the new edge-based gradients evaluation significantly improves the robustness for high-aspect ratio meshes frequently encountered in three-dimensional, Navier-Stokes calculations. The order of accuracy of the proposed method is demonstrated for oblique acoustic wave propagation, shock-wave interaction, and hypersonic flows over a blunt body. The confirmed second-order convergence along with the enhanced robustness in handling hypersonic blunt body flow calculations makes the proposed approach a very competitive CFD framework for 3D Navier-Stokes simulations.
NASA Astrophysics Data System (ADS)
Priymak, V. G.
1995-05-01
We present a new family of algorithms for incompressible 3D Navier-Stokes equations in cylindrical geometry. A model problem of turbulent flow calculation in an infinite circular pipe {(r, ϕ, z): 0 ≤ r ≤ R, 0 ≤ ϕ < 2π, |z| < ∞} is considered and used for accuracy, stability, and efficiency estimations. Algorithms are based on Galerkin trigonometric approximation for uniform variables ϕ, z, on pseudospectral polynomial approximation in the r -direction (with different sets of collocation nodes) and on implicit and predictor-corrector time advancement schemes. In all cases high (infinite order) spatial accuracy is retained despite the presence of coordinate singularity at r = 0. To achieve this we exploit the behaviour of analytic functions of variables r, ϕ, z in the vicinity of r = 0. We analyze the advantages and disadvantages of four Navier-Stokes algorithms. In method A a new splitting technique is developed which makes use of a second-order predictor-corrector scheme and nontraditional fractional step procedure. Stability and efficiency characteristics of this scheme exceed that of the usually used mixed Adams-Bashforth/Crank-Nicolson time advancement. To minimize errors due to splitting, algorithm B is suggested that has no fractional steps. In this method pressure values are eliminated from discretized Navier-Stokes equations by means of equivalent matrix operations. Although conventional Chebyshev collocation nodes rl = R cos(πl/2Q), l = 0, 1, ..., Q, are used in both methods, the discrete boundary conditions at r = 0-consistent with analytic behaviour of solutions for small r-are fully accessible for the first time. In addition, approximations developed prevent the appearance of various pathological (with, e.g., spurious, parasitic modes, etc.) discretizations of Navier-Stokes operators. In algorithm C we propose a new set of collocation nodes rl = (1 - xl)R/2, l = 0, 1, ..., Q, where xl ɛ (-1, 1), l = 1, 2, ..., Q - 1, are the zeros of
NASA Technical Reports Server (NTRS)
Yoon, Seokkwan; Kwak, Dochan
1991-01-01
A numerical method based on the pseudocompressibility concept is developed for solving the three-dimensional incompressible Navier-Stokes equations using the lower-upper symmetric-Gauss-Seidel implicit scheme. Very high efficiency is achieved in a new flow solver, INS3D-LU code, by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.
NASA Astrophysics Data System (ADS)
Miao, Sha; Hendrickson, Kelli; Liu, Yuming; Subramani, Hariprasad
2015-11-01
This work presents a novel and efficient Cartesian-grid based simulation capability for the study of an incompressible, turbulent gas layer over a liquid flow with disparate Reynolds numbers in two phases. This capability couples a turbulent gas-flow solver and a liquid-layer based on a second-order accurate Boundary Data Immersion Method (BDIM) at the deformable interface. The turbulent gas flow solver solves the incompressible Navier-Stokes equations via direct numerical simulation or through turbulence closure (unsteady Reynolds-Averaged Navier-Stokes Models) for Reynolds numbers O(106). In this application, a laminar liquid layer solution is obtained from depth-integrated Navier-Stokes equations utilizing shallow water wave assumptions. The immersed boundary method (BDIM) enforces the coupling at the deformable interface, the boundary conditions to turbulence closure equations and defines the domain geometry on the Cartesian grid. Validations are made for the turbulent gas channel flow over high-viscosity liquid. This simulation capability can be applied to problems in the oil and industrial sector such as channel and pipe flows with heavy oils as well as wind wave generation in shallow waters. Sponsored by the Chevron Energy Technology Company.
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.; Ghaffari, Farhad
2011-01-01
Numerical predictions of the longitudinal aerodynamic characteristics for the Ares I class of vehicles, along with the associated error estimate derived from an iterative convergence grid refinement, are presented. Computational results are based on the unstructured grid, Reynolds-averaged Navier-Stokes flow solver USM3D, with an assumption that the flow is fully turbulent over the entire vehicle. This effort was designed to complement the prior computational activities conducted over the past five years in support of the Ares I Project with the emphasis on the vehicle s last design cycle designated as the A106 configuration. Due to a lack of flight data for this particular design s outer mold line, the initial vehicle s aerodynamic predictions and the associated error estimates were first assessed and validated against the available experimental data at representative wind tunnel flow conditions pertinent to the ascent phase of the trajectory without including any propulsion effects. Subsequently, the established procedures were then applied to obtain the longitudinal aerodynamic predictions at the selected flight flow conditions. Sample computed results and the correlations with the experimental measurements are presented. In addition, the present analysis includes the relevant data to highlight the balance between the prediction accuracy against the grid size and, thus, the corresponding computer resource requirements for the computations at both wind tunnel and flight flow conditions. NOTE: Some details have been removed from selected plots and figures in compliance with the sensitive but unclassified (SBU) restrictions. However, the content still conveys the merits of the technical approach and the relevant results.
A locally stabilized immersed boundary method for the compressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Brehm, C.; Hader, C.; Fasel, H. F.
2015-08-01
A higher-order immersed boundary method for solving the compressible Navier-Stokes equations is presented. The distinguishing feature of this new immersed boundary method is that the coefficients of the irregular finite-difference stencils in the vicinity of the immersed boundary are optimized to obtain improved numerical stability. This basic idea was introduced in a previous publication by the authors for the advection step in the projection method used to solve the incompressible Navier-Stokes equations. This paper extends the original approach to the compressible Navier-Stokes equations considering flux vector splitting schemes and viscous wall boundary conditions at the immersed geometry. In addition to the stencil optimization procedure for the convective terms, this paper discusses other key aspects of the method, such as imposing flux boundary conditions at the immersed boundary and the discretization of the viscous flux in the vicinity of the boundary. Extensive linear stability investigations of the immersed scheme confirm that a linearly stable method is obtained. The method of manufactured solutions is used to validate the expected higher-order accuracy and to study the error convergence properties of this new method. Steady and unsteady, 2D and 3D canonical test cases are used for validation of the immersed boundary approach. Finally, the method is employed to simulate the laminar to turbulent transition process of a hypersonic Mach 6 boundary layer flow over a porous wall and subsonic boundary layer flow over a three-dimensional spherical roughness element.
NASA Technical Reports Server (NTRS)
Smith, Crawford F.; Podleski, Steve D.
1993-01-01
The proper use of a computational fluid dynamics code requires a good understanding of the particular code being applied. In this report the application of CFL3D, a thin-layer Navier-Stokes code, is compared with the results obtained from PARC3D, a full Navier-Stokes code. In order to gain an understanding of the use of this code, a simple problem was chosen in which several key features of the code could be exercised. The problem chosen is a cone in supersonic flow at an angle of attack. The issues of grid resolution, grid blocking, and multigridding with CFL3D are explored. The use of multigridding resulted in a significant reduction in the computational time required to solve the problem. Solutions obtained are compared with the results using the full Navier-Stokes equations solver PARC3D. The results obtained with the CFL3D code compared well with the PARC3D solutions.
Summary of EASM Turbulence Models in CFL3D With Validation Test Cases
NASA Technical Reports Server (NTRS)
Rumsey, Christopher L.; Gatski, Thomas B.
2003-01-01
This paper summarizes the Explicit Algebraic Stress Model in k-omega form (EASM-ko) and in k-epsilon form (EASM-ke) in the Reynolds-averaged Navier-Stokes code CFL3D. These models have been actively used over the last several years in CFL3D, and have undergone some minor modifications during that time. Details of the equations and method for coding the latest versions of the models are given, and numerous validation cases are presented. This paper serves as a validation archive for these models.
Numerical solutions of the complete Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Hassan, H. A.
1986-01-01
Using ideas from the kinetic theory, the Navier-Stokes equations are modified in such a way that they can be cast as a set of first order hyperbolic equations. This is achieved by incorporating time dependent terms into the definition of the stress tensor and the heat flux vectors. The boundary conditions are then determined from the theory of characteristics. Because the resulting equations reduce to the traditional Navier-Stokes equations when the steady state is reached, the present approach provides a straightforward scheme for the determination of inflow and outflow boundary conditions. The method is validated by comparing its predictions with known exact solutions of the steady Navier-Stokes equations.
Navier-Stokes calculations of scramjet-nozzle-afterbody flowfields
NASA Technical Reports Server (NTRS)
Baysal, Oktay
1991-01-01
A comprehensive computational fluid dynamics effort was conducted from 1987 to 1990 to properly design a nozzle and lower aft end of a generic hypersonic vehicle powered by a scramjet engine. The interference of the exhaust on the control surfaces of the vehicle can have adverse effects on its stability. Two-dimensional Navier-Stokes computations were performed, where the exhaust gas was assumed to be air behaving as a perfect gas. Then the exhaust was simulated by a mixture of Freon-12 and argon, which required solving the Navier-Stokes equations for four species: (nitrogen, oxygen, Freon-12, and argon). This allowed gamma to be a field variable during the mixing of the multispecies gases. Two different mixing models were used and comparisons between them as well as the perfect gas air calculations were made to assess their relative merits. Finally, the three dimensional Navier-Stokes computations were made for the full-span scramjet nozzle afterbody module.
A dual potential formulation of the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Gegg, S. G.; Pletcher, R. H.; Steger, J. L.
1989-01-01
A dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented. The velocity field is decomposed using a scalar and vector potential. Vorticity and dilatation are used as the dependent variables in the momentum equations. Test cases in two dimensions verify the capability to solve flows using approximations from potential flow to full Navier-Stokes simulations. A three-dimensional incompressible flow formulation is also described. An interesting feature of this approach to solving the Navier-Stokes equations is the decomposition of the velocity field into a rotational part (vector potential) and an irrotational part (scalar potential). The Helmholtz decomposition theorem allows this splitting of the velocity field. This approach has had only limited use since it increases the number of dependent variables in the solution. However, it has often been used for incompressible flows where the solution scheme is known to be fast and accurate. This research extends the usage of this method to fully compressible Navier-Stokes simulations by using the dilatation variable along with vorticity. A time-accurate, iterative algorithm is used for the uncoupled solution of the governing equations. Several levels of flow approximation are available within the framework of this method. Potential flow, Euler and full Navier-Stokes solutions are possible using the dual potential formulation. Solution efficiency can be enhanced in a straightforward way. For some flows, the vorticity and/or dilatation may be negligible in certain regions (e.g., far from a viscous boundary in an external flow). It is possible to drop the calculation of these variables then and optimize the solution speed. Also, efficient Poisson solvers are available for the potentials. The relative merits of non-primitive variables versus primitive variables for solution of the Navier-Stokes equations are also discussed.
Convergence acceleration of an aeroelastic Navier-Stokes solver
NASA Technical Reports Server (NTRS)
Obayashi, S.; Guruswamy, G.
1994-01-01
New capabilities have been added to a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is completely rewritten with a combination of the LU-SGS (Lower-Upper factored Symmetric Gauss-Seidel) implicit method and the modified HLLE (Harten-Lax-van Leer-Einfeldt) upwind scheme. A pseudo-time marching method is used for the directly coupled structural equations to improve overall convergence rates for static aeroelastic analysis. Results are demonstrated for transonic flows over rigid and flexible wings.
Factorization of the Compressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.
2005-01-01
The Navier-Stokes equations for a Newtonian ideal gas are examined to determine the factorizable form of the equations relevant to the construction of a factorizable relaxation scheme. The principal linearization of the equations is found by examining the relative magnitude of the terms for short-wavelength errors. The principal part of the operator is then found. Comparison of the factors of the Navier-Stokes and Euler equations differ qualitatively because of the coupling of entropy and pressure through thermal diffusion. Special cases of the factorization are considered.
Algorithm implementation on the Navier-Stokes computer
NASA Technical Reports Server (NTRS)
Krist, Steven E.; Zang, Thomas A.
1987-01-01
The Navier-Stokes Computer is a multi-purpose parallel-processing supercomputer which is currently under development at Princeton University. It consists of multiple local memory parallel processors, called Nodes, which are interconnected in a hypercube network. Details of the procedures involved in implementing an algorithm on the Navier-Stokes computer are presented. The particular finite difference algorithm considered in this analysis was developed for simulation of laminar-turbulent transition in wall bounded shear flows. Projected timing results for implementing this algorithm indicate that operation rates in excess of 42 GFLOPS are feasible on a 128 Node machine.
Navier-Stokes computations useful in aircraft design
NASA Technical Reports Server (NTRS)
Holst, Terry L.
1990-01-01
Large scale Navier-Stokes computations about aircraft components as well as reasonably complete aircraft configurations are presented and discussed. Speed and memory requirements are described for various general problem classes, which in some cases are already being used in the industrial design environment. Recent computed results, with experimental comparisons when available, are included to highlight the presentation. Finally, prospects for the future are described and recommendations for areas of concentrated research are indicated. The future of Navier-Stokes computations is seen to be rapidly expanding across a broad front of applications, which includes the entire subsonic-to-hypersonic speed regime.
Pseudo-time algorithms for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Turkel, E.
1986-01-01
A pseudo-time method is introduced to integrate the compressible Navier-Stokes equations to a steady state. This method is a generalization of a method used by Crocco and also by Allen and Cheng. We show that for a simple heat equation that this is just a renormalization of the time. For a convection-diffusion equation the renormalization is dependent only on the viscous terms. We implement the method for the Navier-Stokes equations using a Runge-Kutta type algorithm. This permits the time step to be chosen based on the inviscid model only. We also discuss the use of residual smoothing when viscous terms are present.
Analysis of regularized Navier-Stokes equations, 2
NASA Technical Reports Server (NTRS)
Ou, Yuh-Roung; Sritharan, S. S.
1989-01-01
A practically important regularization of the Navier-Stokes equations was analyzed. As a continuation of the previous work, the structure of the attractors characterizing the solutins was studied. Local as well as global invariant manifolds were found. Regularity properties of these manifolds are analyzed.
Cavitation Modeling in Euler and Navier-Stokes Codes
NASA Technical Reports Server (NTRS)
Deshpande, Manish; Feng, Jinzhang; Merkle, Charles L.
1993-01-01
Many previous researchers have modeled sheet cavitation by means of a constant pressure solution in the cavity region coupled with a velocity potential formulation for the outer flow. The present paper discusses the issues involved in extending these cavitation models to Euler or Navier-Stokes codes. The approach taken is to start from a velocity potential model to ensure our results are compatible with those of previous researchers and available experimental data, and then to implement this model in both Euler and Navier-Stokes codes. The model is then augmented in the Navier-Stokes code by the inclusion of the energy equation which allows the effect of subcooling in the vicinity of the cavity interface to be modeled to take into account the experimentally observed reduction in cavity pressures that occurs in cryogenic fluids such as liquid hydrogen. Although our goal is to assess the practicality of implementing these cavitation models in existing three-dimensional, turbomachinery codes, the emphasis in the present paper will center on two-dimensional computations, most specifically isolated airfoils and cascades. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce consistent predictions. Comparisons with experimental results also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects in both cryogenic and non-cryogenic fluids. The impact on CPU time and the code modifications required suggests that these models are appropriate for incorporation in current generation turbomachinery codes.
A multidimensional flux function with applications to the Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Rumsey, Christopher L.; Van Leer, Bram; Roe, Philip L.
1993-01-01
In the present grid-independent approximate Riemann solver for 2D and 3D flows that are governed by the Euler or Navier-Stokes equations, fluxes on grid faces are obtained by wave decomposition; the assumption of information-propagation in the velocity-difference directions leads to a more accurate resolution of shear and shock waves, when these are are oblique to the grid. The model, which yields significantly greater accuracy in both supersonic and subsonic first-order spatially accurate computations, describes the difference in states at each grid interface by the action of five waves.
Nonlinear Aeroelastic Analysis Using a Time-Accurate Navier-Stokes Equations Solver
NASA Technical Reports Server (NTRS)
Kuruvila, Geojoe; Bartels, Robert E.; Hong, Moeljo S.; Bhatia, G.
2007-01-01
A method to simulate limit cycle oscillation (LCO) due to control surface freeplay using a modified CFL3D, a time-accurate Navier-Stokes computational fluid dynamics (CFD) analysis code with structural modeling capability, is presented. This approach can be used to analyze aeroelastic response of aircraft with structural behavior characterized by nonlinearity in the force verses displacement curve. A limited validation of the method, using very low Mach number experimental data for a three-degrees-of-freedom (pitch/plunge/flap deflection) airfoil model with flap freeplay, is also presented.
Turbomachinery blade optimization using the Navier-Stokes equations
Chand, K.K.; Lee, K.D.
1997-12-01
A method is presented to perform aerodynamic design optimization of turbomachinery blades. The method couples a Navier-Stokes flow solver with a grid generator and numerical optimization algorithm to seek improved designs for transonic turbine blades. A fast and efficient multigrid, finite-volume flow solver provides accurate performance evaluations of potential designs. Design variables consist of smooth perturbations to the blade surface. A unique elliptic-hyperbolic grid generation method is used to regenerate a Navier-Stokes grid after perturbations have been added to the geometry. Designs are sought which improve a design objective while remaining within specified constraints. The method is demonstrated with two transonic turbine blades with different types and numbers of design variables.
Intermittency in two-dimensional Ekman-Navier-Stokes turbulence
NASA Astrophysics Data System (ADS)
Boffetta, G.; Celani, A.; Musacchio, S.; Vergassola, M.
2002-08-01
We study the statistics of the vorticity field in two-dimensional Navier-Stokes turbulence with linear Ekman friction. We show that the small-scale vorticity fluctuations are intermittent, as conjectured by Bernard [Europhys. Lett. 50, 333 (2000)] and Nam et al. [Phys. Rev. Lett. 84, 5134 (2000)]. The small-scale statistics of vorticity fluctuations coincide with that of a passive scalar with finite lifetime transported by the velocity field itself.
Dynamic Stall Computations Using a Zonal Navier-Stokes Model
1988-06-01
COMPUTATIONS USING A ZONAL NAVIER-STOKES MODEL OfOSONA, AUTWOR(S) Conrovd, Jack H. r. __ _ I, ,3 , iOR co T’M( COVERED DATE Of REPORT (Yea, Month Oy) IS PAGE...48 computer and is used to calculate the flow field about a NACA 0012 airfoil oscillating in pitch. Surface pressure distributions and integrated...lift, pitching moment, and drag coefficient versus angle of attack are compared to existing experimental data for four cases and existing computational
Navier-Stokes Simulation of Boundary-Layer Transition
1990-05-01
AUTHOITY 3 DISTRIBUTION/AVAILABILITY OF REPORT Approved for publlo release, distri but ion unmlioe4 ’ AD-A226 351 5 . MONITORING ORGANIZATION REPORT NUMBER...ARJSR 87-0237, "Navier-Stokes Simulation of Boundary-Layer Transition" escrs. 5 w ccessful efforts to computationally model the receptivity of the...3.1 Basic-State Results........................................ 4 3.2 Unsteady-Disturbance Results................................. 5 3.3 Conclusions
Characterization of blowup for the Navier-Stokes equations using vector potentials
NASA Astrophysics Data System (ADS)
Ohkitani, Koji
2017-01-01
We characterize a possible blowup for the 3D Navier-Stokes on the basis of dynamical equations for vector potentials 𝑨 . This is motivated by a known interpolation ∥𝑨∥ BMO≤∥𝒖∥ L3 , together with recent mathematical results. First, by working out an inversion formula for singular integrals that appear in the governing equations, we derive a criterion using the nonlinear term of 𝑨 as ∫0t∗∥∂𝑨/∂t-ν △ 𝑨 ∥ L∞d t =∞ for a blowup at t∗. Second, for a particular form of a scale-invariant singularity of the nonlinear term we show that the vector potential becomes unbounded in its L∞ and BMO norms. Using the stream function, we also consider the 2D Navier-Stokes equations to seek an alternative proof of their known global regularity. It is not yet proven that the BMO norm of vector potentials in 3D (or, the stream function in 2D) serve as a blow up criterion in more general cases.
Navier-Stokes computations of a viscous optimized waverider. M.S. Thesis
NASA Technical Reports Server (NTRS)
Takashima, Naruhisa
1992-01-01
The performance of a Mach 6 viscous optimized waverider was calculated using the 3-D Navier-Stokes equations. The Mach 6 viscous optimized waverider was generated using MAXWARP, a code developed at the University of Maryland. The computations were performed using CFL3D, an implicit upwind-biased finite-volume algorithm developed at NASA Langley. Results show that good agreement was found between the calculated performance by MAXWARP and results from the Mach 6 Navier-Stokes computation. Furthermore, off-design performance of the Mach 6 optimized waverider was computed at Mach 4 and 8. The performance at these Mach numbers compared well with the performance of the viscous optimized waveriders specifically designed for these Mach numbers. Finally, contours of different flow parameters in the cross-flow plane were examined for the three calculations. The results indicate that the flow gradients are relatively small within the captured flow, and the variation itself is well behaved; thus, making the waverider configuration a promising choice for an engine/airframe design, especially for cruise-type applications.
NASA Technical Reports Server (NTRS)
Chaderjian, Neal M.
1986-01-01
A computer code is under development whereby the thin-layer Reynolds-averaged Navier-Stokes equations are to be applied to realistic fighter aircraft configurations. This transonic Navier-Stokes code (TNS) utilizes a zonal approach in order to treat complex geometries and satisfy in-core computer memory constraints. The zonal approach was applied to isolated wing geometries in order to facilitate code development. The TNS finite difference algorithm, zonal methodology, and code validation with experimental data is addressed. Also addressed are some numerical issues such as code robustness, efficiency, and accuracy at high angles of attack. Special free-stream-preserving metrics proved an effective way to treat H-mesh singularities over a large range of severe flow conditions, including strong leading edge flow gradients, massive shock induced separation, and stall. Furthermore, lift and drag coefficients were computed for a wing up through CLmax. Numerical oil flow patterns and particle trajectories are presented both for subcritical and transonic flow. These flow simulations are rich with complex separated flow physics and demonstrate the efficiency and robustness of the zonal approach.
NASA Technical Reports Server (NTRS)
Chaderjian, N. M.
1986-01-01
A computer code is under development whereby the thin-layer Reynolds-averaged Navier-Stokes equations are to be applied to realistic fighter-aircraft configurations. This transonic Navier-Stokes code (TNS) utilizes a zonal approach in order to treat complex geometries and satisfy in-core computer memory constraints. The zonal approach has been applied to isolated wing geometries in order to facilitate code development. Part 1 of this paper addresses the TNS finite-difference algorithm, zonal methodology, and code validation with experimental data. Part 2 of this paper addresses some numerical issues such as code robustness, efficiency, and accuracy at high angles of attack. Special free-stream-preserving metrics proved an effective way to treat H-mesh singularities over a large range of severe flow conditions, including strong leading-edge flow gradients, massive shock-induced separation, and stall. Furthermore, lift and drag coefficients have been computed for a wing up through CLmax. Numerical oil flow patterns and particle trajectories are presented both for subcritical and transonic flow. These flow simulations are rich with complex separated flow physics and demonstrate the efficiency and robustness of the zonal approach.
NASA Technical Reports Server (NTRS)
Viegas, J. R.; Rubesin, M. W.
1983-01-01
To make computer codes for two-dimensional compressible flows more robust and economical, wall functions for these flows, under adiabatic conditions, have been developed and tested. These wall functions have been applied to three two-equation models of turbulence. The tests consist of comparisons of calculated and experimental results for transonic and supersonic flow over a flat plate and for two-dimensional and axisymmetrical transonic shock-wave/boundary-layer interaction flows with and without separation. The calculations are performed with an implicit algorithm that solves the Reynolds-averaged Navier-Stokes equations. It is shown that results obtained agree very well with the data for the complex compressible flows tested, provided criteria for use of the wall functions are followed. The expected savings in cost of the computations and improved robustness of the code were achieved.
Attractors of three-dimensional fast-rotating Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Trahe, Markus
The three-dimensional (3-D) rotating Navier-Stokes equations describe the dynamics of rotating, incompressible, viscous fluids. In this work, they are considered with smooth, time-independent forces and the original statements implied by the classical "Taylor-Proudman Theorem" of geophysics are rigorously proved. It is shown that fully developed turbulence of 3-D fast-rotating fluids is essentially characterized by turbulence of two-dimensional (2-D) fluids in terms of numbers of degrees of freedom. In this context, the 3-D nonlinear "resonant limit equations", which arise in a non-linear averaging process as the rotation frequency O → infinity, are studied and optimal (2-D-type) upper bounds for fractal box and Hausdorff dimensions of the global attractor as well as upper bounds for box dimensions of exponential attractors are determined. Then, the convergence of exponential attractors for the full 3-D rotating Navier-Stokes equations to exponential attractors for the resonant limit equations as O → infinity in the sense of full Hausdorff-metric distances is established. This provides upper and lower semi-continuity of exponential attractors with respect to the rotation frequency and implies that the number of degrees of freedom (attractor dimension) of 3-D fast-rotating fluids is close to that of 2-D fluids. Finally, the algebraic-geometric structure of the Poincare curves, which control the resonances and small divisor estimates for partial differential equations, is further investigated; the 3-D nonlinear limit resonant operators are characterized by three-wave interactions governed by these curves. A new canonical transformation between those curves is constructed; with far-reaching consequences on the density of the latter.
Time-Accurate, Unstructured-Mesh Navier-Stokes Computations with the Space-Time CESE Method
NASA Technical Reports Server (NTRS)
Chang, Chau-Lyan
2006-01-01
Application of the newly emerged space-time conservation element solution element (CESE) method to compressible Navier-Stokes equations is studied. In contrast to Euler equations solvers, several issues such as boundary conditions, numerical dissipation, and grid stiffness warrant systematic investigations and validations. Non-reflecting boundary conditions applied at the truncated boundary are also investigated from the stand point of acoustic wave propagation. Validations of the numerical solutions are performed by comparing with exact solutions for steady-state as well as time-accurate viscous flow problems. The test cases cover a broad speed regime for problems ranging from acoustic wave propagation to 3D hypersonic configurations. Model problems pertinent to hypersonic configurations demonstrate the effectiveness of the CESE method in treating flows with shocks, unsteady waves, and separations. Good agreement with exact solutions suggests that the space-time CESE method provides a viable alternative for time-accurate Navier-Stokes calculations of a broad range of problems.
Navier-Stokes simulation of the supersonic combustion flowfield in a ram accelerator
NASA Technical Reports Server (NTRS)
Yungster, Shaye
1991-01-01
A computational study of the ram accelerator, a ramjet-in-tube device for accelerating projectiles to ultrahigh velocities, is presented. The analysis is performed using a fully implicit TVD scheme that efficiently solves the Reynolds-averaged Navier-Stokes equations and the species continuity equations associated with a finite rate combustion model. Previous analyses of this concept were based on inviscid assumptions. The present results indicate that viscous effects are of primary importance; in all the cases studied, shock-induced combustion always started in the boundary layer. The effects of Mach number, mixture composition, pressure, and turbulence are investigated for various configurations. Two types of combustion processes, one stable and the other unstable, were observed depending on the inflow conditions. In the unstable case, a detonation wave is formed, which propagates upstream and unstarts the ram accelerator. In the stable case, a solution that converges to steady-state is obtained, in which the combustion wave remains stationary with respect to the ram accelerator projectile. The possibility of stabilizing the detonation wave by means of a backward facing step is also investigated. In addition to these studies, two numerical techniques were tested. These two techniques are vector extrapolation to accelerate convergence, and a diagonal formulation that eliminates the expense of inverting large block matrices that arise in chemically reacting flows.
Multitasking a three-dimensional Navier-Stokes algorithm on the Cray-2
NASA Technical Reports Server (NTRS)
Swisshelm, Julie M.
1989-01-01
A three-dimensional computational aerodynamics algorithm has been multitasked for efficient parallel execution on the Cray-2. It provides a means for examining the multitasking performance of a complete CFD application code. An embedded zonal multigrid scheme is used to solve the Reynolds-averaged Navier-Stokes equations for an internal flow model problem. The explicit nature of each component of the method allows a spatial partitioning of the computational domain to achieve a well-balanced task load for MIMD computers with vector-processing capability. Experiments have been conducted with both two- and three-dimensional multitasked cases. The best speedup attained by an individual task group was 3.54 on four processors of the Cray-2, while the entire solver yielded a speedup of 2.67 on four processors for the three-dimensional case. The multiprocessing efficiency of various types of computational tasks is examined, performance on two Cray-2s with different memory access speeds is compared, and extrapolation to larger problems is discussed.
Navier-Stokes computation of compressible turbulent flows with a second order closure, part 1
NASA Technical Reports Server (NTRS)
Haminh, Hieu; Kollmann, Wolfgang; Vandromme, Dany
1990-01-01
A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme.
Navier-Stokes Simulation of a Heavy Lift Slowed-Rotor Compound Helicopter Configuration
NASA Technical Reports Server (NTRS)
Allan, Brian G.; Jenkins, Luther N.; Yao, Chung-Sheng; Bartram, Scott M.; Hallissy, Jim B.; Harris, Jerome; Noonan, Kevin W.; Wong, Oliver D.; Jones, Henry E.; Malovrh, Brendon D.; reis, Deane G.; Mace, W. Derry
2009-01-01
Time accurate numerical simulations were performed using the Reynolds-averaged Navier-Stokes (RANS) flow solver OVERFLOW for a heavy lift, slowed-rotor, compound helicopter configuration, tested at the NASA Langley 14- by 22-Foot Subsonic Tunnel. The primary purpose of these simulations is to provide support for the development of a large field of view Particle Imaging Velocimetry (PIV) flow measurement technique supported by the Subsonic Rotary Wing (SRW) project under the NASA Fundamental Aeronautics program. These simulations provide a better understanding of the rotor and body wake flows and helped to define PIV measurement locations as well as requirements for validation of flow solver codes. The large field PIV system can measure the three-dimensional velocity flow field in a 0.914m by 1.83m plane. PIV measurements were performed upstream and downstream of the vertical tail section and are compared to simulation results. The simulations are also used to better understand the tunnel wall and body/rotor support effects by comparing simulations with and without tunnel floor/ceiling walls and supports. Comparisons are also made to the experimental force and moment data for the body and rotor.
NASA Astrophysics Data System (ADS)
Ghia, K. N.; Ghia, U.
1992-11-01
A two-and-a-quarter-year multi-tasked research project was pursued by the present investigators to study dynamic stall phenomenon under AFOSR sponsorship between Feb. 1990 - May 1992. The major objective was to predict and control the dynamic stall phenomenon in 2-D and 3-D flows. In the process of achieving these objectives, significant effort was directed towards developing mathematical models and the corresponding computational methods which were made available to interested researchers and organizations involved in computational fluid dynamics (CFD) research. The analyses developed included a two-dimensional Navier-Stokes (NS) analysis for a general body undergoing arbitrary three-degree-of-freedom maneuvers; detailed results are provided for this class of flows. For enhancement of accuracy and efficiency, an adaptive-grid time-accurate flow solution technique was developed to enable improved resolution of the various length scales in a vortex-dominated unsteady flow. A multi-block grid generation analysis is developed for a 3-D rectangular planform wing. For the corresponding flow analysis using velocity-vorticity variables and direct-solution philosophy, the difficulties experienced were clearly discussed in the annual report submitted a year ago in November 1991. This 3-D flow analysis was therefore temporarily set aside. It will be pursued further in a subsequent grant, and the progress made on it will be reported in a forthcoming annual report for that grant. In the current grant, the study of 3-D flows was continued, using an iterative solution methodology. Hence, a 3-D unsteady Navier-Stokes analysis, again using velocity-vorticity variables, and an iterative solution technique with multi-grid acceleration were developed.
Analysis of a High-Lift Multi-Element Airfoil using a Navier-Stokes Code
NASA Technical Reports Server (NTRS)
Whitlock, Mark E.
1995-01-01
A thin-layer Navier-Stokes code, CFL3D, was utilized to compute the flow over a high-lift multi-element airfoil. This study was conducted to improve the prediction of high-lift flowfields using various turbulence models and improved glidding techniques. An overset Chimera grid system is used to model the three element airfoil geometry. The effects of wind tunnel wall modeling, changes to the grid density and distribution, and embedded grids are discussed. Computed pressure and lift coefficients using Spalart-Allmaras, Baldwin-Barth, and Menter's kappa-omega - Shear Stress Transport (SST) turbulence models are compared with experimental data. The ability of CFL3D to predict the effects on lift coefficient due to changes in Reynolds number changes is also discussed.
Application of Aeroelastic Solvers Based on Navier Stokes Equations
NASA Technical Reports Server (NTRS)
Keith, Theo G., Jr.; Srivastava, Rakesh
2001-01-01
The propulsion element of the NASA Advanced Subsonic Technology (AST) initiative is directed towards increasing the overall efficiency of current aircraft engines. This effort requires an increase in the efficiency of various components, such as fans, compressors, turbines etc. Improvement in engine efficiency can be accomplished through the use of lighter materials, larger diameter fans and/or higher-pressure ratio compressors. However, each of these has the potential to result in aeroelastic problems such as flutter or forced response. To address the aeroelastic problems, the Structural Dynamics Branch of NASA Glenn has been involved in the development of numerical capabilities for analyzing the aeroelastic stability characteristics and forced response of wide chord fans, multi-stage compressors and turbines. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading is available. To obtain the steady and unsteady aerodynamic forces for the complex flows around the engine components, for the flow regimes encountered by the rotor, an advanced compressible Navier-Stokes solver is required. A finite volume based Navier-Stokes solver has been developed at Mississippi State University (MSU) for solving the flow field around multistage rotors. The focus of the current research effort, under NASA Cooperative Agreement NCC3- 596 was on developing an aeroelastic analysis code (entitled TURBO-AE) based on the Navier-Stokes solver developed by MSU. The TURBO-AE code has been developed for flutter analysis of turbomachine components and delivered to NASA and its industry partners. The code has been verified. validated and is being applied by NASA Glenn and by aircraft engine manufacturers to analyze the aeroelastic stability characteristics of modem fans, compressors
Parabolized Navier-Stokes methods for hypersonic flows
NASA Technical Reports Server (NTRS)
Lawrence, Scott L.
1991-01-01
A representative sampling of the techniques used in the integration of the Parabolized Navier-Stokes (PNS) equations is presented. Special atention is given to recent algorithms developed specifically for application to high speed flows, characterized by the presence of strong embedded shock waves and real gas effects. It is shown that PNS solvers are being used in the analysis of sonic boom signatures. Methods for modeling physical effects are discussed, including an overview of commonly used turbulence models and a more detailed discussion of techniques for including equilibrium and finite rate real gas effects.
Implicit upwind methods for the compressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Coakley, T. J.
1983-01-01
A class of implicit upwind differencing methods for the compressible Navier-Stokes equations is described and applied. The methods are based on the use of local eigenvalues or wave speeds to control spatial differencing of inviscid terms and are aimed at increasing the level of accuracy and stability achievable in computation. Techniques for accelerating the rate of convergence to a steady state solution are also used. Applications to inviscid and viscous transonic flows are discussed and compared with other methods and experimental measurements. It is shown that accurate and efficient transonic airfoil calculations can be made on the Cray-l computer in less than 2 min.
The Navier-Stokes Equations in the Critical Lebesgue Space
NASA Astrophysics Data System (ADS)
Dong, Hongjie; Du, Dapeng
2009-12-01
We study regularity criteria for the d-dimensional incompressible Navier-Stokes equations. We prove in this paper that if {u in L_infty^tLd^x((0,T)× mathbb{R}^d)} is a Leray-Hopf weak solution, then u is smooth and unique in {(0, T)× mathbb{R}^d} . This generalizes a result by Escauriaza, Seregin and Šverák [5]. Additionally, we show that if T = ∞ then u goes to zero as t goes to infinity.
Towards an ideal preconditioner for linearized Navier-Stokes problems
Murphy, M.F.
1996-12-31
Discretizing certain linearizations of the steady-state Navier-Stokes equations gives rise to nonsymmetric linear systems with indefinite symmetric part. We show that for such systems there exists a block diagonal preconditioner which gives convergence in three GMRES steps, independent of the mesh size and viscosity parameter (Reynolds number). While this {open_quotes}ideal{close_quotes} preconditioner is too expensive to be used in practice, it provides a useful insight into the problem. We then consider various approximations to the ideal preconditioner, and describe the eigenvalues of the preconditioned systems. Finally, we compare these preconditioners numerically, and present our conclusions.
Smooth solutions of the Navier-Stokes equations
Pokhozhaev, S I
2014-02-28
We consider smooth solutions of the Cauchy problem for the Navier-Stokes equations on the scale of smooth functions which are periodic with respect to x∈R{sup 3}. We obtain existence theorems for global (with respect to t>0) and local solutions of the Cauchy problem. The statements of these depend on the smoothness and the norm of the initial vector function. Upper bounds for the behaviour of solutions in both classes, which depend on t, are also obtained. Bibliography: 10 titles.
Implicit multiblock Euler and Navier-Stokes calculations
NASA Astrophysics Data System (ADS)
Jenssen, Carl B.
1994-09-01
Implicit multiblock computations have been carried out for a large number of blocks using explicit coupling between the blocks. The convergence rate of this method is very sensitive to the block partitioning. For the Navier-Stokes equations the height of the blocks should be greater than the boundary-layer thickness. Also, excessively thin blocks will cause breakdown of the algorithm. For transonic calculations the best convergence rate was obtained using a red-black Gauss-Seidel approach. It is concluded that the method is well suited for massively parallel computers.
Time-accurate Navier-Stokes calculations with multigrid acceleration
NASA Technical Reports Server (NTRS)
Melson, N. D.; Sanetrik, Mark D.; Atkins, Harold L.
1993-01-01
An efficient method for calculating unsteady flows is presented, with emphasis on a modified version of the thin-layer Navier-Stokes equations. Fourier stability analysis is used to illustrate the effect of treating the source term implicitly instead of explicity, as well as to illustrate other algorithmic choices. A 2D circular cylinder (with a Reynolds number of 1200 and a Mach number of 0.3) is calculated. The present scheme requires only about 10 percent of the computer time required by global minimum time stepping.
PAB3D: Its History in the Use of Turbulence Models in the Simulation of Jet and Nozzle Flows
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.; Pao, S. Paul; Hunter, Craig A.; Deere, Karen A.; Massey, Steven J.; Elmiligui, Alaa
2006-01-01
This is a review paper for PAB3D s history in the implementation of turbulence models for simulating jet and nozzle flows. We describe different turbulence models used in the simulation of subsonic and supersonic jet and nozzle flows. The time-averaged simulations use modified linear or nonlinear two-equation models to account for supersonic flow as well as high temperature mixing. Two multiscale-type turbulence models are used for unsteady flow simulations. These models require modifications to the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k-epsilon) model with a RANS/LES transition function, dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier-Stokes (PANS) formulation. All of these models are implemented in the three-dimensional Navier-Stokes code PAB3D. This paper discusses computational methods, code implementation, computed results for a wide range of nozzle configurations at various operating conditions, and comparisons with available experimental data. Very good agreement is shown between the numerical solutions and available experimental data over a wide range of operating conditions.
Algorithmic Enhancements to the VULCAN Navier-Stokes Solver
NASA Technical Reports Server (NTRS)
Litton, D. K.; Edwards, J. R.; White, J. A.
2003-01-01
VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M less than or equal to 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can solve the Navier-Stokes equations for very low Mach numbers.
Reliability enhancement of Navier-Stokes codes through convergence acceleration
NASA Technical Reports Server (NTRS)
Merkle, Charles L.; Dulikravich, George S.
1995-01-01
Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.
Modeling Vortex Generators in a Navier-Stokes Code
NASA Technical Reports Server (NTRS)
Dudek, Julianne C.
2011-01-01
A source-term model that simulates the effects of vortex generators was implemented into the Wind-US Navier-Stokes code. The source term added to the Navier-Stokes equations simulates the lift force that would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, subsonic flow in an S-duct with 22 corotating vortex generators, and supersonic flow in a rectangular duct with a counter-rotating vortex-generator pair. The model was also used to successfully simulate microramps in supersonic flow by treating each microramp as a pair of vanes with opposite angles of incidence. The validation results indicate that the source-term vortex-generator model provides a useful tool for screening vortex-generator configurations and gives comparable results to solutions computed using gridded vanes.
NASA Technical Reports Server (NTRS)
Kandula, M.; Pearce, D. G.
1991-01-01
A steady incompressible three-dimensional viscous flow analysis has been conducted for the Space Shuttle external tank/orbiter propellant feed line disconnect flapper valves with upstream elbows. The Navier-Stokes code, INS3D, is modified to handle interior obstacles and a simple turbulence model. The flow solver is tested for stability and convergence in the presence of interior flappers. An under-relaxation scheme has been incorporated to improve the solution stability. Important flow characteristics such as secondary flows, recirculation, vortex and wake regions, and separated flows are observed. Computed values for forces, moments, and pressure drop are in satisfactory agreement with water flow test data covering a maximum tube Reynolds number of 3.5 million. The predicted hydrodynamical stability of the flappers correlates well with the measurements.
Parallelizing Navier-Stokes Computations on a Variety of Architectural Platforms
NASA Technical Reports Server (NTRS)
Jayasimha, D. N.; Hayder, M. E.; Pillay, S. K.
1997-01-01
We study the computational, communication, and scalability characteristics of a Computational Fluid Dynamics application, which solves the time accurate flow field of a jet using the compressible Navier-Stokes equations, on a variety of parallel architectural platforms. The platforms chosen for this study are a cluster of workstations (the LACE experimental testbed at NASA Lewis), a shared memory multiprocessor (the Cray YMP), distributed memory multiprocessors with different topologies-the IBM SP and the Cray T3D. We investigate the impact of various networks, connecting the cluster of workstations, on the performance of the application and the overheads induced by popular message passing libraries used for parallelization. The work also highlights the importance of matching the memory bandwidth to the processor speed for good single processor performance. By studying the performance of an application on a variety of architectures, we are able to point out the strengths and weaknesses of each of the example computing platforms.
An Evaluation of Architectural Platforms for Parallel Navier-Stokes Computations
NASA Technical Reports Server (NTRS)
Jayasimha, D. N.; Hayder, M. E.; Pillay, S. K.
1996-01-01
We study the computational, communication, and scalability characteristics of a computational fluid dynamics application, which solves the time accurate flow field of a jet using the compressible Navier-Stokes equations, on a variety of parallel architecture platforms. The platforms chosen for this study are a cluster of workstations (the LACE experimental testbed at NASA Lewis), a shared memory multiprocessor (the Cray YMP), and distributed memory multiprocessors with different topologies - the IBM SP and the Cray T3D. We investigate the impact of various networks connecting the cluster of workstations on the performance of the application and the overheads induced by popular message passing libraries used for parallelization. The work also highlights the importance of matching the memory bandwidth to the processor speed for good single processor performance. By studying the performance of an application on a variety of architectures, we are able to point out the strengths and weaknesses of each of the example computing platforms.
Investigation of Navier-Stokes Code Verification and Design Optimization
NASA Technical Reports Server (NTRS)
Vaidyanathan, Rajkumar
2004-01-01
With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization
Navier-Stokes analysis of turbomachinery blade external heat transfer
NASA Technical Reports Server (NTRS)
Ameri, A. A.; Sockol, P. M.; Gorla, R. S. R.
1992-01-01
The two-dimensional, compressible, thin-layer Navier-Stokes and energy equations were solved numerically to obtain heat transfer rates on turbomachinery blades. The Baldwin-Lomax algebraic model and the q - omega low Reynolds number, two-equation model were used for modeling of turbulence. For the numerical solution of the governing equations a four-stage Runge-Kutta solver was employed. The turbulence model equations were solved using an implicit scheme. Numerical solutions are presented for two-dimensional flow within two vane cascades. The heat transfer results and the pressure distributions were compared with published experimental data. The agreement between the numerical calculations and the experimental values were found to be generally favorable. The position of transition from laminar to turbulent flow was also predicted accurately.
Navier-Stokes analysis of turbomachinery blade external heat transfer
NASA Technical Reports Server (NTRS)
Gorla, Rama S. R.
1991-01-01
The two-dimensional, compressible, thin-layer Navier-Stokes and energy equations were solved numerically to obtain heat transfer rates on turbomachinery blades. The Baldwin-Lomax algebraic model and the q-omega low Reynolds number two-equation model were used for modeling of turbulence. For the numerical solution of the governing equations a four-stage Runge-Kutta solver was employed. The turbulence model equations were solved using an implicit scheme. Numerical solutions are presented for two-dimensional flow within two vane cascades. The heat transfer results and the pressure distributions were compared with published experimental data. The agreement between the numerical calculations and the experimental values were found to be generally favorable. The position of transition from laminar to turbulent flow was also predicted accurately.
Turbulence modeling methods for the compressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Coakley, T. J.
1983-01-01
Turbulence modeling methods for the compressible Navier-Stokes equations, including several zero- and two-equation eddy-viscosity models, are described and applied. Advantages and disadvantages of the models are discussed with respect to mathematical simplicity, conformity with physical theory, and numerical compatibility with methods. A new two-equation model is introduced which shows advantages over other two-equation models with regard to numerical compatibility and the ability to predict low-Reynolds-number transitional phenomena. Calculations of various transonic airfoil flows are compared with experimental results. A new implicit upwind-differencing method is used which enhances numerical stability and accuracy, and leads to rapidly convergent steady-state solutions.
Navier-Stokes simulation of real gas flows in nozzles
NASA Technical Reports Server (NTRS)
Nagaraj, N.; Lombard, C. K.
1987-01-01
Air flow in a hypersonic nozzle causes real gas effects due to reaction among the species constituting air. Such reactions may be in chemical equilibrium or in chemical nonequilibrium. Here using the CSCM upwind scheme for the compressible Navier-Stokes equations, the real gas flowfield in an arcjet nozzle is computed for both the equilibrium case and the nonequilibrium case. A hypersonic nozzle flow arising from a pebble bed heated plenum is also computed for the equilibrium situation. Between the equilibrium cases, the chemistry is treated by two different schemes and comments are made as to computational complexity. For the nonequilibrium case, a full set of seventeen reactions and full implicit coupling of five species with gasdynamics is employed to compute the flowfield. For all cases considered here the gas is assumed to be a calorically imperfect mixture of ideal gases in thermal equilibrium.
Perturbation of eigenvalues of preconditioned Navier-Stokes operators
Elman, H.C.
1996-12-31
We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steady-state Navier-Stokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on perturbations of eigenvalues as functions of the viscosity and discretization mesh size. The bounds suggest that the sensitivity of the eigenvalues is at worst linear in the inverse of the viscosity and quadratic in the inverse of the mesh size, and that scaling can be used to decrease the sensitivity in some cases. Experimental results supplement these results and confirm the relatively mild dependence on viscosity. They also indicate a dependence on the mesh size of magnitude smaller than the analysis suggests.
Iterative methods for compressible Navier-Stokes and Euler equations
Tang, W.P.; Forsyth, P.A.
1996-12-31
This workshop will focus on methods for solution of compressible Navier-Stokes and Euler equations. In particular, attention will be focused on the interaction between the methods used to solve the non-linear algebraic equations (e.g. full Newton or first order Jacobian) and the resulting large sparse systems. Various types of block and incomplete LU factorization will be discussed, as well as stability issues, and the use of Newton-Krylov methods. These techniques will be demonstrated on a variety of model transonic and supersonic airfoil problems. Applications to industrial CFD problems will also be presented. Experience with the use of C++ for solution of large scale problems will also be discussed. The format for this workshop will be four fifteen minute talks, followed by a roundtable discussion.
Towards Optimal Multigrid Efficiency for the Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Swanson, R. C.
2001-01-01
A fast multigrid solver for the steady incompressible Navier-Stokes equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Numerical solutions are shown for flow over a flat plate and a Karman-Trefftz airfoil. Using collective Gauss-Seidel line relaxation in both the vertical and horizontal directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of a Runge-Kutta based multigrid method.
Computation of turbine flowfields with a Navier-Stokes code
NASA Technical Reports Server (NTRS)
Hobson, G. V.; Lakshminarayana, B.
1990-01-01
A new technique has been developed for the solution of the incompressible Navier-Stokes equations. The numerical technique, derived from a pressure substitution method (PSM), overcomes many of the deficiencies of the pressure crrection method. This technique allows for the direct solution of the actual pressure in the form of a Poisson equation which is derived from the pressure weighted substitution of the full momentum equations into the continuity equation. In two-dimensions a turbine flowfield, including heat transfer, has been computed with this method and the prediction of the cascade performance is presented. The extension of the pressure correction method for the solution of three-dimensional flows is also presented for laminar flow in an S-shaped duct and turbulent flow in the end-wall region of a turbine cascade.
Navier-Stokes Dynamics by a Discrete Boltzmann Model
NASA Technical Reports Server (NTRS)
Rubinstein, Robet
2010-01-01
This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.
Analysis of an Incompressible Navier-Stokes-Maxwell-Stefan System
NASA Astrophysics Data System (ADS)
Chen, Xiuqing; Jüngel, Ansgar
2015-12-01
The Maxwell-Stefan equations for the molar fluxes, supplemented by the incompressible Navier-Stokes equations governing the fluid velocity dynamics, are analyzed in bounded domains with no-flux boundary conditions. The system models the dynamics of a multicomponent gaseous mixture under isothermal conditions. The global-in-time existence of bounded weak solutions to the strongly coupled model and their exponential decay to the homogeneous steady state are proved. The mathematical difficulties are due to the singular Maxwell-Stefan diffusion matrix, the cross-diffusion terms, and the different molar masses of the fluid components. The key idea of the proof is the use of a new entropy functional and entropy variables, which allows for a proof of positive lower and upper bounds of the mass densities without the use of a maximum principle.
High accuracy solutions of incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Gupta, Murli M.
1990-01-01
In recent years, high accuracy finite difference approximations were developed for partial differential equations of elliptic type, with particular emphasis on the convection-diffusion equation. These approximations are of compact type, have a local truncation error of fourth order, and allow the use of standard iterative schemes to solve the resulting systems of algebraic equations. These high accuracy approximations are extended to the solution of Navier-Stokes equations. Solutions are obtained for the model problem of driven cavity and are compared with solutions obtained using other approximations and those obtained by other authors. It is discovered that the high order approximations do indeed produce high accuracy solutions and have a potential for use in solving important problems of viscous fluid flows.
SSME thrust chamber simulation using Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Przekwas, A. J.; Singhal, A. K.; Tam, L. T.
1984-01-01
The capability of the PHOENICS fluid dynamics code in predicting two-dimensional, compressible, and reacting flow in the combustion chamber and nozzle of the space shuttle main engine (SSME) was evaluated. A non-orthogonal body fitted coordinate system was used to represent the nozzle geometry. The Navier-Stokes equations were solved for the entire nozzle with a turbulence model. The wall boundary conditions were calculated based on the wall functions which account for pressure gradients. Results of the demonstration test case reveal all expected features of the transonic nozzle flows. Of particular interest are the locations of normal and barrel shocks, and regions of highest temperature gradients. Calculated performance (global) parameters such as thrust chamber flow rate, thrust, and specific impulse are also in good agreement with available data.
NASA Astrophysics Data System (ADS)
Gibbon, John D.; Pal, Nairita; Gupta, Anupam; Pandit, Rahul
2016-12-01
We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter ϕ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984), 10.1007/BF01212349]. By taking an L∞ norm of the energy of the full binary system, designated as E∞, we have shown that ∫0tE∞(τ ) d τ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with 1283 to 5123 collocation points and over the duration of our DNSs confirm that E∞ remains bounded as far as our computations allow.
Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP
NASA Technical Reports Server (NTRS)
Vadyak, Joseph; Shrewsbury, George E.; Narramore, Jim C.; Montry, Gary; Holst, Terry; Kwak, Dochan (Technical Monitor)
1995-01-01
The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time
Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces
NASA Technical Reports Server (NTRS)
Wang, Chi R.
2005-01-01
This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one
NASA Technical Reports Server (NTRS)
Bonhaus, Daryl L.; Wornom, Stephen F.
1991-01-01
Two codes which solve the 3-D Thin Layer Navier-Stokes (TLNS) equations are used to compute the steady state flow for two test cases representing typical finite wings at transonic conditions. Several grids of C-O topology and varying point densities are used to determine the effects of grid refinement. After a description of each code and test case, standards for determining code efficiency and accuracy are defined and applied to determine the relative performance of the two codes in predicting turbulent transonic wing flows. Comparisons of computed surface pressure distributions with experimental data are made.
The use of a Navier-Stokes code in the wing design process
NASA Technical Reports Server (NTRS)
Mcmillin, S. Naomi
1989-01-01
The feasibility was determined of incorporating the Navier-Stokes computational code, CFL3D, into the supersonic wing design process. The approach taken is of two steps. The first step was to calibrate CFL3D against existing experimental data sets obtained on thin sharp edged delta wings. The experimental data identified six flow types which are dependent on the similarity parameters of Mach number and angle of attack normal to the leading edge. The calibration showed CFL3D capable of simulating these various separated and attached flow conditions. The second step was to use CFL3D to study the initial formation of leading edge separation over delta wings at supersonic speeds. This consisted of examining solutions obtained on a 65 deg delta wing at Mach number of 1.6 with varying cross sectional shapes. Reynolds number was held constant at 1000000 and the Baldwin-Lomax turbulence model was used. The study showed that through the use of leading edge radius and/or camber, the onset of leading edge separation can be delayed to a higher angle of attack than observed on a flat sharp edged wing. Based on the geometries studied, three wind tunnel models are being designed to verify these results.
Navier-Stokes and viscous shock-layer solutions for radiating hypersonic flows
NASA Technical Reports Server (NTRS)
Gupta, Roop N.
1987-01-01
Results are presented from the Navier-Stokes and viscous shock-layer (VSL) calculations with nonequilibrium and equilibrium chemistry, respectively. These calculations contain coupling to the Aerotherm radiation code RAD. A simplified form of the electron energy equation is used to obtain an electron temperature in the Navier-Stokes calculations. The radiation in the flowfield is calculated using this temperature. The Navier-Stokes code is used at high altitude only, whereas the VSL code is employed for the entire entry period to make estimates of the radiative and convective heating to the Fire II vehicle. Results from the Navier-Stokes code have also been compared with the predictions of Lee and Kawamura, who used gray-gas radiation model and thin-layer Navier-Stokes equations. Quite good agreement is obtained between the measured and computed values of radiative and convective heating from the VSL code in th medium-to-low altitude flight regime of the Fire II vehicle. At high altitudes, the Navier-Stokes calculations considerably overpredict the Fire II flight data for radiative intensity. This is attributed to the deficiencies in the Aerotherm radiation model when used for low-density flight conditions. This model contains the thermal equilibrium assumption and precludes accounting for the collision-limiting phenomenon at high altitudes. Present Navier-Stokes calculations highlight the effect of these assumptions on radiative heating calculations for such conditions.
NASA Technical Reports Server (NTRS)
Shyam, Vikram
2010-01-01
A preprocessor for the Computational Fluid Dynamics (CFD) code TURBO has been developed and tested. The preprocessor converts grids produced by GridPro (Program Development Company (PDC)) into a format readable by TURBO and generates the necessary input files associated with the grid. The preprocessor also generates information that enables the user to decide how to allocate the computational load in a multiple block per processor scenario.
NASA Technical Reports Server (NTRS)
Iannetti, Anthony C.; Moder, Jeffery P.
2010-01-01
Developing physics-based tools to aid in reducing harmful combustion emissions, like Nitrogen Oxides (NOx), Carbon Monoxide (CO), Unburnt Hydrocarbons (UHC s), and Sulfur Dioxides (SOx), is an important goal of aeronautics research at NASA. As part of that effort, NASA Glenn Research Center is performing a detailed assessment and validation of an in-house combustion CFD code known as the National Combustion Code (NCC) for turbulent reacting flows. To assess the current capabilities of NCC for simulating turbulent reacting flows with liquid jet fuel injection, a set of Single Swirler Lean Direct Injection (LDI) experiments performed at the University of Cincinnati was chosen as an initial validation data set. This Jet-A/air combustion experiment operates at a lean equivalence ratio of 0.75 at atmospheric pressure and has a 4 percent static pressure drop across the swirler. Detailed comparisons of NCC predictions for gas temperature and gaseous emissions (CO and NOx) against this experiment are considered in a previous work. The current paper is focused on detailed comparisons of the spray characteristics (radial profiles of drop size distribution and at several radial rakes) from NCC simulations against the experimental data. Comparisons against experimental data show that the use of the correlation for primary spray break-up implemented by Raju in the NCC produces most realistic results, but this result needs to be improved. Given the single or ten step chemical kinetics models, use of a spray size correlation gives similar, acceptable results
Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions
NASA Technical Reports Server (NTRS)
Tidriri, M. D.
1995-01-01
One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.
Stable boundary conditions and difference schemes for Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Dutt, P.
1985-01-01
The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.
Wadawadigi, G.; Tannehill, J.C.; Buelow, P.E.; Lawrence, S.L. NASA, Ames Research Center, Moffett Field, CA )
1992-07-01
A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional (3D) chemically reacting flow in scramjet (supersonic combustion ramjet) engines. The code is a modification of the 3D upwind PNS (UPS) airflow code which has been extended in the present study to permit internal flow calculations with hydrogen-air chemistry. With these additions, the new code has the capability of computing aerodynamic and propulsive flowfields simultaneously. The algorithm solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that has been modified to account for 'real gas' effects. The fluid medium is assumed to be a chemically reacting mixture of thermally perfect (but calorically imperfect) gases in thermal equilibrium. The new code has been applied to two test cases. These include the Burrows-Kurkov supersonic combustion experiment and a generic 3D scramjet flowfield. The computed results compare favorably with the available experimental data. 38 refs.
High-lift calculations using Navier-Stokes methods
NASA Astrophysics Data System (ADS)
Larsson, Torbjoern
Wing sections on an aircraft are designed for optimal cruise performance, whereas during the take-off and landing phase totally different lift-to-drag characteristics are needed. High lift and low drag is essential while taking off, on the other hand high lift and high drag is favorable when landing. The design and shaping of the high-lift system can have a major influence on the overall economy and safety of the aircraft. In a historical perspective experimental investigations have been the only way to gain any deeper knowledge of the performance of a given wing-flap configuration. Today, computational methods for high-lift systems based on the viscid-inviscid interaction approach with integral methods for boundary layers and wakes are quite common. Although fast solutions can be obtained with these methods it is highly desirable to have a numerical method that captures the flow physics in a more detailed and adequate way. The present wotk demonstrates that Navier-Stokes methods can be used with good results for simulating high-lift flow fields, but also points to the area where further research is needed.
A Data Parallel Multizone Navier-Stokes Code
NASA Technical Reports Server (NTRS)
Jespersen, Dennis C.; Levit, Creon; Kwak, Dochan (Technical Monitor)
1995-01-01
We have developed a data parallel multizone compressible Navier-Stokes code on the Connection Machine CM-5. The code is set up for implicit time-stepping on single or multiple structured grids. For multiple grids and geometrically complex problems, we follow the "chimera" approach, where flow data on one zone is interpolated onto another in the region of overlap. We will describe our design philosophy and give some timing results for the current code. The design choices can be summarized as: 1. finite differences on structured grids; 2. implicit time-stepping with either distributed solves or data motion and local solves; 3. sequential stepping through multiple zones with interzone data transfer via a distributed data structure. We have implemented these ideas on the CM-5 using CMF (Connection Machine Fortran), a data parallel language which combines elements of Fortran 90 and certain extensions, and which bears a strong similarity to High Performance Fortran (HPF). One interesting feature is the issue of turbulence modeling, where the architecture of a parallel machine makes the use of an algebraic turbulence model awkward, whereas models based on transport equations are more natural. We will present some performance figures for the code on the CM-5, and consider the issues involved in transitioning the code to HPF for portability to other parallel platforms.
Reliability enhancement of Navier-Stokes codes through convergence enhancement
NASA Technical Reports Server (NTRS)
Choi, K.-Y.; Dulikravich, G. S.
1993-01-01
Reduction of total computing time required by an iterative algorithm for solving Navier-Stokes equations is an important aspect of making the existing and future analysis codes more cost effective. Several attempts have been made to accelerate the convergence of an explicit Runge-Kutta time-stepping algorithm. These acceleration methods are based on local time stepping, implicit residual smoothing, enthalpy damping, and multigrid techniques. Also, an extrapolation procedure based on the power method and the Minimal Residual Method (MRM) were applied to the Jameson's multigrid algorithm. The MRM uses same values of optimal weights for the corrections to every equation in a system and has not been shown to accelerate the scheme without multigriding. Our Distributed Minimal Residual (DMR) method based on our General Nonlinear Minimal Residual (GNLMR) method allows each component of the solution vector in a system of equations to have its own convergence speed. The DMR method was found capable of reducing the computation time by 10-75 percent depending on the test case and grid used. Recently, we have developed and tested a new method termed Sensitivity Based DMR or SBMR method that is easier to implement in different codes and is even more robust and computationally efficient than our DMR method.
Design and Navier-Stokes analysis of hypersonic wind tunnel nozzles. M.S. Thesis
NASA Technical Reports Server (NTRS)
Benton, James R.
1989-01-01
Four hypersonic wind tunnel nozzles ranging in Mach number from 6 to 17 are designed with the method of characteristics and boundary layer approach (MOC/BL) and analyzed with a Navier-Stokes solver. Limitations of the MOC/BL approach when applied to thick high speed boundary layers with non-zero normal pressure gradients are investigated. Working gases include ideal air, thermally perfect nitrogen and virial CF4. Agreement between the design conditions and Navier-Stokes solutions for ideal air at Mach 6 is good. Thermally perfect nitrogen showed poor agreement at Mach 13.5 and Mach 17. Navier-Stokes solutions for CF4 are not obtained, but comparison of the effects of low gamma to those of high Mach number suggests that the Navier-Stokes solution would not compare well with design.
Short Communication: A Parallel Newton-Krylov Method for Navier-Stokes Rotorcraft Codes
NASA Astrophysics Data System (ADS)
Ekici, Kivanc; Lyrintzis, Anastasios S.
2003-05-01
The application of Krylov subspace iterative methods to unsteady three-dimensional Navier-Stokes codes on massively parallel and distributed computing environments is investigated. Previously, the Euler mode of the Navier-Stokes flow solver Transonic Unsteady Rotor Navier-Stokes (TURNS) has been coupled with a Newton-Krylov scheme which uses two Conjugate-Gradient-like (CG) iterative methods. For the efficient implementation of Newton-Krylov methods to the Navier-Stokes mode of TURNS, efficient preconditioners must be used. Parallel implicit operators are used and compared as preconditioners. Results are presented for two-dimensional and three-dimensional viscous cases. The Message Passing Interface (MPI) protocol is used, because of its portability to various parallel architectures.
Investigation of vortex breakdown on a delta wing using Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Agrawal, S.; Barnett, R. M.; Robinson, B. A.
1991-01-01
A numerical investigation of leading edge vortex breakdown in a delta wing at high angles of attack is presented. The analysis was restricted to low speed flows on a flat plate wing with sharp leading edges. Both Euler and Navier-Stokes equations were used and the results were compared with experimental data. Predictions of vortex breakdown progression with angle of attack with both Euler and Navier-Stokes equations are shown to be consistent with the experimental data. However, the Navier-Stokes predictions show significant improvements in breakdown location at angles of attack where the vortex breakdown approaches the wing apex. The predicted trajectories of the primary vortex are in very good agreement with the test data, the laminar solutions providing the overall best comparison. The Euler shows a small displacement of the primary vortex, relative to experiment, due to the lack of secondary vortices. The turbulent Navier-Stokes, in general, fall between the Euler and laminar solutions.
Euler and Navier-Stokes solutions for the leeside flow over delta wings at supersonic speeds
NASA Technical Reports Server (NTRS)
Mcmillin, S. N.; Thomas, J. L.; Murman, E. M.
1987-01-01
Distinctly different types of leeside flowfields over highly swept sharp leading edge delta wings in supersonic flow were numerically simulated using Euler and Navier-Stokes solvers. The Euler code was seen to be adequate only in predicting primary flow structures (leading edge vortex and cross flow shock) whereas the Navier-Stokes code was capable of predicting secondary flow structures (i.e., secondary vortex). A comparison of laminar and turbulent Navier-Stokes solutions indicated that the turbulent boundary layer model is more accurate in predicting the effect of the boundary layer model on the flowfield. Also, the Navier-Stokes code indicated detailed flow structures not observed in the qualitative experimental data available (i.e., vapor screen photographs) indicating a need for quantitative flow field data.
NASA Astrophysics Data System (ADS)
Zhang, Ting; Fang, Daoyuan
2008-03-01
In this paper, we study the free boundary problem for 1D compressible Navier-Stokes equations with density-dependent viscosity. We focus on the case where the viscosity coefficient vanishes on vacuum. We prove the global existence and uniqueness for discontinuous solutions to the Navier-Stokes equations when the initial density is a bounded variation function, and give a decay result for the density as t-->+[infinity].
Far-Field Boundary Conditions in Numerical Solutions of the Navier-Stokes Equations.
2014-09-26
nonlinear system of mixed parabolic- hyperbolic type in two space dimensions and time, with four independent variables must be solved in an exterior...conditions. * III THE NAVIER-STOKES EQUATIONS AND CHARACTERISTIC VARIABLES : We now begin our discussion of the equations of gas dynamics. We will neglect...8217 Far-Field Boundary Conditions in Numerical Solutions of the Navier-Stokes Equations L°O * (. P.J. McKenna LA. DTIC * E.LECTE Final Report AFOSR Grant
Inviscid Limit for Damped and Driven Incompressible Navier-Stokes Equations in mathbb R^2
NASA Astrophysics Data System (ADS)
Constantin, P.; Ramos, F.
2007-10-01
We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in mathbb R^2 . We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstrophy balance.
Adapting a Navier-Stokes code to the ICL-DAP
NASA Technical Reports Server (NTRS)
Grosch, C. E.
1985-01-01
The results of an experiment are reported, i.c., to adapt a Navier-Stokes code, originally developed on a serial computer, to concurrent processing on the CL Distributed Array Processor (DAP). The algorithm used in solving the Navier-Stokes equations is briefly described. The architecture of the DAP and DAP FORTRAN are also described. The modifications of the algorithm so as to fit the DAP are given and discussed. Finally, performance results are given and conclusions are drawn.
Single-grid spectral collocation for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Bernardi, Christine; Canuto, Claudio; Maday, Yvon; Metivet, Brigitte
1988-01-01
The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.
Partial implicitization. [numerical stability of Burger equation model for Navier-Stokes equation
NASA Technical Reports Server (NTRS)
Graves, R. A., Jr.
1973-01-01
The steady-state solution to the full Navier-Stokes equations for complicated flows is generally difficult to obtain. The Burgers (1948) equation is used as a model of the Navier-Stokes equations. The steady-state solution is obtained by a one-step explicit technique resulting from a partial implicitization of the difference equation. Stability analysis shows that the technique is unconditionally stable, and numerical tests show the technique to be accurate.
Gehrer, A.; Jericha, H.
1999-07-01
External heat transfer predictions are performed for two-dimensional turbine blade cascades. The Reynolds-averaged Navier-Stokes equations with algebraic (Arnone and Pacciani, 1998), one-equation (Spalart and Allmaras, 1994), and two-equation (low-Re {kappa}-{epsilon}, Biswas and Fukuyama, 1994) turbulence closures are solved with a fully implicit time-marching finite volume method. Comparisons with measurements (Arts et al., 1990; Arts, 1994) for a highly loaded transonic turbine nozzle guide vane cascade show good agreement in some cases, but also reveal problems with transition prediction and turbulence modeling. Special attention has been focused on the low-Re {kappa}-{epsilon} model concerning the influence of the inlet boundary condition for the {epsilon}-equation and problems in the stagnation point region.
Global smooth flows for compressible Navier-Stokes-Maxwell equations
NASA Astrophysics Data System (ADS)
Xu, Jiang; Cao, Hongmei
2016-08-01
Umeda et al. (Jpn J Appl Math 1:435-457, 1984) considered a rather general class of symmetric hyperbolic-parabolic systems: A0zt+sum_{j=1}nAjz_{xj}+Lz=sum_{j,k=1}nB^{jk}z_{xjxk} and showed optimal decay rates with certain dissipative assumptions. In their results, the dissipation matrices {L} and {B^{jk}(j,k=1,ldots,n)} are both assumed to be real symmetric. So far there are no general results in case that {L} and {B^{jk}} are not necessarily symmetric, which is left open now. In this paper, we investigate compressible Navier-Stokes-Maxwell (N-S-M) equations arising in plasmas physics, which is a concrete example of hyperbolic-parabolic composite systems with non-symmetric dissipation. It is observed that the Cauchy problem for N-S-M equations admits the dissipative mechanism of regularity-loss type. Consequently, extra higher regularity is usually needed to obtain the optimal decay rate of {L1({mathbb{R}}^3)}-{L^2({mathbb{R}}^3)} type, in comparison with that for the global-in-time existence of smooth solutions. In this paper, we obtain the minimal decay regularity of global smooth solutions to N-S-M equations, with aid of {L^p({mathbb{R}}^n)}-{Lq({mathbb{R}}^n)}-{Lr({mathbb{R}}^n)} estimates. It is worth noting that the relation between decay derivative orders and the regularity index of initial data is firstly found in the optimal decay estimates.
Navier-Stokes Computations of a Wing-Flap Model With Blowing Normal to the Flap Surface
NASA Technical Reports Server (NTRS)
Boyd, D. Douglas, Jr.
2005-01-01
A computational study of a generic wing with a half span flap shows the mean flow effects of several blown flap configurations. The effort compares and contrasts the thin-layer, Reynolds averaged, Navier-Stokes solutions of a baseline wing-flap configuration with configurations that have blowing normal to the flap surface through small slits near the flap side edge. Vorticity contours reveal a dual vortex structure at the flap side edge for all cases. The dual vortex merges into a single vortex at approximately the mid-flap chord location. Upper surface blowing reduces the strength of the merged vortex and moves the vortex away from the upper edge. Lower surface blowing thickens the lower shear layer and weakens the merged vortex, but not as much as upper surface blowing. Side surface blowing forces the lower surface vortex farther outboard of the flap edge by effectively increasing the aerodynamic span of the flap. It is seen that there is no global aerodynamic penalty or benefit from the particular blowing configurations examined.
Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Schwab, John R.; Bui, Trong T.
1993-01-01
A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.
PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady
1990-01-01
A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 2 is the User's Guide, and describes the program's general features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.
Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Schwab, John R.; Bui, Trong T.
1993-01-01
A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.
Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 2: User's guide
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Schwab, John R.; Bui, Trong T.
1993-01-01
A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the User's Guide, and describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.
PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady
1990-01-01
A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 1 is the Analysis Description, and describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.
PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference
NASA Technical Reports Server (NTRS)
Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady
1990-01-01
A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram.
NASA Technical Reports Server (NTRS)
Reznick, Steve
1988-01-01
Transonic Euler/Navier-Stokes computations are accomplished for wing-body flow fields using a computer program called Transonic Navier-Stokes (TNS). The wing-body grids are generated using a program called ZONER, which subdivides a coarse grid about a fighter-like aircraft configuration into smaller zones, which are tailored to local grid requirements. These zones can be either finely clustered for capture of viscous effects, or coarsely clustered for inviscid portions of the flow field. Different equation sets may be solved in the different zone types. This modular approach also affords the opportunity to modify a local region of the grid without recomputing the global grid. This capability speeds up the design optimization process when quick modifications to the geometry definition are desired. The solution algorithm embodied in TNS is implicit, and is capable of capturing pressure gradients associated with shocks. The algebraic turbulence model employed has proven adequate for viscous interactions with moderate separation. Results confirm that the TNS program can successfully be used to simulate transonic viscous flows about complicated 3-D geometries.
NASA Technical Reports Server (NTRS)
Mizukami, M.; Saunders, J. D.
1995-01-01
The supersonic diffuser of a Mach 2.68 bifurcated, rectangular, mixed-compression inlet was analyzed using a two-dimensional (2D) Navier-Stokes flow solver. Parametric studies were performed on turbulence models, computational grids and bleed models. The computer flowfield was substantially different from the original inviscid design, due to interactions of shocks, boundary layers, and bleed. Good agreement with experimental data was obtained in many aspects. Many of the discrepancies were thought to originate primarily from 3D effects. Therefore, a balance should be struck between expending resources on a high fidelity 2D simulation, and the inherent limitations of 2D analysis. The solutions were fairly insensitive to turbulence models, grids and bleed models. Overall, the k-e turbulence model, and the bleed models based on unchoked bleed hole discharge coefficients or uniform velocity are recommended. The 2D Navier-Stokes methods appear to be a useful tool for the design and analysis of supersonic inlets, by providing a higher fidelity simulation of the inlet flowfield than inviscid methods, in a reasonable turnaround time.
Improved Convergence and Robustness of USM3D Solutions on Mixed Element Grids (Invited)
NASA Technical Reports Server (NTRS)
Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.
2015-01-01
Several improvements to the mixed-element USM3D discretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Scheme (HANIS), has been developed and implemented. It provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier Stokes (RANS) equations and a nonlinear control of the solution update. Two variants of the new methodology are assessed on four benchmark cases, namely, a zero-pressure gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the baseline solver technology.
CFL3D Contribution to the AIAA Supersonic Shock Boundary Layer Interaction Workshop
NASA Technical Reports Server (NTRS)
Rumsey, Christopher L.
2010-01-01
This paper documents the CFL3D contribution to the AIAA Supersonic Shock Boundary Layer Interaction Workshop, held in Orlando, Florida in January 2010. CFL3D is a Reynolds-averaged Navier-Stokes code. Four shock boundary layer interaction cases are computed using a one-equation turbulence model widely used for other aerodynamic problems of interest. Two of the cases have experimental data available at the workshop, and two of the cases do not. The effect of grid, flux scheme, and thin-layer approximation are investigated. Comparisons are made to the available experimental data. All four cases exhibit strong three-dimensional behavior in and near the interaction regions, resulting from influences of the tunnel side-walls.
NASA Technical Reports Server (NTRS)
Grossman, Bernard
1999-01-01
The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based
NASA Technical Reports Server (NTRS)
Grossman, Bernard
1999-01-01
Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. An efficient surface parameterization based on a free-form deformation technique has been
Automated Euler and Navier-Stokes Database Generation for a Glide-Back Booster
NASA Technical Reports Server (NTRS)
Chaderjian, Neal M.; Rogers, Stuart E.; Aftosmis, Mike J.; Pandya, Shishir A.; Ahmad, Jasim U.; Tejnil, Edward
2004-01-01
The past two decades have seen a sustained increase in the use of high fidelity Computational Fluid Dynamics (CFD) in basic research, aircraft design, and the analysis of post-design issues. As the fidelity of a CFD method increases, the number of cases that can be readily and affordably computed greatly diminishes. However, computer speeds now exceed 2 GHz, hundreds of processors are currently available and more affordable, and advances in parallel CFD algorithms scale more readily with large numbers of processors. All of these factors make it feasible to compute thousands of high fidelity cases. However, there still remains the overwhelming task of monitoring the solution process. This paper presents an approach to automate the CFD solution process. A new software tool, AeroDB, is used to compute thousands of Euler and Navier-Stokes solutions for a 2nd generation glide-back booster in one week. The solution process exploits a common job-submission grid environment, the NASA Information Power Grid (IPG), using 13 computers located at 4 different geographical sites. Process automation and web-based access to a MySql database greatly reduces the user workload, removing much of the tedium and tendency for user input errors. The AeroDB framework is shown. The user submits/deletes jobs, monitors AeroDB's progress, and retrieves data and plots via a web portal. Once a job is in the database, a job launcher uses an IPG resource broker to decide which computers are best suited to run the job. Job/code requirements, the number of CPUs free on a remote system, and queue lengths are some of the parameters the broker takes into account. The Globus software provides secure services for user authentication, remote shell execution, and secure file transfers over an open network. AeroDB automatically decides when a job is completed. Currently, the Cart3D unstructured flow solver is used for the Euler equations, and the Overflow structured overset flow solver is used for the
NASA Technical Reports Server (NTRS)
Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.
2016-01-01
An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.
NASA Astrophysics Data System (ADS)
Lanzafame, Giuseppe
2015-02-01
In the nonlinear Navier-Stokes viscous flow dynamics, physical damping is mathematically accomplished by a braking term in the momentum equation, corresponding to a heating term in the energy equation, both responsible of the conversion of mechanical energy into heat. In such two terms, it is essential the role of the viscous stress tensor, relative to contiguous macroscopic moving flow components, depending on the macroscopic viscosity coefficient ν. A working formulation for ν can always be found analytically, tuning some arbitrary parameters in the current known formulations, according to the geometry, morphology and physics of the flow. Instead, in this paper, we write an alternative hybrid formulation for ν, where molecular parameters are also included. Our expression for ν has a more physical interpretation of the internal damping in dilute gases because the macroscopic viscosity is related to the small scale molecular dissipation, not strictly dependent on the flow morphology, as well as it is free of any arbitrary parameter. Results for some basic 2D tests are shown in the smoothed particle hydrodynamics (SPH) framework. An application to the 3D accretion disc modeling for low mass cataclysmic variables is also discussed. Consequences of the macroscopic viscosity coefficient reformulation in a more strictly physical terms on the thermal conductivity coefficient for dilute gases are also discussed.
NASA Technical Reports Server (NTRS)
Rogers, S. E.; Kwak, D.; Chang, J. L. C.
1986-01-01
Numerically solving the incompressible Navier-Stokes equations is known to be time consuming and expensive. Testing of the INS3D computers code, which solves these equations with the use of the pseudocompressibility method, shows this method to be an efficient way to obtain the steady state solution. The effects of the waves introduced by the pseudocompressibility method are analyzed and criteria are set and tested for the choice of the pseudocompressibility parameter which governs the artificial sound speed. The code is tested using laminar flow over a two dimensional backward-facing step, and laminar flow over a two dimensional circular cylinder. The results of the computations over the backward-facing step are in excellent agreement with experimental results. The transient solution of the flow over the cylinder impulsively started from rest is in good agreement with experimental results. However, the computed frequency of periodic shedding of vortices behind the cylinder is not in agreement with the experimental value. For a three dimensional test case, computations were conducted for a cylinder end wall junction. The saddle point separation and horseshoe vortex system appear in the computed field. The solution also shows secondary vortex filaments which wrap around the cylinder and spiral up in the wake.
Xiaodong Liu; Lijun Xuan; Hong Luo; Yidong Xia
2001-01-01
A reconstructed discontinuous Galerkin (rDG(P1P2)) method, originally introduced for the compressible Euler equations, is developed for the solution of the compressible Navier- Stokes equations on 3D hybrid grids. In this method, a piecewise quadratic polynomial solution is obtained from the underlying piecewise linear DG solution using a hierarchical Weighted Essentially Non-Oscillatory (WENO) reconstruction. The reconstructed quadratic polynomial solution is then used for the computation of the inviscid fluxes and the viscous fluxes using the second formulation of Bassi and Reay (Bassi-Rebay II). The developed rDG(P1P2) method is used to compute a variety of flow problems to assess its accuracy, efficiency, and robustness. The numerical results demonstrate that the rDG(P1P2) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to the large eddy simulation (LES) and direct numerical simulation (DNS) of compressible turbulent flows.
Algorithm and code development for unsteady three-dimensional Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Obayashi, Shigeru
1991-01-01
A streamwise upwind algorithm for solving the unsteady 3-D Navier-Stokes equations was extended to handle the moving grid system. It is noted that the finite volume concept is essential to extend the algorithm. The resulting algorithm is conservative for any motion of the coordinate system. Two extensions to an implicit method were considered and the implicit extension that makes the algorithm computationally efficient is implemented into Ames's aeroelasticity code, ENSAERO. The new flow solver has been validated through the solution of test problems. Test cases include three-dimensional problems with fixed and moving grids. The first test case shown is an unsteady viscous flow over an F-5 wing, while the second test considers the motion of the leading edge vortex as well as the motion of the shock wave for a clipped delta wing. The resulting algorithm has been implemented into ENSAERO. The upwind version leads to higher accuracy in both steady and unsteady computations than the previously used central-difference method does, while the increase in the computational time is small.
Exponential integrators for the incompressible Navier-Stokes equations.
Newman, Christopher K.
2004-07-01
We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size. Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step. Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L{sup 2} inner product. We examine this L{sup 2} projection and an H{sup 1} projection induced by the H{sup 1} semi-inner product. The H
An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Korte, John J.
1991-01-01
An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required
A gas-kinetic BGK scheme for the compressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Xu, Kun
2000-01-01
This paper presents an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations. The current method extends the previous gas-kinetic Navier-Stokes solver developed by Xu and Prendergast by implementing a general nonequilibrium state to represent the gas distribution function at the beginning of each time step. As a result, the requirement in the previous scheme, such as the particle collision time being less than the time step for the validity of the BGK Navier-Stokes solution, is removed. Therefore, the applicable regime of the current method is much enlarged and the Navier-Stokes solution can be obtained accurately regardless of the ratio between the collision time and the time step. The gas-kinetic Navier-Stokes solver developed by Chou and Baganoff is the limiting case of the current method, and it is valid only under such a limiting condition. Also, in this paper, the appropriate implementation of boundary condition for the kinetic scheme, different kinetic limiting cases, and the Prandtl number fix are presented. The connection among artificial dissipative central schemes, Godunov-type schemes, and the gas-kinetic BGK method is discussed. Many numerical tests are included to validate the current method.
NASA Technical Reports Server (NTRS)
Deese, J. E.; Agarwal, R. K.
1989-01-01
Computational fluid dynamics has an increasingly important role in the design and analysis of aircraft as computer hardware becomes faster and algorithms become more efficient. Progress is being made in two directions: more complex and realistic configurations are being treated and algorithms based on higher approximations to the complete Navier-Stokes equations are being developed. The literature indicates that linear panel methods can model detailed, realistic aircraft geometries in flow regimes where this approximation is valid. As algorithms including higher approximations to the Navier-Stokes equations are developed, computer resource requirements increase rapidly. Generation of suitable grids become more difficult and the number of grid points required to resolve flow features of interest increases. Recently, the development of large vector computers has enabled researchers to attempt more complex geometries with Euler and Navier-Stokes algorithms. The results of calculations for transonic flow about a typical transport and fighter wing-body configuration using thin layer Navier-Stokes equations are described along with flow about helicopter rotor blades using both Euler/Navier-Stokes equations.
NASA Astrophysics Data System (ADS)
Cheng, Jian; Yang, Xiaoquan; Liu, Xiaodong; Liu, Tiegang; Luo, Hong
2016-12-01
A Direct Discontinuous Galerkin (DDG) method is developed for solving the compressible Navier-Stokes equations on arbitrary grids in the framework of DG methods. The DDG method, originally introduced for scalar diffusion problems on structured grids, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations. Two approaches of implementing the DDG method to compute numerical diffusive fluxes for the Navier-Stokes equations are presented: one is based on the conservative variables, and the other is based on the primitive variables. The importance of the characteristic cell size used in the DDG formulation on unstructured grids is examined. The numerical fluxes on the boundary by the DDG method are discussed. A number of test cases are presented to assess the performance of the DDG method for solving the compressible Navier-Stokes equations. Based on our numerical results, we observe that DDG method can achieve the designed order of accuracy and is able to deliver the same accuracy as the widely used BR2 method at a significantly reduced cost, clearly demonstrating that the DDG method provides an attractive alternative for solving the compressible Navier-Stokes equations on arbitrary grids owning to its simplicity in implementation and its efficiency in computational cost.
NASA Technical Reports Server (NTRS)
Gabrielsen, R. E.; Karel, S.
1975-01-01
An algorithm for solving the nonlinear stationary Navier-Stokes problem is developed. Explicit error estimates are given. This mathematical technique is potentially adaptable to the separation problem.
Validation of a Node-Centered Wall Function Model for the Unstructured Flow Code FUN3D
NASA Technical Reports Server (NTRS)
Carlson, Jan-Renee; Vasta, Veer N.; White, Jeffery
2015-01-01
In this paper, the implementation of two wall function models in the Reynolds averaged Navier-Stokes (RANS) computational uid dynamics (CFD) code FUN3D is described. FUN3D is a node centered method for solving the three-dimensional Navier-Stokes equations on unstructured computational grids. The first wall function model, based on the work of Knopp et al., is used in conjunction with the one-equation turbulence model of Spalart-Allmaras. The second wall function model, also based on the work of Knopp, is used in conjunction with the two-equation k-! turbulence model of Menter. The wall function models compute the wall momentum and energy flux, which are used to weakly enforce the wall velocity and pressure flux boundary conditions in the mean flow momentum and energy equations. These wall conditions are implemented in an implicit form where the contribution of the wall function model to the Jacobian are also included. The boundary conditions of the turbulence transport equations are enforced explicitly (strongly) on all solid boundaries. The use of the wall function models is demonstrated on four test cases: a at plate boundary layer, a subsonic di user, a 2D airfoil, and a 3D semi-span wing. Where possible, different near-wall viscous spacing tactics are examined. Iterative residual convergence was obtained in most cases. Solution results are compared with theoretical and experimental data for several variations of grid spacing. In general, very good comparisons with data were achieved.
Existence and Regularity of the Pressure for the Stochastic Navier-Stokes Equations
Langa, Jose A. Real, Jose Simon, Jacques
2003-10-15
We prove, on one hand, that for a convenient body force with value sin the distribution space (H{sup -1}(D)){sup d}, where D is the geometric domain of the fluid, there exist a velocity u and a pressure p solution of the stochastic Navier-Stokes equation in dimension 2, 3 or 4. On the other hand, we prove that, for a body force with values in the dual space V' of the divergence free subspace V of (H{sup 1}{sub 0}(D)){sup d},in general it is not possible to solve the stochastic Navier-Stokes equations. More precisely, although such body forces have been considered, there is no topological space in which Navier-Stokes equations could be meaningful for them.
Navier-Stokes Analysis of the Flowfield Characteristics of an Ice Contaminated Aircraft Wing
NASA Technical Reports Server (NTRS)
Chung, J.; Choo, Y.; Reehorst, A.; Potapczuk, M.; Slater, J.
1999-01-01
An analytical study was performed as part of the NASA Lewis support of a National Transportation Safety Board (NTSB) aircraft accident investigation. The study was focused on the performance degradation associated with ice contamination on the wing of a commercial turbo-prop-powered aircraft. Based upon the results of an earlier numerical study conducted by the authors, a prominent ridged-ice formation on the subject aircraft wing was selected for detailed flow analysis using 2-dimensional (2-D), as well as, 3-dimensional (3-D) Navier-Stokes computations. This configuration was selected because it caused the largest lift decrease and drag increase among all the ice shapes investigated in the earlier study. A grid sensitivity test was performed to find out the influence of grid spacing on the lift, drag, and associated angle-of-attack for the maximum lift (C(sub lmax)). This study showed that grid resolution is important and a sensitivity analysis is an essential element of the process in order to assure that the final solution is independent of the grid. The 2-D results suggested that a severe stability and control difficulty could have occurred at a slightly higher angle-of-attack (AOA) than the one recorded by the Flight Data Recorder (FDR). This stability and control problem was thought to have resulted from a decreased differential lift on the wings with respect to the normal loading for the configuration. The analysis also indicated that this stability and control problem could have occurred whether or not natural ice shedding took place. Numerical results using an assumed 3-D ice shape showed an increase of the angle at which this phenomena occurred of about 4 degrees. As it occurred with the 2-D case, the trailing edge separation was observed but started only when the AOA was very close to the angle at which the maximum lift occurred.
Performance of a three-dimensional Navier-Stokes code on CYBER 205 for high-speed juncture flows
NASA Technical Reports Server (NTRS)
Lakshmanan, B.; Tiwari, S. N.
1987-01-01
A vectorized 3D Navier-Stokes code has been implemented on CYBER 205 for solving the supersonic laminar flow over a swept fin/flat plate junction. The code extends MacCormack's predictor-corrector finite volume scheme to a generalized coordinate system in a locally one dimensional time split fashion. A systematic parametric study is conducted to examine the effect of fin sweep on the computed flow field. Calculated results for the pressure distribution on the flat plate and fin leading edge are compared with the experimental measurements of a right angle blunt fin/flat plate junction. The decrease in the extent of the separated flow region and peak pressure on the fin leading edge, and weakening of the two reversed supersonic zones with increase in fin sweep have been clearly observed in the numerical simulation.
Shadid, J.N.; Tuminaro, R.S.; Walker, H.F.
1997-02-01
The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.
Full Navier-Stokes analysis of a two-dimensional mixer/ejector nozzle for noise suppression
NASA Technical Reports Server (NTRS)
Debonis, James R.
1992-01-01
A three-dimensional full Navier-Stokes (FNS) analysis was performed on a mixer/ejector nozzle designed to reduce the jet noise created at takeoff by a future supersonic transport. The PARC3D computational fluid dynamics (CFD) code was used to study the flow field of the nozzle. The grid that was used in the analysis consisted of approximately 900,000 node points contained in eight grid blocks. Two nozzle configurations were studied: a constant area mixing section and a diverging mixing section. Data are presented for predictions of pressure, velocity, and total temperature distributions and for evaluations of internal performance and mixing effectiveness. The analysis provided good insight into the behavior of the flow.
NASA Astrophysics Data System (ADS)
Klaij, C. M.; van der Vegt, J. J. W.; van der Ven, H.
2006-12-01
The space-time discontinuous Galerkin discretization of the compressible Navier-Stokes equations results in a non-linear system of algebraic equations, which we solve with pseudo-time stepping methods. We show that explicit Runge-Kutta methods developed for the Euler equations suffer from a severe stability constraint linked to the viscous part of the equations and propose an alternative to relieve this constraint while preserving locality. To evaluate its effectiveness, we compare with an implicit-explicit Runge-Kutta method which does not suffer from the viscous stability constraint. We analyze the stability of the methods and illustrate their performance by computing the flow around a 2D airfoil and a 3D delta wing at low and moderate Reynolds numbers.
FUN3D Analyses in Support of the Second Aeroelastic Prediction Workshop
NASA Technical Reports Server (NTRS)
Chwalowski, Pawel; Heeg, Jennifer
2016-01-01
This paper presents the computational aeroelastic results generated in support of the second Aeroelastic Prediction Workshop for the Benchmark Supercritical Wing (BSCW) configurations and compares them to the experimental data. The computational results are obtained using FUN3D, an unstructured grid Reynolds- Averaged Navier-Stokes solver developed at NASA Langley Research Center. The analysis results include aerodynamic coefficients and surface pressures obtained for steady-state, static aeroelastic equilibrium, and unsteady flow due to a pitching wing or flutter prediction. Frequency response functions of the pressure coefficients with respect to the angular displacement are computed and compared with the experimental data. The effects of spatial and temporal convergence on the computational results are examined.
Multilevel local refinement and multigrid methods for 3-D turbulent flow
Liao, C.; Liu, C.; Sung, C.H.; Huang, T.T.
1996-12-31
A numerical approach based on multigrid, multilevel local refinement, and preconditioning methods for solving incompressible Reynolds-averaged Navier-Stokes equations is presented. 3-D turbulent flow around an underwater vehicle is computed. 3 multigrid levels and 2 local refinement grid levels are used. The global grid is 24 x 8 x 12. The first patch is 40 x 16 x 20 and the second patch is 72 x 32 x 36. 4th order artificial dissipation are used for numerical stability. The conservative artificial compressibility method are used for further improvement of convergence. To improve the accuracy of coarse/fine grid interface of local refinement, flux interpolation method for refined grid boundary is used. The numerical results are in good agreement with experimental data. The local refinement can improve the prediction accuracy significantly. The flux interpolation method for local refinement can keep conservation for a composite grid, therefore further modify the prediction accuracy.
Convergence Acceleration of a Navier-Stokes Solver for Efficient Static Aeroelastic Computations
NASA Technical Reports Server (NTRS)
Obayashi, Shigeru; Guruswamy, Guru P.
1995-01-01
New capabilities have been developed for a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is based on a combination of the lower-upper factored symmetric Gauss-Seidel implicit method and the modified Harten-Lax-van Leer-Einfeldt upwind scheme. A numerically stable and efficient pseudo-time-marching method is also developed for computing steady flows over flexible wings. Results are demonstrated for transonic flows over rigid and flexible wings.
Navier-Stokes computations on swept-tapered wings, including flexibility
NASA Technical Reports Server (NTRS)
Guruswamy, Guru P.
1990-01-01
A procedure to couple the Navier-Stokes solutions with modal structural equations of motion is presented for computing aeroelastic responses of flexible fighter wings. The Navier-Stokes flow equations are solved by a finite-difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear-acceleration method. The configuration-adaptive dynamic grids are time-accurately generated using the aeroelastically deformed shape of the wing. The coupled calculations are compared with experiments when available. Effects of flexibility and pitch rate are demonstrated for flows with vortices. Turbulent flow computations are also compared with laminar flow computations.
A stable penalty method for the compressible Navier-Stokes equations. 1: Open boundary conditions
NASA Technical Reports Server (NTRS)
Hesthaven, J. S.; Gottlieb, D.
1994-01-01
The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization and localization at the boundaries based on these variables. The proposed boundary conditions are applied through a penalty procedure, thus ensuring correct behavior of the scheme as the Reynolds number tends to infinity. The versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder.
Navier-Stokes computations of separated vortical flows past prolate spheroid at incidence
NASA Technical Reports Server (NTRS)
Wong, Tin-Chee; Kandil, Osama A.; Liu, C. H.
1989-01-01
The problem of steady incompressible viscous flow past prolate spheroids at incidence is formulated using the unsteady incompressible and compressible thin-layer Navier-Stokes equations. The two sets of Navier-Stokes equations are solved using a pseudotime stepping of the implicit flux-difference splitting scheme on a curvilinear grid, which is generated by a transfinite grid generator. The Baldwin and Lomax (1978) algebraic eddy-viscosity model is used to model the turbulent flow. The computational applications cover a 6:1 prolate spheroid at different angles of attack and Reynolds numbers. The results are compared with experimental data.
Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations
Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C.; Michalowski, Nicholas
2015-07-15
The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.
Determining finite volume elements for the 2D Navier-Stokes equations
Jones, D.A. . Dept. of Mathematics); Titi, E.S. . Dept. of Mathematics Cornell Univ., Ithaca, NY . Mathematical Sciences Inst.)
1991-01-01
We consider the 2D Navier-Stokes equations on a square with periodic boundary conditions. Dividing the square into N equal subsquares, we show that if the asymptotic behavior of the average of solutions on these subsquares (finite volume elements) is known, then the large time behavior of the solution itself is completely determined, provided N is large enough. We also establish a rigorous upper bound for N needed to determine the solutions to the Navier-Stokes equation in terms of the physical parameters of the problem. 34 refs.
Cao, Yong; Chu, Yuchuan; He, Xiaoming; ...
2013-01-01
This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.
An Exact Mapping from Navier-Stokes Equation to Schr"odinger Equation via Riccati Equation
NASA Astrophysics Data System (ADS)
Christianto, Vic; Smarandache, Florentin
2010-03-01
In the present article we argue that it is possible to write down Schr"odinger representation of Navier-Stokes equation via Riccati equation. The proposed approach, while differs appreciably from other method such as what is proposed by R. M. Kiehn, has an advantage, i.e. it enables us extend further to quaternionic and biquaternionic version of Navier-Stokes equation, for instance via Kravchenko's and Gibbon's route. Further observation is of course recommended in order to refute or verify this proposition.
First-Order System Least-Squares for the Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Bochev, P.; Cai, Z.; Manteuffel, T. A.; McCormick, S. F.
1996-01-01
This paper develops a least-squares approach to the solution of the incompressible Navier-Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the Navier-Stokes equations as a first-order system by introducing a velocity flux variable and associated curl and trace equations. We show that the resulting system is well-posed, and that an associated least-squares principle yields optimal discretization error estimates in the H(sup 1) norm in each variable (including the velocity flux) and optimal multigrid convergence estimates for the resulting algebraic system.
3D pressure imaging of an aircraft propeller blade-tip flow by phase-locked stereoscopic PIV
NASA Astrophysics Data System (ADS)
Ragni, D.; van Oudheusden, B. W.; Scarano, F.
2012-02-01
The flow field at the tip region of a scaled DHC Beaver aircraft propeller, running at transonic speed, has been investigated by means of a multi-plane stereoscopic particle image velocimetry setup. Velocity fields, phase-locked with the blade rotational motion, are acquired across several planes perpendicular to the blade axis and merged to form a 3D measurement volume. Transonic conditions have been reached at the tip region, with a revolution frequency of 19,800 rpm and a relative free-stream Mach number of 0.73 at the tip. The pressure field and the surface pressure distribution are inferred from the 3D velocity data through integration of the momentum Navier-Stokes equation in differential form, allowing for the simultaneous flow visualization and the aerodynamic loads computation, with respect to a reference frame moving with the blade. The momentum and pressure data are further integrated by means of a contour-approach to yield the aerodynamic sectional force components as well as the blade torsional moment. A steady Reynolds averaged Navier-Stokes numerical simulation of the entire propeller model has been used for comparison to the measurement data.
Parameter investigation with line-implicit lower-upper symmetric Gauss-Seidel on 3D stretched grids
NASA Astrophysics Data System (ADS)
Otero, Evelyn; Eliasson, Peter
2015-03-01
An implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-averaged Navier-Stokes (RANS) simulation on stretched meshes. The computational fluid dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the left-hand side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimised settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.
Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach
NASA Technical Reports Server (NTRS)
Kiris, Cetin; Kwak, Dochan
1999-01-01
A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.
Williams, P.T.
1993-09-01
As the field of computational fluid dynamics (CFD) continues to mature, algorithms are required to exploit the most recent advances in approximation theory, numerical mathematics, computing architectures, and hardware. Meeting this requirement is particularly challenging in incompressible fluid mechanics, where primitive-variable CFD formulations that are robust, while also accurate and efficient in three dimensions, remain an elusive goal. This dissertation asserts that one key to accomplishing this goal is recognition of the dual role assumed by the pressure, i.e., a mechanism for instantaneously enforcing conservation of mass and a force in the mechanical balance law for conservation of momentum. Proving this assertion has motivated the development of a new, primitive-variable, incompressible, CFD algorithm called the Continuity Constraint Method (CCM). The theoretical basis for the CCM consists of a finite-element spatial semi-discretization of a Galerkin weak statement, equal-order interpolation for all state-variables, a 0-implicit time-integration scheme, and a quasi-Newton iterative procedure extended by a Taylor Weak Statement (TWS) formulation for dispersion error control. Original contributions to algorithmic theory include: (a) formulation of the unsteady evolution of the divergence error, (b) investigation of the role of non-smoothness in the discretized continuity-constraint function, (c) development of a uniformly H{sup 1} Galerkin weak statement for the Reynolds-averaged Navier-Stokes pressure Poisson equation, (d) derivation of physically and numerically well-posed boundary conditions, and (e) investigation of sparse data structures and iterative methods for solving the matrix algebra statements generated by the algorithm.
A Navier-Stokes Solution for Transonic Flow through a Cascade.
1982-01-01
McDonald (Ref. 13). 25. Thompson , J . F ., F. C. Thames and C. W. Mastin: Boundary Fitted Curvi- linear Coordinate Systems for Solution of Partial...Navier-Stokes Equations with Application to Shock Boundary Layer Inter- actions. AIAA Paper 75-1, 1975. 25. Thompson , J . F ., F. C. Thames and C. W
Numerical solution of the Navier-Stokes equations for unsteady separated flows
NASA Astrophysics Data System (ADS)
Hankey, W. L.
By use of the time-dependent Navier-Stokes equations, simplifying assumptions are no longer necessary to investigate many classes of unsteady separated flows. The projected advancement of computer capability over the next few years renders questionable the wisdom of supporting basic research on short-cut approximate methods for analyzing unsteady separated flows.
An implicit flux-split algorithm for the compressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Thomas, James L.; Rumsey, Christopher L.; Walters, Robert W.; Van Leer, Bram
1987-01-01
An implicit upwind scheme for the compressible Navier-Stokes equations is described and applied to the internal flow in a dual-throat nozzle. The method is second-order accurate spatially and naturally dissipative. A spatially-split approximate factorization method is used to obtain efficient steady-state solutions on the NASA Langley VPS-32 (CYBER 205) supercomputer.
Implementation of multigrid methods for solving Navier-Stokes equations on a multiprocessor system
NASA Technical Reports Server (NTRS)
Naik, Vijay K.; Taasan, Shlomo
1987-01-01
Presented are schemes for implementing multigrid algorithms on message based MIMD multiprocessor systems. To address the various issues involved, a nontrivial problem of solving the 2-D incompressible Navier-Stokes equations is considered as the model problem. Three different multigrid algorithms are considered. Results from implementing these algorithms on an Intel iPSC are presented.
Splitting methods for low Mach number Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Abarbanel, Saul; Dutt, Pravir; Gottlieb, David
1987-01-01
Examined are some splitting techniques for low Mach number Euler flows. Shortcomings of some of the proposed methods are pointed out and an explanation for their inadequacy suggested. A symmetric splitting for both the Euler and Navier-Stokes equations is then presented which removes the stiffness of these equations when the Mach number is small. The splitting is shown to be stable.
Optimal Control for Two-Dimensional Stochastic Navier-Stokes Equations
Cutland, Nigel J. Grzesiak, Katarzyna
2007-01-15
Loeb space methods are used to prove the existence of an optimal control for the two-dimensional stochastic Navier--Stokes equations in a variety of settings-including that of control based on digital observations of the evolution of the solution.
Numerical Experiments in Unsteady Flows Through the Use of Full Navier- Stokes Equations
1991-06-01
Murashige , Hinatsu and Kinoshita (1989) have used a similar method to analyze three cases (K = 5, 7, and 10) at higher Reynolds numbers around 104. The flow... Murashige , S., Hinatsu, M., and Kinoshita, T., 1989, "Direct Calculations of the Navier-Stokes Equations for Forces Acting on a Cylinder in Oscillatory
Solving Navier-Stokes' equation using Castillo-Grone's mimetic difference operators on GPUs
NASA Astrophysics Data System (ADS)
Abouali, Mohammad; Castillo, Jose
2012-11-01
This paper discusses the performance and the accuracy of Castillo-Grone's (CG) mimetic difference operator in solving the Navier-Stokes' equation in order to simulate oceanic and atmospheric flows. The implementation is further adapted to harness the power of the many computing cores available on the Graphics Processing Units (GPUs) and the speedup is discussed.
A Comparison of Three Navier-Stokes Solvers for Exhaust Nozzle Flowfields
NASA Technical Reports Server (NTRS)
Georgiadis, Nicholas J.; Yoder, Dennis A.; Debonis, James R.
1999-01-01
A comparison of the NPARC, PAB, and WIND (previously known as NASTD) Navier-Stokes solvers is made for two flow cases with turbulent mixing as the dominant flow characteristic, a two-dimensional ejector nozzle and a Mach 1.5 elliptic jet. The objective of the work is to determine if comparable predictions of nozzle flows can be obtained from different Navier-Stokes codes employed in a multiple site research program. A single computational grid was constructed for each of the two flows and used for all of the Navier-Stokes solvers. In addition, similar k-e based turbulence models were employed in each code, and boundary conditions were specified as similarly as possible across the codes. Comparisons of mass flow rates, velocity profiles, and turbulence model quantities are made between the computations and experimental data. The computational cost of obtaining converged solutions with each of the codes is also documented. Results indicate that all of the codes provided similar predictions for the two nozzle flows. Agreement of the Navier-Stokes calculations with experimental data was good for the ejector nozzle. However, for the Mach 1.5 elliptic jet, the calculations were unable to accurately capture the development of the three dimensional elliptic mixing layer.
Hong Luo; Luqing Luo; Robert Nourgaliev; Vincent A. Mousseau
2010-01-01
A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.
Numerical simulation of compressible Navier-Stokes flow in a double throat nozzle
NASA Astrophysics Data System (ADS)
Scott, James N.; Visbal, Miguel R.
The flow through a double-throat nozzle is computed using the complete time-dependent compressible Navier-Stokes equations. The computations were performed by using an existing working code with no special modifications for this particular application. The computations were performed on a Cyber 845 computer and a CRAY XMP-48 computer using three different grid sizes.
On spectral multigrid methods for the time-dependent Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Zang, T. A.; Hussaini, M. Y.
1985-01-01
A splitting scheme is proposed for the numerical solution of the time-dependent, incompressible Navier-Stokes equations by spectral methods. A staggered grid is used for the pressure, improved intermediate boundary conditions are employed in the split step for the velocity, and spectral multigrid techniques are used for the solution of the implicit equations.
Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray
2014-11-25
A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.
Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray
2014-01-01
A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design. PMID:25404761
NASA Astrophysics Data System (ADS)
Starodubtsev, Y. V.; Gogolev, I. G.; Solodov, V. G.
2005-06-01
The paper describes 3D numerical Reynolds Averaged Navier-Stokes (RANS) model and approximate sector approach for viscous turbulent flow through flow path of one stage axial supercharge gas turbine of marine diesel engine. Computational data are tested by comparison with experimental data. The back step flow path opening and tip clearance jet are taken into account. This approach could be applied for variety of turbine theory and design tasks: for offer optimal design in order to minimize kinetic energy stage losses; for solution of partial supply problem; for analysis of flow pattern in near extraction stages; for estimation of rotational frequency variable forces on blades; for sector vane adjustment (with thin leading edges mainly), for direct flow modeling in the turbine etc. The development of this work could be seen in the direction of unsteady stage model application.
NASA Technical Reports Server (NTRS)
Boger, David A.; Govindan, T. R.; McDonald, Henry
1997-01-01
Previous work at NASA LeRC has shown that flow distortions in aircraft engine inlet ducts can be significantly reduced by mounting vortex generators, or small wing sections, on the inside surface of the engine inlet. The placement of the vortex generators is an important factor in obtaining the optimal effect over a wide operating envelope. In this regard, the only alternative to a long and expensive test program which would search out this optimal configuration is a good prediction procedure which could narrow the field of search. Such a procedure has been developed in collaboration with NASA LeRC, and results obtained by NASA personnel indicate that it shows considerable promise for predicting the viscous turbulent flow in engine inlet ducts in the presence of vortex generators. The prediction tool is a computer code which numerically solves the reduced Navier-Stokes equations and so is commonly referred to as RNS3D. Obvious deficiencies in RNS3D have been addressed in previous work. Primarily, it is known that the predictions of the mean velocity field of a turbulent boundary layer flow approaching separation are not in good agreement with data. It was suggested that the use of an algebraic mixing-length turbulence model in RNS3D is at least partly to blame for this. Additionally, the current turbulence model includes an assumption of isotropy which will ultimately fail to capture turbulence-driven secondary flow known to exist in noncircular ducts.
NASA Technical Reports Server (NTRS)
Holst, T. L.; Thomas, S. D.; Kaynak, U.; Gundy, K. L.; Flores, J.; Chaderjian, N. M.
1985-01-01
Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The flow field immediately adjacent to the wing surface is resolved with fine grid zones and solved using a Navier-Stokes algorithm. Flow field regions removed from the wing are resolved with less finely clustered grid zones and are solved with an Euler algorithm. Computational issues associated with this zonal approach, including data base management aspects, are discussed. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects. Additional cases with significant shock induced separation on the upper wing surface are also presented.
Application of multi-grid methods for solving the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Demuren, A. O.
This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.
A comparative study of turbulence decay using Navier-Stokes and a discrete particle simulation
NASA Technical Reports Server (NTRS)
Goswami, A.; Baganoff, D.; Lele, S.; Feiereisen, W.
1993-01-01
A comparative study of the two dimensional temporal decay of an initial turbulent state of flow is presented using a direct Navier-Stokes simulation and a particle method, ranging from the near continuum to more rarefied regimes. Various topics related to matching the initial conditions between the two simulations are considered. The determination of the initial velocity distribution function in the particle method was found to play an important role in the comparison. This distribution was first developed by matching the initial Navier-Stokes state of stress, but was found to be inadequate beyond the near continuum regime. An alternative approach of using the Lees two-sided Maxwellian to match the initial strain-rate is discussed. Results of the comparison of the temporal decay of mean kinetic energy are presented for a range of Knudsen numbers. As expected, good agreement was observed for the near continuum regime, but the differences found for the more rarefied conditions were unexpectedly small.
Application of multi-grid methods for solving the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1989-01-01
The application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems is discussed. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line-, or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to that of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.
Application of multi-grid methods for solving the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1989-01-01
This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.
Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Lawrence, J. L.; Tannehill, J. C.; Chaussee, D. S.
1984-01-01
MacCormack's implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method for solving the PNS equations does not require the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed. The advantages and disadvantages of the present adaptation are discussed in relation to those of the conventional Beam-Warming scheme for a flat plate boundary layer test case. Comparisons are made for accuracy, stability, computer time, computer storage, and ease of implementation. The present method was also applied to a second test case of hypersonic laminar flow over a 15% compression corner. The computed results compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.
Numerical solution of the Navier-Stokes equations for arbitrary blunt bodies in supersonic flows
NASA Technical Reports Server (NTRS)
Warsi, Z. U. A.; Devarayalu, K.; Thompson, J. F.
1978-01-01
A time-dependent, two-dimensional Navier-Stokes code employing the body-fitted coordinate technique has been developed for supersonic flows past blunt bodies of arbitrary shape. The computer program is based on the finite-difference approximation of the compressible Navier-Stokes equations transformed to nonorthogonal curvilinear coordinates with the contravariant components of the velocity vector as dependent variables. The bow shock ahead of the body is obtained as part of the solution, by 'shock capturing'. Numerical solutions of the complete equations are presented in detail for free-stream Mach number 4.6, Reynolds number 10,000, and an isothermal wall temperature of 556 K for a circular cylinder with the free-stream outer boundaries forming a hyperbola in the front and a circular arc in the back.
Prediction of Business Jet Airloads Using The Overflow Navier-Stokes Code
NASA Technical Reports Server (NTRS)
Bounajem, Elias; Buning, Pieter G.
2001-01-01
The objective of this work is to evaluate the application of Navier-Stokes computational fluid dynamics technology, for the purpose of predicting off-design condition airloads on a business jet configuration in the transonic regime. The NASA Navier-Stokes flow solver OVERFLOW with Chimera overset grid capability, availability of several numerical schemes and convergence acceleration techniques was selected for this work. A set of scripts which have been compiled to reduce the time required for the grid generation process are described. Several turbulence models are evaluated in the presence of separated flow regions on the wing. Computed results are compared to available wind tunnel data for two Mach numbers and a range of angles-of-attack. Comparisons of wing surface pressure from numerical simulation and wind tunnel measurements show good agreement up to fairly high angles-of-attack.
Three-dimensional Navier-Stokes heat transfer predictions for turbine blade rows
NASA Technical Reports Server (NTRS)
Boyle, Robert J.; Giel, Paul W.
1992-01-01
Results are shown for a three-dimensional Navier-Stokes analysis of both the flow and the surface heat transfer for turbine applications. Heat transfer comparisons are made with the experimental shock-tunnel data of Dunn and Kim, and with the data of Blair for the rotor of the large scale rotating turbine. The analysis was done using the steady-state, three-dimensional, thin-layer Navier-Stokes code developed by Chima, which uses a multistage Runge-Kutta scheme with implicit residual smoothing. An algebraic mixing length turbulence model is used to calculate turbulent eddy viscosity. The variation in heat transfer due to variations in grid parameters is examined. The effects of rotation, tip clearance, and inlet boundary layer thickness variation on the predicted blade and endwall heat transfer are examined.
A finite element solution algorithm for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Baker, A. J.
1974-01-01
A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.
Bypass Transitional Flow Calculations Using a Navier-Stokes Solver and Two-Equation Models
NASA Technical Reports Server (NTRS)
Liuo, William W.; Shih, Tsan-Hsing; Povinelli, L. A. (Technical Monitor)
2000-01-01
Bypass transitional flows over a flat plate were simulated using a Navier-Stokes solver and two equation models. A new model for the bypass transition, which occurs in cases with high free stream turbulence intensity (TI), is described. The new transition model is developed by including an intermittency correction function to an existing two-equation turbulence model. The advantages of using Navier-Stokes equations, as opposed to boundary-layer equations, in bypass transition simulations are also illustrated. The results for two test flows over a flat plate with different levels of free stream turbulence intensity are reported. Comparisons with the experimental measurements show that the new model can capture very well both the onset and the length of bypass transition.
Programming the Navier-Stokes computer: An abstract machine model and a visual editor
NASA Technical Reports Server (NTRS)
Middleton, David; Crockett, Tom; Tomboulian, Sherry
1988-01-01
The Navier-Stokes computer is a parallel computer designed to solve Computational Fluid Dynamics problems. Each processor contains several floating point units which can be configured under program control to implement a vector pipeline with several inputs and outputs. Since the development of an effective compiler for this computer appears to be very difficult, machine level programming seems necessary and support tools for this process have been studied. These support tools are organized into a graphical program editor. A programming process is described by which appropriate computations may be efficiently implemented on the Navier-Stokes computer. The graphical editor would support this programming process, verifying various programmer choices for correctness and deducing values such as pipeline delays and network configurations. Step by step details are provided and demonstrated with two example programs.
NASA Technical Reports Server (NTRS)
Truong, K. V.; Tobak, M.
1990-01-01
The indicial response approach is recast in a form appropriate to the study of vortex induced oscillations phenomena. An appropriate form is demonstrated for the indicial response of the velocity field which may be derived directly from the Navier-Stokes equations. On the basis of the Navier-Stokes equations, it is demonstrated how a form of the velocity response to an arbitrary motion may be determined. To establish its connection with the previous work, the new approach is applied first to the simple situation wherein the indicial response has a time invariant equilibrium state. Results for the aerodynamic response to an arbitrary motion are shown to confirm to the form obtained previously.
A cell-vertex multigrid method for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Radespiel, R.
1989-01-01
A cell-vertex scheme for the Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing, a multigrid method, and carefully controlled artificial dissipative terms, very good convergence rates are obtained for a wide range of two- and three-dimensional flows over airfoils and wings. The accuracy of the code is examined by grid refinement studies and comparison with experimental data. For an accurate prediction of turbulent flows with strong separations, a modified version of the nonequilibrium turbulence model of Johnson and King is introduced, which is well suited for an implementation into three-dimensional Navier-Stokes codes. It is shown that the solutions for three-dimensional flows with strong separations can be dramatically improved, when a nonequilibrium model of turbulence is used.
A comparison of numerical flux formulas for the Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Van Leer, Bram; Thomas, James L.; Roe, Philip L.; Newsome, Richard W.
1987-01-01
Numerical flux formulas for the convection terms in the Euler or Navier-Stokes equations are analyzed with regard to their accuracy in representing steady nonlinear and linear waves (shocks and entropy/shear waves, respectively). Numerical results are obtained for a one-dimensional conical Navier-Stokes flow including both a shock and a boundary layer. Analysis and experiments indicate that for an accurate representation of both layers the flux formula must include information about all different waves by which neighboring cells interact, as in Roe's flux-difference splitting. In comparison, Van Leer's flux-vector splitting, which ignores the linear waves, badly diffuses the boundary layer. The results of MacCormack's scheme, if properly tuned, are significantly better. The use of a sufficiently detailed flux formula appears to reduce the number of cells required to resolve a boundary layer by a factor 1/2 to 1/4 and thus pays off.
NASA Technical Reports Server (NTRS)
Holst, T. L.
1976-01-01
Four explicit finite difference techniques designed to solve the time-dependent, compressible Navier Stokes equations are compared. These techniques are: (1) MacCormack, (2) modified Du Fort-Frankel, (3) modified hopscotch, and (4) Brailovskaya. The comparison was made numerically by solving the quasi-one dimensional Navier Stokes equations for the flow in a converging-diverging nozzle. Solutions with and without standing normal shock waves were computed for unit Reynolds numbers (based on total conditions) ranging from 45374 to 2269. The results indicate that all four techniques are comparable in accuracy; however, the modified hopscotch scheme is two to three times faster than the Brailovskaya and MacCormack schemes and three to six times faster than the modified Du Fort-Frankel scheme.
A p-adaptive LCP formulation for the compressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Cagnone, J. S.; Vermeire, B. C.; Nadarajah, S.
2013-01-01
This paper presents a polynomial-adaptive lifting collocation penalty (LCP) formulation for the compressible Navier-Stokes equations. The LCP formulation is a high-order nodal scheme in differential form. This format, although computationally efficient, complicates the treatment of non-uniform polynomial approximations. In Cagnone and Nadarajah (2012) [9], we proposed to circumvent this difficulty by employing specially designed elements inserted at the interface where the interpolation degree varies. In the present study we examine the applicability of this approach to the discretization of the Navier-Stokes equations, with focus put on the treatment of the viscous fluxes. The stability of the scheme is analyzed with the scalar diffusion equation and the merits of the approach are demonstrated with various p-adaptive simulations.
NASA Technical Reports Server (NTRS)
Chen, Y. K.; Henline, W. D.
1993-01-01
The general boundary conditions including mass and energy balances of chemically equilibrated or nonequilibrated gas adjacent to ablating surfaces have been derived. A computer procedure based on these conditions was developed and interfaced with the Navier-Stokes solver for predictions of the flow field, surface temperature, and surface ablation rates over re-entry space vehicles with ablating Thermal Protection Systems (TPS). The Navier-Stokes solver with general surface thermochemistry boundary conditions can predict more realistic solutions and provide useful information for the design of TPS. A test case with a proposed hypersonic test vehicle configuration and associated free stream conditions was developed. Solutions with various surface boundary conditions were obtained, and the effect of nonequilibrium gas as well as surface chemistry on surface heating and ablation rate were examined. The solutions of the GASP code with complete ablating surface conditions were compared with those of the ASC code. The direction of future work is also discussed.
Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Swanson, R. C.
2004-01-01
A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.
Numerical study of singularity formation in a class of Euler and Navier-Stokes flows
NASA Astrophysics Data System (ADS)
Ohkitani, Koji; Gibbon, John D.
2000-12-01
We study numerically a class of stretched solutions of the three-dimensional Euler and Navier-Stokes equations identified by Gibbon, Fokas, and Doering (1999). Pseudo-spectral computations of a Euler flow starting from a simple smooth initial condition suggests a breakdown in finite time. Moreover, this singularity apparently persists in the Navier-Stokes case. Independent evidence for the existence of a singularity is given by a Taylor series expansion in time. The mechanism underlying the formation of this singularity is the two-dimensionalization of the vorticity vector under strong compression; that is, the intensification of the azimuthal components associated with the diminishing of the axial component. It is suggested that the hollowing of the vortex accompanying this phenomenon may have some relevance to studies in vortex breakdown.
Numerical solution of transonic wing flows using an Euler/Navier-Stokes zonal approach
NASA Technical Reports Server (NTRS)
Holst, T. L.; Gundy, K. L.; Thomas, S. D.; Chaderjian, N. M.; Flores, J.
1985-01-01
Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The grid zones immediately adjacent to the wing surface are suitably clustered and solved with the Navier-Stokes equations. Grid zones removed from the wing are less finely clustered and are solved with the Euler equations. Wind tunnel wall effects are easily and accurately modeled with the new grid-zoning algorithm because the wind tunnel grid is constructed as an exact subset of the corresponding free-air grid. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects and shock-induced separation on the upper wing surface.
Navier-Stokes cascade analysis with a stiff Kappa-Epsilon turbulence solver
NASA Technical Reports Server (NTRS)
Liu, Jong-Shang; Sockol, Peter M.; Prahl, Joseph M.
1987-01-01
The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data.
Navier-Stokes cascade analysis with a stiff k-epsilon turbulence solver
NASA Technical Reports Server (NTRS)
Liu, Jong-Shang; Sockol, Peter M.; Prahl, Joseph M.
1988-01-01
The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data.
NASA Astrophysics Data System (ADS)
Zhang, Xiangxiong
2017-01-01
We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to multiple dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta time discretizations satisfy a weak positivity property. With a simple and efficient positivity-preserving limiter, high order explicit Runge-Kutta DG schemes are rendered preserving the positivity of density and internal energy without losing local conservation or high order accuracy. Numerical tests suggest that the positivity-preserving flux and the positivity-preserving limiter do not induce excessive artificial viscosity, and the high order positivity-preserving DG schemes without other limiters can produce satisfying non-oscillatory solutions when the nonlinear diffusion in compressible Navier-Stokes equations is accurately resolved.
Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains
NASA Astrophysics Data System (ADS)
Kast, Steven M.; Fidkowski, Krzysztof J.
2013-11-01
We present an output-based mesh adaptation strategy for Navier-Stokes simulations on deforming domains. The equations are solved with an arbitrary Lagrangian-Eulerian (ALE) approach, using a discontinuous Galerkin finite-element discretization in both space and time. Discrete unsteady adjoint solutions, derived for both the state and the geometric conservation law, provide output error estimates and drive adaptation of the space-time mesh. Spatial adaptation consists of dynamic order increment or decrement on a fixed tessellation of the domain, while a combination of coarsening and refinement is used to provide an efficient time step distribution. Results from compressible Navier-Stokes simulations in both two and three dimensions demonstrate the accuracy and efficiency of the proposed approach. In particular, the method is shown to outperform other common adaptation strategies, which, while sometimes adequate for static problems, struggle in the presence of mesh motion.
A two-level subgrid stabilized Oseen iterative method for the steady Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Shang, Yueqiang
2013-01-01
Based on two-grid finite element discretization and a recent subgrid-scale model, a two-level subgrid stabilized Oseen iterative method for the convection dominated Navier-Stokes equations is proposed and analyzed. This method combines the best algorithmic features of the two-grid discretization and subgrid stabilization methods. It first solves a subgrid stabilized nonlinear Navier-Stokes problem by applying m Oseen iterations on a coarse grid, and then solves a linear problem on a finer grid where the nonlinear convection term is fixed by the coarse grid solution. Stability of the method and error estimates of the discrete solution are analyzed. The algorithmic parameter scalings are also derived. Numerical results on an example with known analytical solution, the lid-driven cavity flow and the backward-facing step flow are given to verify the theoretical predictions and demonstrate the method's promise.
NASA Astrophysics Data System (ADS)
Thompson, D. S.
1980-05-01
The full Navier-Stokes equations for incompressible turbulent flow must be solved to accurately represent all flow phenomena which occur in a high Reynolds number incompressible flow. A two layer algebraic eddy viscosity turbulence model is used to represent the Reynolds stress in the primitive variable formulation. The development of the boundary-fitted coordinate systems makes the numerical solution of these equations feasible for arbitrarily shaped bodies. The nondimensional time averaged Navier-Stokes equations, including the turbulence mode, are represented by finite difference approximations in the transformed plane. The resulting coupled system of nonlinear algebraic equations is solved using a point successive over relaxation iteration. The test case considered was a NACA 64A010 airfoil section at an angle of attack of two degrees and a Reynolds number of 2,000,000.
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.
2013-01-01
Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.
Time-Filtered Navier-Stokes Approach and Emulation of Turbulence-Chemistry Interaction
NASA Technical Reports Server (NTRS)
Liu, Nan-Suey; Wey, Thomas; Shih, Tsan-Hsing
2013-01-01
This paper describes the time-filtered Navier-Stokes approach capable of capturing unsteady flow structures important for turbulent mixing and an accompanying subgrid model directly accounting for the major processes in turbulence-chemistry interaction. They have been applied to the computation of two-phase turbulent combustion occurring in a single-element lean-direct-injection combustor. Some of the preliminary results from this computational effort are presented in this paper.
A combined geometric approach for solving the Navier-Stokes equations on dynamic grids
NASA Technical Reports Server (NTRS)
Slater, John W.
1995-01-01
A combined geometric approach for solving the Navier-Stokes equations is presented for the analysis of planar, unsteady flow about mechanisms with components in moderate relative motion. The approach emphasizes the relationships between the geometry model, grid, and flow model for the benefit of the total dynamics problem. One application is the analysis of the restart operation of a variable-geometry, high-speed inlet.
Verification of a low Mach variable-density Navier-Stokes solver for turbulent combustion
NASA Astrophysics Data System (ADS)
Mullyadzhanov, R.; Palkin, E.; Nićeno, B.; Vervisch, L.; Hanjalić, K.
2016-10-01
We describe the low Mach variable-density Navier-Stokes numerical iterative solution procedure implemented in the finite-volume unstructured T-FlowS code. As the test cases we use a number of analytic manufactured solutions and Rayleigh-Taylor instability problem from the literature for algorithm verification purposes. The tests show that the code is second-order accurate in agreement with the spatial discretization scheme. We outline the recent combustion ADEF model implemented in the program.
Numerical solution of the Navier-Stokes equations for arbitrary 2-dimensional multi-element airfoils
NASA Technical Reports Server (NTRS)
Thompson, J. F.
1983-01-01
Numerical solutions of the Navier-Stokes equations, with an algebraic turbulence model, for time-dependent two dimensional flow about multi-element airfoils were developed. Fundamental to these solutions was the use of numerically-generated boundary-conforming curvilinear coordinate systems to allow bodies of arbitrary shape to be treated. A general two dimensional grid generation code for multiple-body configuration was written as a part of this project and made available through the COSMIC code library.
TURNS - A free-wake Euler/Navier-Stokes numerical method for helicopter rotors
NASA Technical Reports Server (NTRS)
Srinivasan, G. R.; Baeder, J. D.
1993-01-01
Computational capabilities of a numerical procedure, called TURNS (transonic unsteady rotor Navier-Stokes), to calculate the aerodynamics and acoustics (high-speed impulsive noise) out to several rotor diameters are summarized. The procedure makes it possible to obtain the aerodynamics and acoustics information in one single calculation. The vortical wave and its influence, as well as the acoustics, are captured as part of the overall flowfield solution. The accuracy and suitability of the TURNS method is demonstrated through comparisons with experimental data.
Some observations on a new numerical method for solving Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Kumar, A.
1981-01-01
An explicit-implicit technique for solving Navier-Stokes equations is described which, is much less complex than other implicit methods. It is used to solve a complex, two-dimensional, steady-state, supersonic-flow problem. The computational efficiency of the method and the quality of the solution obtained from it at high Courant-Friedrich-Lewy (CFL) numbers are discussed. Modifications are discussed and certain observations are made about the method which may be helpful in using it successfully.
An Anisotropic Partial Regularity Criterion for the Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Kukavica, Igor; Rusin, Walter; Ziane, Mohammed
2017-03-01
In this paper, we address the partial regularity of suitable weak solutions of the incompressible Navier-Stokes equations. We prove an interior regularity criterion involving only one component of the velocity. Namely, if ( u, p) is a suitable weak solution and a certain scale-invariant quantity involving only u 3 is small on a space-time cylinder {{Qr^{*}}(x_0,t_0)}, then u is regular at ( x 0, t 0).
Generalized INF-SUP condition for Chebyshev approximation of the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Bernardi, Christine; Canuto, Claudio; Maday, Yvon
1986-01-01
An abstract mixed problem and its approximation are studied; both are well-posed if and only if several inf-sup conditions are satisfied. These results are applied to a spectral Galerkin method for the Stokes problem in a square, when it is formulated in Chebyshev weighted Sobolev spaces. Finally, a collocation method for the Navier-Stokes equations at Chebyshev nodes is analyzed.
Navier-Stokes computations of laminar compressible and incompressible vortex flows in a channel
NASA Astrophysics Data System (ADS)
Brockmeier, U.; Mitra, N. K.; Fiebig, M.
To investigate the structure of compressible and incompressible vortices behind a small delta wing in a channel at low Reynolds and Mach numbers, computer programs have been developed to solve complete three-dimensional Navier-Stokes and energy equations. Results show qualitatively similar vortex formation, flattening of the vortex core, and movement of the core away from the channel center and towards the bottom wall for both incompressible and compressible flows.
Solution of three-dimensional afterbody flow using reduced Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Almahroos, H. M. H.; Khosla, P. K.; Rubin, S. G.
1991-01-01
The flow over afterbody geometries was investigated using the reduced Navier-Stokes (RNS) approximation. Both pressure velocity flux-split and composites velocity primitive variable formulations were considered. Pressure or pseudopotential relaxation procedures are combined with sparse matrix or coupled strongly implicit algorithms to form a three-dimensional solver for general non-orthogonal coordinates. Three-dimensional subsonic and transonic viscous/inviscid interacting flows were evaluated. Solutions with and without regions of recirculation were obtained.
Complete Galilean-Invariant Lattice BGK Models for the Navier-Stokes Equation
NASA Technical Reports Server (NTRS)
Qian, Yue-Hong; Zhou, Ye
1998-01-01
Galilean invariance has been an important issue in lattice-based hydrodynamics models. Previous models concentrated on the nonlinear advection term. In this paper, we take into account the nonlinear response effect in a systematic way. Using the Chapman-Enskog expansion up to second order, complete Galilean invariant lattice BGK models in one dimension (theta = 3) and two dimensions (theta = 1) for the Navier-Stokes equation have been obtained.
Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method
NASA Technical Reports Server (NTRS)
Chen, Hudong; Chen, Shiyi; Matthaeus, William H.
1992-01-01
A lattice Boltzmann model is presented which gives the complete Navier-Stokes equation and may provide an efficient parallel numerical method for solving various fluid problems. The model uses the single-time relaxation approximation and a particular Maxwell-type distribution. The model eliminates exactly (1) the non-Galilean invariance caused by a density-dependent coefficient in the convection term and (2) a velocity-dependent equation of state.
Isogeometric Divergence-conforming B-splines for the Steady Navier-Stokes Equations
2012-04-01
important simplification of fully unsteady Navier- Stokes flow . Many low speed, laminar fluid flows may be accurately described by the steady Navier...medium- and large-Reynolds number flows are inherently unsteady in both laminar and turbulent regimes. 2 Notation We begin this paper with some basic... Laminar flow behind a two-dimensional grid. Mathematical Proceedings of the Cambridge Philosophical Society, 44:58–62, 1948. [28] R J Labeur and G N
NASA Astrophysics Data System (ADS)
Hartmann, Ralf; Houston, Paul
2008-11-01
In this article we propose a new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the compressible Navier-Stokes equations. Here, particular emphasis is devoted to the construction of an optimal numerical method for the evaluation of certain target functionals of practical interest, such as the lift and drag coefficients of a body immersed in a viscous fluid. With this in mind, the key ingredients in the construction of the method include: (i) an adjoint consistent imposition of the boundary conditions; (ii) an adjoint consistent reformulation of the underlying target functional of practical interest; (iii) design of appropriate interior penalty stabilization terms. Numerical experiments presented within this article clearly indicate the optimality of the proposed method when the error is measured in terms of both the L2-norm, as well as for certain target functionals. Computational comparisons with other discontinuous Galerkin schemes proposed in the literature, including the second scheme of Bassi and Rebay, cf. [F. Bassi, S. Rebay, GMRES discontinuous Galerkin solution of the compressible Navier-Stokes equations, in: B. Cockburn, G. Karniadakis, C.-W. Shu (Eds.), Discontinuous Galerkin Methods, Lecture Notes in Comput. Sci. Engrg., vol. 11, Springer, Berlin, 2000, pp. 197-208; F. Bassi, S. Rebay, Numerical evaluation of two discontinuous Galerkin methods for the compressible Navier-Stokes equations, Int. J. Numer. Methods Fluids 40 (2002) 197-207], the standard SIPG method outlined in [R. Hartmann, P. Houston, Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. I: Method formulation, Int. J. Numer. Anal. Model. 3(1) (2006) 1-20], and an NIPG variant of the new scheme will be undertaken.
Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Tran, Chuong V.; Yu, Xinwei
2017-01-01
In this article, we prove new regularity criteria of the Prodi-Serrin-Ladyzhenskaya type for the Cauchy problem of the three-dimensional incompressible Navier-Stokes equations. Our results improve the classical Lr(0, T; Ls) regularity criteria for both velocity and pressure by factors of certain negative powers of the scaling invariant norms ↑" separators=" u ↑ L 3 and ↑" separators=" u ↑ H ˙ 1 / 2 .
An Incompressible Navier-Stokes with Particles Algorithm andParallel Implementation
Martin, Daniel F.; Colella, Phillip; Keen, Noel D.
2006-11-28
We present a variation of an adaptive projection method forcomputing solutions to the incompressible Navier-Stokes equations withsuspended particles. To compute the divergence-free component of themomentum forcing due to the particle drag, we employ an approach whichexploits the locality and smoothness of the Laplacian of the projectionoperator applied to the discretized particle drag force. We presentconvergence and performance results to demonstrate the effectiveness ofthis approach.
On the asymptotic limit of the Navier-Stokes system on domains with rough boundaries
NASA Astrophysics Data System (ADS)
Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka; Wolf, Joerg
We study the asymptotic behavior of solutions to the incompressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations are non-degenerate, meaning not oriented in a single direction.
Ergodicity of stochastic 2D Navier-Stokes equation with Lévy noise
NASA Astrophysics Data System (ADS)
Dong, Zhao; Xie, Yingchao
In this paper we deal with the 2D Navier-Stokes equation perturbed by a Lévy noise force whose white noise part is non-degenerate and that the intensity measure of Poisson measure is σ-finite. Existence and uniqueness of invariant measure for this equation is obtained, two main properties of the Markov semigroup associated with this equation are proved. In other words, strong Feller property and irreducibility hold in the same space.
Properties of solutions of certain control problems associated with the Navier-Stokes system
NASA Astrophysics Data System (ADS)
Fursikov, A. V.
The paper examines the properties of solutions of certain problems involving the control of systems described by the Navier-Stokes equations with periodic boundary conditions and without constraints on the controlling parameter. The uniqueness of the solutions is considered; necessary and sufficient conditions of the absolute minimum are obtained; and the smoothness of the solutions is demonstrated. The corresponding Euler-Lagrange equations are also examined.
FUN3D and CFL3D Computations for the First High Lift Prediction Workshop
NASA Technical Reports Server (NTRS)
Park, Michael A.; Lee-Rausch, Elizabeth M.; Rumsey, Christopher L.
2011-01-01
Two Reynolds-averaged Navier-Stokes codes were used to compute flow over the NASA Trapezoidal Wing at high lift conditions for the 1st AIAA CFD High Lift Prediction Workshop, held in Chicago in June 2010. The unstructured-grid code FUN3D and the structured-grid code CFL3D were applied to several different grid systems. The effects of code, grid system, turbulence model, viscous term treatment, and brackets were studied. The SST model on this configuration predicted lower lift than the Spalart-Allmaras model at high angles of attack; the Spalart-Allmaras model agreed better with experiment. Neglecting viscous cross-derivative terms caused poorer prediction in the wing tip vortex region. Output-based grid adaptation was applied to the unstructured-grid solutions. The adapted grids better resolved wake structures and reduced flap flow separation, which was also observed in uniform grid refinement studies. Limitations of the adaptation method as well as areas for future improvement were identified.
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.
2015-01-01
Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
Finite-time Properties of the Navier-Stokes Equations Under Lebesque Space Disturbances
NASA Astrophysics Data System (ADS)
Bobba, Kumar
2006-11-01
A complete understanding of the stability characteristics of the Navier-Stokes equations involve understanding both the transient response and the steady state response. The steady state (or infinite-time) response of the Navier-Stokes equations is characterized by the point spectrum and has been well studied. In this work, we study the transient (or finite-time) response of the unsteady Navier-Stokes equations linearized about plane Couette base flow under spatial and temporal varying disturbance forcing. The forcing and response are assumed to belong to infinite-dimensional Lebesque function spaces, L2 and L∞. An analytical characterization is given for the induced norms that characterize the response. It is shown that the L2 induced norm is tightly bounded by the H∞ norm of the transfer function operator and the L∞ induced norm is upper bounded by the L1 norm of the impulse response operator. The structure of the worst case disturbances and their amplification rates are computed using spectral methods---with Fourier modes in homogeneous direction and Chebyshev collocation in non-homogeneous direction. The relevance of the present results to the channel flow laminar-turbulent transition experiments will be discussed.
NASA Astrophysics Data System (ADS)
Yang, Xiaoquan; Cheng, Jian; Liu, Tiegang; Luo, Hong
2015-11-01
The direct discontinuous Galerkin (DDG) method based on a traditional discontinuous Galerkin (DG) formulation is extended and implemented for solving the compressible Navier-Stokes equations on arbitrary grids. Compared to the widely used second Bassi-Rebay (BR2) scheme for the discretization of diffusive fluxes, the DDG method has two attractive features: first, it is simple to implement as it is directly based on the weak form, and therefore there is no need for any local or global lifting operator; second, it can deliver comparable results, if not better than BR2 scheme, in a more efficient way with much less CPU time. Two approaches to perform the DDG flux for the Navier- Stokes equations are presented in this work, one is based on conservative variables, the other is based on primitive variables. In the implementation of the DDG method for arbitrary grid, the definition of mesh size plays a critical role as the formation of viscous flux explicitly depends on the geometry. A variety of test cases are presented to demonstrate the accuracy and efficiency of the DDG method for discretizing the viscous fluxes in the compressible Navier-Stokes equations on arbitrary grids.
A Second Order Continuum Theory of Fluids - Beyond the Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Paolucci, Samuel
2016-11-01
The Navier-Stokes equations have proved very valuable in modeling fluid flows over the last two centuries. However, there are some cases where it has been demonstrated that they do not provide accurate results. In such cases, very large variations in velocity and/or thermal fields occur in the flows. It is recalled that the Navier-Stokes equations result from linear approximations of constitutive quantities. Using continuum mechanics principles, we derive a second order constitutive theory that application of which should provide more accurate results is such cases. One important case is the structure of gas-dynamic shock waves. It has been demonstrated experimentally that the Navier-Stokes formulation yields incorrect shock profiles even at moderate Mach numbers. Current continuum theories, and indeed most statistical mechanics theories, that have been advanced to reconcile such discrepancies have not been fully successful. Thus, application of the second order theory based solely on a continuum formulation provides an excellent test problem. Results of the second-order equations applied to the shock structure are obtained for monatomic and diatomic gases over a large range of Mach numbers and are compared to experimental results.
Relative advantages of thin-layer Navier-Stokes and interactive boundary-layer procedures
NASA Technical Reports Server (NTRS)
Mehta, U.; Chang, K. C.; Cebeci, T.
1985-01-01
Numerical procedures for solving the thin-shear-layer Navier-Stokes equations and for the interaction of solutions to inviscid and boundary-layer equations are described and evaluated. To allow appraisal of the numerical and fluid dynamic abilities of the two schemes, they have been applied to one airfoil as a function of angle of attack at two slightly different Reynolds numbers. The NACA 0012 airfoil has been chosen because it allows comparison with measured lift, drag, and moment and with surface-pressure distributions. Calculations have been performed with algebraic eddy-viscosity formulations, and they include consideration of transition. The results are presented in a form that allows easy appraisal of the accuracy of both procedures and of the relative costs. The interactive procedure is computationally efficient but restrictive relative to the thin-layer Navier-Stokes procedure. The latter procedure does a better job of predicting drag than does the former. In both procedures, the location of transition is crucial for accurate or detailed computations, particularly at high angles of attack. When the upstream influence of pressure field through the shear layer is important, the thin-layer Navier-Stokes procedure has an edge over the interactive procedure.
A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.
1989-01-01
A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.
Hypersonic Navier-Stokes Comparisons to Orbiter Flight Data
NASA Technical Reports Server (NTRS)
Candler, Graham V.; Campbell, Charles H.
2010-01-01
During the STS-119 flight of Space Shuttle Discovery, two sets of surface temperature measurements were made. Under the HYTHIRM program3 quantitative thermal images of the windward side of the Orbiter with a were taken. In addition, the Boundary Layer Transition Flight Experiment 4 made thermocouple measurements at discrete locations on the Orbiter wind side. Most of these measurements were made downstream of a surface protuberance designed to trip the boundary layer to turbulent flow. In this paper, we use the US3D computational fluid dynamics code to simulate the Orbiter flow field at conditions corresponding to the STS-119 re-entry. We employ a standard two-temperature, five-species finite-rate model for high-temperature air, and the surface catalysis model of Stewart.1 This work is similar to the analysis of Wood et al . 2 except that we use a different approach for modeling turbulent flow. We use the one-equation Spalart-Allmaras turbulence model8 with compressibility corrections 9 and an approach for tripping the boundary layer at discrete locations. In general, the comparison between the simulations and flight data is remarkably good
NASA Astrophysics Data System (ADS)
Tavelli, Maurizio; Dumbser, Michael
2016-08-01
unstructured meshes allows to discretize even complex physical domains with very coarse grids in both, space and time. The proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3D test problems and by comparing the obtained numerical results with available exact analytical solutions, or with other numerical or experimental reference data. To the knowledge of the authors, this is the first time that a space-time discontinuous Galerkin finite element method is presented for the three-dimensional incompressible Navier-Stokes equations on staggered unstructured tetrahedral grids.
NASA Astrophysics Data System (ADS)
Lerat, A.
2016-10-01
Residual-Based Compact (RBC) schemes approximate the 3-D compressible Euler equations with a 5th- or 7th-order accuracy on a 5 × 5 × 5-point stencil and capture shocks pretty well without correction. For unsteady flows however, they require a costly algebra to extract the time-derivative occurring at several places in the scheme. A new high-order time formulation has been recently proposed [13] for simplifying the RBC schemes and increasing their temporal accuracy. The present paper goes much further in this direction and deeply reconsiders the method. An avatar of the RBC schemes is presented that greatly reduces the computing time and the memory requirements while keeping the same type of successful numerical dissipation. Two and three-dimensional linear stability are analyzed and the method is extended to the 3-D compressible Navier-Stokes equations. The new compact scheme is validated for several unsteady problems in two and three dimension. In particular, an accurate DNS at moderate cost is presented for the evolution of the Taylor-Green Vortex at Reynolds 1600 and Prandtl 0.71. The effects of the mesh size and of the accuracy order in the approximation of Euler and viscous terms are discussed.
NASA Technical Reports Server (NTRS)
Ameri, Ali A.; Shyam, Vikram; Rigby, David; Poinsatte, Phillip; Thurman, Douglas; Steinthorsson, Erlendur
2014-01-01
Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.
NASA Technical Reports Server (NTRS)
Ameri, Ali; Shyam, Vikram; Rigby, David; Poinsatte, Philip; Thurman, Douglas; Steinthorsson, Erlendur
2014-01-01
Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations which are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminarturbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes which take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-HT code and applied to film cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30 holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and four blowing ratios of 0.5, 1.0, 1.5 and 2.0 are shown. Flow features under those conditions are also described.
NASA Technical Reports Server (NTRS)
Ameri, Ali; Shyam, Vikram; Rigby, David; Poinsatte, Phillip; Thurman, Douglas; Steinthorsson, Erlendur
2014-01-01
Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.
NASA Technical Reports Server (NTRS)
Bardina, J. E.; Coakley, T. J.
1994-01-01
An investigation of the numerical simulation with two-equation turbulence models of a three-dimensional hypersonic intersecting (SWTBL) shock-wave/turbulent boundary layer interaction flow is presented. The flows are solved with an efficient implicit upwind flux-difference split Reynolds-averaged Navier-Stokes code. Numerical results are compared with experimental data for a flow at Mach 8.28 and Reynolds number 5.3x10(exp 6) with crossing shock-waves and expansion fans generated by two lateral 15 fins located on top of a cold-wall plate. This experiment belongs to the hypersonic database for modeling validation. Simulations show the development of two primary counter-rotating cross-flow vortices and secondary turbulent structures under the main vortices and in each corner singularity inside the turbulent boundary layer. A significant loss of total pressure is produced by the complex interaction between the main vortices and the uplifted jet stream of the boundary layer. The overall agreement between computational and experimental data is generally good. The turbulence modeling corrections show improvements in the predictions of surface heat transfer distribution and an increase in the strength of the cross-flow vortices. Accurate predictions of the outflow flowfield is found to require accurate modeling of the laminar/turbulent boundary layers on the fin walls.
Progress Toward Generation of a Navier-Stokes Database for a Harrier in Ground Effect
NASA Technical Reports Server (NTRS)
Chaderjian, Neal M.; Ahmad, Jasim U.; Pandya, Shishir A.; Murman, Scott A.; Kwak, Dochan (Technical Monitor)
2002-01-01
The Harrier YAV-8B aircraft is capable of vertical and short-field take-off and landing (V/STOL) by directing its four exhaust nozzles toward the ground, or conventional flight by rotating its nozzles into a horizontal position. The British Royal Air Force and the United States Marine Corps have used this aircraft for more than 30 years to provide a quick reaction time for troop support, and reduce the need for long runways. The success of this powered-lift (PL) vehicle has also prompted the more recent design of the Joint Strike Fighter (JSF). However there are significant safety issues that must be addressed when operating a PL vehicle in close proximity to the ground. Hot Gas Ingestion (HGI) by the inlets can result in a rapid loss of powered lift; and high-speed jet flows along the ground plane can induce low pressures underneath the vehicle, causing a 'suck-down' effect. Under these conditions, departure from controlled flight may occur. Moreover, unsteady ground vortices and jet fountains can affect the aircraft,s controllability and its proximity to ground troops. The viscous, time-dependent flow fields of PL vehicles are difficult to accurately and efficiently predict using Computational Fluid Dynamics (CFD). A number of researchers have used the time-dependent Reynolds-averaged Navier-Stokes (RANS) equations to compute flows for single and multiple jets in a cross-flow. A few have added some geometric complexity to the problem by computing flows for jet-augmented delta wings near a ground plane. Smith et.al. computed for the first time a single RANS solution about a simplified Harrier. This geometry included a fuselage, wing, leading edge root extension (LERX), inlets, and exhaust nozzles. All of these investigations cite two practical problems with computing these flows: 1) the need for improved solution accuracy; and, 2) the need for faster solution methods. We view the need for faster solution methods as key to improving the solution accuracy and making
NASA Technical Reports Server (NTRS)
Reddy, D. R.; Rubin, S. G.
1988-01-01
A consistent and efficient set of boundary conditions is developed for the multi-sweep space-marching pressure-elliptic Reduced Navier-Stokes (RNS) scheme as applied for 3-D internal viscous flow problems. No-slip boundary conditions are directly imposed on the solid walls. There is no iteration procedure required in the cross plane to ensure mass conservation across each marching plane. The finite difference equations forming the coefficient matrix are ordered such that the surface normal velocity is specified on all the solid walls; unlike external flows, a pressure boundary condition in the cross plane is not required. Since continuity is directly satisfied at all points in the flow domain, the first order momentum equations can be solved directly for the pressure without the need for a Poisson pressure correction equation. The procedure developed herein can also be applied with periodic boundary conditions. The analysis is given for general compressible flows. Incompressible flow solutions are obtained, for straight and curved ducts of square cross section, to validate the procedure. These solutions are used to demonstrate the applicability of the RNS scheme, with the improved boundary conditions for internal flows with strong interaction, as would be encountered in ducts and turbomachinery geometries.
NASA Astrophysics Data System (ADS)
Spyropoulos, John T.
This thesis extends earlier research in numerical analysis and computational fluid dynamics (CFD) to obtain a novel finite element method for the transient, 3-D, incompressible Navier-Stokes equations, along with efficient, parallelizable algorithms to carry out an implementation of the method in such a fashion as to be useful in mainstream industrial settings. This new finite element procedure employs alternating-direction operator splittings to model problems of increasing complexity in a step-by-step and natural manner. The scheme employs a characteristic-Galerkin method for the numerical treatment of the nonlinear advection operator. Non-overlapping domain decomposition schemes are employed for the solution of linear Stokes-type subproblems and for the matching of the inviscid and viscous solutions in different subdomains. These problems are solved by Bramble-Pasciak-Schatz wirebasket domain decomposition methods in a stabilized mixed finite element method formulation. The scheme is coupled to an existing grid generator code that provides globally unstructured, but locally structured grids, within each subdomain. Numerical results obtained include incompressible viscous flows over a backward facing steps at various Reynolds numbers and show very good to excellent agreement with experiments as well as other published numerical results.
Wang, Z J
2012-12-06
The overriding objective for this project is to develop an efficient and accurate method for capturing strong discontinuities and fine smooth flow structures of disparate length scales with unstructured grids, and demonstrate its potentials for problems relevant to DOE. More specifically, we plan to achieve the following objectives: 1. Extend the SV method to three dimensions, and develop a fourth-order accurate SV scheme for tetrahedral grids. Optimize the SV partition by minimizing a form of the Lebesgue constant. Verify the order of accuracy using the scalar conservation laws with an analytical solution; 2. Extend the SV method to Navier-Stokes equations for the simulation of viscous flow problems. Two promising approaches to compute the viscous fluxes will be tested and analyzed; 3. Parallelize the 3D viscous SV flow solver using domain decomposition and message passing. Optimize the cache performance of the flow solver by designing data structures minimizing data access times; 4. Demonstrate the SV method with a wide range of flow problems including both discontinuities and complex smooth structures. The objectives remain the same as those outlines in the original proposal. We anticipate no technical obstacles in meeting these objectives.
NASA Technical Reports Server (NTRS)
Liu, N. S.; Shamroth, S. J.; Mcdonald, H.
1983-01-01
The multidimensional ensemble averaged compressible time dependent Navier Stokes equations in conjunction with mixing length turbulence model and shock capturing technique were used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations were carried out: (1) 2 D, steady, subsonic; (2) 2 D, steady, transonic with normal shock; (3) 2 D, steady, supersonic with terminal shock; (4) 2 D, transient process of shock development and (5) 3 D, steady, transonic with normal shock. The numerical results obtained for the 2 D and 3 D transonic shocked flows were compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data.
Chaotic Behaviuor of the Navier-Stokes Solutions, Gyroscopes and Storm Surging
NASA Astrophysics Data System (ADS)
Tchiguirinskaia, Ioulia; Schertzer, Daniel
2015-04-01
Storm surges are phenomena inflicting wide damages all over the planet. Unfortunately they are badly represented in classical forecast model schemes because their multiscale nature is at odd with the scale truncation of these models. For similar reasons, classical data analysis often compelled to considered them as 'outliers' of the normal atmospheric activity, whereas as in fact they result from the same physical mechanisms that create less extreme behavior. A better representation of storm surges requires a multicale understanding of how a cascade of seemingly harmless instabilities can generate major ones. This correspond to the conjectured, outstanding intermittency.of the chaotic behaviour of the Navier-Stokes solutions. However, our limited, mathematical understanding of the Navier-Stokes equations prevent us to directly use them to investigate this question. We therefore use the most relevant cascade model to theoretically tackle this question of intermittency, i.e. the Scaling Gyroscopes Cascade (SGC). Indeed, this model is obtained with the help of a non trivial tree-decomposition of the Lie structure of the Navier-Stokes equations. the SGC model is deduced from these equations by preserving only a certain type of direct interactions, while the resulting indirect interactions are built dynamically along the tree-structure of the cascade. Because its fundamental element corresponds to a 'top' -i.e., an object with which almost anyone began to discover the puzzling nonlinear properties of rotation!- the SGC model remains rather simple, yet not simplistic! In particular, the SGC model enables us to investigate in details the occurrence of the critical singularity of a first order multifractal phase transition, which theoretically define storm surges. Overall, these theoretical findings could significantly reduce numerous uncertainties of environmental risk assessments.
Large Scale Flutter Data for Design of Rotating Blades Using Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Guruswamy, Guru P.
2012-01-01
A procedure to compute flutter boundaries of rotating blades is presented; a) Navier-Stokes equations. b) Frequency domain method compatible with industry practice. Procedure is initially validated: a) Unsteady loads with flapping wing experiment. b) Flutter boundary with fixed wing experiment. Large scale flutter computation is demonstrated for rotating blade: a) Single job submission script. b) Flutter boundary in 24 hour wall clock time with 100 cores. c) Linearly scalable with number of cores. Tested with 1000 cores that produced data in 25 hrs for 10 flutter boundaries. Further wall-clock speed-up is possible by performing parallel computations within each case.
Navier-Stokes calculations for the vortex of a rotor in hover
NASA Technical Reports Server (NTRS)
Liu, C. H.; Thomas, J. L.; Tung, C.
1984-01-01
An efficient finite-difference scheme for the solution of the incompressible Navier-Stokes equation is used to study the vortex wake of a rotor in hover. The solution Procedure uses a vorticity-stream function formulation and incorporates an asymptotic far-field boundary condition enabling the size of the computational domain to be reduced in comparison to other methods. The results from the present method are compared with experimental data obtained by smoke flow visualization and hot-wire measurements for several rotor blade configurations.
Decay rates to viscous contact waves for the compressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Ma, Shixiang; Wang, Jing
2016-02-01
In this paper, we study the large-time asymptotic behavior of contact wave for the Cauchy problem of one-dimensional compressible Navier-Stokes equations with zero viscosity. When the Riemann problem for the Euler system admits a contact discontinuity solution, we can construct a contact wave, which approximates the contact discontinuity on any finite-time interval for small heat conduction and then runs away from it for large time, and proves that it is nonlinearly stable provided that the strength of the contact discontinuity and the perturbation of the initial data are suitably small.
Evaluation of a research circulation control airfoil using Navier-Stokes methods
NASA Technical Reports Server (NTRS)
Shrewsbury, George D.
1987-01-01
The compressible Reynolds time averaged Navier-Stokes equations were used to obtain solutions for flows about a two dimensional circulation control airfoil. The governing equations were written in conservation form for a body-fitted coordinate system and solved using an Alternating Direction Implicit (ADI) procedure. A modified algebraic eddy viscosity model was used to define the turbulent characteristics of the flow, including the wall jet flow over the Coanda surface at the trailing edge. Numerical results are compared to experimental data obtained for a research circulation control airfoil geometry. Excellent agreement with the experimental results was obtained.
On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows
Venetis, J.
2015-01-01
A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces. PMID:25918743
1979-09-01
ithm for Computational Fluid Dynamics," Ph.D. Dissertation, Univ. of Tennessee, Report ESM 78-1, 1978. 18. Thames, F. C., Thompson , J . F ., and Mastin...C. W., "Numerical Solution of the Navier-Stokes Equations for Arbitrary Two-Dimensional Air- foils," NASA SP-347, 1975. 19. Thompson , J . F ., Thames...Number of Arbitrary Two-Dimensional Bodies," NASA CR-2729, 1976. 20. Thames, F. C., Thompson , J . F ., Mastin, C. W., and Walker, R. L., "Numerical
Continuum Navier-Stokes modelling of water flow past fullerene molecules
NASA Astrophysics Data System (ADS)
Walther, J. H.; Popadic, A.; Koumoutsakos, P.; Praprotnik, M.
2015-11-01
We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the computational cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently by continuum flow solvers, allowing for investigations into spatiotemporal scales inaccessible to atomistic simulations.
A least-squares finite element method for incompressible Navier-Stokes problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1989-01-01
A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method, and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.
Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations.
Fedotov, Aleksandr A; Akulova, Anna S; Akulov, Sergey A
2016-08-01
Mathematical modeling for composition distal arterial pulse wave in the blood vessels of the upper limbs was considered. Formation of distal arterial pulse wave is represented as a composition of forward and reflected pulse waves propagating along the arterial vessels. The formal analogy between pulse waves propagation along the human arterial system and the propagation of electrical oscillations in electrical transmission lines with distributed parameters was proposed. Dependencies of pulse wave propagation along the human arterial system were obtained by solving the one-dimensional Navier-Stokes equations for a few special cases.
Navier-Stokes in Aperture Domains:. Existence with Bounded Flux and Qualitative Properties
NASA Astrophysics Data System (ADS)
Maremonti, P.
2008-04-01
In this note we show a result of existence and some qualitative properties of solution to the Navier-Stokes equations in aperture domains. Roughly speaking, an aperture domain is an open connected consisting of two separated half-spaces connected by a hole. As it is known, in this special but physically interesting geometry the IBVP is a well posed if a flux condition trhough the hole is given as data. Our results correspond to an assumption on the flux that we consider physically reasonable. The results of this note will appear in the papers [2,18].
NASA Technical Reports Server (NTRS)
Chan, J. S.; Freeman, J. A.
1984-01-01
The viscous, axisymmetric flow in the thrust chamber of the space shuttle main engine (SSME) was computed on the CRAY 205 computer using the general interpolants method (GIM) code. Results show that the Navier-Stokes codes can be used for these flows to study trends and viscous effects as well as determine flow patterns; but further research and development is needed before they can be used as production tools for nozzle performance calculations. The GIM formulation, numerical scheme, and computer code are described. The actual SSME nozzle computation showing grid points, flow contours, and flow parameter plots is discussed. The computer system and run times/costs are detailed.
Quasiconservation laws for compressible three-dimensional Navier-Stokes flow.
Gibbon, J D; Holm, D D
2012-10-01
We formulate the quasi-Lagrangian fluid transport dynamics of mass density ρ and the projection q=ω·∇ρ of the vorticity ω onto the density gradient, as determined by the three-dimensional compressible Navier-Stokes equations for an ideal gas, although the results apply for an arbitrary equation of state. It turns out that the quasi-Lagrangian transport of q cannot cross a level set of ρ. That is, in this formulation, level sets of ρ (isopycnals) are impermeable to the transport of the projection q.
Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers
NASA Technical Reports Server (NTRS)
Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.
2014-01-01
This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.
Navier-Stokes Simulation of Homogeneous Turbulence on the CYBER 205
NASA Technical Reports Server (NTRS)
Wu, C. T.; Ferziger, J. H.; Chapman, D. R.; Rogallo, R. S.
1984-01-01
A computer code which solves the Navier-Stokes equations for three dimensional, time-dependent, homogenous turbulence has been written for the CYBER 205. The code has options for both 64-bit and 32-bit arithmetic. With 32-bit computation, mesh sizes up to 64 (3) are contained within core of a 2 million 64-bit word memory. Computer speed timing runs were made for various vector lengths up to 6144. With this code, speeds a little over 100 Mflops have been achieved on a 2-pipe CYBER 205. Several problems encountered in the coding are discussed.
Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Soh, Woo Y.
1992-01-01
A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.
A Navier-Stokes solver for high speed equilibrium flows and application to blunt bodies
NASA Technical Reports Server (NTRS)
Prabhu, Ramadas K.; Stewart, James R.; Thareja, Rajiv R.
1989-01-01
This paper presents a finite element method for the solution of Navier-Stokes equations with the assumption of thermodynamic and chemical equilibrium. The method employs an upwind finite element technique with an implicit time-marching scheme for the solution, and uses an adaptively generated unstructured triangular mesh with several layers of quadrilateral elements near solid walls. The complexity associated with the assumption that the flow is in equilibrium is treated consistently, and the inviscid flux Jacobian matrices are derived. Several problems involving inviscid and viscous hypersonic flow past blunt are solved. Results are compared with other numerical results and experimental data, and generally good agreement is observed.
A solution to the Navier-Stokes equations based upon the Newton Kantorovich method
NASA Technical Reports Server (NTRS)
Davis, J. E.; Gabrielsen, R. E.; Mehta, U. B.
1977-01-01
An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.
Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows
NASA Technical Reports Server (NTRS)
Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.
2009-01-01
A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.
A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
Kupiainen, M; Sjogreen, B
2008-03-21
We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in [6] and for the Euler equations of compressible fluid flow in [11], to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.
NASA Technical Reports Server (NTRS)
Rudy, D. H.; Morris, D. J.; Blanchard, D. K.; Cooke, C. H.; Rubin, S. G.
1975-01-01
The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.
Fischer, P.F.
1996-12-31
Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.
NASA Technical Reports Server (NTRS)
Kandil, Osama A.
1993-01-01
Research on Navier-Stokes, dynamics, and aeroelastic computations for vortical flows, buffet, and flutter applications was performed. Progress during the period from 1 Oct. 1992 to 30 Sep. 1993 is included. Papers on the following topics are included: vertical tail buffet in vortex breakdown flows; simulation of tail buffet using delta wing-vertical tail configuration; shock-vortex interaction over a 65-degree delta wing in transonic flow; supersonic vortex breakdown over a delta wing in transonic flow; and prediction and control of slender wing rock.
NASA Technical Reports Server (NTRS)
Thomas, J. L.; Diskin, B.; Brandt, A.
1999-01-01
The distributed-relaxation multigrid and defect- correction methods are applied to the two- dimensional compressible Navier-Stokes equations. The formulation is intended for high Reynolds number applications and several applications are made at a laminar Reynolds number of 10,000. A staggered- grid arrangement of variables is used; the coupled pressure and internal energy equations are solved together with multigrid, requiring a block 2x2 matrix solution. Textbook multigrid efficiencies are attained for incompressible and slightly compressible simulations of the boundary layer on a flat plate. Textbook efficiencies are obtained for compressible simulations up to Mach numbers of 0.7 for a viscous wake simulation.
Time-Accurate Incompressible Navier-Stokes Computations with Overlapped Moving Grids
NASA Technical Reports Server (NTRS)
Kiris, Cetin; Kwak, Dochan; Rogers, Stuart; Lee, Yu-Tai; Kutler, Paul (Technical Monitor)
1994-01-01
MIT flapping foil experiment was used as a validation case to evaluate the current incompressible Navier-Stokes approach with overlapped grid schemes. Steady-state calculations were carried out for overlapped and patched grids. The grid dependency, turbulence model effects, and the effect of order of differencing were investigated. Numerical results were compared against experimental data. The resulting procedure were applied to unsteady flapping foil calculations. Two upstream NACA 0025 foils perform high-frequency synchronized motion and generate unsteady flow conditions to the downstream larger stationary foil. Comparison between unsteady experimental data and numerical results from two different moving boundary procedures will be presented.
A three-dimensional structured/unstructured hybrid Navier-Stokes method for turbine blade rows
NASA Astrophysics Data System (ADS)
Tsung, F.-L.; Loellbach, J.; Kwon, O.; Hah, C.
1994-12-01
A three-dimensional viscous structured/unstructured hybrid scheme has been developed for numerical computation of high Reynolds number turbomachinery flows. The procedure allows an efficient structured solver to be employed in the densely clustered, high aspect-ratio grid around the viscous regions near solid surfaces, while employing an unstructured solver elsewhere in the flow domain to add flexibility in mesh generation. Test results for an inviscid flow over an external transonic wing and a Navier-Stokes flow for an internal annular cascade are presented.
Inverse airfoil design procedure using a multigrid Navier-Stokes method
NASA Technical Reports Server (NTRS)
Malone, J. B.; Swanson, R. C.
1991-01-01
The Modified Garabedian McFadden (MGM) design procedure was incorporated into an existing 2-D multigrid Navier-Stokes airfoil analysis method. The resulting design method is an iterative procedure based on a residual correction algorithm and permits the automated design of airfoil sections with prescribed surface pressure distributions. The new design method, Multigrid Modified Garabedian McFadden (MG-MGM), is demonstrated for several different transonic pressure distributions obtained from both symmetric and cambered airfoil shapes. The airfoil profiles generated with the MG-MGM code are compared to the original configurations to assess the capabilities of the inverse design method.
NASA Technical Reports Server (NTRS)
Jentink, Thomas Neil; Usab, William J., Jr.
1990-01-01
An explicit, Multigrid algorithm was written to solve the Euler and Navier-Stokes equations with special consideration given to the coarse mesh boundary conditions. These are formulated in a manner consistent with the interior solution, utilizing forcing terms to prevent coarse-mesh truncation error from affecting the fine-mesh solution. A 4-Stage Hybrid Runge-Kutta Scheme is used to advance the solution in time, and Multigrid convergence is further enhanced by using local time-stepping and implicit residual smoothing. Details of the algorithm are presented along with a description of Jameson's standard Multigrid method and a new approach to formulating the Multigrid equations.
Propulsive-jet flow field analysis using the three-dimensional Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Reed, C. L.
1988-01-01
A three-dimensional Navier-Stokes code has been applied to the analysis of flow fields containing propulsive jets. Specifically, the application was made to a flow field containing a supersonic jet injected at an angle of 90 degrees to a subsonic free stream. Although wind tunnel data were available, the computational results were not readily comparable to the experimental data because of significant differences between the two plume trajectories. Reasons for the differences are suggested in the report and include: (1) incomplete convergence, (2) inadequate grid resolution in the high gradient regions, and (3) use of a low-order turbulence closure model.
Global strong solutions to radial symmetric compressible Navier-Stokes equations with free boundary
NASA Astrophysics Data System (ADS)
Li, Hai-liang; Zhang, Xingwei
2016-12-01
In this paper, we consider the two-dimensional barotropic compressible Navier-Stokes equations with stress free boundary condition imposed on the free surface. As the viscosity coefficients satisfies μ (ρ) = 2 μ, λ (ρ) =ρβ, β > 1, we establish the existence of global strong solution for arbitrarily large spherical symmetric initial data even if the density vanishes across the free boundary. In particular, we show that the density is strictly positive and bounded from the above and below in any finite time if the initial density is strictly positive, and the free boundary propagates along the particle path and expand outwards at an algebraic rate.
Accuracy of upwind schemes applied to the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Von Lavante, E.
1990-01-01
A systematic comparison was carried out of the different forms of the van Leer et al. (1987) flux-vector splitting scheme (FVSS) for solving the Navier-Stokes equations with Roe's (1981) implicit flux-difference splitting scheme (FDSS) as applied to a simple viscous configuration. Particular attention is given to the effects of spacial accuracy, grid resolution, and grid stretching on the accuracy of the resulting flow field. It was found that, on coarse highly stretched grids, the FDSS produces more accurate results than the FVSS.
An incremental block-line-Gauss-Seidel method for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Napolitano, M.; Walters, R. W.
1985-01-01
A block-line-Gauss-Seidel (LGS) method is developed for solving the incompressible and compressible Navier-Stokes equations in two dimensions. The method requires only one block-tridiagonal solution process per iteration and is consequently faster per step than the linearized block-ADI methods. Results are presented for both incompressible and compressible separated flows: in all cases the proposed block-LGS method is more efficient than the block-ADI methods. Furthermore, for high Reynolds number weakly separated incompressible flow in a channel, which proved to be an impossible task for a block-ADI method, solutions have been obtained very efficiently by the new scheme.
The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1989-01-01
The Navier-Stokes equations in an implicit flux-split difference formulation are solved numerically using a Gauss-Seidel line-relaxation procedure. Particular attention is given to the selection of flux-vector splitting method and flux splitting in boundary layers. Results for sample problems involving (1) turbulent supersonic flow over a cone and (2) the viscous hypersonic flow of a chemically reacting gas in thermal nonequilibrium past a blunted cone are presented in extensive graphs and briefly characterized. The present flux-split procedures are shown to provide accurate shear-layer calculations.
Compressible Navier-Stokes equations: A study of leading edge effects
NASA Technical Reports Server (NTRS)
Hariharan, S. I.; Karbhari, P. R.
1987-01-01
A computational method is developed that allows numerical calculations of the time dependent compressible Navier-Stokes equations.The current results concern a study of flow past a semi-infinite flat plate.Flow develops from given inflow conditions upstream and passes over the flat plate to leave the computational domain without reflecting at the downstream boundary. Leading edge effects are included in this paper. In addition, specification of a heated region which gets convected with the flow is considered. The time history of this convection is obtained, and it exhibits a wave phenomena.
Development of a Navier-Stokes analysis for the flow in disk pumps
NASA Astrophysics Data System (ADS)
Kim, Y. N.; Buggeln, R. C.; McDonald, H.
1985-04-01
A technique has been developed to solve the Navier-Stokes equations for the flow in disk pumps. The technique uses a linearized block implicit-alternating direction technique to efficiently solve the unsteady governing equations to a steady state with appropriate boundary conditions and initial conditions. The resulting code was used to calculate the flow in two different geometries under the same flow conditions. Demonstration calculation indicates that the code will be a valuable tool in analytically evaluating the performance of existing and future disk pumps.
Development of a Navier-Stokes Analysis for the Flow in Disk Pumps.
1985-04-01
oiRD-AIS5 454 DEVELOPMENT OF A NAVIER-STOKES ANALYSIS FOR THE FLOW IN i/i DISK PUMPS .. (U) SCIENTIFIC RESEARCH ASSOCIATES INC GLASTONBURY CT Y N KIM...FLOW 7L, IN DISK PUMPS I: Y,-N. KIM R. C. BUGGELN H. MCDONALD SCIENTIFIC RESEARCH ASSOCIATES, INC. P. O. BOX 498 GLASTONBURY, CONNECTICUT 06033 APRIL...SUPPLEMENTARY NOTATION 17 COSATI CODES 18. SUBJECT TERMS (Continue on reverse if neceuary and id(tify by block number) FIELD GROUP SUB. GR. Disk Pumps , Navier
Upwind differencing and LU factorization for chemical non-equilibrium Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Shuen, Jian-Shun
1992-01-01
By means of either the Roe or the Van Leer flux-splittings for inviscid terms, in conjunction with central differencing for viscous terms in the explicit operator and the Steger-Warming splitting and lower-upper approximate factorization for the implicit operator, the present, robust upwind method for solving the chemical nonequilibrium Navier-Stokes equations yields formulas for finite-volume discretization in general coordinates. Numerical tests in the illustrative cases of a hypersonic blunt body, a ramped duct, divergent nozzle flows, and shock wave/boundary layer interactions, establish the method's efficiency.
Space-Time Error Representation and Estimation in Navier-Stokes Calculations
NASA Technical Reports Server (NTRS)
Barth, Timothy J.
2006-01-01
The mathematical framework for a-posteriori error estimation of functionals elucidated by Eriksson et al. [7] and Becker and Rannacher [3] is revisited in a space-time context. Using these theories, a hierarchy of exact and approximate error representation formulas are presented for use in error estimation and mesh adaptivity. Numerical space-time results for simple model problems as well as compressible Navier-Stokes flow at Re = 300 over a 2D circular cylinder are then presented to demonstrate elements of the error representation theory for time-dependent problems.
Application of a Scalable, Parallel, Unstructured-Grid-Based Navier-Stokes Solver
NASA Technical Reports Server (NTRS)
Parikh, Paresh
2001-01-01
A parallel version of an unstructured-grid based Navier-Stokes solver, USM3Dns, previously developed for efficient operation on a variety of parallel computers, has been enhanced to incorporate upgrades made to the serial version. The resultant parallel code has been extensively tested on a variety of problems of aerospace interest and on two sets of parallel computers to understand and document its characteristics. An innovative grid renumbering construct and use of non-blocking communication are shown to produce superlinear computing performance. Preliminary results from parallelization of a recently introduced "porous surface" boundary condition are also presented.
Quantum Brownian Motions and Navier-Stokes Weakly Turbulence — a Path Integral Study
NASA Astrophysics Data System (ADS)
Botelho, Luiz C. L.
In this paper, we present a new method to solve exactly the Schrödinger Harmonic oscillator wave equation in the presence of time-dependent parameter. We also apply such technique to solve exactly the problem of random frequency averaged quantum propagator of a harmonic oscillator with white-noise statistics frequency. We still apply our technique to solve exactly the Brownian Quantum Oscillator in the presence of an electric field. Finally, we use these quantum mechanic techniques to solve exactly the Statistical-Turbulence of the Navier-Stokes in a region of fluid random stirring weakly (analytical) coupling through time-dependent Euclidean-Quantum oscillators path-integrals.
Multiwavelet characterization of function spaces adapted to the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Lakey, Joseph D.; Obeidat, S.; Pereyra, M. Cristina
2000-12-01
We use wavelets based ona modification of the Geronimo- Hardin-Massopust construction to define localized extension/restriction operators form half-spaces to their full spaces/boundaries respectively. These operations are continuous in Sobolev and Morrey space norms. We also prove estimates for multiresolution projections of pointwise products of functions in these spaces. These are two of the key steps in extending results of Federbush and of Cannone and Meyer concerning solutions of Navier-Stokes with initial data in Sobolev and Morrey spaces to the case of half spaces and, ultimately, to more general domains with boundary.
Local stabilization of the compressible Navier-Stokes system, around null velocity, in one dimension
NASA Astrophysics Data System (ADS)
Chowdhury, Shirshendu; Maity, Debayan; Ramaswamy, Mythily; Raymond, Jean-Pierre
2015-07-01
In this paper we study the exponential stabilization of the one dimensional compressible Navier-Stokes system, in a bounded interval (0, π), locally around a constant steady state (ρ bar, 0), ρ bar > 0, by a localized distributed control acting only in the velocity equation. We determine a linear feedback law able to stabilize a nonlinear transformed system. Coming back to the original nonlinear system, we obtain a nonlinear feedback law able to stabilize locally this nonlinear system. To the best of our knowledge, the results of the paper are the first ones providing feedback control laws stabilizing compressible fluid flows.
Propulsion-related flowfields using the preconditioned Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Venkateswaran, S.; Weiss, J. M.; Merkle, C. L.; Choi, Y.-H.
1992-01-01
A previous time-derivative preconditioning procedure for solving the Navier-Stokes is extended to the chemical species equations. The scheme is implemented using both the implicit ADI and the explicit Runge-Kutta algorithms. A new definition for time-step is proposed to enable grid-independent convergence. Several examples of both reacting and non-reacting propulsion-related flowfields are considered. In all cases, convergence that is superior to conventional methods is demonstrated. Accuracy is verified using the example of a backward facing step. These results demonstrate that preconditioning can enhance the capability of density-based methods over a wide range of Mach and Reynolds numbers.
A least-squares finite element method for incompressible Navier-Stokes problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1992-01-01
A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.
A Navier-Stokes phase-field crystal model for colloidal suspensions
Praetorius, Simon Voigt, Axel
2015-04-21
We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier-Stokes Phase-Field Crystal model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and is used to analyze colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.
NASA Astrophysics Data System (ADS)
Suzuki, Kensuke
A new analysis tool, an unsteady Hybrid Navier-Stokes/Vortex Model, for a horizontal axis wind turbine (HAWT) in yawed flow is presented, and its convergence and low cost computational performance are demonstrated. In earlier work, a steady Hybrid Navier-Stokes/Vortex Model was developed with a view to improving simulation results obtained by participants of the NASA Ames blind comparison workshop, following the NREL Unsteady Aerodynamics Experiment. The hybrid method was shown to better predict rotor torque and power over the range of wind speeds, from fully attached to separated flows. A decade has passed since the workshop was held and three dimensional unsteady Navier-Stokes analyses have become available using super computers. In the first chapter, recent results of unsteady Euler and Navier-Stokes computations are reviewed as standard references of what is currently possible and are contrasted with results of the Hybrid Navier-Stokes/Vortex Model in steady flow. In Chapter 2, the computational method for the unsteady Hybrid model is detailed. The grid generation procedure, using ICEM CFD, is presented in Chapter 3. Steady and unsteady analysis results for the NREL Phase IV rotor and for a modified "swept NREL rotor" are presented in Chapter 4-Chapter 7.
NASA Technical Reports Server (NTRS)
Mcmillin, S. Naomi; Thomas, James L.; Murman, Earll M.
1990-01-01
An Euler flow solver and a thin layer Navier-Stokes flow solver were used to numerically simulate the supersonic leeside flow fields over delta wings which were observed experimentally. Three delta wings with 75, 67.5, and 60 deg leading edge sweeps were computed over an angle-of-attack range of 4 to 20 deg at a Mach number 2.8. The Euler code and Navier-Stokes code predict equally well the primary flow structure where the flow is expected to be separated or attached at the leading edge based on the Stanbrook-Squire boundary. The Navier-Stokes code is capable of predicting both the primary and the secondary flow features for the parameter range investigated. For those flow conditions where the Euler code did not predict the correct type of primary flow structure, the Navier-Stokes code illustrated that the flow structure is sensitive to boundary layer model. In general, the laminar Navier-Stokes solutions agreed better with the experimental data, especially for the lower sweep delta wings. The computational results and a detailed re-examination of the experimental data resulted in a refinement of the flow classifications. This refinement in the flow classification results in the separation bubble with the shock flow type as the intermediate flow pattern between separated and attached flows.
Verification and Validation of the k-kL Turbulence Model in FUN3D and CFL3D Codes
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.; Carlson, Jan-Renee; Rumsey, Christopher L.
2015-01-01
The implementation of the k-kL turbulence model using multiple computational uid dy- namics (CFD) codes is reported herein. The k-kL model is a two-equation turbulence model based on Abdol-Hamid's closure and Menter's modi cation to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's equation is well suited for term-by-term mod- eling and displays useful features compared to other two-equation models. An important di erence is that this formulation leads to the inclusion of higher-order velocity derivatives in the source terms of the scale equations. This can enhance the ability of the Reynolds- averaged Navier-Stokes (RANS) solvers to simulate unsteady ows. The present report documents the formulation of the model as implemented in the CFD codes Fun3D and CFL3D. Methodology, veri cation and validation examples are shown. Attached and sepa- rated ow cases are documented and compared with experimental data. The results show generally very good comparisons with canonical and experimental data, as well as matching results code-to-code. The results from this formulation are similar or better than results using the SST turbulence model.
Further Development of a New, Flux-Conserving Newton Scheme for the Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Scott, James R.
1996-01-01
This paper is one of a series of papers describing the development of a new numerical approach for solving the steady Navier-Stokes equations. The key features in the current development are (1) the discrete representation of the dependent variables by way of high order polynomial expansions, (2) the retention of all derivatives in the expansions as unknowns to be explicitly solved for, (3) the automatic balancing of fluxes at cell interfaces, and (4) the discrete simulation of both the integral and differential forms of the governing equations. The main purpose of this paper is, first, to provide a systematic and rigorous derivation of the conditions that are used to simulate the differential form of the Navier-Stokes equations, and second, to extend our previously-presented internal flow scheme to external flows and nonuniform grids. Numerical results are presented for high Reynolds number flow (Re = 100,000) around a finite flat plate, and detailed comparisons are made with the Blasius flat plate solution and Goldstein wake solution. It is shown that the error in the streamwise velocity decreases like r(sup alpha)(Delta)y(exp 2), where alpha approx. 0.25 and r = delta(y)/delta(x) is the grid aspect ratio.
Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations
Walters, R.A.; Carey, G.F.
1983-01-01
The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations. ?? 1983.
A Galerkin-free model reduction approach for the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Shinde, Vilas; Longatte, Elisabeth; Baj, Franck; Hoarau, Yannick; Braza, Marianna
2016-03-01
Galerkin projection of the Navier-Stokes equations on Proper Orthogonal Decomposition (POD) basis is predominantly used for model reduction in fluid dynamics. The robustness for changing operating conditions, numerical stability in long-term transient behavior and the pressure-term consideration are generally the main concerns of the Galerkin Reduced-Order Models (ROM). In this article, we present a novel procedure to construct an off-reference solution state by using an interpolated POD reduced basis. A linear interpolation of the POD reduced basis is performed by using two reference solution states. The POD basis functions are optimal in capturing the averaged flow energy. The energy dominant POD modes and corresponding base flow are interpolated according to the change in operating parameter. The solution state is readily built without performing the Galerkin projection of the Navier-Stokes equations on the reduced POD space modes as well as the following time-integration of the resulted Ordinary Differential Equations (ODE) to obtain the POD time coefficients. The proposed interpolation based approach is thus immune from the numerical issues associated with a standard POD-Galerkin ROM. In addition, a posteriori error estimate and a stability analysis of the obtained ROM solution are formulated. A detailed case study of the flow past a cylinder at low Reynolds numbers is considered for the demonstration of proposed method. The ROM results show good agreement with the high fidelity numerical flow simulation.
Navier-Stokes symmetry in the phenomenological transport theory for bacterial chemotaxis
NASA Astrophysics Data System (ADS)
Rosen, Gerald
1984-05-01
It is observed that the Navier-Stokes space-time dilatation invariance (x-->-->λx-->,t-->λ2t) implies that the random motility and chemotactic flux function take the forms observed experimentally for motile Escherichia coli attracted by low concentrations of oxygen; moreover, the rate function for E. coli consumption of dissolved oxygen is required to have the form (const) × (local oxygen concentration)2/3. It is also noteworthy that the Schrödinger-Bloch function for redistribution of chemotactic bacteria cells is invariant under the space-time dilatation transformations if and only if the chemotactic flux coefficient-random motility ratio equals 2, a value in the range 1.1 to 2.5 observed experimentally by Holz and Chen in the oxygen chemotaxis of motile E. coli. Suitably specialized governing equations for the phenomenological transport theory also admit a Galilean transformation invariance symmetry if and only if the chemotactic flux coefficient-critical substrate diffusivity ratio equals -2 and the consumption rate function is simply linear in the local oxygen concentration. Applicable to the regime of viscous incompressible flows with Reynolds numbers much less than unity, the Navier-Stokes superposition invariance may also give rise to a corresponding invariance symmetry in equivalent but linear phenomenological transport equations.
Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1995-01-01
A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.
Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Hafez, Mohammed; Dacles, Jennifer
1989-01-01
The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.
A point implicit unstructured grid solver for the Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Thareja, Rajiv R.; Stewart, James R.; Hassan, Obey; Morgan, Ken; Peraire, Jaime
1988-01-01
An upwind finite element technique that uses cell centered quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive unstructured triangular grids. A structured grid of quadrilaterals is laid out near the body surface. For inviscid flows the method is stable at Courant numbers of over 100,000. A first order basic scheme and a higher order flux corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view of simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are very distinctly captured with a sequence of adaptively generated grids. The adaptive mesh generator and the upwind Navier-Stokes solver are combined in a set of programs called LARCNESS, an acronym for Langley Adaptive Remeshing Code and Navier-Stokes Solver.
Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations
NASA Technical Reports Server (NTRS)
Frink, Neal T.; Pirzadeh, Shahyar Z.
1998-01-01
A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.
Turbulent solution of the Navier-Stokes equations for uniform shear flow
NASA Technical Reports Server (NTRS)
Deissler, R. G.
1981-01-01
To study the nonlinear physics of uniform turbulent shear flow, the unaveraged Navier-Stokes equations are solved numerically. This extends our previous work in which mean gradients were absent. For initial conditions, modified three-dimensional-cosine velocity fluctuations are used. The boundary conditions are modified periodic conditions on a stationary three-dimensional numerical grid. A uniform mean shear is superimposed on the initial and boundary conditions. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. As in the case of no shear the initially nonrandom flow develops into an apparently random turbulence at higher Reynolds number. Thus, randomness or turbulence can apparently arise as a consequence of the structure of the Navier-Stokes equations. Except for an initial period of adjustment, all fluctuating components grow with time. The initial equality of the three intensity components is destroyed by the shear, the transverse components becoming smaller than the longitudinal one, in agreement with experiment. Also, the shear creates a small-scale structure in the turbulence. The nonlinear solutions are compared with linearized ones.
Flowfield Comparisons from Three Navier-Stokes Solvers for an Axisymmetric Separate Flow Jet
NASA Technical Reports Server (NTRS)
Koch, L. Danielle; Bridges, James; Khavaran, Abbas
2002-01-01
To meet new noise reduction goals, many concepts to enhance mixing in the exhaust jets of turbofan engines are being studied. Accurate steady state flowfield predictions from state-of-the-art computational fluid dynamics (CFD) solvers are needed as input to the latest noise prediction codes. The main intent of this paper was to ascertain that similar Navier-Stokes solvers run at different sites would yield comparable results for an axisymmetric two-stream nozzle case. Predictions from the WIND and the NPARC codes are compared to previously reported experimental data and results from the CRAFT Navier-Stokes solver. Similar k-epsilon turbulence models were employed in each solver, and identical computational grids were used. Agreement between experimental data and predictions from each code was generally good for mean values. All three codes underpredict the maximum value of turbulent kinetic energy. The predicted locations of the maximum turbulent kinetic energy were farther downstream than seen in the data. A grid study was conducted using the WIND code, and comments about convergence criteria and grid requirements for CFD solutions to be used as input for noise prediction computations are given. Additionally, noise predictions from the MGBK code, using the CFD results from the CRAFT code, NPARC, and WIND as input are compared to data.
Consequences of the Brenner modification to the Navier Stokes equations for dynamic light scattering
NASA Astrophysics Data System (ADS)
Bardow, André; Christian Öttinger, Hans
2007-01-01
A modification of the classical Navier-Stokes equations has recently been proposed by Brenner [Is the tracer velocity of a fluid continuum equal to its mass velocity? Phys. Rev. E 70 (2004) Art. No. 061201; Kinematics of volume transport, Physica A 349 (2005) 11-59; Navier-Stokes revisited, Physica A 349 (2005) 60-132] and then formalized by Öttinger [Beyond Equilibrium Thermodynamics, Wiley, Hoboken, 2005]. In the modified theory, a contribution for mass diffusion is included in the continuity equation. The argument was based on experimental support from thermophoresis which however depends on the correct formulation of boundary conditions. The controversy therefore remained. Since such an additional mass diffusion transport mode should contribute to dynamic light scattering spectra, the consequences of the modified theory for light scattering spectra are discussed in this work. For liquids, the new theory is consistent with measured scattering data since the modification to the spectrum is usually negligible. The effect could, however, be observable in gases.
Looking for O(N) Navier-Stokes solutions on non-structured meshes
NASA Technical Reports Server (NTRS)
Morano, Eric; Dervieux, Alain
1993-01-01
Multigrid methods are good candidates for the resolution of the system arising in Numerical Fluid Dynamics. However, the question is to know if those algorithms which are efficient for the Poissan equation on structured meshes will still apply well to the Euler and Navier-Stokes equations on unstructured meshes. The study of elliptic problems leads us to define the conditions where a Full Multigrid strategy has O(N) complexity. The aim of this paper is to build a comparison between the elliptic theory and practical CFD problems. First, as an introduction, we will recall some basic definitions and theorems applied to a model problem. The goal of this section is to point out the different properties that we need to produce an FMG algorithm with O(N) complexity. Then, we will show how we can apply this theory to the fluid dynamics equations such as Euler and Navier-Stokes equations. At last, we present some results which are 2nd-order accurate and some explanations about the behavior of the FMG process.
Looking for O(N) Navier-Stokes solutions on non-structured meshes
NASA Technical Reports Server (NTRS)
Morano, Eric; Dervieux, Alain
1993-01-01
Multigrid methods are good candidates for the resolution of the system arising in numerical fluid dynamics. However, the question is to know if those algorithms which are efficient for the Poisson equation on structured meshes will still apply well to the Euler and Navier-Stokes equations on unstructured meshes. The study of elliptic problems leads us to define the conditions where a full multigrid strategy has O(N) complexity. The aim of this paper is to build a comparison between the elliptic theory and practical CFD problems. First, as an introduction, we will recall some basic definitions and theorems applied to a model problem. The goal of this section is to point out the different properties that we need to produce an FMG algorithm with O(N) complexity. Then, we will show how we can apply this theory to the fluid dynamics equations such as Euler and Navier-Stokes equations. At last, we present some results which are 2nd-order accurate and some explanations about the behavior of the FMG process.
Hypersonic blunt body wake computations using DSMC and Navier-Stokes solvers
NASA Technical Reports Server (NTRS)
Moss, James N.; Mitcheltree, Robert A.; Dogra, Virendra K.; Wilmoth, Richard G.
1993-01-01
Numerical results obtained with direct simulation Monte Carlo (DSMC) and Navier-Stokes methods are presented for Mach 20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how does the wake structure change as a function of rarefaction, what are the afterbody levels of heating, and to what limits are continuum models realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the afterbody sting are emphasized in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.
Direct simulation Monte Carlo and Navier-Stokes simulations of blunt body wake flows
NASA Technical Reports Server (NTRS)
Moss, James N.; Mitcheltree, Robert A.; Dogra, Virendra K.; Wilmoth, Richard G.
1994-01-01
Numerical results obtained with direct simulation Monte Carlo and Navier-Stokes methods are presented for a Mach-20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how the wake structure changes as a function of rare faction, what the afterbody levels of heating are, and to what limits the continuum models are realistic as rarefunction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the afterbody sting are emphasized in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.
Direct simulation Monte Carlo and Navier-Stokes simulations of blunt body wake flows
NASA Technical Reports Server (NTRS)
Moss, James N.; Mitcheltree, Robert A.; Dogra, Virendra K.; Wilmoth, Richard G.
1994-01-01
Numerical results obtained with direct simulation Monte Carlo and Navier-Stokes methods are presented for a Mach-20 nitrogen flow about a 70-deg blunted cone. The flow conditions simuulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how the wake structure changes as a function of rarefaction, what the afterbody levels of heating are, and to what limits the continuum models are realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the after body sting are emphasizes in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.
Navier-Stokes turbine heat transfer predictions using two-equation turbulence
NASA Astrophysics Data System (ADS)
Ameri, Ali A.; Arnone, Andrea
1992-08-01
Navier-Stokes calculations were carried out in order to predict the heat transfer rates on turbine blades. The calculations were performed using TRAF2D which is a two-dimensional, explicit, finite volume mass-averaged Navier-Stokes solver. Turbulence was modeled using q-omega and k-epsilon two-equation models and the Baldwin-Lomax algebraic model. The model equations along with the flow equations were solved explicitly on a non-periodic C grid. Implicit residual smoothing (IRS) or a combination of multigrid technique and IRS was applied to enhance convergence rates. Calculations were performed to predict the Stanton number distributions on the first stage vane and blade row as well as the second stage vane row of the Rocketdyne Space Shuttle Main Engine (SSME) high pressure fuel turbine. The comparison with the experimental results, although generally favorable, serves to highlight the weaknesses of the turbulence models and the possible areas of improving these models for use in turbomachinery heat transfer calculations.
Algorithm and code development for unsteady three-dimensional Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Obayashi, Shigeru
1994-01-01
Aeroelastic tests require extensive cost and risk. An aeroelastic wind-tunnel experiment is an order of magnitude more expensive than a parallel experiment involving only aerodynamics. By complementing the wind-tunnel experiments with numerical simulations, the overall cost of the development of aircraft can be considerably reduced. In order to accurately compute aeroelastic phenomenon it is necessary to solve the unsteady Euler/Navier-Stokes equations simultaneously with the structural equations of motion. These equations accurately describe the flow phenomena for aeroelastic applications. At ARC a code, ENSAERO, is being developed for computing the unsteady aerodynamics and aeroelasticity of aircraft, and it solves the Euler/Navier-Stokes equations. The purpose of this cooperative agreement was to enhance ENSAERO in both algorithm and geometric capabilities. During the last five years, the algorithms of the code have been enhanced extensively by using high-resolution upwind algorithms and efficient implicit solvers. The zonal capability of the code has been extended from a one-to-one grid interface to a mismatching unsteady zonal interface. The geometric capability of the code has been extended from a single oscillating wing case to a full-span wing-body configuration with oscillating control surfaces. Each time a new capability was added, a proper validation case was simulated, and the capability of the code was demonstrated.
Navier-Stokes turbine heat transfer predictions using two-equation turbulence
NASA Technical Reports Server (NTRS)
Ameri, Ali A.; Arnone, Andrea
1992-01-01
Navier-Stokes calculations were carried out in order to predict the heat transfer rates on turbine blades. The calculations were performed using TRAF2D which is a two-dimensional, explicit, finite volume mass-averaged Navier-Stokes solver. Turbulence was modeled using q-omega and k-epsilon two-equation models and the Baldwin-Lomax algebraic model. The model equations along with the flow equations were solved explicitly on a non-periodic C grid. Implicit residual smoothing (IRS) or a combination of multigrid technique and IRS was applied to enhance convergence rates. Calculations were performed to predict the Stanton number distributions on the first stage vane and blade row as well as the second stage vane row of the Rocketdyne Space Shuttle Main Engine (SSME) high pressure fuel turbine. The comparison with the experimental results, although generally favorable, serves to highlight the weaknesses of the turbulence models and the possible areas of improving these models for use in turbomachinery heat transfer calculations.
Discontinuous Galerkin solution of the Navier-Stokes equations on deformable domains
Persson, P.-O.; Bonet, J.; Peraire, J.
2009-01-13
We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain, By writing the Navier-Stokes equations as a conservation law for the independent variables in the reference configuration, the complexity introduced by variable geometry is reduced to solving a transformed conservation law in a fixed reference configuration, The spatial discretization is carried out using the Discontinuous Galerkin method on unstructured meshes of triangles, while the time integration is performed using an explicit Runge-Kutta method, For general domain changes, the standard scheme fails to preserve exactly the free-stream solution which leads to some accuracy degradation, especially for low order approximations. This situation is remedied by adding an additional equation for the time evolution of the transformation Jacobian to the original conservation law and correcting for the accumulated metric integration errors. A number of results are shown to illustrate the flexibility of the approach to handle high order approximations on complex geometries.
Implementation and analysis of a Navier-Stokes algorithm on parallel computers
NASA Technical Reports Server (NTRS)
Fatoohi, Raad A.; Grosch, Chester E.
1988-01-01
The results of the implementation of a Navier-Stokes algorithm on three parallel/vector computers are presented. The object of this research is to determine how well, or poorly, a single numerical algorithm would map onto three different architectures. The algorithm is a compact difference scheme for the solution of the incompressible, two-dimensional, time-dependent Navier-Stokes equations. The computers were chosen so as to encompass a variety of architectures. They are the following: the MPP, an SIMD machine with 16K bit serial processors; Flex/32, an MIMD machine with 20 processors; and Cray/2. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. The basic comparison is among SIMD instruction parallelism on the MPP, MIMD process parallelism on the Flex/32, and vectorization of a serial code on the Cray/2. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Finally, conclusions are presented.
Energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Sanderse, B.
2013-01-01
Energy-conserving methods have recently gained popularity for the spatial discretization of the incompressible Navier-Stokes equations. In this paper implicit Runge-Kutta methods are investigated which keep this property when integrating in time. Firstly, a number of energy-conserving Runge-Kutta methods based on Gauss, Radau and Lobatto quadrature are constructed. These methods are suitable for convection-dominated problems (such as turbulent flows), because they do not introduce artificial diffusion and are stable for any time step. Secondly, to obtain robust time-integration methods that work also for stiff problems, the energy-conserving methods are extended to a new class of additive Runge-Kutta methods, which combine energy conservation with L-stability. In this class, the Radau IIA/B method has the best properties. Results for a number of test cases on two-stage methods indicate that for pure convection problems the additive Radau IIA/B method is competitive with the Gauss methods. However, for stiff problems, such as convection-dominated flows with thin boundary layers, both the higher order Gauss and Radau IIA/B method suffer from order reduction. Overall, the Gauss methods are the preferred method for energy-conserving time integration of the incompressible Navier-Stokes equations.
On the Navier-Stokes equations with rotating effect and prescribed outflow velocity
NASA Astrophysics Data System (ADS)
Hansel, Tobias
2011-09-01
We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in {mathbb R^d} subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the prescribed velocity vector is assumed to be parallel to the axis of rotation, in this paper we are interested in a general outflow velocity. In order to use L p -techniques we introduce a new coordinate system, in which we obtain a non-autonomous partial differential equation with an unbounded drift term. We prove that the linearized problem in {mathbb R^d} is solved by an evolution system on {L^p_{σ}(mathbb R^d)} for 1 < p < ∞. For this we use results about time-dependent Ornstein-Uhlenbeck operators. Finally, we prove, for p ≥ d and initial data {u_0in L^p_{σ}(mathbb R^d)}, the existence of a unique mild solution to the full Navier-Stokes system.
The Quantum-Kinetic Chemical Reaction Model for Navier-Stokes Codes
NASA Astrophysics Data System (ADS)
Gallis, Michael A.; Wagnild, Ross M.; Torczynski, John R.
2013-11-01
The Quantum-Kinetic chemical reaction model of Bird is formulated as a non-equilibrium chemical reaction model for Navier-Stokes codes. The model is based solely on thermophysical, molecular-level information and is capable of reproducing measured equilibrium reaction rates without using any experimentally measured reaction-rate information. The model recognizes the principal role of vibrational energy in overcoming the reaction energy threshold. The effect of rotational non-equilibrium is introduced as a perturbation to the effect of vibrational non-equilibrium. Since the model uses only molecular-level properties, it is inherently able to predict reaction rates for arbitrary non-equilibrium conditions. This ability is demonstrated in the context of both Navier-Stokes and DSMC codes. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Besov Space Regularity Conditions for Weak Solutions of the Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner
2014-06-01
Consider a bounded domain with smooth boundary, some initial value , and a weak solution u of the Navier-Stokes system in . Our aim is to develop regularity and uniqueness conditions for u which are based on the Besov space with ; here A denotes the Stokes operator. This space, introduced by Farwig et al. (Ann. Univ. Ferrara 55:89-110,
Navier-Stokes solutions with surface catalysis for Martian atmospheric entry
NASA Technical Reports Server (NTRS)
Chen, Y.-K.; Henline, W. D.; Stewart, D. A.; Candler, G. V.
1992-01-01
In this study numerical solutions have been obtained for two-dimensional axisymmetric hypersonic nonequilibrium CO2 flow over a high angle blunt cone with appropriate surface boundary conditions to account for energy and mass conservation at the body surface. The flowfield is described by the Navier-Stokes equations and multicomponent conservation laws which account for both translational and internal vibrational nonequilibrium effects. Complete forebody solutions have been obtained for the peak heating point of the Mars entry trajectory specified in the proposed NASA MESUR (Mars Environmental Survey) project. In these solutions, radiative equilibrium wall temperature and surface heating distributions are determined over the MESUR aeroshell forebody for entry velocity equal to 7 km/sec with varying degrees of surface catalysis. The effects of gas kinetics, surface catalysis, transport properties, and vibrational relaxation times on the surface heating are examined. The results identify some important issues in the prediction of surface heating for flows in thermochemical nonequilibrium and show that the Navier-Stokes code used herein is effective for thermal protection system design and materials selection.
Evaluation of Navier-Stokes and Euler solutions for leading-edge separation vortices
NASA Technical Reports Server (NTRS)
Fujii, K.; Gavali, S.; Holst, T. L.
1987-01-01
Extensive study on the numerical simulation of the vortical flow over a double delta wing is carried out using the thin layer Navier-Stokes and Euler equations. Two important flow characteristics, vortex interaction and vortex breakdown, are successfully simulated. Grid resolution is one of the most important factors associated with the vortex problem. Computations were performed on a series of grids with various levels of refinement, coarse, medium, and fine. Computations using either the coarse or medium grids fail to capture the proper physical phenomena. The computed result using a fine grid shows flow unsteadiness once the vortex breakdown takes place. The C sub L - alpha characteristics are well predicted up to the breakdown angle of attack for all the grid distributions. The Euler solutions show fairly good agreement with the experiment on the C sub L - alpha characteristics. However, other aspects of the solution at each angle of attack, such as the locus of the leading edge separation vortex, are not consistent with the experiment. Even for the fine grid Navier-Stokes computations, further grid resolution is required to obtain good quantitative agreement with the experiment.
Ducted-Fan Engine Acoustic Predictions Using a Navier-Stokes Code
NASA Technical Reports Server (NTRS)
Rumsey, C. L.; Biedron, R. T.; Farassat, F.; Spence, P. L.
1998-01-01
A Navier-Stokes computer code is used to predict one of the ducted-fan engine acoustic modes that results from rotor-wake/stator-blade interaction. A patched sliding-zone interface is employed to pass information between the moving rotor row and the stationary stator row. The code produces averaged aerodynamic results downstream of the rotor that agree well with a widely used average-passage code. The acoustic mode of interest is generated successfully by the code and is propagated well upstream of the rotor, temporal and spatial numerical resolution are fine enough such that attenuation of the signal is small. Two acoustic codes are used to find the far-field noise. Near-field propagation is computed by using Eversman's wave envelope code, which is based on a finite-element model. Propagation to the far field is accomplished by using the Kirchhoff formula for moving surfaces with the results of the wave envelope code as input data. Comparison of measured and computed far-field noise levels show fair agreement in the range of directivity angles where the peak radiation lobes from the inlet are observed. Although only a single acoustic mode is targeted in this study, the main conclusion is a proof-of-concept: Navier Stokes codes can be used both to generate and propagate rotor-stator acoustic modes forward through an engine, where the results can be coupled to other far-field noise prediction codes.
Fast non-symmetric iterations and efficient preconditioning for Navier-Stokes equations
Silvester, D.; Elman, H.
1994-12-31
Discretisation of the steady-state Navier-Stokes equations: (u.grad)u-{nu}{del}{sup 2}u + grad p = 0; div u = 0 [1]. in some flow domain {Omega} {contained_in} IR{sup d}, (d = 2 or 3), gives a system of non-linear algebraic equations for discretised variables u (the velocity), and p (the pressure). The authors assume that appropriate boundary conditions are imposed. The non-linear equation system can be linearised using a fixed-point (Picard) iteration to give a matrix system which must be solved at every iteration. Part of this matrix is block diagonal, and consists of d convection-diffusion operators, one for each component of velocity. Two difficulties arise when solving this matrix equation. Firstly, the block diagonal part is not symmetric, although under certain conditions the symmetric part is positive definite. Secondly, the overall system is indefinite. This makes the design of fast and efficient iterative solvers for discretised Navier-Stokes operators an extremely challenging task.
Computation of transonic separated wing flows using an Euler/Navier-Stokes zonal approach
NASA Technical Reports Server (NTRS)
Kaynak, Uenver; Holst, Terry L.; Cantwell, Brian J.
1986-01-01
A computer program called Transonic Navier Stokes (TNS) has been developed which solves the Euler/Navier-Stokes equations around wings using a zonal grid approach. In the present zonal scheme, the physical domain of interest is divided into several subdomains called zones and the governing equations are solved interactively. The advantages of the Zonal Grid approach are as follows: (1) the grid for any subdomain can be generated easily; (2) grids can be, in a sense, adapted to the solution; (3) different equation sets can be used in different zones; and, (4) this approach allows for a convenient data base organization scheme. Using this code, separated flows on a NACA 0012 section wing and on the NASA Ames WING C have been computed. First, the effects of turbulence and artificial dissipation models incorporated into the code are assessed by comparing the TNS results with other CFD codes and experiments. Then a series of flow cases is described where data are available. The computed results, including cases with shock-induced separation, are in good agreement with experimental data. Finally, some futuristic cases are presented to demonstrate the abilities of the code for massively separated cases which do not have experimental data.
Ducted-Fan Engine Acoustic Predictions using a Navier-Stokes Code
NASA Technical Reports Server (NTRS)
Rumsey, C. L.; Biedron, R. T.; Farassat, F.; Spence, P. L.
1998-01-01
A Navier-Stokes computer code is used to predict one of the ducted-fan engine acoustic modes that results from rotor-wake/stator-blade interaction. A patched sliding-zone interface is employed to pass information between the moving rotor row and the stationary stator row. The code produces averaged aerodynamic results downstream of the rotor that agree well with a widely used average-passage code. The acoustic mode of interest is generated successfully by the code and is propagated well upstream of the rotor; temporal and spatial numerical resolution are fine enough such that attenuation of the signal is small. Two acoustic codes are used to find the far-field noise. Near-field propagation is computed by using Eversman's wave envelope code, which is based on a finite-element model. Propagation to the far field is accomplished by using the Kirchhoff formula for moving surfaces with the results of the wave envelope code as input data. Comparison of measured and computed far-field noise levels show fair agreement in the range of directivity angles where the peak radiation lobes from the inlet are observed. Although only a single acoustic mode is targeted in this study, the main conclusion is a proof-of-concept: Navier-Stokes codes can be used both to generate and propagate rotor/stator acoustic modes forward through an engine, where the results can be coupled to other far-field noise prediction codes.
Partially implicit motion of a sharp interface in Navier-Stokes flow
NASA Astrophysics Data System (ADS)
Thomas Beale, J.
2012-07-01
We develop a numerical method for the coupled motion of Navier-Stokes flow with an elastic interface of zero thickness which exerts tension and bending forces on the fluid. The interface motion is made partially implicit by approximating a backward Euler step in the high wavenumbers as in the small scale decomposition method of Hou, Lowengrub and Shelley. This modified step is combined with the method of Beale and Layton [J.T. Beale, A.T. Layton, A velocity decomposition approach for moving interfaces in viscous fluids, J. Comput. Phys. 228 (2009) 3358-67]; the fluid velocity is found by computing the Stokes velocity and a more regular remainder. The resulting scheme is second order in space and first order in time; it can be made second order in time by extrapolation. The discontinuities in the pressure and velocity gradient are preserved. The partially implicit method allows much larger time steps than an explicit method with negligible added effort. The formulas in the Fourier transform for the implicit approximation in high wavenumbers are similar to those derived in Hou and Shi [T.Y. Hou, Z. Shi, An efficient semi-implicit immersed boundary method for the Navier-Stokes equations, J. Comput. Phys. 227 (2008) 9138-69] in a different context.
Theoretical study of the incompressible Navier-Stokes equations by the least-squares method
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Loh, Ching Y.; Povinelli, Louis A.
1994-01-01
Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.
Local feedback regularization of three-dimensional Navier-Stokes equations on bounded domains
NASA Astrophysics Data System (ADS)
Balogh, Andras
One of the outstanding open problems in applied mathematics is the question of well-posedness of the initial boundary value problem associated with the three-dimensional fluid flow. At the same time, due to important applications in control theory, numerical analysis and turbulence, various types of regularizations and controls are gaining new interest. The specific problem we consider here is inspired by recent advances in the control of nonlinear distributed parameter systems and its possible applications to hydrodynamics. The main objective is to investigate the extent to which the 3-dimensional Navier-Stokes system can be regularized using a particular, physically motivated, feedback control law. The feedback is introduced in the form of an additional nonlinear viscosity term. Since control over the whole domain is not feasible in general, i.e., it is not usually possible to measure the entire state of the system, we consider a feedback supported only on a subdomain. On the rest of the domain the classical Navier-Stokes equations govern the fluid flow. The additional viscosity term is physically meaningful in the sense that it is proportional to the energy dissipation functional on the subdomain. For the controlled system we prove the existence, uniqueness and stability of the strong solution for initial data and forcing term which are arbitrary on the subdomain of control and are sufficiently small (in appropriate function spaces) outside this subdomain.
On L3,∞-stability of the Navier-Stokes system in exterior domains
NASA Astrophysics Data System (ADS)
Koba, Hajime
2017-02-01
This paper studies the stability of a stationary solution of the Navier-Stokes system with a constant velocity at infinity in an exterior domain. More precisely, this paper considers the stability of the Navier-Stokes system governing the stationary solution which belongs to the weak L3-space L 3 , ∞. Under the condition that the initial datum belongs to a solenoidal L 3 , ∞-space, we prove that if both the L 3 , ∞-norm of the initial datum and the L 3 , ∞-norm of the stationary solution are sufficiently small then the system admits a unique global-in-time strong L 3 , ∞-solution satisfying both L 3 , ∞-asymptotic stability and L∞-asymptotic stability. Moreover, we investigate L 3 , r-asymptotic stability of the global-in-time solution. Using Lp-Lq type estimates for the Oseen semigroup and applying an equivalent norm on the Lorentz space are key ideas to establish both the existence of a unique global-in-time strong (or mild) solution of our system and the stability of our solution.
NASA Technical Reports Server (NTRS)
Kandil, Osama A.; Chuang, Andrew H.; Shifflette, James M.
1987-01-01
A unified central-difference finite-volume Euler and Navier-Stokes solver with four-stage Runge-Kutta time stepping is presented. The computer code developed for this purpose is capable of solving the standard set and nonstandard sets (zero-total-pressure loss) of Euler equations and the thin-layer and full Navier-Stokes equations. Applications are presented for conical supersonic flows with weak shocks using the standard and nonstandard sets of Euler equations, and the thin-layer and full Navier-Stokes equations for sharp and round-edged delta wings. Applications are also presented for three-dimensional transonic and subsonic flows using the standard set of Euler equations for sharp-edged delta wings. The computational results of the different sets of equations are compared with each other and with the experimental results and conclusions on the validity of these sets to these applications, are presented.
An, Hongli; Yuen, Manwai
2014-05-15
In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen [M. W. Yuen, “Analytical solutions to the Navier-Stokes equations,” J. Math. Phys. 49, 113102 (2008)], our solutions constitute a generalization of that obtained by Yuen. Interestingly, numerical simulations show that the analytical solutions can be used to explain the drifting phenomena of the propagation wave like Tsunamis in oceans.
NASA Technical Reports Server (NTRS)
Kapoor, Kamlesh; Anderson, Bernhard H.; Shaw, Robert J.
1994-01-01
A full Navier-Stokes analysis was performed to evaluate the performance of the subsonic diffuser of a NASA Lewis Research Center 70/30 mixed-compression bifurcated supersonic inlet for high speed civil transport application. The PARC3D code was used in the present study. The computations were also performed when approximately 2.5 percent of the engine mass flow was allowed to bypass through the engine bypass doors. The computational results were compared with the available experimental data which consisted of detailed Mach number and total pressure distribution along the entire length of the subsonic diffuser. The total pressure recovery, flow distortion, and crossflow velocity at the engine face were also calculated. The computed surface ramp and cowl pressure distributions were compared with experiments. Overall, the computational results compared well with experimental data. The present CFD analysis demonstrated that the bypass flow improves the total pressure recovery and lessens flow distortions at the engine face.
Grid-Adapted FUN3D Computations for the Second High Lift Prediction Workshop
NASA Technical Reports Server (NTRS)
Lee-Rausch, E. M.; Rumsey, C. L.; Park, M. A.
2014-01-01
Contributions of the unstructured Reynolds-averaged Navier-Stokes code FUN3D to the 2nd AIAA CFD High Lift Prediction Workshop are described, and detailed comparisons are made with experimental data. Using workshop-supplied grids, results for the clean wing configuration are compared with results from the structured code CFL3D Using the same turbulence model, both codes compare reasonably well in terms of total forces and moments, and the maximum lift is similarly over-predicted for both codes compared to experiment. By including more representative geometry features such as slat and flap brackets and slat pressure tube bundles, FUN3D captures the general effects of the Reynolds number variation, but under-predicts maximum lift on workshop-supplied grids in comparison with the experimental data, due to excessive separation. However, when output-based, off-body grid adaptation in FUN3D is employed, results improve considerably. In particular, when the geometry includes both brackets and the pressure tube bundles, grid adaptation results in a more accurate prediction of lift near stall in comparison with the wind-tunnel data. Furthermore, a rotation-corrected turbulence model shows improved pressure predictions on the outboard span when using adapted grids.
A high-order gas-kinetic Navier-Stokes flow solver
Li Qibing; Xu Kun; Fu Song
2010-09-20
The foundation for the development of modern compressible flow solver is based on the Riemann solution of the inviscid Euler equations. The high-order schemes are basically related to high-order spatial interpolation or reconstruction. In order to overcome the low-order wave interaction mechanism due to the Riemann solution, the temporal accuracy of the scheme can be improved through the Runge-Kutta method, where the dynamic deficiencies in the first-order Riemann solution is alleviated through the sub-step spatial reconstruction in the Runge-Kutta process. The close coupling between the spatial and temporal evolution in the original nonlinear governing equations seems weakened due to its spatial and temporal decoupling. Many recently developed high-order methods require a Navier-Stokes flux function under piece-wise discontinuous high-order initial reconstruction. However, the piece-wise discontinuous initial data and the hyperbolic-parabolic nature of the Navier-Stokes equations seem inconsistent mathematically, such as the divergence of the viscous and heat conducting terms due to initial discontinuity. In this paper, based on the Boltzmann equation, we are going to present a time-dependent flux function from a high-order discontinuous reconstruction. The theoretical basis for such an approach is due to the fact that the Boltzmann equation has no specific requirement on the smoothness of the initial data and the kinetic equation has the mechanism to construct a dissipative wave structure starting from an initially discontinuous flow condition on a time scale being larger than the particle collision time. The current high-order flux evaluation method is an extension of the second-order gas-kinetic BGK scheme for the Navier-Stokes equations (BGK-NS). The novelty for the easy extension from a second-order to a higher order is due to the simple particle transport and collision mechanism on the microscopic level. This paper will present a hierarchy to construct such
NASA Technical Reports Server (NTRS)
Kiris, Cetin C.; Kwak, Dochan; Rogers, Stuart E.
2002-01-01
This paper reviews recent progress made in incompressible Navier-Stokes simulation procedures and their application to problems of engineering interest. Discussions are focused on the methods designed for complex geometry applications in three dimensions, and thus are limited to primitive variable formulation. A summary of efforts in flow solver development is given followed by numerical studies of a few example problems of current interest. Both steady and unsteady solution algorithms and their salient features are discussed. Solvers discussed here are based on a structured-grid approach using either a finite -difference or a finite-volume frame work. As a grand-challenge application of these solvers, an unsteady turbopump flow simulation procedure has been developed which utilizes high performance computing platforms. In the paper, the progress toward the complete simulation capability of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of two parallel computing algorithms that have been implemented in the INS3D code. The relative motion of the grid systems for the rotorstator interaction was obtained using overact grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on SCSI Origin 3000 systems at NASA Ames Research Center. The same procedure has been extended to the development of NASA-DeBakey Ventricular Assist Device (VAD) that is based on an axial blood pump. Computational, and clinical analysis of this device are presented.
Slat Cove Unsteadiness Effect of 3D Flow Structures
NASA Technical Reports Server (NTRS)
Choudhari, Meelan M.; Khorrami, Mehdi R.
2006-01-01
Previous studies have indicated that 2D, time accurate computations based on a pseudo-laminar zonal model of the slat cove region (within the framework of the Reynolds-Averaged Navier-Stokes equations) are inadequate for predicting the full unsteady dynamics of the slat cove flow field. Even though such computations could capture the large-scale, unsteady vorticity structures in the slat cove region without requiring any external forcing, the simulated vortices were excessively strong and the recirculation zone was unduly energetic in comparison with the PIV measurements for a generic high-lift configuration. To resolve this discrepancy and to help enable physics based predictions of slat aeroacoustics, the present paper is focused on 3D simulations of the slat cove flow over a computational domain of limited spanwise extent. Maintaining the pseudo-laminar approach, current results indicate that accounting for the three-dimensionality of flow fluctuations leads to considerable improvement in the accuracy of the unsteady, nearfield solution. Analysis of simulation data points to the likely significance of turbulent fluctuations near the reattachment region toward the generation of broadband slat noise. The computed acoustic characteristics (in terms of the frequency spectrum and spatial distribution) within short distances from the slat resemble the previously reported, subscale measurements of slat noise.
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
NASA Technical Reports Server (NTRS)
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
On the control of the chaotic attractors of the 2-d Navier-Stokes equations.
Smaoui, Nejib; Zribi, Mohamed
2017-03-01
The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.
LDV measurement and Navier-Stokes computation of parallel jet mixing in a rectangular confinement
Kunz, R.F.; D`Amico, S.W.; Vassallo, P.F.; Zaccaria, M.A.; Aksoy, H.; So, R.M.C.
1995-06-01
Laser Doppler Velocimetry (LDV) measurements were taken in a rectangular confinement into which issues a row of parallel jets. Two-component measurements were taken with two optics orientations yielding three mean velocity components and four Reynolds stress components. As observed in isolated three dimensional wall bounded jets, the transverse diffusion of the jets is quite large. The data indicates that this rapid mixing process is due to strong secondary flows, transport of large inlet intensities and Reynolds stress anisotropy effects. Navier-Stokes analyses of this configuration underpredict the rate of transverse jet diffusion. Detailed numerical accuracy studies show that this is attributed to shortcomings in low-Reynolds number two-equation turbulence modelling. A low-Reynolds number full-Reynolds stress model is shown to provide improvement.
Euler/Navier-Stokes flow computations on flexible configurations for stability analysis
NASA Technical Reports Server (NTRS)
Guruswamy, G.; Tu, E.
1995-01-01
Longitudinal dynamic stability derivatives required for design of aircraft are computed by using the state-of-the-art numerical methods for wing-body configurations. The flow is modeled using the Euler/Navier-Stokes equations with turbulence models and solved using an efficient finite-difference scheme suitable for patched structured grids. Computations are made at a flow regime that is beyond the limits of the current linear methods mostly used for computing stability derivatives. Flow conditions include shockwaves and viscous dominated vortical flows. Effect of Mach number and angle-of-attack on stability derivatives are demonstrated for a typical wing-body configuration. For the same configuration the effects of wing flexibility on the magnitude and phase angles of stability derivatives are also demonstrated.
Numerical solution of the Navier-Stokes equations using orthogonal boundary-fitted coordinates
NASA Astrophysics Data System (ADS)
Bramley, J. S.; Sloan, D. M.
The Navier-Stokes equations for laminar viscous flow in a bifurcating channel are solved numerically, applying the boundary-fitted coordinate method of Ryskin and Leal (1983) to generate orthogonal grids with grid lines clustered in the boundary layers of the flow. The theoretical basis of the method is outlined, and results for Re = 50, 100, and 500 are presented in graphs and briefly characterized. It is shown that the present approach reduces the number of grid points required to calculate the separation and recirculation regions by half (as compared with the method of Bramley and Sloan, 1986), with significant savings in computation time. The need for an improved vorticity boundary condition to permit smaller grids at the solid boundaries is indicated.
An asymptotic-preserving method for a relaxation of the Navier-Stokes-Korteweg equations
NASA Astrophysics Data System (ADS)
Chertock, Alina; Degond, Pierre; Neusser, Jochen
2017-04-01
The Navier-Stokes-Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flows. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a relaxation of the NSK system, for which robust numerical methods can be designed. However, time steps for explicit numerical schemes depend on the relaxation parameter and therefore numerical simulations in the relaxation limit are very inefficient. To overcome this restriction, we propose an implicit-explicit asymptotic-preserving finite volume method. We prove that the new scheme provides a consistent discretization of the NSK system in the relaxation limit and demonstrate that it is capable of accurately and efficiently computing numerical solutions of problems with realistic density ratios and small interfacial widths.
On solving the compressible Navier-Stokes equations for unsteady flows at very low Mach numbers
NASA Technical Reports Server (NTRS)
Pletcher, R. H.; Chen, K.-H.
1993-01-01
The properties of a preconditioned, coupled, strongly implicit finite difference scheme for solving the compressible Navier-Stokes equations in primitive variables are investigated for two unsteady flows at low speeds, namely the impulsively started driven cavity and the startup of pipe flow. For the shear-driven cavity flow, the computational effort was observed to be nearly independent of Mach number, especially at the low end of the range considered. This Mach number independence was also observed for steady pipe flow calculations; however, rather different conclusions were drawn for the unsteady calculations. In the pressure-driven pipe startup problem, the compressibility of the fluid began to significantly influence the physics of the flow development at quite low Mach numbers. The present scheme was observed to produce the expected characteristics of completely incompressible flow when the Mach number was set at very low values. Good agreement with incompressible results available in the literature was observed.
Calculation of steady and unsteady airfoil flow fields via the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Shamroth, S. J.
1985-01-01
A compressible time-dependent procedure for the two-dimensional ensemble averaged Navier-Stokes equations has been applied to the isolated airfoil problem in steady and unsteady flows. The procedure solves the governing equations via the linearized block implicit technique. Turbulence is modeled either via a mixing length or turbulence energy approach. The equations are solved in general non-orthogonal form with no-slip boundary conditions applied at the airfoil surface. Results are presented for airfoils at constant incidence, an airfoil in ramp motion and an airfoil oscillating through a dynamic stall loop. In general, steady converged solutions are obtained within 70 time steps over the range of Mach numbers considered. Comparisons with measured data show good agreement between computation and measurement.
Three-dimensional Navier-Stokes simulations of turbine rotor-stator interaction
NASA Technical Reports Server (NTRS)
Rai, Man Mohan
1988-01-01
Fluid flows within turbomachinery tend to be extremely complex in nature. Understanding such flows is crucial to improving current designs of turbomachinery. The computational approach can be used to great advantage in understanding flows in turbomachinery. A finite difference, unsteady, thin layer, Navier-Stokes approach to calculating the flow within an axial turbine stage is presented. The relative motion between the stator and rotor airfoils is made possible with the use of patched grids that move relative to each other. The calculation includes endwall and tip leakage effects. An introduction to the rotor-stator problem and sample results in the form of time averaged surface pressures are presented. The numerical data are compared with experimental data and the agreement between the two is found to be good.
Numerical solutions of the Navier-Stokes equations for transonic afterbody flows
NASA Technical Reports Server (NTRS)
Swanson, R. C., Jr.
1980-01-01
The time dependent Navier-Stokes equations in mass averaged variables are solved for transonic flow over axisymmetric boattail plume simulator configurations. Numerical solution of these equations is accomplished with the unsplit explict finite difference algorithm of MacCormack. A grid subcycling procedure and computer code vectorization are used to improve computational efficiency. The two layer algebraic turbulence models of Cebeci-Smith and Baldwin-Lomax are employed for investigating turbulence closure. Two relaxation models based on these baseline models are also considered. Results in the form of surface pressure distribution for three different circular arc boattails at two free stream Mach numbers are compared with experimental data. The pressures in the recirculating flow region for all separated cases are poorly predicted with the baseline turbulence models. Significant improvements in the predictions are usually obtained by using the relaxation models.
Navier-Stokes computation of wing leading edge tangential blowing for a tilt rotor in hover
NASA Technical Reports Server (NTRS)
Fejtek, Ian; Roberts, Leonard
1992-01-01
The effect of a thin tangential jet located at the leading edge of the wing of a tilt rotor configuration in hover is computed using the thin-layer Navier-stokes equations. Computations showed that leading edge tangential blowing is effective in reducing the download caused by the impingement of the rotor download caused by the impingement of the rotor downwash on the wing. Results from the numerical model support previous experimental findings that download reduction is due mainly to a decrease in upper surface pressure and not an increase in pressure on the lower surface. The numerical solution clearly shows that because of the three-dimensionality of the flow field, the download could be reduced further by allowing a spanwise variation in blowing strength.
NASA Astrophysics Data System (ADS)
Buzzicotti, Michele; Bhatnagar, Akshay; Biferale, Luca; Lanotte, Alessandra S.; Sankar Ray, Samriddhi
2016-11-01
We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under Fourier-mode reduction. The Navier-Stokes equations are evolved on a restricted set of modes, obtained as a projection on a fractal or homogeneous Fourier set. We find a strong sensitivity (reduction) of the high-frequency variability of the Lagrangian velocity fluctuations on the degree of mode decimation, similarly to what is already reported for Eulerian statistics. This is quantified by a tendency towards a quasi-Gaussian statistics, i.e., to a reduction of intermittency, at all scales and frequencies. This can be attributed to a strong depletion of vortex filaments and of the vortex stretching mechanism. Nevertheless, we found that Eulerian and Lagrangian ensembles are still connected by a dimensional bridge-relation which is independent of the degree of Fourier-mode decimation.
Development of a three-dimensional Navier-Stokes code on CDC star-100 computer
NASA Technical Reports Server (NTRS)
Vatsa, V. N.; Goglia, G. L.
1978-01-01
A three-dimensional code in body-fitted coordinates was developed using MacCormack's algorithm. The code is structured to be compatible with any general configuration, provided that the metric coefficients for the transformation are available. The governing equations are developed in primitive variables in order to facilitate the incorporation of physical boundary conditions and turbulence-closure models. MacCormack's two-step, unsplit, time-marching algorithm is used to solve the unsteady Navier-Stokes equations until steady-state solution is achieved. Cases discussed include (1) flat plate in supersonic free stream; (2) supersonic flow along an axial corner; (3) subsonic flow in an axial corner at M infinity = 0.95; and (4) supersonic flow in an axial corner at M infinity 1.5.
On solving the compressible Navier-Stokes equations for unsteady flows at very low Mach numbers
NASA Technical Reports Server (NTRS)
Pletcher, R. H.; Chen, K.-H.
1993-01-01
The properties of a preconditioned, coupled, strongly implicit finite-difference scheme for solving the compressible Navier-Stokes equations in primitive variables are investigated for two unsteady flows at low speeds, namely the impulsively started driven cavity and the startup of pipe flow. For the shear-driven cavity flow, the computational effort was observed to be nearly independent of Mach number, especially at the low end of the range considered. This Mach number independence was also observed for steady pipe flow calculations; however, rather different conclusions were drawn for the unsteady calculations. In the pressure-driven pipe startup problem, the compressibility of the fluid began to significantly influence the physics of the flow development at quite low Mach numbers. The present scheme was observed to produce the expected characteristics of completely incompressible flow when the Mach number was set at very low values. Good agreement with incompressible results available in the literature was observed.
Prediction of airfoil stall using Navier-Stokes equations in streamline coordinates
NASA Technical Reports Server (NTRS)
Choi, D. H.; Sohn, C. H.; Oh, C. S.
1992-01-01
A Navier-Stokes procedure to calculate the flow about an airfoil at incidence was developed. The parabolized equations are solved in the streamline coordinates generated for an arbitrary airfoil shape using conformal mapping. A modified k-epsilon turbulence model is applied in the entire domain, but the eddy viscosity in the laminar region is suppressed artificially to simulate the region correctly. The procedure was applied to airfoils at various angles of attack, and the results are quite satisfactory for both laminar and turbulent flows. It is shown that the present choice of the coordinate system reduces the error due to numerical diffusion, and that the lift is accurately predicted for a wide range of incidence.
The Navier-Stokes equation and solution generating symmetries from holography
NASA Astrophysics Data System (ADS)
Berkeley, Joel; Berman, David S.
2013-04-01
The fluid-gravity correspondence provides us with explicit spacetime metrics that are holographically dual to (non-)relativistic nonlinear hydrodynamics. The vacuum Einstein equations, in the presence of a Killing vector, possess solution-generating symmetries known as spacetime Ehlers transformations. These form a subgroup of the larger generalized Ehlers group acting on spacetimes with arbitrary matter content. We apply this generalized Ehlers group, in the presence of Killing isometries, to vacuum metrics with hydrodynamic duals to develop a formalism for solution-generating transformations of incompressible Navier-Stokes fluids. Using this we provide examples of a linear energy scaling from RG flow under vanishing vorticity, and a set of {{{Z}}_2} symmetries for fixed viscosity.
Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas.
Kolvin, Itamar; Livne, Eli; Meerson, Baruch
2010-08-01
We show that, in dimension higher than one, heat diffusion and viscosity cannot arrest thermal collapse in a freely evolving dilute granular gas, even in the absence of gravity. Thermal collapse involves a finite-time blowup of the gas density. It was predicted earlier in ideal, Euler hydrodynamics of dilute granular gases in the absence of gravity, and in nonideal, Navier-Stokes granular hydrodynamics in the presence of gravity. We determine, analytically and numerically, the dynamic scaling laws that characterize the gas flow close to collapse. We also investigate bifurcations of a freely evolving dilute granular gas in circular and wedge-shaped containers. Our results imply that, in general, thermal collapse can only be arrested when the gas density becomes comparable with the close-packing density of grains. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.
Navier-Stokes predictions of pitch damping for axisymmetric shell using steady coning motion
NASA Technical Reports Server (NTRS)
Weinacht, Paul; Sturek, Walter B.; Schiff, Lewis B.
1991-01-01
Previous theoretical investigations have proposed that the side force and moment acting on a body of revolution in steady coning motion could be related to the pitch-damping force and moment. In the current research effort, this approach is applied to produce predictions of the pitch damping for axisymmetric shell. The flow fields about these projectiles undergoing steady coning motion are successfully computed using a parabolized Navier-Stokes computational approach which makes use of a rotating coordinate frame. The governing equations are modified to include the centrifugal and Coriolis force terms due to the rotating coordinate frame. From the computed flow field, the side moments due to coning motion, spinning motion, and combined spinning and coning motion are used to determine the pitch-damping coefficients. Computations are performed for two generic shell configurations, a secant-ogive-cylinder and a secant-ogive-cylinder-boattail.
Navier-Stokes solution on the CYBER-203 by a pseudospectral technique
NASA Technical Reports Server (NTRS)
Lambiotte, J. J.; Hussaini, M. Y.; Bokhari, S.; Orszag, S. A.
1983-01-01
A three-level, time-split, mixed spectral/finite difference method for the numerical solution of the three-dimensional, compressible Navier-Stokes equations has been developed and implemented on the Control Data Corporation (CDC) CYBER-203. This method uses a spectral representation for the flow variables in the streamwise and spanwise coordinates, and central differences in the normal direction. The five dependent variables are interleaved one horizontal plane at a time and the array of their values at the grid points of each horizontal plane is a typical vector in the computation. The code is organized so as to require, per time step, a single forward-backward pass through the entire data base. The one-and two-dimensional Fast Fourier Transforms are performed using software especially developed for the CYBER-203.
A split finite element algorithm for the compressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Baker, A. J.
1979-01-01
An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.
NASA Technical Reports Server (NTRS)
Kiris, Cetin; Kwak, Dochan
2001-01-01
Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two method are compared by obtaining unsteady solutions for the evolution of twin vortices behind a at plate. Calculated results are compared with experimental and other numerical results. For an un- steady ow which requires small physical time step, pressure projection method was found to be computationally efficient since it does not require any subiterations procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in our computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.
A compressible solution of the Navier-Stokes equations for turbulent flow about an airfoil
NASA Technical Reports Server (NTRS)
Shamroth, S. J.; Gibeling, H. J.
1979-01-01
A compressible time dependent solution of the Navier-Stokes equations including a transition turbulence model is obtained for the isolated airfoil flow field problem. The equations are solved by a consistently split linearized block implicit scheme. A nonorthogonal body-fitted coordinate system is used which has maximum resolution near the airfoil surface and in the region of the airfoil leading edge. The transition turbulence model is based upon the turbulence kinetic energy equation and predicts regions of laminar, transitional, and turbulent flow. Mean flow field and turbulence field results are presented for an NACA 0012 airfoil at zero and nonzero incidence angles of Reynolds number up to one million and low subsonic Mach numbers.
Boundary Layer for the Navier-Stokes-alpha Model of Fluid Turbulence
NASA Astrophysics Data System (ADS)
Cheskidov, A.
We study boundary-layer turbulence using the Navier-Stokes-alpha model obtaining an extension of the Prandtl equations for the averaged flow in a turbulent boundary layer. In the case of a zero pressure gradient flow along a flat plate, we derive a nonlinear fifth-order ordinary differential equation, which is an extension of the Blasius equation. We study it analytically and prove the existence of a two-parameter family of solutions satisfying physical boundary conditions. Matching these parameters with the skin-friction coefficient and the Reynolds number based on momentum thickness, we get an agreement of the solutions with experimental data in the laminar and transitional boundary layers, as well as in the turbulent boundary layer for moderately large Reynolds numbers.
Convergence acceleration for a three-dimensional Euler/Navier-Stokes zonal approach
NASA Technical Reports Server (NTRS)
Flores, J.
1985-01-01
A fast diagonal algorithm is coupled with a zonal approach to solve the three-dimensional Euler/Navier-Stokes equations. Transonic viscous solutions are obtained on a 150,000 point mesh for a NACA 0012 wing. The new computational approach yields a speedup by as much as a factor of 40 over the standard Beam-Warming algorithm/zonal method originally coded. A three-order-of-magnitude drop in the L2-norm of the residual requires approximately 500 iterations, which takes about 45 min of CPU time on a Cray-XMP. The numerically computed solutions are in good agreement with experimental results. Effects on convergence rate owing to increasing the zonal boundary overlap regions, different stretching distributions in the viscous regions, and different CFL values are also explored.
NASA Astrophysics Data System (ADS)
Serson, D.; Meneghini, J. R.; Sherwin, S. J.
2016-07-01
This paper presents methods of including coordinate transformations into the solution of the incompressible Navier-Stokes equations using the velocity-correction scheme, which is commonly used in the numerical solution of unsteady incompressible flows. This is important when the transformation leads to symmetries that allow the use of more efficient numerical techniques, like employing a Fourier expansion to discretize a homogeneous direction. Two different approaches are presented: in the first approach all the influence of the mapping is treated explicitly, while in the second the mapping terms related to convection are treated explicitly, with the pressure and viscous terms treated implicitly. Through numerical results, we demonstrate how these methods maintain the accuracy of the underlying high-order method, and further apply the discretisation strategy to problems where mixed Fourier-spectral/hp element discretisations can be applied, thereby extending the usefulness of this discretisation technique.
Dynamics and Control of the 2-d Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Smaoui, Nejib; Zribi, Mohamed
2013-11-01
The control problem of the dynamics of the two-dimensional (2-d) Navier-Stokes (N-S) equations with spatially periodic and temporally steady forcing is studied. First, we devise a dynamical system of several nonlinear differential equations by a truncation of the 2-d N-S equations. Then, we study the dynamics of the obtained Galerkin system by analyzing the system's attractors for different values of the Reynolds number, Re. By applying the symmetry of the equation on one of the system's attractors, a symmetric limit trajectory that is part of the dynamics is obtained. Next, a control strategy to drive the dynamics from one attractor to another attractor for a given Re is designed. Finally, numerical simulations are undertaken to validate the theoretical developments. This work was supported and funded by Kuwait University Research Grant No. SM02/13.
Dynamics and Control of a Reduced Order System of the 2-d Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Smaoui, Nejib; Zribi, Mohamed
2014-11-01
The dynamics and control problem of a reduced order system of the 2-d Navier-Stokes (N-S) equations is analyzed. First, a seventh order system of nonlinear ordinary differential equations (ODE) which approximates the dynamical behavior of the 2-d N-S equations is obtained by using the Fourier Galerkin method. We show that the dynamics of this ODE system transforms from periodic solutions to chaotic attractors through a sequence of bifurcations including a period doubling scenarios. Then three Lyapunov based controllers are designed to either control the system of ODEs to a desired fixed point or to synchronize two ODE systems obtained from the truncation of the 2-d N-S equations under different conditions. Numerical simulations are presented to show the effectiveness of the proposed controllers. This research was supported and funded by the Research Sector, Kuwait University under Grant No. SM02/14.
NASA Technical Reports Server (NTRS)
Bart, Timothy J.; Kutler, Paul (Technical Monitor)
1998-01-01
Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.
Comparisons of TVD schemes applied to the Navier-Stokes equations. [total variation diminishing
NASA Technical Reports Server (NTRS)
Buelow, Philip E.
1989-01-01
In this study, the following total variation diminishing (TVD) schemes for solving the Navier-Stokes equations have been tested: the Chakravarthy and Szema (1985) upwind biased TVD scheme, the Harten's upwind TVD scheme described by Yee et al. (1983), and the Yee's (1985) symmetric TVD scheme. The schemes have been compared using three test cases. The first case was the one-dimensional shock tube problem which tested the shock-capturing abilities of the schemes. Chakravarthy's and Harten's schemes gave similar results which were found to be more accurate than the results from Yee's scheme. The second case was a compressible boundary layer which tested the schemes's abilities to solve fiscous flows. In this case, the three schemes yielded almost identical results. Finally, the shock/boundary-layer interaction case studied experimentally by Hakkinen et al. (1959) was computed. Here, Chakravarthy's and Yee's schemes compared most favorably with the published data, with Yee's scheme giving slightly better results.
Navier-Stokes Computations on Full Wing-Body Configuration with Oscillating Control Surfaces
NASA Technical Reports Server (NTRS)
Obayashi, Shigeru; Chiu, Ing-Tsau; Guruswamy, Guru P.
1995-01-01
Unsteady Navier-Stokes simulations have been performed for vortical flows over an "arrow-wing" configuration of a supersonic transport in the transonic regime. Computed steady pressures and integrated force coefficients with and without control surface deflection at a moderate angle of attack are compared with experiment. For unsteady cases, oscillating trailing-edge control surfaces are modeled by using moving grids. Response characteristics between symmetric and antisymmetric oscillatory motions of the control surfaces on the left and right wings are studied. The antisymmetric case produces higher lift than the steady case with no deflection and the unsteady symmetric case produces higher lift than the antisymmetric case. The detailed analysis of the wake structure revealed a strong interaction between the primary vortex and the wake vortex sheet from the flap region when the flap is deflected up.
Navier-Stokes solutions for two-dimensional subsonic base flow
NASA Technical Reports Server (NTRS)
Rudy, D. H.
1984-01-01
Methods for determining the effects of mass injection from the trailing edge of a bluff body at low speeds and in transonic flow were numerically studied along with an unmodified blunt-based body to gain insight into the effects of vortex shedding on the base drag. The methodology used to obtain finite-difference solutions to the Navier-Stokes equations for subsonic compressible two-dimensional near-wake flows is presented. The effectiveness of an introduced outflow boundary condition which minimizes reflections back into the computational domain was demonstrated with the solution of a model vortex problem. Calculations of the near-wake flow past a circular cylinder were in excellent agreement with experimental data. Laminar-flow solutions for a blunt-based model with and without a base cavity and with mass injection into the wake agreed qualitatively with experimental observations. The drag reduction capability provided by such base modifications was demonstrated.
About the coupling of turbulence closure models with averaged Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Vandromme, D.; Ha Minh, H.
1986-01-01
The MacCormack implicit predictor-corrector model (1981) for numerical solution of the coupled Navier-Stokes equations for turbulent flows is extended to nonconservative multiequation turbulence models, as well as the inclusion of second-order Reynolds stress turbulence closure. A scalar effective pressure turbulent contribution to the pressure field is defined to approximate the effects of the Reynolds stress in strongly sheared flows. The Jacobian matrices of the transport equations are diagonalized to reduce the required computer memory and run time. Techniques are defined for including turbulence in the diagonalization. Application of the method is demonstrated with solutions generated for transonic nozzle flow and for the interaction between a supersonic flat plate boundary layer and a 12 deg compression-expansion ramp.
Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows
NASA Technical Reports Server (NTRS)
Warsi, Z. U. A.; Devarayalu, K.; Thompson, J. F.
1978-01-01
A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.
Convergence acceleration of rational Runge-Kutta scheme for Euler and Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Morinishi, Koji; Nobuyuki, Satofuka
Modifications introduced to improve the performance of the rational-Runge-Kutta Euler/Navier-Stokes solver of Morishini and Satofuka (1987 and 1988) are discussed, summarizing the results of recent investigations. The derivation of the governing equations and the basic numerical procedure are outlined, and the use of the residual-averaging technique and multigrid methods to accelerate convergence is explained. Results are presented in graphs for (1) two-dimensional inviscid flow on a NACA 0012 airfoil at Mach 0.8 and angle of attack alpha = 1.25 deg, (2) two-dimensional viscous flow on an RAE 2822 airfoil at Mach 0.73 and alpha = 2.80 deg, and (3) three-dimensional inviscid flow on the ONERA M6 wing at Mach 0.84 and alpha = 3.06 deg. The steady-state convergence of the method is shown to be comparable to that of diagonalized implicit approximate-factorization schemes.
Numerical solution of the Navier-Stokes equations by a multigrid method
NASA Astrophysics Data System (ADS)
Cambier, L.; Couaillier, V.; Veuillot, J. P.
This article describes the use of a multigrid method to compute compressible two-dimensional turbulent flows by solving the averaged Navier-Stokes equations, complemented by a turbulence model. The numerical method is described in detail. It is based on an explicit, centered scheme of the Lax-Wendroff type, the convergence of which is accelerated by a multigrid phase similar to the one proposed by Ni. The effect of the parameters introduced in the multigrid acceleration phase is studied in numerical simulations to increase their effectiveness. The applications covered relate to high-Reynolds flows around a wing profile and in a two-dimensional cascade. Comparisons with experimental data are given for these two types of application.