A GPU-accelerated flow solver for incompressible two-phase fluid flows
NASA Astrophysics Data System (ADS)
Codyer, Stephen; Raessi, Mehdi; Khanna, Gaurav
2011-11-01
We present a numerical solver for incompressible, immiscible, two-phase fluid flows that is accelerated by using Graphics Processing Units (GPUs). The Navier-Stokes equations are solved by the projection method, which involves solving a pressure Poisson problem at each time step. A second-order discretization of the Poisson problem leads to a sparse matrix with five and seven diagonals for two- and three-dimensional simulations, respectively. Running a serial linear algebra solver on a single CPU can take 50-99.9% of the total simulation time to solve the above system for pressure. To remove this bottleneck, we utilized the large parallelization capabilities of GPUs; we developed a linear algebra solver based on the conjugate gradient iterative method (CGIM) by using CUDA 4.0 libraries and compared its performance with CUSP, an open-source, GPU library for linear algebra. Compared to running the CGIM solver on a single CPU core, for a 2D case, our GPU solver yields speedups of up to 88x in solver time and 81x overall time on a single GPU card. In 3D cases, the speedups are up to 81x (solver) and 15x (overall). Speedup is faster at higher grid resolutions and our GPU solver outperforms CUSP. Current work examines the acceleration versus a parallel CGIM CPU solver.
Incompressible Flows Free Surfaces
Energy Science and Technology Software Center (ESTSC)
1992-02-01
NASA-VOF3D is a three-dimensional, transient, free surface, incompressible fluid dynamics program. It is specifically designed to calculate confined flows in a low gravity environment in which surface physics must be accurately treated. It allows multiple free surfaces with surface tension and wall adhesion and includes a partial cell treatment that allows curved boundaries and internal obstacles. Variable mesh spacing is permitted in all three coordinate directions. Boundary conditions available are rigid free-slip wall, rigid no-slipmore » wall, continuative, periodic, and specified pressure outflow boundary.« less
Unified approach for incompressible flows
NASA Technical Reports Server (NTRS)
Chang, Tyne-Hsien
1995-01-01
A unified approach for solving incompressible flows has been investigated in this study. The numerical CTVD (Centered Total Variation Diminishing) scheme used in this study was successfully developed by Sanders and Li for compressible flows, especially for the high speed. The CTVD scheme possesses better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that the CTVD scheme can equally well apply to solve incompressible flows. Because of the mathematical difference between the governing equations for incompressible and compressible flows, the scheme can not directly apply to the incompressible flows. However, if one can modify the continuity equation for incompressible flows by introducing pseudo-compressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of the algorithm to incompressible flows thus becomes feasible. In this study, the governing equations for incompressible flows comprise continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the physical and numerical boundary conditions are properly implemented by the characteristic boundary conditions. Accordingly, a CFD code has been developed for this research and is currently under testing. Flow past a circular cylinder was chosen for numerical experiments to determine the accuracy and efficiency of the code. The code has shown some promising results.
Unified approach for incompressible flows
NASA Technical Reports Server (NTRS)
Chang, Tyne-Hsien
1993-01-01
An unified approach for solving both compressible and incompressible flows was investigated in this study. The difference in CFD code development between incompressible and compressible flows is due to the mathematical characteristics. However, if one can modify the continuity equation for incompressible flows by introducing pseudocompressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of a compressible flow code to solve incompressible flows becomes feasible. Among numerical algorithms developed for compressible flows, the Centered Total Variation Diminishing (CTVD) schemes possess better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that CTVD schemes can equally well solve incompressible flows. In this study, the governing equations for incompressible flows include the continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the boundary conditions including physical and numerical boundary conditions must be properly specified to obtain accurate solution. The CFD code for this research is currently in progress. Flow past a circular cylinder will be used for numerical experiments to determine the accuracy and efficiency of the code before applying this code to more specific applications.
Computation of viscous incompressible flows
NASA Technical Reports Server (NTRS)
Kwak, Dochan
1989-01-01
Incompressible Navier-Stokes solution methods and their applications to three-dimensional flows are discussed. A brief review of existing methods is given followed by a detailed description of recent progress on development of three-dimensional generalized flow solvers. Emphasis is placed on primitive variable formulations which are most promising and flexible for general three-dimensional computations of viscous incompressible flows. Both steady- and unsteady-solution algorithms and their salient features are discussed. Finally, examples of real world applications of these flow solvers are given.
Reduced Order Modeling Incompressible Flows
NASA Technical Reports Server (NTRS)
Helenbrook, B. T.
2010-01-01
The details: a) Need stable numerical methods; b) Round off error can be considerable; c) Not convinced modes are correct for incompressible flow. Nonetheless, can derive compact and accurate reduced-order models. Can be used to generate actuator models or full flow-field models
Computational Challenges of Viscous Incompressible Flows
NASA Technical Reports Server (NTRS)
Kwak, Dochan; Kiris, Cetin; Kim, Chang Sung
2004-01-01
Over the past thirty years, numerical methods and simulation tools for incompressible flows have been advanced as a subset of the computational fluid dynamics (CFD) discipline. Although incompressible flows are encountered in many areas of engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to the rather stringent requirements for predicting aerodynamic performance characteristics of flight vehicles, while flow devices involving low-speed or incompressible flow could be reasonably well designed without resorting to accurate numerical simulations. As flow devices are required to be more sophisticated and highly efficient CFD took become increasingly important in fluid engineering for incompressible and low-speed flow. This paper reviews some of the successes made possible by advances in computational technologies during the same period, and discusses some of the current challenges faced in computing incompressible flows.
Successes and Challenges of Incompressible Flow Simulation
NASA Technical Reports Server (NTRS)
Kwak, Dochan; Kiris, Cetin
2003-01-01
During the past thirty years, numerical methods and simulation tools for incompressible flows have been advanced as a subset of CFD discipline. Even though incompressible flows are encountered in many areas of engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to rather stringent requirements for predicting aerodynamic performance characteristics of flight vehicles, while flow devices involving low speed or incompressible flow could be reasonably well designed without resorting to accurate numerical simulations. As flow devices are required to be more sophisticated and highly efficient, CFD tools become indispensable in fluid engineering for incompressible and low speed flow. This paper is intended to review some of the successes made possible by advances in computational technologies during the same period, and discuss some of the current challenges.
Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach
Cicogna, G.; Pegoraro, F.
2015-02-15
We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and, in particular, a special type of “weak” symmetries.
Potential flow and forces for incompressible viscous flow
NASA Astrophysics Data System (ADS)
Chang, Chien-Cheng
1992-06-01
Forces on a finite body in an incompressible viscous flow are shown to be contributed by a potential flow and fluid elements of nonzero vorticity in a revealing formulation. The present study indicates that the potential flow pay also a geometric role in determining the contribution of the fluid elements. Consideration is given to a solid body moving through a fluid, fluid accelerating past a solid body and a solid body which oscillates in a uniform stream. The effects of induced-mass and inertial forces appear naturally in the formulation and are separated from the contribution due to the surface vorticity and that due to the vorticity within the flow. Physical significance of the present analysis for vortical flows about a finite body is illustrated by examples, e.g., flow past a circular cylinder or an ellipsoid of revolution.
Computing Incompressible Flows With Free Surfaces
NASA Technical Reports Server (NTRS)
Kothe, D.
1994-01-01
RIPPLE computer program models transient, two-dimensional flows of incompressible fluids with surface tension on free surfaces of general shape. Surface tension modeled as volume force derived from continuum-surface-force model, giving RIPPLE both robustness and accuracy in modeling surface-tension effects at free surface. Also models wall adhesion effects. Written in FORTRAN 77.
Equilibria with incompressible flows from symmetry analysis
Kuiroukidis, Ap E-mail: gthroum@cc.uoi.gr; Throumoulopoulos, G. N. E-mail: gthroum@cc.uoi.gr
2015-08-15
We identify and study new nonlinear axisymmetric equilibria with incompressible flow of arbitrary direction satisfying a generalized Grad Shafranov equation by extending the symmetry analysis presented by Cicogna and Pegoraro [Phys. Plasmas 22, 022520 (2015)]. In particular, we construct a typical tokamak D-shaped equilibrium with peaked toroidal current density, monotonically varying safety factor, and sheared electric field.
Maximal mixing by incompressible fluid flows
NASA Astrophysics Data System (ADS)
Seis, Christian
2013-12-01
We consider a model for mixing binary viscous fluids under an incompressible flow. We prove the impossibility of perfect mixing in finite time for flows with finite viscous dissipation. As measures of mixedness we consider a Monge-Kantorovich-Rubinstein transportation distance and, more classically, the H-1 norm. We derive rigorous a priori lower bounds on these mixing norms which show that mixing cannot proceed faster than exponentially in time. The rate of the exponential decay is uniform in the initial data.
On the propagation of acceleration waves in incompressible hyperelastic solids
NASA Astrophysics Data System (ADS)
Gültop, T.
2003-07-01
The conditions for the propagation of acceleration waves (sound waves) in incompressible elastic media undergoing finite deformation are investigated. The incompressible hyperelastic solid media is considered in accordance with the general constitutive theory of materials subject to internal mechanical constraints. The equation of motion of acceleration waves is obtained using the theory of singular surfaces. A general comparison is made between the magnitudes of the propagation speeds of waves in incompressible and unconstrained solid media by the use of Mandel's inequalities. The magnitudes of the speeds of propagation of acceleration waves in the incompressible hyperelastic material classes of neo-Hookean, Mooney-Rivlin, and St. Venant-Kirchhoff solids are determined. Comparisons are made of the specific results concerning the magnitudes of wave propagation speeds making use of the corresponding material parameters.
Triangular spectral elements for incompressible fluid flow
NASA Technical Reports Server (NTRS)
Mavriplis, C.; Vanrosendale, John
1993-01-01
We discuss the use of triangular elements in the spectral element method for direct simulation of incompressible flow. Triangles provide much greater geometric flexibility than quadrilateral elements and are better conditioned and more accurate when small angles arise. We employ a family of tensor product algorithms for triangles, allowing triangular elements to be handled with comparable arithmetic complexity to quadrilateral elements. The triangular discretizations are applied and validated on the Poisson equation. These discretizations are then applied to the incompressible Navier-Stokes equations and a laminar channel flow solution is given. These new triangular spectral elements can be combined with standard quadrilateral elements, yielding a general and flexible high order method for complex geometries in two dimensions.
High-End Computing for Incompressible Flows
NASA Technical Reports Server (NTRS)
Kwak, Dochan; Kiris, Cetin
2001-01-01
The objective of the First MIT Conference on Computational Fluid and Solid Mechanics (June 12-14, 2001) is to bring together industry and academia (and government) to nurture the next generation in computational mechanics. The objective of the current talk, 'High-End Computing for Incompressible Flows', is to discuss some of the current issues in large scale computing for mission-oriented tasks.
Multigrid Approach to Incompressible Viscous Cavity Flows
NASA Technical Reports Server (NTRS)
Wood, William A.
1996-01-01
Two-dimensional incompressible viscous driven-cavity flows are computed for Reynolds numbers on the range 100-20,000 using a loosely coupled, implicit, second-order centrally-different scheme. Mesh sequencing and three-level V-cycle multigrid error smoothing are incorporated into the symmetric Gauss-Seidel time-integration algorithm. Parametrics on the numerical parameters are performed, achieving reductions in solution times by more than 60 percent with the full multigrid approach. Details of the circulation patterns are investigated in cavities of 2-to-1, 1-to-1, and 1-to-2 depth to width ratios.
Skin-Friction Measurements in Incompressible Flow
NASA Technical Reports Server (NTRS)
Smith, Donald W.; Walker, John H.
1959-01-01
Experiments have been conducted to measure the local surface-shear stress and the average skin-friction coefficient in Incompressible flow for a turbulent boundary layer on a smooth flat plate having zero pressure gradient. Data were obtained for a range of Reynolds numbers from 1 million to 45 million. The local surface-shear stress was measured by a floating-element skin-friction balance and also by a calibrated total head tube located on the surface of the test wall. The average skin-friction coefficient was obtained from boundary-layer velocity profiles.
Preconditioning and the limit to the incompressible flow equations
NASA Technical Reports Server (NTRS)
Turkel, E.; Fiterman, A.; Vanleer, B.
1993-01-01
The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations are considered. The relation between them for both the continuous problem and the finite difference approximation is also considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Hence, the steady state of the preconditioned system is the same as the steady state of the original system. For finite difference methods the preconditioning can change and improve the steady state solutions. An application to flow around an airfoil is presented.
Pseudo-compressibility methods for the incompressible flow equations
NASA Technical Reports Server (NTRS)
Turkel, Eli; Arnone, A.
1993-01-01
Preconditioning methods to accelerate convergence to a steady state for the incompressible fluid dynamics equations are considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Thus the steady state of the preconditioned system is the same as the steady state of the original system. The method is compared to other types of pseudo-compressibility. For finite difference methods preconditioning can change and improve the steady state solutions. An application to viscous flow around a cascade with a non-periodic mesh is presented.
Supercomputing Aspects for Simulating Incompressible Flow
NASA Technical Reports Server (NTRS)
Kwak, Dochan; Kris, Cetin C.
2000-01-01
The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. 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
Efficient solutions of two-dimensional incompressible steady viscous flows
NASA Technical Reports Server (NTRS)
Morrison, J. H.; Napolitano, M.
1986-01-01
A simple, efficient, and robust numerical technique is provided for solving two dimensional incompressible steady viscous flows at moderate to high Reynolds numbers. The proposed approach employs an incremental multigrid method and an extrapolation procedure based on minimum residual concepts to accelerate the convergence rate of a robust block-line-Gauss-Seidel solver for the vorticity-stream function Navier-Stokes equations. Results are presented for the driven cavity flow problem using uniform and nonuniform grids and for the flow past a backward facing step in a channel. For this second problem, mesh refinement and Richardson extrapolation are used to obtain useful benchmark solutions in the full range of Reynolds numbers at which steady laminar flow is established.
Incompressible flow in stepped labyrinth seals
NASA Technical Reports Server (NTRS)
Morrison, G. L.; Chi, D.
1985-01-01
A steped labyrinth seal was experimentally investigated to determine the effects of pressure ratio, shaft speed, number of teeth, and tooth/step location upon the leakage through the seal for incompressible flow. The dependence of the flow coefficient upon the number of throttles and pressure ratio are similar to those for straight-through labyrinth seals. It can be noted that the axial location of the throttle with respect to the step had a special effect upon the flow coefficient. That is, the dependency of the flow coefficient upon rotation rate and the number of throttles changes with axial location. It was found that the minimum flow coefficient was obtained when the seal teeth were centered on the step surface. Axial pressure distribution measurements show that when the teeth are centered on the step, the pressure drop from cavity to cavity is almost uniform. It is speculated that the obtaining of this uniform pressure gradient is the cause for the enhanced performance of the stepped labyrinth seal when operated in that configuration.
A vectorized solution for incompressible flow
NASA Technical Reports Server (NTRS)
Patel, N. R.; Thompson, J. F.
1984-01-01
An algorithm is developed to obtain solutions to the unsteady Reynolds-averaged incompressible Navier-Stokes equations in general curvilinear coordinates on a vector processor. The governing equations are in nonconservative form with the velocity and pressure as dependent variables. Two momentum equations and the Poisson equation for pressure form a set of three governing equations for three flow field unknowns: u, v, and p. The governing equations and boundary conditions are expressed in terms of boundary-conforming curvilinear coordinates, and a checkerboard SOR iteration is used to solve the governing equations. Several possible sequences for a checkerboard SOR iteration are investigated for finding the best overall convergence rate. The efficiency and capability of the present algorithm was assessed using the example of an 18 percent thick NACA 66(3)018 airfoil at zero degree angle of attack for chord Reynolds number range 1000-40,000.
AN IMMERSED BOUNDARY METHOD FOR COMPLEX INCOMPRESSIBLE FLOWS
An immersed boundary method for time-dependant, three- dimensional, incompressible flows is presented in this paper. The incompressible Navier-Stokes equations are discretized using a low-diffusion flux splitting method for the inviscid fluxes and a second order central differenc...
HELENA code with incompressible parallel plasma flow
NASA Astrophysics Data System (ADS)
Throumoulopoulos, George; Poulipoulis, George; Konz, Christian; EFDA ITM-TF Team
2015-11-01
It has been established that plasma rotation in connection to both zonal and equilibrium flow can play a role in the transitions to the advanced confinement regimes in tokamaks, as the L-H transition and the formation of Internal Transport Barriers. For incompressible rotation the equilibrium is governed by a generalized Grad-Shafranov (GGS) equation and a decoupled Bernoulli-type equation for the pressure. For parallel flow the GGS equation can be transformed to one identical in form with the usual Grad-Shafranov equation. In the present study on the basis of the latter equation we have extended HELENA, an equilibrium fixed boundary solver integrated in the ITM-TF modeling infrastructure. The extended code solves the GGS equation for a variety of the two free-surface-function terms involved for arbitrary Afvén Mach functions. We have constructed diverted-boundary equilibria pertinent to ITER and examined their characteristics, in particular as concerns the impact of rotation. It turns out that the rotation affects noticeably the pressure and toroidal current density with the impact on the current density being stronger in the parallel direction than in the toroidal one. Also, the linear stability of the equilibria constructed is examined This work has been carried out within the framework of the EUROfuion Consortium and has received funding from the National Programme for the Controlled Thermonuclear Fusion, Hellenic Republic.
Acoustic waves superimposed on incompressible flows
NASA Technical Reports Server (NTRS)
Hodge, Steve
1990-01-01
The use of incompressible approximations in deriving solutions to the Lighthill wave equation was investigated for problems where an analytical solution could be found. A particular model problem involves the determination of the sound field of a spherical oscillating bubble in an ideal fluid. It is found that use of incompressible boundary conditions leads to good approximations in the important region of high acoustic wave number.
Statistical theory of turbulent incompressible multimaterial flow
Kashiwa, B.
1987-10-01
Interpenetrating motion of incompressible materials is considered. ''Turbulence'' is defined as any deviation from the mean motion. Accordingly a nominally stationary fluid will exhibit turbulent fluctuations due to a single, slowly moving sphere. Mean conservation equations for interpenetrating materials in arbitrary proportions are derived using an ensemble averaging procedure, beginning with the exact equations of motion. The result is a set of conservation equations for the mean mass, momentum and fluctuational kinetic energy of each material. The equation system is at first unclosed due to integral terms involving unknown one-point and two-point probability distribution functions. In the mean momentum equation, the unclosed terms are clearly identified as representing two physical processes. One is transport of momentum by multimaterial Reynolds stresses, and the other is momentum exchange due to pressure fluctuations and viscous stress at material interfaces. Closure is approached by combining careful examination of multipoint statistical correlations with the traditional physical technique of kappa-epsilon modeling for single-material turbulence. This involves representing the multimaterial Reynolds stress for each material as a turbulent viscosity times the rate of strain based on the mean velocity of that material. The multimaterial turbulent viscosity is related to the fluctuational kinetic energy kappa, and the rate of fluctuational energy dissipation epsilon, for each material. Hence a set of kappa and epsilon equations must be solved, together with mean mass and momentum conservation equations, for each material. Both kappa and the turbulent viscosities enter into the momentum exchange force. The theory is applied to (a) calculation of the drag force on a sphere fixed in a uniform flow, (b) calculation of the settling rate in a suspension and (c) calculation of velocity profiles in the pneumatic transport of solid particles in a pipe.
General Equation Set Solver for Compressible and Incompressible Turbomachinery Flows
NASA Technical Reports Server (NTRS)
Sondak, Douglas L.; Dorney, Daniel J.
2002-01-01
Turbomachines for propulsion applications operate with many different working fluids and flow conditions. The flow may be incompressible, such as in the liquid hydrogen pump in a rocket engine, or supersonic, such as in the turbine which may drive the hydrogen pump. Separate codes have traditionally been used for incompressible and compressible flow solvers. The General Equation Set (GES) method can be used to solve both incompressible and compressible flows, and it is not restricted to perfect gases, as are many compressible-flow turbomachinery solvers. An unsteady GES turbomachinery flow solver has been developed and applied to both air and water flows through turbines. It has been shown to be an excellent alternative to maintaining two separate codes.
A monolithic mass tracking formulation for bubbles in incompressible flow
Aanjaneya, Mridul Patkar, Saket Fedkiw, Ronald
2013-08-15
We devise a novel method for treating bubbles in incompressible flow that relies on the conservative advection of bubble mass and an associated equation of state in order to determine pressure boundary conditions inside each bubble. We show that executing this algorithm in a traditional manner leads to stability issues similar to those seen for partitioned methods for solid–fluid coupling. Therefore, we reformulate the problem monolithically. This is accomplished by first proposing a new fully monolithic approach to coupling incompressible flow to fully nonlinear compressible flow including the effects of shocks and rarefactions, and then subsequently making a number of simplifying assumptions on the air flow removing not only the nonlinearities but also the spatial variations of both the density and the pressure. The resulting algorithm is quite robust, has been shown to converge to known solutions for test problems, and has been shown to be quite effective on more realistic problems including those with multiple bubbles, merging and pinching, etc. Notably, this approach departs from a standard two-phase incompressible flow model where the air flow preserves its volume despite potentially large forces and pressure differentials in the surrounding incompressible fluid that should change its volume. Our bubbles readily change volume according to an isothermal equation of state.
Minimal surfaces, incompressible flows and the geometric phase
NASA Astrophysics Data System (ADS)
Martinez, J. C.
1995-02-01
We show that the Berry phase may be associated with an incompressible flow issuing through a minimal surface. An example based on the linear Jahn-Teller effect is given and found to be related to a Clifford torus rather than the usual magnetic monopole in S 3.
Incompressible and anelastic flow simulations on numerically generated grids
NASA Technical Reports Server (NTRS)
Sharman, R. D.; Keller, T. L.; Wurtele, M. G.
1988-01-01
In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property of orthogonality has been preserved. Flow equations in general curvilinear coordinates maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible models, using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.
Stability of axisymmetric swirl flows of viscous incompressible fluid
NASA Astrophysics Data System (ADS)
Aktershev, S. P.; Kuibin, P. A.
2013-09-01
A new method of solution to the problem of stability of the swirl flow of viscous incompressible fluid is developed. The method based on expansion of the required function into power series of radial coordinate allows an avoidance of difficulties related to numerical integration of the system of differential equations with a singular point. Stability of the Poiseuille flow in a rotating pipe is considered as an example.
Conservative properties of finite difference schemes for incompressible flow
NASA Technical Reports Server (NTRS)
Morinishi, Youhei
1995-01-01
The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.
Local mesh refinement for incompressible fluid flow with free surfaces
Terasaka, H.; Kajiwara, H.; Ogura, K.
1995-09-01
A new local mesh refinement (LMR) technique has been developed and applied to incompressible fluid flows with free surface boundaries. The LMR method embeds patches of fine grid in arbitrary regions of interest. Hence, more accurate solutions can be obtained with a lower number of computational cells. This method is very suitable for the simulation of free surface movements because free surface flow problems generally require a finer computational grid to obtain adequate results. By using this technique, one can place finer grids only near the surfaces, and therefore greatly reduce the total number of cells and computational costs. This paper introduces LMR3D, a three-dimensional incompressible flow analysis code. Numerical examples calculated with the code demonstrate well the advantages of the LMR method.
Incompressible Turbulent Wing-Body Junction Flow
NASA Technical Reports Server (NTRS)
Krishnamurthy, R.; Cagle, Corey D.; Chandra, S.
1998-01-01
The overall objective of this study is to contribute to the optimized design of fan bypass systems in advanced turbofan engines. Increasing the engine bypass ratios have provided a major boost in engine performance improvement over the last fifty years. An engine with high bypass ratio (11-16:1) such as the Advanced Ducted Propulsion (ADP) is being developed and is expected to provide an additional 25% improvement in overall efficiency over the early turbofans. Such significant improvements in overall efficiency would reduce the cost per seat mile, which is a major government and Industry challenge for the 21th century. The research is part of the Advanced Subsonic Technology (AST) program that involves a NASA, U.S. Industry and FAA partnership with the goal of a safe and highly productive global air transportation system. The immediate objective of the study is to perform numerical simulation of duct-strut interactions to elucidate the loss mechanisms associated with this configuration that is typical of advanced turbofan engines such as ADP. However, at present experimental data for a duct-strut configuration are not available. Thus, as a first step a wing-body junction flow would be studied and is the specific objective of the present study. At the outset it is to be recognized that while duct-strut interaction flow is similar to that of wing-body junction flows, there are some differences owing to the presence of a wall at both ends of the strut. Likewise, some differences are due to the sheared inflow (as opposed to a uniform inflow) velocity profile. It is however expected that some features of a wing-body junction flow would persist. Next, some of the salient aspects of the complex flow near a wing-body junction, as revealed by various studies reported in the literature will be reviewed. One of the principle characteristics of the juncture flow, is the presence of the mean flow components in a plane perpendicular to the direction of the oncoming free
Incompressible Turbulent Wing-Body Junction Flow
NASA Technical Reports Server (NTRS)
Krishnamurthy, R.; Cagle, Corey D.; Chandra, S.
1998-01-01
The overall objective of this study is to contribute to the optimized design of fan bypass systems in advanced turbofan engines. Increasing the engine bypass ratios have provided a major boost in engine performance improvement over the last fifty years. An engine with high bypass ratio (11-16:1) such as the Advanced Ducted Propulsion (ADP) is being developed and is expected to provide an additional 25% improvement in overall efficiency over the early turbofans. Such significant improvements in overall efficiency would reduce the cost per seat mile, which is a major government and Industry challenge for the 21th century. The research is part of the Advanced Subsonic Technology (AST) program that involves a NASA, U.S. Industry and FAA partnership with the goal of a safe and highly productive global air transportation system. The immediate objective of the study is to perform numerical simulation of duct-strut interactions to elucidate the loss mechanisms associated with this configuration that is typical of advanced turbofan engines such as ADP. However, at present experimental data for a duct-strut configuration are not available. Thus, as a first step a wing-body junction flow would be studied and is the specific objective of the present study. At the outset it is to be recognized that while duct-strut interaction flow is similar to that of wing-body junction flows, there are some differences owing to the presence of a wall at both ends of the strut. Likewise, some differences are due to the sheared inflow (as opposed to a uniform inflow) velocity profile. It is however expected that some features of a wing-body junction flow would persist. Next, some of the salient aspects of the complex flow near a wing-body junction, as revealed by various studies reported in the literature will be reviewed. One of the principle characteristics of the juncture flow, is the presence of the mean flow components in a plane perpendicular to the direction of the oncoming free
Consistent lattice Boltzmann methods for incompressible axisymmetric flows.
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei
2016-08-01
In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified. PMID:27627407
Consistent lattice Boltzmann methods for incompressible axisymmetric flows
NASA Astrophysics Data System (ADS)
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei
2016-08-01
In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.
Mathematical aspects of finite element methods for incompressible viscous flows
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.
1986-01-01
Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
Optimized profiles for incompressible flow metering nozzles
NASA Astrophysics Data System (ADS)
Lakshminarayanan, R.; Haji-Sheikh, A.; Lou, D. Y. S.; Spindler, M.
1988-04-01
The Euler-Lagrange equation was used to minimize shear stress in designing a flow-metering nozzle. The flow field in the nozzle was computed by solving the momentum equation in integral form. The profile of the nozzle was obtained by minimizing the shear losses in the converging section of the nozzle. Following computation of the profile, a metering nozzle was designed, constructed, and subsequently tested to evaluate the validity of the analysis. The nozzle was designed for a pipe diameter of 15.24 cm (6 in.) and a throat diameter of 9.266 cm (3.648 in.). The test results indicated a marked increase in the value of the discharge coefficient when it is compared with that for the ASME standard nozzle. The computed pressure distribution is in good agreement with the experimental data.
RIPPLE - A new model for incompressible flows with free surfaces
NASA Technical Reports Server (NTRS)
Kothe, D. B.; Mjolsness, R. C.
1991-01-01
A new free surface flow model, RIPPLE, is summarized. RIPPLE obtains finite difference solutions for incompressible flow problems having strong surface tension forces at free surfaces of arbitrarily complex topology. The key innovation is the continuum surface force model which represents surface tension as a (strongly) localized volume force. Other features include a higher-order momentum advection model, a volume-of-fluid free surface treatment, and an efficient two-step projection solution method. RIPPLE's unique capabilities are illustrated with two example problems: low-gravity jet-induced tank flow, and the collision and coalescence of two cylindrical rods.
Incompressible viscous flow simulations of the NFAC wind tunnel
NASA Technical Reports Server (NTRS)
Champney, Joelle Milene
1986-01-01
The capabilities of an existing 3-D incompressible Navier-Stokes flow solver, INS3D, are extended and improved to solve turbulent flows through the incorporation of zero- and two-equation turbulence models. The two-equation model equations are solved in their high Reynolds number form and utilize wall functions in the treatment of solid wall boundary conditions. The implicit approximate factorization scheme is modified to improve the stability of the two-equation solver. Applications to the 3-D viscous flow inside the 80 by 120 feet open return wind tunnel of the National Full Scale Aerodynamics Complex (NFAC) are discussed and described.
Numerical Simulation of Incompressible Flows with Moving Interfaces
NASA Astrophysics Data System (ADS)
Medale, Marc; Jaeger, Marc
1997-03-01
A numerical model has been developed for the 2D simulation of free surface flows or, more generally speaking, moving interface ones. The bulk fluids on both sides of the interface are taken into account in simulating the incompressible laminar flow state. In the case of heat transfer the whole system, i.e. walls as well as possible obstacles, is considered. This model is based on finite element analysis with an Eulerian approach and an unstructured fixed mesh. A special technique to localize the interface allows its temporal evolution through this mesh. Several numerical examples are presented to demonstrate the capabilities of the model.
STREMR: Numerical model for depth-averaged incompressible flow
NASA Astrophysics Data System (ADS)
Roberts, Bernard
1993-09-01
The STREMR computer code is a two-dimensional model for depth-averaged incompressible flow. It accommodates irregular boundaries and nonuniform bathymetry, and it includes empirical corrections for turbulence and secondary flow. Although STREMR uses a rigid-lid surface approximation, the resulting pressure is equivalent to the displacement of a free surface. Thus, the code can be used to model free-surface flow wherever the local Froude number is 0.5 or less. STREMR uses a finite-volume scheme to discretize and solve the governing equations for primary flow, secondary flow, and turbulence energy and dissipation rate. The turbulence equations are taken from the standard k-Epsilon turbulence model, and the equation for secondary flow is developed herein. Appendices to this report summarize the principal equations, as well as the procedures used for their discrete solution.
Viscous Incompressible Flow Computations for 3-D Steady and Unsteady Flows
NASA Technical Reports Server (NTRS)
Kwak, Dochan
2001-01-01
This viewgraph presentation gives an overview of viscous incompressible flow computations for three-dimensional steady and unsteady flows. Details are given on the use of computational fluid dynamics (CFD) as an engineering tool, solution methods for incompressible Navier-Stokes equations, numerical and physical characteristics of the primitive variable approach, and the role of CFD in the past and in current engineering and research applications.
Incompressible Navier-Stokes computations of rotating flows
NASA Astrophysics Data System (ADS)
Kiris, Cetin; Chang, Leon; Kwak, Dochan; Rogers, Stuart
1993-01-01
Flow through pump components, such as an inducer and an impeller, is efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. The resulting computer code is applied to the flow analysis inside a generic rocket engine pump inducer, a fuel pump impeller, and SSME high-pressure fuel turbopump impeller. Numerical results of inducer flow are compared with experimental measurements. Flow analyses at 80-, 100-, and 120-percent of design conditions are presented.
High order parallel numerical schemes for solving incompressible flows
NASA Technical Reports Server (NTRS)
Lin, Avi; Milner, Edward J.; Liou, May-Fun; Belch, Richard A.
1992-01-01
The use of parallel computers for numerically solving flow fields has gained much importance in recent years. This paper introduces a new high order numerical scheme for computational fluid dynamics (CFD) specifically designed for parallel computational environments. A distributed MIMD system gives the flexibility of treating different elements of the governing equations with totally different numerical schemes in different regions of the flow field. The parallel decomposition of the governing operator to be solved is the primary parallel split. The primary parallel split was studied using a hypercube like architecture having clusters of shared memory processors at each node. The approach is demonstrated using examples of simple steady state incompressible flows. Future studies should investigate the secondary split because, depending on the numerical scheme that each of the processors applies and the nature of the flow in the specific subdomain, it may be possible for a processor to seek better, or higher order, schemes for its particular subcase.
Pressure boundary conditions for incompressible flow using unstructured meshes
Mathur, S.R.; Murthy, J.Y.
1997-10-01
A large variety of industrial problems require the specification of pressure boundary conditions. In many industrial pipe flows, for example, the mass flow rate is not known a priori; the flow is driven by a specified pressure difference between inlet and outlet. This article presents a numerical method for computing incompressible flows with given pressure boundary conditions. Unstructured meshes composed of arbitrary polyhedra are considered in a cell-centered, co-located pressure-velocity formulation. The SIMPLE algorithm of Patankar and Spalding is extended to develop correction equations for boundary static pressure and boundary mass flux through an added-dissipation scheme. The procedure is validated against published benchmarks and shown to perform satisfactorily.
NASA Technical Reports Server (NTRS)
Krolik, J. H.
1977-01-01
The paper examines the behavior of linear perturbations in an incompressible fluid undergoing acceleration by radiation pressure, with reference to processes occurring in quasars, supernovae, and planetary nebulae. It is shown that, contrary to prior expectation, fluids accelerated by radiation pressure, are not always unstable to Rayleigh-Taylor modes. Some are, in fact, unstable, but the nature of the instability is qualitatively different.
A multilevel approximate projections for incompressible flow calculations
Howell, L.H.
1994-12-31
An adaptive-mesh projection algorithm for unsteady, variable-density, incompressible flow at high Reynolds number has been developed in the Applied Mathematics Group at LLNL. A grid-based refinement scheme combines the theoretical efficiencies of adaptive methods with the computational advantages of uniform grids, while a second-order Godunov method provides a robust and accurate treatment of advection in the presence of discontinuities without excessive dissipation. This paper focuses on the work of the present author concerning the approximate projection itself, which involves the numerical inversion of the operator {del} {center_dot} (1/{rho}){del} on various subsets of the adaptive grid hierarchy.
New discretization and solution techniques for incompressible viscous flow problems
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.
1983-01-01
Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.
A boundary element method for steady incompressible thermoviscous flow
NASA Technical Reports Server (NTRS)
Dargush, G. F.; Banerjee, P. K.
1991-01-01
A boundary element formulation is presented for moderate Reynolds number, steady, incompressible, thermoviscous flows. The governing integral equations are written exclusively in terms of velocities and temperatures, thus eliminating the need for the computation of any gradients. Furthermore, with the introduction of reference velocities and temperatures, volume modeling can often be confined to only a small portion of the problem domain, typically near obstacles or walls. The numerical implementation includes higher order elements, adaptive integration and multiregion capability. Both the integral formulation and implementation are discussed in detail. Several examples illustrate the high level of accuracy that is obtainable with the current method.
Nested Cartesian grid method in incompressible viscous fluid flow
NASA Astrophysics Data System (ADS)
Peng, Yih-Ferng; Mittal, Rajat; Sau, Amalendu; Hwang, Robert R.
2010-09-01
In this work, the local grid refinement procedure is focused by using a nested Cartesian grid formulation. The method is developed for simulating unsteady viscous incompressible flows with complex immersed boundaries. A finite-volume formulation based on globally second-order accurate central-difference schemes is adopted here in conjunction with a two-step fractional-step procedure. The key aspects that needed to be considered in developing such a nested grid solver are proper imposition of interface conditions on the nested-block boundaries, and accurate discretization of the governing equations in cells that are with block-interface as a control-surface. The interpolation procedure adopted in the study allows systematic development of a discretization scheme that preserves global second-order spatial accuracy of the underlying solver, and as a result high efficiency/accuracy nested grid discretization method is developed. Herein the proposed nested grid method has been widely tested through effective simulation of four different classes of unsteady incompressible viscous flows, thereby demonstrating its performance in the solution of various complex flow-structure interactions. The numerical examples include a lid-driven cavity flow and Pearson vortex problems, flow past a circular cylinder symmetrically installed in a channel, flow past an elliptic cylinder at an angle of attack, and flow past two tandem circular cylinders of unequal diameters. For the numerical simulations of flows past bluff bodies an immersed boundary (IB) method has been implemented in which the solid object is represented by a distributed body force in the Navier-Stokes equations. The main advantages of the implemented immersed boundary method are that the simulations could be performed on a regular Cartesian grid and applied to multiple nested-block (Cartesian) structured grids without any difficulty. Through the numerical experiments the strength of the solver in effectively
Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Rausch, Russ D.; Bonhaus, Daryl L.
1997-01-01
An implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described. The foundation of the code is a backward Euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned Generalized Minimal Residual (GMRES) technique. For the GMRES calculations, several techniques are investigated for forming the matrix-vector product. Convergence acceleration is achieved through a multigrid scheme that uses non-nested coarse grids that are generated using a technique described in the present paper. Convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four-element airfoil. Viscous results, which are compared with experimental data, include the turbulent flow over a NACA 4412 airfoil, a three-element airfoil for which Mach number effects are investigated, and three-dimensional flow over a wing with a partial-span flap.
Nested Grid Iteration for Incompressible Viscous Flow and Transport
NASA Astrophysics Data System (ADS)
Kirk, B.; Lipnikov, K.; Carey, G. F.
2003-07-01
We investigate the use of one-way cascadic multigrid strategies (CMG) in the solution of incompressible viscous flow using the finite element method. First we describe the basic CMG approach for representative elliptic boundary value problems and summarize the theoretical error estimates from approximation theory, desired smoother properties, and arithmetic complexity of the method. The extension of these error and complexity estimates to adaptive grids is also given. Then we present the mathematical formulation and the finite element approximation scheme for the class of fluid-thermal problems of interest. In supporting numerical experiments, we examine performance of the algorithm on both serial and distributed parallel systems. We carry out comparison studies with a standard BCG solution strategy on the fine level grid and study diagonal treatments for the zero pressure block.
Lattice Boltzmann modeling of three-phase incompressible flows.
Liang, H; Shi, B C; Chai, Z H
2016-01-01
In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems. PMID:26871191
Incompressible Navier-Stokes calculations in pump flows
NASA Astrophysics Data System (ADS)
Kiris, Cetin; Chang, Leon; Kwak, Dochan
1993-07-01
Flow through pump components, such as the SSME-HPFTP Impeller and an advanced rocket pump impeller, is efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved in steadily rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. The resulting computer code is applied to the flow analysis inside an 11-inch SSME High Pressure Fuel Turbopump impeller, and an advanced rocket pump impeller. Numerical results of SSME-HPFTP impeller flow are compared with experimental measurements. In the advanced pump impeller, the effects of exit and shroud cavities are investigated. Flow analyses at design conditions will be presented.
Incompressible Navier-Stokes Calculations in Pump Flows
NASA Technical Reports Server (NTRS)
Kiris, Cetin; Chang, Leon; Kwak, Dochan
1993-01-01
Flow through pump components, such as the SSME-HPFTP Impeller and an advanced rocket pump impeller, is efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved in steadily rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. The resulting computer code is applied to the flow analysis inside an 11-inch SSME High Pressure Fuel Turbopump impeller, and an advanced rocket pump impeller. Numerical results of SSME-HPFTP impeller flow are compared with experimental measurements. In the advanced pump impeller, the effects of exit and shroud cavities are investigated. Flow analyses at design conditions will be presented.
Lattice Boltzmann modeling of three-phase incompressible flows
NASA Astrophysics Data System (ADS)
Liang, H.; Shi, B. C.; Chai, Z. H.
2016-01-01
In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.
A multilevel adaptive projection method for unsteady incompressible flow
NASA Technical Reports Server (NTRS)
Howell, Louis H.
1993-01-01
There are two main requirements for practical simulation of unsteady flow at high Reynolds number: the algorithm must accurately propagate discontinuous flow fields without excessive artificial viscosity, and it must have some adaptive capability to concentrate computational effort where it is most needed. We satisfy the first of these requirements with a second-order Godunov method similar to those used for high-speed flows with shocks, and the second with a grid-based refinement scheme which avoids some of the drawbacks associated with unstructured meshes. These two features of our algorithm place certain constraints on the projection method used to enforce incompressibility. Velocities are cell-based, leading to a Laplacian stencil for the projection which decouples adjacent grid points. We discuss features of the multigrid and multilevel iteration schemes required for solution of the resulting decoupled problem. Variable-density flows require use of a modified projection operator--we have found a multigrid method for this modified projection that successfully handles density jumps of thousands to one. Numerical results are shown for the 2D adaptive and 3D variable-density algorithms.
Three-dimensional incompressible flow calculations with alternative discretization schemes
NASA Astrophysics Data System (ADS)
Tamamidis, Panos; Assanis, Dennis N.
1993-08-01
A finite-volume calculation procedure for steady, incompressible, elliptic flows in complex geometries is presented. The methodology uses generalized body-fitted coordinates to model the shape of the boundary accurately. All variables are stored at the centroids of the elements, thus achieving simplicity and low cost of computations. Turbulence is modeled by using the standard two-equation k-epsilon model. The purpose of this work is to evaluate the performance and accuracy of flow calculations under different discretization schemes in the light of experimental results. The discretization schemes that are incorporated in the code include the classical hybrid scheme, the third-order QUICK scheme, and a fifth-order upwind scheme. Benchmark tests are performed for laminar and turbulent flows in 90 deg curved ducts of square and circular cross sections. Flaw solutions obtained using the classical hybrid scheme are compared with solutions obtained with the higher-order schemes. The results show that accurate solutions can be efficiently obtained on grids of moderate size by using high-order-accuracy schemes. Overall, the potential of the methodology for calculating real-life engineering flows is demonstrated.
Computation of incompressible viscous flows through turbopump components
NASA Astrophysics Data System (ADS)
Kiris, Cetin; Chang, Leon
1993-02-01
Flow through pump components, such as an inducer and an impeller, is efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. the equations are solved in steadily rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. Current computations use a one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. The resulting computer code is applied to the flow analysis inside a generic rocket engine pump inducer, a fuel pump impeller, and SSME high pressure fuel turbopump impeller. Numerical results of inducer flow are compared with experimental measurements. In the fuel pump impeller, the effect of downstream boundary conditions is investigated. Flow analyses at 80 percent, 100 percent, and 120 percent of design conditions are presented.
Adjoint operator approach to shape design for internal incompressible flows
NASA Technical Reports Server (NTRS)
Cabuk, H.; Sung, C.-H.; Modi, V.
1991-01-01
The problem of determining the profile of a channel or duct that provides the maximum static pressure rise is solved. Incompressible, laminar flow governed by the steady state Navier-Stokes equations is assumed. Recent advances in computational resources and algorithms have made it possible to solve the direct problem of determining such a flow through a body of known geometry. It is possible to obtain a set of adjoint equations, the solution to which permits the calculation of the direction and relative magnitude of change in the diffuser profile that leads to a higher pressure rise. The solution to the adjoint problem can be shown to represent an artificially constructed flow. This interpretation provides a means to construct numerical solutions to the adjoint equations that do not compromise the fully viscous nature of the problem. The algorithmic and computational aspects of solving the adjoint equations are addressed. The form of these set of equations is similar but not identical to the Navier-Stokes equations. In particular some issues related to boundary conditions and stability are discussed.
Consistent and conservative framework for incompressible multiphase flow simulations
NASA Astrophysics Data System (ADS)
Owkes, Mark; Desjardins, Olivier
2015-11-01
We present a computational methodology for convection that handles discontinuities with second order accuracy and maintains conservation to machine precision. We use this method in the context of an incompressible gas-liquid flow to transport the phase interface, momentum, and scalars. Using the same methodology for all the variables ensures discretely consistent transport, which is necessary for robust and accurate simulations of turbulent atomizing flows with high-density ratios. The method achieves conservative transport by computing consistent fluxes on a refined mesh, which ensures all conserved quantities are fluxed with the same discretization. Additionally, the method seamlessly couples semi-Lagrangian fluxes used near the interface with finite difference fluxes used away from the interface. The semi-Lagrangian fluxes are three-dimensional, un-split, and conservatively handle discontinuities. Careful construction of the fluxes ensures they are divergence-free and no gaps or overlaps form between neighbors. We have tested and used the scheme for many cases and demonstrate a simulation of an atomizing liquid jet.
Implicit lower-upper/approximate-factorization schemes for incompressible flows
Briley, W.R.; Neerarambam, S.S.; Whitfield, D.L.
1996-10-01
A lower-upper/approximate-factorization (LU/AF) scheme is developed for the incompressible Euler or Navier-Stokes equations. The LU/AF scheme contains an iteration parameter that can be adjusted to improve iterative convergence rate. The LU/AF scheme is to be used in conjunction with linearized implicit approximations and artificial compressibility to compute steady solutions, and within sub-iterations to compute unsteady solutions. Formulations based on time linearization with and without sub-iteration and on Newton linearization are developed using spatial difference operators. The spatial approximation used includes upwind differencing based on Roe`s approximate Riemann solver and van Leer`s MUSCL scheme, with numerically computed implicit flux linearizations. Simple one-dimensional diffusion and advection/diffusion problems are first studied analytically to provide insight for development of the Navier-Stokes algorithm. The optimal values of both time step and LU/AF parameter are determined for a test problem consisting of two-dimensional flow past a NACA 0012 airfoil, with a highly stretched grid. The optimal parameter provides a consistent improvement in convergence rate for four test cases having different grids and Reynolds numbers and, also, for an inviscid case. The scheme can be easily extended to three dimensions and adapted for compressible flows. 24 refs., 11 figs., 2 tabs.
Mixing of spherical bubbles with time-dependent radius in incompressible flows
NASA Astrophysics Data System (ADS)
Pérez-Muñuzuri, Vicente; Garaboa-Paz, Daniel
2016-02-01
The motion of contracting and expanding bubbles in an incompressible chaotic flow is analyzed in terms of the finite-time Lyapunov exponents. The viscous forces acting on the bubble surface depend not only on the relative acceleration but also on the time dependence of the bubble volume, which is modeled by the Rayleigh-Plesset equation. The effect of bubble coalescence on the coherent structures that develop in the flow is studied using a simplified bubble merger model. Contraction and expansion of the bubbles is favored in the vicinity of the coherent structures. Time evolution of coalescence bubbles follows a Lévy distribution with an exponent that depends on the initial distance between bubbles. Mixing patterns were found to depend heavily on merging and on the time-dependent volume of the bubbles.
The exact calculation of quadrupole sources for some incompressible flows
NASA Technical Reports Server (NTRS)
Brentner, Kenneth S.
1988-01-01
This paper is concerned with the application of the acoustic analogy of Lighthill to the acoustic and aerodynamic problems associated with moving bodies. The Ffowcs Williams-Hawkings equation, which is an interpretation of the acoustic analogy for sound generation by moving bodies, manipulates the source terms into surface and volume sources. Quite often in practice the volume sources, or quadrupoles, are neglected for various reasons. Recently, Farassat, Long and others have attempted to use the FW-H equation with the quadrupole source and neglected to solve for the surface pressure on the body. The purpose of this paper is to examine the contribution of the quadrupole source to the acoustic pressure and body surface pressure for some problems for which the exact solution is known. The inviscid, incompressible, 2-D flow, calculated using the velocity potential, is used to calculate the individual contributions of the various surface and volume source terms in the FW-H equation. The relative importance of each of the sources is then assessed.
Accurate and robust methods for variable density incompressible flows with discontinuities
Rider, W.J.; Kothe, D.B.; Puckett, E.G.
1996-09-01
We are interested in the solution of incompressible flows which are characterized by large density variations, interfacial physics, arbitrary material topologies and strong vortical content. The issues present in constant density incompressible flow are exacerbated by the presence of density discontinuities. A much greater premium requirement is placed the positivity of computed quantities The mechanism of baroclinc vorticity generation exists ({gradient}p x {gradient}p) to further complicate the physics.
An explicit Runge-Kutta method for 3D turbulent incompressible flows
NASA Technical Reports Server (NTRS)
Sung, Chao-Ho; Lin, Cheng-Wen; Hung, C. M.
1988-01-01
A computer code has been developed to solve for the steady-state solution of the 3D incompressible Reynolds-averaged Navier-Stokes equations. The approach is based on the cell-center, central-difference, finite-volume formulation and an explicit one-step, multistage Runge-Kutta time-stepping scheme. The Baldwin-Lomax turbulence model is used. Techniques to accelerate the rate of convergence to a steady-state solution include the preconditioned method, the local time stepping, and the implicit residual smoothing. Improvements in computational efficiency have been demonstrated in several areas. This numerical procedure has been used to simulate the turbulent horseshoe vortex flow around an airfoil/flat-plate juncture.
Preconditioned High-order WENO Scheme for Incompressible Viscous Flows Simulation
NASA Astrophysics Data System (ADS)
Qian, Z. S.; Zhang, J. B.; Li, C. X.
2011-09-01
A high-order accurate and highly-efficient finite difference algorithm for numerical simulation of the incompressible viscous flows has been developed. This algorithm is based on the pseudo-compressibility formulation, which combines the preconditioning technique for accelerating the time marching for stiff hyperbolic equations. Third-, fifth- and seventh-order accurate WENO schemes are used to discrete the inviscid fluxes and fourth- and sixth-order central schemes are employed for the viscous fluxes and metric terms. Implicit lower-upper symmetric Gauss-Seidel (LU-SGS) time marching procedure is performed for temporal discretization. The accuracy and the efficiency of the proposed method are demonstrated for several numerical test cases.
NASA Astrophysics Data System (ADS)
Moawad, S. M.; Ibrahim, D. A.
2016-08-01
The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.
An efficient algorithm for incompressible N-phase flows
NASA Astrophysics Data System (ADS)
Dong, S.
2014-11-01
We present an efficient algorithm within the phase field framework for simulating the motion of a mixture of N (N⩾2) immiscible incompressible fluids, with possibly very different physical properties such as densities, viscosities, and pairwise surface tensions. The algorithm employs a physical formulation for the N-phase system that honors the conservations of mass and momentum and the second law of thermodynamics. We present a method for uniquely determining the mixing energy density coefficients involved in the N-phase model based on the pairwise surface tensions among the N fluids. Our numerical algorithm has several attractive properties that make it computationally very efficient: (i) it has completely de-coupled the computations for different flow variables, and has also completely de-coupled the computations for the (N-1) phase field functions; (ii) the algorithm only requires the solution of linear algebraic systems after discretization, and no nonlinear algebraic solve is needed; (iii) for each flow variable the linear algebraic system involves only constant and time-independent coefficient matrices, which can be pre-computed during pre-processing, despite the variable density and variable viscosity of the N-phase mixture; (iv) within a time step the semi-discretized system involves only individual de-coupled Helmholtz-type (including Poisson) equations, despite the strongly-coupled phase-field system of fourth spatial order at the continuum level; (v) the algorithm is suitable for large density contrasts and large viscosity contrasts among the N fluids. Extensive numerical experiments have been presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts. In particular, we compare our simulations with the de Gennes theory, and demonstrate that our method produces physically accurate results for multiple fluid phases. We also demonstrate the significant and sometimes dramatic effects of the
An efficient algorithm for incompressible N-phase flows
Dong, S.
2014-11-01
We present an efficient algorithm within the phase field framework for simulating the motion of a mixture of N (N⩾2) immiscible incompressible fluids, with possibly very different physical properties such as densities, viscosities, and pairwise surface tensions. The algorithm employs a physical formulation for the N-phase system that honors the conservations of mass and momentum and the second law of thermodynamics. We present a method for uniquely determining the mixing energy density coefficients involved in the N-phase model based on the pairwise surface tensions among the N fluids. Our numerical algorithm has several attractive properties that make it computationally very efficient: (i) it has completely de-coupled the computations for different flow variables, and has also completely de-coupled the computations for the (N−1) phase field functions; (ii) the algorithm only requires the solution of linear algebraic systems after discretization, and no nonlinear algebraic solve is needed; (iii) for each flow variable the linear algebraic system involves only constant and time-independent coefficient matrices, which can be pre-computed during pre-processing, despite the variable density and variable viscosity of the N-phase mixture; (iv) within a time step the semi-discretized system involves only individual de-coupled Helmholtz-type (including Poisson) equations, despite the strongly-coupled phase–field system of fourth spatial order at the continuum level; (v) the algorithm is suitable for large density contrasts and large viscosity contrasts among the N fluids. Extensive numerical experiments have been presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts. In particular, we compare our simulations with the de Gennes theory, and demonstrate that our method produces physically accurate results for multiple fluid phases. We also demonstrate the significant and sometimes dramatic effects of the
NASA Astrophysics Data System (ADS)
Wu, Heng
2000-10-01
In this thesis, an a-posteriori error estimator is presented and employed for solving viscous incompressible flow problems. In an effort to detect local flow features, such as vortices and separation, and to resolve flow details precisely, a velocity angle error estimator e theta which is based on the spatial derivative of velocity direction fields is designed and constructed. The a-posteriori error estimator corresponds to the antisymmetric part of the deformation-rate-tensor, and it is sensitive to the second derivative of the velocity angle field. Rationality discussions reveal that the velocity angle error estimator is a curvature error estimator, and its value reflects the accuracy of streamline curves. It is also found that the velocity angle error estimator contains the nonlinear convective term of the Navier-Stokes equations, and it identifies and computes the direction difference when the convective acceleration direction and the flow velocity direction have a disparity. Through benchmarking computed variables with the analytic solution of Kovasznay flow or the finest grid of cavity flow, it is demonstrated that the velocity angle error estimator has a better performance than the strain error estimator. The benchmarking work also shows that the computed profile obtained by using etheta can achieve the best matching outcome with the true theta field, and that it is asymptotic to the true theta variation field, with a promise of fewer unknowns. Unstructured grids are adapted by employing local cell division as well as unrefinement of transition cells. Using element class and node class can efficiently construct a hierarchical data structure which provides cell and node inter-reference at each adaptive level. Employing element pointers and node pointers can dynamically maintain the connection of adjacent elements and adjacent nodes, and thus avoids time-consuming search processes. The adaptive scheme is applied to viscous incompressible flow at different
A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems
NASA Astrophysics Data System (ADS)
Geissert, Matthias; Hieber, Matthias; Nguyen, Thieu Huy
2016-06-01
This article develops a general approach to time periodic incompressible fluid flow problems and semilinear evolution equations. It yields, on the one hand, a unified approach to various classical problems in incompressible fluid flow and, on the other hand, gives new results for periodic solutions to the Navier-Stokes-Oseen flow, the Navier-Stokes flow past rotating obstacles, and, in the geophysical setting, for Ornstein-Uhlenbeck and various diffusion equations with rough coefficients. The method is based on a combination of interpolation and topological arguments, as well as on the smoothing properties of the linearized equation.
Mittal, R.; Dong, H.; Bozkurttas, M.; Najjar, F.M.; Vargas, A.; von Loebbecke, A.
2010-01-01
A sharp interface immersed boundary method for simulating incompressible viscous flow past three-dimensional immersed bodies is described. The method employs a multi-dimensional ghost-cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three-dimensional, stationary, moving and/or deforming bodies. The complex immersed surfaces are represented by grids consisting of unstructured triangular elements; while the flow is computed on non-uniform Cartesian grids. The paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries. Simulations of a number of canonical two- and three-dimensional flows are used to verify the accuracy and fidelity of the solver over a range of Reynolds numbers. Flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems. Finally two cases inspired from biology with highly complex three-dimensional bodies are simulated in order to demonstrate the versatility of the method. PMID:20216919
The solution of the two-dimensional incompressible flow equations on unstructured triangular meshes
NASA Astrophysics Data System (ADS)
Williams, Morgan
1993-05-01
A numerical method for calculating two-dimensional turbulent incompressible flow on unstructured triangular meshes is developed. A primitive variable formulation is used. The Helmholtz pressure equation algorithm is used to enforce the velocity continuity relation for incompressible flow. A careful treatment of the pressure dissipation model is presented. A standard k-epsilon turbulence model with wall functions is used to provide closure for the governing equations. A backward-facing step turbulent flow is calculated using an unstructured triangular mesh, and the results are compared to experimental and computational data.
Front Speed Enhancement by Incompressible Flows in Three or Higher Dimensions
NASA Astrophysics Data System (ADS)
El Smaily, Mohammad; Kirsch, Stéphane
2014-07-01
We study, in dimensions N ≥ 3, the family of first integrals of an incompressible flow: these are functions whose level surfaces are tangential to the streamlines of the advective incompressible field. One main motivation for this study comes from earlier results proving that the existence of nontrivial first integrals of an incompressible flow q is the main key that leads to a "linear speed up" by a large advection of pulsating traveling fronts solving a reaction-advection-diffusion equation in a periodic heterogeneous framework. The family of first integrals is not well understood in dimensions N ≥ 3 due to the randomness of the trajectories of q and this is in contrast with the case N = 2. By looking at the domain of propagation as a union of different components produced by the advective field, we provide more information about first integrals and we give a class of incompressible flows which exhibit "ergodic components" of positive Lebesgue measure (and hence are not shear flows) and which, under certain sharp geometric conditions, speed up the KPP fronts linearly with respect to the large amplitude. In the proofs, we establish a link between incompressibility, ergodicity, first integrals and the dimension to give a sharp condition about the asymptotic behavior of the minimal KPP speed in terms of the configuration of ergodic components.
Approximate factorization with an elliptic pressure solver for incompressible flow
NASA Technical Reports Server (NTRS)
Bernard, R. S.; Thompson, J. F.
1982-01-01
Two-dimensional curvilinear coordinates are used to solve the incompressible Navier-Stokes equations, in conjunction with approximate factorization for the solution of the momentum equation and the successive overrelaxation by lines method for the solution of a Poisson equation for the pressure. The combined algorithm, although not fully explicit, is marginally stable at Reynolds numbers lower than 10,000 and time increments of 0.01. Pressure distributions calculated for attack angles of zero and 6 deg are of the same shape as the experimental curves, but are shifted to one side.
Multi-material incompressible flow simulation using the moment-of-fluid method
Garimella, R V; Schofield, S P; Lowrie, R B; Swartz, B K; Christon, M A; Dyadechko, V
2009-01-01
The Moment-of-Fluid interface reconstruction technique is implemented in a second order accurate, unstructured finite element variable density incompressible Navier-Stokes solver. For flows with multiple materials, MOF significantly outperforms existing first and second order interface reconstruction techniques. For two material flows, the performance of MOF is similar to other interface reconstruction techniques. For strongly driven bouyant flows, the errors in the flow solution dominate and all the interface reconstruction techniques perform similarly.
Paraelectric gas flow accelerator
NASA Technical Reports Server (NTRS)
Sherman, Daniel M. (Inventor); Wilkinson, Stephen P. (Inventor); Roth, J. Reece (Inventor)
2001-01-01
A substrate is configured with first and second sets of electrodes, where the second set of electrodes is positioned asymmetrically between the first set of electrodes. When a RF voltage is applied to the electrodes sufficient to generate a discharge plasma (e.g., a one-atmosphere uniform glow discharge plasma) in the gas adjacent to the substrate, the asymmetry in the electrode configuration results in force being applied to the active species in the plasma and in turn to the neutral background gas. Depending on the relative orientation of the electrodes to the gas, the present invention can be used to accelerate or decelerate the gas. The present invention has many potential applications, including increasing or decreasing aerodynamic drag or turbulence, and controlling the flow of active and/or neutral species for such uses as flow separation, altering heat flow, plasma cleaning, sterilization, deposition, etching, or alteration in wettability, printability, and/or adhesion.
Design method for the flow field and drag of bodies of revolution in incompressible flow
Wolfe, W.P.; Oberkampf, W.L.
1982-01-01
A design method has been developed for determining the flow field, pressure distribution, boundary layer separation point, and drag of bodies of revolution at zero angle of attack in incompressible flow. The approach taken is the classical coupling of potential and boundary solutions to obtain the flow field about the body. The potential solution is obtained by modeling the body with an axial distribution of source/sink elements whose strengths vary linearly along their length. The laminar and turbulent boundary layer solutions are obtained from conventional solutions of the momentum integral equation. An approximate method is used to estimate the boundary layer transition point on the body. An empirical base pressure correlation is used to determine the base drag. Body surface pressure distributions and drag predictions are compared with experimental measurements.
Projection methods for incompressible flow problems with WENO finite difference schemes
NASA Astrophysics Data System (ADS)
de Frutos, Javier; John, Volker; Novo, Julia
2016-03-01
Weighted essentially non-oscillatory (WENO) finite difference schemes have been recommended in a competitive study of discretizations for scalar evolutionary convection-diffusion equations [20]. This paper explores the applicability of these schemes for the simulation of incompressible flows. To this end, WENO schemes are used in several non-incremental and incremental projection methods for the incompressible Navier-Stokes equations. Velocity and pressure are discretized on the same grid. A pressure stabilization Petrov-Galerkin (PSPG) type of stabilization is introduced in the incremental schemes to account for the violation of the discrete inf-sup condition. Algorithmic aspects of the proposed schemes are discussed. The schemes are studied on several examples with different features. It is shown that the WENO finite difference idea can be transferred to the simulation of incompressible flows. Some shortcomings of the methods, which are due to the splitting in projection schemes, become also obvious.
A comparison of two incompressible Navier-Stokes algorithms for unsteady internal flow
NASA Technical Reports Server (NTRS)
Wiltberger, N. Lyn; Rogers, Stuart E.; Kwak, Dochan
1993-01-01
A comparative study of two different incompressible Navier-Stokes algorithms for solving an unsteady, incompressible, internal flow problem is performed. The first algorithm uses an artificial compressibility method coupled with upwind differencing and a line relaxation scheme. The second algorithm uses a fractional step method with a staggered grid, finite volume approach. Unsteady, viscous, incompressible, internal flow through a channel with a constriction is computed using the first algorithm. A grid resolution study and parameter studies on the artificial compressibility coefficient and the maximum allowable residual of the continuity equation are performed. The periodicity of the solution is examined and several periodic data sets are generated using the first algorithm. These computational results are compared with previously published results computed using the second algorithm and experimental data.
Equation-free/Galerkin-free POD-assisted computation of incompressible flows
NASA Astrophysics Data System (ADS)
Sirisup, Sirod; Karniadakis, George Em; Xiu, Dongbin; Kevrekidis, Ioannis G.
2005-08-01
We present a Galerkin-free, proper orthogonal decomposition (POD)-assisted computational methodology for numerical simulations of the long-term dynamics of the incompressible Navier-Stokes equations. The approach is based on the "equation-free" framework: we use short, appropriate initialized bursts of full direct numerical simulations (DNS) of the Navier-Stokes equations to observe, estimate, and accelerate, through "projective integration", the evolution of the flow dynamics. The main assumption is that the long-term dynamics of the flow lie on a low-dimensional, attracting, and invariant manifold, which can be parametrized, not necessarily spanned, by a few POD basis functions. We start with a discussion of the consistency and accuracy of the approach, and then illustrate it through numerical examples: two-dimensional periodic and quasi-periodic flows past a circular cylinder. We demonstrate that the approach can successfully resolve complex flow dynamics at a reduced computational cost and that it can capture the long-term asymptotic state of the flow in cases where traditional Galerkin-POD models fail. The approach trades the overhead involved in developing POD-Galerkin and POD-nonlinear Galerkin codes, for the repeated (yet short, and on demand) use of an existing full DNS simulator. Moreover, since in this approach the POD modes are used to observe rather than span the true system dynamics, the computation is much less sensitive than POD-Galerkin to values of the system parameters (e.g., the Reynolds number) and the particular simulation data ensemble used to obtain the POD basis functions.
NASA Astrophysics Data System (ADS)
Park, Hyunwook; Pan, Xiaomin; Lee, Changhoon; Choi, Jung-Il
2016-06-01
A novel immersed boundary (IB) method based on an implicit direct forcing (IDF) scheme is developed for incompressible viscous flows. The key idea for the present IDF method is to use a block LU decomposition technique in momentum equations with Taylor series expansion to construct the implicit IB forcing in a recurrence form, which imposes more accurate no-slip boundary conditions on the IB surface. To accelerate the IB forcing convergence during the iterative procedure, a pre-conditioner matrix is introduced in the recurrence formulation of the IB forcing. A Jacobi-type parameter is determined in the pre-conditioner matrix by minimizing the Frobenius norm of the matrix function representing the difference between the IB forcing solution matrix and the pre-conditioner matrix. In addition, the pre-conditioning parameter is restricted due to the numerical stability in the recurrence formulation. Consequently, the present pre-conditioned IDF (PIDF) enables accurate calculation of the IB forcing within a few iterations. We perform numerical simulations of two-dimensional flows around a circular cylinder and three-dimensional flows around a sphere for low and moderate Reynolds numbers. The result shows that PIDF yields a better imposition of no-slip boundary conditions on the IB surfaces for low Reynolds number with a fairly larger time step than IB methods with different direct forcing schemes due to the implicit treatment of the diffusion term for determining the IB forcing. Finally, we demonstrate the robustness of the present PIDF scheme by numerical simulations of flow around a circular array of cylinders, flows around a falling sphere, and two sedimenting spheres in gravity.
Towards entropy detection of anomalous mass and momentum exchange in incompressible fluid flow
NASA Astrophysics Data System (ADS)
Naterer, G. F.; Rinn, D.
2002-08-01
An entropy-based approach is presented for assessment of computational accuracy in incompressible flow problems. It is shown that computational entropy can serve as an effective parameter in detecting erroneous or anomalous predictions of mass and momentum transport in the flow field. In the present paper, the fluid flow equations and second law of thermodynamics are discretized by a Galerkin finite-element method with linear, isoparametric triangular elements. It is shown that a weighted entropy residual is closely related to truncation error; this relationship is examined in an application problem involving incompressible flow through a converging channel. In particular, regions exhibiting anomalous flow behaviour, such as under-predicted velocities, appear together with analogous trends in the weighted entropy residual. It is anticipated that entropy-based error detection can provide important steps towards improved accuracy in computational fluid flow. Copyright
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.
On the rotation and skew-symmetric forms for incompressible flow simulations
NASA Technical Reports Server (NTRS)
Zang, Thomas A.
1991-01-01
A variety of numerical simulations of transition and turbulence in incompressible flow are presented to compare the commonly used rotation form with the skew-symmetric (and other) forms of the nonlinear terms. The results indicate that the rotation form is much less accurate than the other forms for spectral algorithms which include aliasing errors. For de-aliased methods the difference is minimal.
Numerical simulation of the incompressible internal flow through a tilting disk valve
NASA Technical Reports Server (NTRS)
Chang, I-Dee; Rogers, Stuart E.; Kwak, Dochan; Kiris, Cetin
1990-01-01
A numerical simulation of the incompressible viscous flow through a prosthetic tilting disk heart valve is presented in order to demonstrate the current capability to model unsteady flows with moving boundaries. Both steady and unsteady flow calculations are performed by solving the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates. In order to handle the moving boundary problems, the chimera grid embedding scheme which decomposes a complex computational domain into several simple subdomains is used. An algebraic turbulence model for internal flows is incorporated to reach the physiological values of Reynolds number. Good agreement is obtained between the numerical results and experimental measurements. It is found that the tilting disk valve causes large regions of separated flow, and regions of high shear.
An anisotropic flow law for incompressible polycrystalline materials
NASA Astrophysics Data System (ADS)
Placidi, Luca; Hutter, Kolumban
2005-11-01
New and explicit anisotropic constitutive equations between the stretching and deviatoric stress tensors for the two- and three-dimensional cases of incompressible polycrystalline materials are presented. The anisotropy is assumed to be driven by an Orientation Distribution Function (ODF). The polycrystal is composed of transversally isotropic crystallites, the lattice orientation of which can be characterized by a single unit vector. The proposed constitutive equations are valid for any frame of reference and for every state of deformation. The basic assumption of this method is that the principle directions of the stretching and of the stress deviator are the same in the isotropic as well as in the anisotropic case. This means that the proposed constitutive laws are able to model the effects of anisotropy only via a change of the fluidity due to a change of the ODF. Such an assumption is justified to guarantee that, besides knowledge of the parameters involved in the isotropic constitutive equation, the anisotropic material response is completely characterized by only one additional parameter, a type of enhancement factor. Explicit comparisons with experimental data are conducted for Ih ice.
Incompressible viscous flow computations for the pump components and the artificial heart
NASA Technical Reports Server (NTRS)
Kiris, Cetin
1992-01-01
A finite-difference, three-dimensional incompressible Navier-Stokes formulation to calculate the flow through turbopump components is utilized. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Both steady and unsteady flow calculations can be performed using the current algorithm. In this work, the equations are solved in steadily rotating reference frames by using the steady-state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using an algebraic mixing-length turbulence model. Numerical results are compared with experimental measurements and a good agreement is found between the two. Included in the appendix is a paper on incompressible viscous flow through artificial heart devices with moving boundaries. Time-accurate calculations, such as impeller and diffusor interaction, will be reported in future work.
On the origins of vortex shedding in two-dimensional incompressible flows
NASA Astrophysics Data System (ADS)
Boghosian, M. E.; Cassel, K. W.
2016-04-01
An exegesis of a novel mechanism leading to vortex splitting and subsequent shedding that is valid for two-dimensional incompressible, inviscid or viscous, and external or internal or wall-bounded flows, is detailed in this research. The mechanism, termed the vortex shedding mechanism (VSM) is simple and intuitive, requiring only two coincident conditions in the flow: (1) the existence of a location with zero momentum and (2) the presence of a net force having a positive divergence. Numerical solutions of several model problems illustrate causality of the VSM. Moreover, the VSM criteria is proved to be a necessary and sufficient condition for a vortex splitting event in any two-dimensional, incompressible flow. The VSM is shown to exist in several canonical problems including the external flow past a circular cylinder. Suppression of the von Kármán vortex street is demonstrated for Reynolds numbers of 100 and 400 by mitigating the VSM.
On a modification of GLS stabilized FEM for solving incompressible viscous flows
NASA Astrophysics Data System (ADS)
Burda, P.; Novotný, J.; Ístek, J.
2006-07-01
We deal with 2D flows of incompressible viscous fluids with high Reynolds numbers. Galerkin Least Squares technique of stabilization of the finite element method is studied and its modification is described. We present a number of numerical results obtained by the developed method, showing its contribution to solving flows with high Reynolds numbers. Several recommendations and remarks are included. We are interested in positive as well as negative aspects of stabilization, which cannot be divorced.
Direct pore-level modeling of incompressible fluid flow in porous media
Ovaysi, Saeed; Piri, Mohammad
2010-09-20
We present a dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media. The model is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples. It is based on moving particle semi-implicit (MPS) method. We modify this technique in order to improve its stability for flow in porous media problems. Using the micro-CT image of a rock sample, the entire medium, i.e., solid and fluid, is discretized into particles. The incompressible Navier-Stokes equations are then solved for each particle using the MPS summations. The model handles highly irregular fluid-solid boundaries effectively. An algorithm to split and merge fluid particles is also introduced. To handle the computational load, we present a parallel version of the model that runs on distributed memory computer clusters. The accuracy of the model is validated against the analytical, numerical, and experimental data available in the literature. The validated model is then used to simulate both unsteady- and steady-state flow of an incompressible fluid directly in a representative elementary volume (REV) size micro-CT image of a naturally-occurring sandstone with 3.398 {mu}m resolution. We analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady-state flow rate.
Computation of incompressible flow around the DARPA SUBOFF bodies
NASA Astrophysics Data System (ADS)
Gorski, Joseph J.; Coleman, Roderick M.; Haussling, Henry J.
1990-07-01
This report describes the application of the DTNS flow solvers, both axisymmetric (DTNSA) and three-dimensional (DTNS3D) versions, and the NUGGET grid generation code to the Defense Advanced Research Projects Agency (DARPA) SUBOFF bodies.
NASA Technical Reports Server (NTRS)
Chang, J. L. C.; Kwak, D.; Rogers, S. E.; Yang, R.-J.
1988-01-01
Incompressible Navier-Stokes solution methods are discussed with an emphasis on the pseudocompressibility method. A steady-state flow solver based on the pseudocompressibility approach is then described. This flow-solver code was used to analyze the internal flow in the Space Shuttle main engine hot-gas manifold. Salient features associated with this three-dimensional realistic flow simulation are discussed. Numerical solutions relevant to the current engine analysis and the redesign effort are discussed along with experimental results. This example demonstrates the potential of computational fluid dynamics as a design tool for aerospace applications.
NASA Technical Reports Server (NTRS)
Beatty, T. D.
1975-01-01
A theoretical method is presented for the computation of the flow field about an axisymmetric body operating in a viscous, incompressible fluid. A potential flow method was used to determine the inviscid flow field and to yield the boundary conditions for the boundary layer solutions. Boundary layer effects in the forces of displacement thickness and empirically modeled separation streamlines are accounted for in subsequent potential flow solutions. This procedure is repeated until the solutions converge. An empirical method was used to determine base drag allowing configuration drag to be computed.
NASA Astrophysics Data System (ADS)
Sun, Y.; Shu, C.; Teo, C. J.; Wang, Y.; Yang, L. M.
2015-11-01
In this paper, a gas-kinetic flux solver (GKFS) is presented for the simulation of incompressible and compressible viscous flows. In this solver, the finite volume method is applied to discretize the Navier-Stokes equations. The inviscid and viscous fluxes at the interface are obtained simultaneously via the gas-kinetic scheme, which locally reconstruct the solution for the continuous Boltzmann equation. Different from the conventional gas-kinetic BGK scheme [1], a simple way is presented in this work to evaluate the non-equilibrium distribution function, which is calculated by the difference of equilibrium distribution functions at the cell interface and its surrounding points. As a consequence, explicit formulations for computing the conservative flow variables and fluxes are simply derived. In particular, three specific schemes are proposed and validated via several incompressible and compressible test examples. Numerical results show that all three schemes can provide accurate numerical results for incompressible flows. On the other hand, Scheme III is much more stable and consistent in simulation of compressible flows.
Distribution of incompressible flow within interdigitated channels and porous electrodes
NASA Astrophysics Data System (ADS)
Kee, Robert J.; Zhu, Huayang
2015-12-01
This paper develops a general model with which to evaluate flow uniformity and pressure drop within interdigitated-channel structures, especially in the context of redox flow batteries. The governing equations are cast in dimensionless variables, leading to a set of characteristic dimensionless parameter groups. The systems of governing equations are solved computationally, with the results presented graphically. Because the results are general, the underlying model itself is not needed to apply the quantitative design guidelines. However, the paper presents and discusses all the information required to recreate the model as needed.
2D Mixed Convection Thermal Incompressible Viscous Flows
NASA Astrophysics Data System (ADS)
Bermudez, Blanca; Nicolas, Alfredo
2005-11-01
Mixed convection thermal incomprressible viscous fluid flows in rectangular cavities are presented. These kind of flows may be governed by the time-dependent Boussinesq approximation in terms of the stream function-vorticity variables formulation. The results are obtained with a simple numerical scheme based mainly on a fixed point iterative process applied to the non-linear system of elliptic equations that is obtained after a second order time discretization. Numerical experiments are reported for the problem of a cavity with fluid boundary motion on the top. Some results correspond to validation examples and others, to the best of our knowledge, correspond to new results. To show that the new results are correct, a mesh size and time independence studies are carried out, and the acceptable errors are measured point-wise. For the optimal mesh size and time step the final times when the steady state is reached, as solution from the unsteady problem, are reported; it should be seen that they are larger than the ones for natural convection which, physically speaking, show the agreement that mixed convection flows are more active than those of natural convection due to the fluid boundary motion on the top of the cavity. The flow parameters are: the Reynolds number, the Grashof number and the aspect ratio.
Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows
NASA Technical Reports Server (NTRS)
Wilson, Robert V.; Demuren, Ayodeji O.; Carpenter, Mark
1998-01-01
A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.
Steady incompressible potential flow around lifting bodies immersed in a fluid. M.S. Thesis
NASA Technical Reports Server (NTRS)
Chiuchiolo, E. A.
1974-01-01
The refinement was investigated of a method for evaluating the pressure distribution on a body surface of arbitrary shape in incompressible flow. The solution was obtained in terms of the velocity potential, through numerical approximations which require the use of a high speed digital computer. The box method and the modal method are described in detail, and were applied to a very thin, rectangular wing in incompressible, steady flow. The box method is found to be more practical as it is applicable to more general geometries (the modal method requires a new set of functions for each geometry), and requires less computer time (fifty percent of that required by the modal method for the same problem).
A nested iterative scheme for computation of incompressible flows in long domains
NASA Astrophysics Data System (ADS)
Manguoglu, Murat; Sameh, Ahmed H.; Tezduyar, Tayfun E.; Sathe, Sunil
2008-12-01
We present an effective preconditioning technique for solving the nonsymmetric linear systems encountered in computation of incompressible flows in long domains. The application category we focus on is arterial fluid mechanics. These linear systems are solved using a nested iterative scheme with an outer Richardson scheme and an inner iteration that is handled via a Krylov subspace method. Test computations that demonstrate the robustness of our nested scheme are presented.
A p-version finite element method for steady incompressible fluid flow and convective heat transfer
NASA Technical Reports Server (NTRS)
Winterscheidt, Daniel L.
1993-01-01
A new p-version finite element formulation for steady, incompressible fluid flow and convective heat transfer problems is presented. The steady-state residual equations are obtained by considering a limiting case of the least-squares formulation for the transient problem. The method circumvents the Babuska-Brezzi condition, permitting the use of equal-order interpolation for velocity and pressure, without requiring the use of arbitrary parameters. Numerical results are presented to demonstrate the accuracy and generality of the method.
Velocity-vorticity formulation of three-dimensional, steady, viscous, incompressible flows
Meir, A.J.
1994-12-31
In this work we discuss some aspects of the velocity-vorticity formulation of three-dimensional, steady, viscous, incompressible flows. We describe reasonable boundary conditions that should be imposed on the vorticity and a compatibility condition that the vorticity must satisfy. This formulation may give rise to efficient numerical algorithms for approximating solutions of the Stokes problem, which in turn yields an iterative method for approximating solutions of the Navier-Stokes equations.
VOF Method for Simulation of Multiphase Incompressible Flows with Phase Change
NASA Astrophysics Data System (ADS)
Zhang, S. P.; Ni, M. J.; Ma, H. Y.
2011-09-01
A volume-of-fluid method for simulation of incompressible multiphase flows with phase change is studied. We have simulated a series of processes of the vapor bubble deformation in a three-dimensional film boiling using volume of fluid (VOF) method, which include the generation, detachment and rising deformation of the bubble. Our numerical results show that the VOF method is a useful method to handle complex deformation of the liquid-vapor interface during film boiling.
Fully consistent CFD methods for incompressible flow computations
NASA Astrophysics Data System (ADS)
Kolmogorov, D. K.; Shen, W. Z.; Sørensen, N. N.; Sørensen, J. N.
2014-06-01
Nowadays collocated grid based CFD methods are one of the most efficient tools for computations of the flows past wind turbines. To ensure the robustness of the methods they require special attention to the well-known problem of pressure-velocity coupling. Many commercial codes to ensure the pressure-velocity coupling on collocated grids use the so-called momentum interpolation method of Rhie and Chow [1]. As known, the method and some of its widely spread modifications result in solutions, which are dependent of time step at convergence. In this paper the magnitude of the dependence is shown to contribute about 0.5% into the total error in a typical turbulent flow computation. Nevertheless if coarse grids are used, the standard interpolation methods result in much higher non-consistent behavior. To overcome the problem, a recently developed interpolation method, which is independent of time step, is used. It is shown that in comparison to other time step independent method, the method may enhance the convergence rate of the SIMPLEC algorithm up to 25 %. The method is verified using turbulent flow computations around a NACA 64618 airfoil and the roll-up of a shear layer, which may appear in wind turbine wake.
Conditions at the downstream boundary for simulations of viscous incompressible flow
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1990-01-01
The proper specification of boundary conditions at artificial boundaries for the simulation of time-dependent fluid flows has long been a matter of controversy. A general theory of asymptotic boundary conditions for dissipative waves is applied to the design of simple, accurate conditions at downstream boundary for incompressible flows. For Reynolds numbers far enough below the critical value for linear stability, a scaling is introduced which greatly simplifies the construction of the asymptotic conditions. Numerical experiments with the nonlinear dynamics of vortical disturbances to plane Poiseuille flow are presented which illustrate the accuracy of our approach. The consequences of directly applying the scalings to the equations are also considered.
Incompressible viscous flow computations for the pump components and the artificial heart
NASA Technical Reports Server (NTRS)
Kiris, Cetin
1992-01-01
A finite difference, three dimensional incompressible Navier-Stokes formulation to calculate the flow through turbopump components is utilized. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. Both steady and unsteady flow calculations can be performed using the current algorithm. Here, equations are solved in steadily rotating reference frames by using the steady state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using an algebraic mixing-length turbulence model. Numerical results are compared with experimental measurements and a good agreement is found between the two.
Transient radiative energy transfer in incompressible laminar flows
NASA Technical Reports Server (NTRS)
Tiwari, S. N.; Singh, D. J.
1987-01-01
Analysis and numerical procedures are presented to investigate the transient radiative interactions of nongray absorbing-emitting species in laminar fully-developed flows between two parallel plates. The particular species considered are OH, CO, CO2, and H2O and different mixtures of these. Transient and steady-state results are obtained for the temperaure distribution and bulk temperature for different plate spacings, wall temperatures, and pressures. Results, in general, indicate that the rate of radiative heating can be quite high during earlier times. This information is useful in designing thermal protection systems for transient operations.
Large eddy simulation of incompressible turbulent channel flow
NASA Technical Reports Server (NTRS)
Moin, P.; Reynolds, W. C.; Ferziger, J. H.
1978-01-01
The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.
Notes on Newton-Krylov based Incompressible Flow Projection Solver
Robert Nourgaliev; Mark Christon; J. Bakosi
2012-09-01
The purpose of the present document is to formulate Jacobian-free Newton-Krylov algorithm for approximate projection method used in Hydra-TH code. Hydra-TH is developed by Los Alamos National Laboratory (LANL) under the auspices of the Consortium for Advanced Simulation of Light-Water Reactors (CASL) for thermal-hydraulics applications ranging from grid-to-rod fretting (GTRF) to multiphase flow subcooled boiling. Currently, Hydra-TH is based on the semi-implicit projection method, which provides an excellent platform for simulation of transient single-phase thermalhydraulics problems. This algorithm however is not efficient when applied for very slow or steady-state problems, as well as for highly nonlinear multiphase problems relevant to nuclear reactor thermalhydraulics with boiling and condensation. These applications require fully-implicit tightly-coupling algorithms. The major technical contribution of the present report is the formulation of fully-implicit projection algorithm which will fulfill this purpose. This includes the definition of non-linear residuals used for GMRES-based linear iterations, as well as physics-based preconditioning techniques.
NASA Astrophysics Data System (ADS)
German, Brian Joseph
This research develops a technique for the solution of incompressible equivalents to planar steady subsonic potential flows. Riemannian geometric formalism is used to develop a gauge transformation of the length measure followed by a curvilinear coordinate transformation to map the given subsonic flow into a canonical Laplacian flow with the same boundary conditions. The effect of the transformation is to distort both the immersed profile shape and the domain interior nonuniformly as a function of local flow properties. The method represents the full nonlinear generalization of the classical methods of Prandtl-Glauert and Karman-Tsien. Unlike the classical methods which are "corrections," this method gives exact results in the sense that the inverse mapping produces the subsonic full potential solution over the original airfoil, up to numerical accuracy. The motivation for this research was provided by an observed analogy between linear potential flow and the special theory of relativity that emerges from the invariance of the d'Alembert wave equation under Lorentz transformations. This analogy is well known in an operational sense, being leveraged widely in linear unsteady aerodynamics and acoustics, stemming largely from the work of Kussner. Whereas elements of the special theory can be invoked for compressibility effects that are linear and global in nature, the question posed in this work was whether other mathematical techniques from the realm of relativity theory could be used to similar advantage for effects that are nonlinear and local. This line of thought led to a transformation leveraging Riemannian geometric methods common to the general theory of relativity. A gauge transformation is used to geometrize compressibility through the metric tensor of the underlying space to produce an equivalent incompressible flow that lives not on a plane but on a curved surface. In this sense, forces owing to compressibility can be ascribed to the geometry of space in
NASA Astrophysics Data System (ADS)
Lavery, N.; Taylor, C.
1999-07-01
Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright
Study of spatial growth of disturbances in an Incompressible Double Shear Layer flow configuration
NASA Astrophysics Data System (ADS)
Natarajan, Hareshram; Jacobs, Gustaaf
2014-11-01
The spatial growth of disturbance within the linear instability regime in an incompressible 2D double shear layer flow configuration is studied by performing a Direct Numerical Simulation. The motivation of this study is to characterize the effect of the presence of an additional shear layer on the spatial growth of a shear layer instability. Initially, a DNS of an incompressible single shear layer is performed and the spatial growth rate of various disturbance frequency modes are validated with Linear Stability Analysis. The addtional shear layer is found to impact the spatial growth rates of the different disturbances and the frequency of the mode with the maximum growth rate is found to be shifted.
Flow-Induced Vibration of Flexible Hydrofoils in Incompressible, Turbulent Flows
NASA Astrophysics Data System (ADS)
Chae, Eun Jung; Akcabay, Deniz Tolga; Young, Yin Lu
2014-11-01
Flexible lifting bodies can be used to enhance the energy-efficiency and maneuverability of propulsion devices compared to their rigid counterparts. To take advantage of advances in materials and active/passive control techniques, an improved understanding of the fluid-structure interaction physics is needed. This numerical study focuses on flexible hydrofoil in incompressible, turbulent flows. The spanwise bending and twisting of a rectangular, cantilevered hydrofoil was modeled as 2DOF equations of motion coupled with the unsteady RANS equation. The results, which have been validated with experimental measurements, showed that the natural frequencies are lower in water compared to those in air due to the added mass effect, and the natural frequencies vary slightly with speed and angle of attack due to hydrodynamic bend-twist coupling and viscous effects. Lock-in of the vortex shedding frequencies with the natural frequencies was observed, along with modification of the wake patterns due to hydrodynamic bend-twist coupling. The hydrodynamic damping was found to be much greater than structural damping, and depends on the relative velocity, angle of attack, as well as structural stiffness and density, and can lead to destabilizing condition of structure in particular cases.
Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows
Fu, S.C.; So, R.M.C.; Leung, W.W.F.
2010-08-20
With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.
A Quantitative Comparison of Leading-edge Vortices in Incompressible and Supersonic Flows
NASA Technical Reports Server (NTRS)
Wang, F. Y.; Milanovic, I. M.; Zaman, K. B. M. Q.
2002-01-01
When requiring quantitative data on delta-wing vortices for design purposes, low-speed results have often been extrapolated to configurations intended for supersonic operation. This practice stems from a lack of database owing to difficulties that plague measurement techniques in high-speed flows. In the present paper an attempt is made to examine this practice by comparing quantitative data on the nearwake properties of such vortices in incompressible and supersonic flows. The incompressible flow data are obtained in experiments conducted in a low-speed wind tunnel. Detailed flow-field properties, including vorticity and turbulence characteristics, obtained by hot-wire and pressure probe surveys are documented. These data are compared, wherever possible, with available data from a past work for a Mach 2.49 flow for the same wing geometry and angles-of-attack. The results indicate that quantitative similarities exist in the distributions of total pressure and swirl velocity. However, the streamwise velocity of the core exhibits different trends. The axial flow characteristics of the vortices in the two regimes are examined, and a candidate theory is discussed.
A pressure based method for the solution of viscous incompressible turbomachinery flows
NASA Technical Reports Server (NTRS)
Hobson, Garth Victor; Lakshminarayana, B.
1991-01-01
A new technique was 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 correction 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. Two dimensional internal flows are computed with this method. The prediction of cascade performance is presented. The extention of the pressure correction method for the solution of three dimensional flows is also presented.
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.; Ganjoo, D. K.
1990-01-01
Finite element procedures and computations based on the velocity-pressure and vorticity-stream function formulations of incompressible flows are presented. Two new multistep velocity-pressure formulations are proposed and compared with the vorticity-stream function and one-step formulations. The example problems chosen are the standing vortex problem and flow past a circular cylinder. Benchmark quality computations are performed for the cylinder problem. The numerical results indicate that the vorticity-stream function formulation and one of the two new multistep formulations involve much less numerical dissipation than the one-step formulation.
NASA Technical Reports Server (NTRS)
Thiede, P.
1978-01-01
The transition of the laminar boundary layer into the turbulent state, which results in an increased drag, can be avoided by sucking of the boundary layer particles near the wall. The technically-interesting case of sucking the particles using individual slits is investigated for bodies of revolution in incompressible flow. The results of the variational calculations show that there is an optimum suction height, where the slot separations are maximum. Combined with favorable shaping of the body, it is possible to keep the boundary layer over bodies of revolution laminar at high Reynolds numbers using relatively few suction slits and small amounts of suction flow.
Frequency-selection mechanism in incompressible open-cavity flows via reflected instability waves.
Tuerke, F; Sciamarella, D; Pastur, L R; Lusseyran, F; Artana, G
2015-01-01
We present an alternative perspective on nonharmonic mode coexistence, commonly found in the shear layer spectrum of open-cavity flows. Modes obtained by a local linear stability analysis of perturbations to a two-dimensional, incompressible, and inviscid sheared flow over a cavity of finite length and depth were conditioned by a so-called coincidence condition first proposed by Kulikowskii [J. Appl. Math. Mech. 30, 180 (1966)] which takes into account instability wave reflection within the cavity. The analysis yields a set of discrete, nonharmonic frequencies, which compare well with experimental results [Phys. Fluids 20, 114101 (2008); Exp. Fluids 50, 905 (2010)]. PMID:25679706
NASA Technical Reports Server (NTRS)
Chang, J. L. C.; Rosen, R.; Dao, S. C.; Kwak, D.
1985-01-01
An implicit finite difference code cast in general curvilinear coordinates is further developed for three-dimensional incompressible turbulent flows. The code is based on the method of pseudocompressibility and utilizes the Beam and Warming implicit approximate factorization algorithm to achieve computational efficiency. A multiple-zone method is further extended to include composite-grids to overcome the excessive computer memory required for solving turbulent flows in complex three-dimensional geometries. A simple turbulence model is proposed for internal flows. The code is being used for the Space Shuttle Main Engine (SSME) internal flow analyses.
Computation of incompressible viscous flows through artificial heart devices with moving boundaries
NASA Technical Reports Server (NTRS)
Kiris, Cetin; Rogers, Stuart; Kwak, Dochan; Chang, I.-DEE
1991-01-01
The extension of computational fluid dynamics techniques to artificial heart flow simulations is illustrated. Unsteady incompressible Navier-Stokes equations written in 3-D generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. The efficiency and robustness of the time accurate formulation of the algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated with experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapping grid embedding scheme are used, respectively. Steady state solutions for the flow through a tilting disk heart valve was compared against experimental measurements. Good agreement was obtained. The flow computation during the valve opening and closing is carried out to illustrate the moving boundary capability.
Borazjani, Iman; Ge, Liang; Le, Trung; Sotiropoulos, Fotis
2013-01-01
We develop an overset-curvilinear immersed boundary (overset-CURVIB) method in a general non-inertial frame of reference to simulate a wide range of challenging biological flow problems. The method incorporates overset-curvilinear grids to efficiently handle multi-connected geometries and increase the resolution locally near immersed boundaries. Complex bodies undergoing arbitrarily large deformations may be embedded within the overset-curvilinear background grid and treated as sharp interfaces using the curvilinear immersed boundary (CURVIB) method (Ge and Sotiropoulos, Journal of Computational Physics, 2007). The incompressible flow equations are formulated in a general non-inertial frame of reference to enhance the overall versatility and efficiency of the numerical approach. Efficient search algorithms to identify areas requiring blanking, donor cells, and interpolation coefficients for constructing the boundary conditions at grid interfaces of the overset grid are developed and implemented using efficient parallel computing communication strategies to transfer information among sub-domains. The governing equations are discretized using a second-order accurate finite-volume approach and integrated in time via an efficient fractional-step method. Various strategies for ensuring globally conservative interpolation at grid interfaces suitable for incompressible flow fractional step methods are implemented and evaluated. The method is verified and validated against experimental data, and its capabilities are demonstrated by simulating the flow past multiple aquatic swimmers and the systolic flow in an anatomic left ventricle with a mechanical heart valve implanted in the aortic position. PMID:23833331
A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains
NASA Astrophysics Data System (ADS)
Liska, Sebastian; Colonius, Tim
2016-07-01
A computationally efficient method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier-Stokes equations on an unbounded staggered Cartesian grid. Operations are limited to a finite computational domain through a lattice Green's function technique. This technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discrete operators. The differential algebraic equations describing the temporal evolution of the discrete momentum equation and incompressibility constraint are numerically solved by combining an integrating factor technique for the viscous term and a half-explicit Runge-Kutta scheme for the convective term. A projection method that exploits the mimetic and commutativity properties of the discrete operators is used to efficiently solve the system of equations that arises in each stage of the time integration scheme. Linear complexity, fast computation rates, and parallel scalability are achieved using recently developed fast multipole methods for difference equations. The accuracy and physical fidelity of solutions are verified through numerical simulations of vortex rings.
A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains
NASA Astrophysics Data System (ADS)
Liska, Sebastian; Colonius, Tim
2015-11-01
A novel, parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier-Stokes equations on an infinite staggered Cartesian grid. Operations are limited to a finite computational domain through a lattice Green's function technique. This technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discrete operators. The differential algebraic equations describing the temporal evolution of the discrete momentum equation, incompressibility constraint, and the no-slip constraint are numerically solved by combining an integrating factor technique for the viscous term and a half-explicit Runge-Kutta scheme for the convective term. A nested projection that exploits the mimetic and commutativity properties of the discrete operators is used to efficiently solve the system of equations that arises in each stage of the time integration scheme. Linear complexity, fast computation rate, and parallel scalability are achieved using recently developed fast multipole methods for difference equations. Results for three-dimensional test problems are presented, and the performance and scaling of the present implementation are discussed.
Lift due to thickness for low aspect ratio wings in incompressible flow
NASA Technical Reports Server (NTRS)
Dodbele, S. S.; Plotkin, A.
1985-01-01
The problem under consideration is a numerical study of the effects of thickness on lift for low aspect ratio wings in steady incompressible inviscid flow at moderate angles of attack. At these angles of attack the flow separates along the leading edge giving rise to a lift substantially higher than that computed by classical attached flow potential theory. The problem is treated as a perturbation expansion in a small thickness parameter. The lifting elements of the flow are modeled using a nonlinear vortex lattice method which replaces the leading and trailing edge vortex sheets by segmented straight vortex filaments. The thickness elements of the flow are modeled with a mean plane source distribution and a modification to the wing boundary conditions. Results are obtained for wings with biconvex and NACA 0012 sections which compare well with available experimental data. The important observation that the effect of thickness is to decrease the lift is made.
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1991-01-01
An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1991-01-01
An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.
Cauchy's almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow
NASA Astrophysics Data System (ADS)
Frisch, Uriel; Villone, Barbara
2014-09-01
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to Göttingen University, contain major discoveries on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy's formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation theorem was to be rediscovered independently by William Thomson (Kelvin) in 1869. Cauchy's invariants were only occasionally cited in the 19th century - besides Hankel, foremost by George Stokes and Maurice Lévy - and even less so in the 20th until they were rediscovered via Emmy Noether's theorem in the late 1960, but reattributed to Cauchy only at the end of the 20th century by Russian scientists.
Towards a segregated time spectral solution method for incompressible viscous flows
NASA Astrophysics Data System (ADS)
Sabine, Baumbach
2016-06-01
Considering the growth of interest in understanding flow phenomena in rotational machines, computational fluid dynamics (CFD) is a powerful tool to reach this goal. Especially unsteady simulations are becoming a focus of interest. Nevertheless, unsteady simulations require huge computational times and ressources, thus it is necessary to investigate other methods to find more appropriate approaches to model time-periodic cases. For time-periodic flows the time spectral method (TSM) presents an interesting alternative to the regular time marching solvers. The TSM is well-known for computation of compressible time-periodic flows, but applications to incompressible cases are limited. This paper presents an extension of the TSM to incompressible flows. While there have been previous implementations using pressure correction method with an explicit treatment of time coupling, here an implicit treatment is chosen. To increase efficiency and employ a more robust coupling of the individual time instances the momentum equations are solved in block-coupled fashion. The pressure correction term is solved segregatedly. To consider cases with dynamic mesh motion an arbitrary lagrange Euler (ALE) formulation is also used in the solver. The efficiency of the method is demonstrated using a basic 2D aerodynamic test case and the results are compared to traditional time-stepping approaches.
Energy stable, collocated high order schemes for incompressible flows on distorted grids
NASA Astrophysics Data System (ADS)
Reiss, Julius
2012-09-01
An energy preserving finite difference scheme for incompressible, constant density flows is presented. It is building on the idea of the skew-symmetric rewriting of the non-linear transport term. In contrast to former schemes collocated grids can be used, while exactly preserving the energy conservation and still avoiding the odd-even decoupling of the Laplacian. High order derivatives can be utilized. A formulation for curvilinear grids is discussed and strict skew-symmetry and perfect conservation is found for arbitrary transformations in two dimensions and quite general, but not fully general transformations in three dimensions.
A Multiblock Approach for Calculating Incompressible Fluid Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Sheng, Chunhua; Whitfield, David L.; Anderson, W. Kyle
1997-01-01
A multiblock approach is presented for solving two-dimensional incompressible turbulent flows on unstructured grids. The artificial compressibility form of the governing equations is solved by a vertex-centered, finite-volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work introduces a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements while not increasing the CPU time. Results presented in this work shows that the current multiblock algorithm requires 70% less memory than the single block algorithm.
NASA Technical Reports Server (NTRS)
Sohn, J. L.; Heinrich, J. C.
1990-01-01
The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.
Wave Number Selection for Incompressible Parallel Jet Flows Periodic in Space
NASA Technical Reports Server (NTRS)
Miles, Jeffrey Hilton
1997-01-01
The temporal instability of a spatially periodic parallel flow of an incompressible inviscid fluid for various jet velocity profiles is studied numerically using Floquet Analysis. The transition matrix at the end of a period is evaluated by direct numerical integration. For verification, a method based on approximating a continuous function by a series of step functions was used. Unstable solutions were found only over a limited range of wave numbers and have a band type structure. The results obtained are analogous to the behavior observed in systems exhibiting complexity at the edge of order and chaos.
NASA Astrophysics Data System (ADS)
Gartling, D. K.
1987-04-01
The theoretical and numerical background for the finite element computer program, NACHOS 2, is presented in detail. The NACHOS 2 code is designed for the two-dimensional analysis of viscous incompressible fluid flows, including the effects of heat transfer and/or other transport processes. A general description of the boundary value problems treated by the program is presented. The finite element formulations and the associated numerical methods used in the NACHOS 2 code are also outlined. Instructions for use of the program are documented in SAND-86-1817; examples of problems analyzed by the code are provided in SAND-86-1818.
Approximate indicial lift function for tapered, swept wings in incompressible flow
NASA Technical Reports Server (NTRS)
Queijo, M. J.; Wells, W. R.; Keskar, D. A.
1978-01-01
An approximate indicial lift function associated with circulation was developed for tapered, swept wings in incompressible flow. The function is derived by representing the wings with a simple vortex system. The results from the derived equations compare well with the limited available results from more rigorous and complex methods. The equations, as derived, are not very convenient for calculating the dynamic response of aircraft, parameter extraction, or for determining frequency-response curves for wings. Therefore, an expression is developed to convert the indicial response function to an exponential form which is more convenient for these purposes.
NASA Astrophysics Data System (ADS)
Chagelishvili, George; Hau, Jan-Niklas; Khujadze, George; Oberlack, Martin
2016-08-01
The linear dynamics of perturbations in smooth shear flows covers the transient exchange of energies between (1) the perturbations and the basic flow and (2) different perturbations modes. Canonically, the linear exchange of energies between the perturbations and the basic flow can be described in terms of the Orr and the lift-up mechanisms, correspondingly for two-dimensional (2D) and three-dimensional (3D) perturbations. In this paper the mechanical basis of the linear transient dynamics is introduced and analyzed for incompressible plane constant shear flows, where we consider the dynamics of virtual fluid particles in the framework of plane perturbations (i.e., perturbations with plane surfaces of constant phase) for the 2D and 3D case. It is shown that (1) the formation of a pressure perturbation field is the result of countermoving neighboring sets of incompressible fluid particles in the flow, (2) the keystone of the energy exchange mechanism between the basic flow and perturbations is the collision of fluid particles with the planes of constant pressure in accordance with the classical theory of elastic collision of particles with a rigid wall, making the pressure field the key player in this process, (3) the interplay of the collision process and the shear flow kinematics describes the transient growth of plane perturbations and captures the physics of the growth, and (4) the proposed mechanical picture allows us to reconstruct the linearized Euler equations in spectral space with a time-dependent shearwise wave number, the linearized Euler equations for Kelvin modes. This confirms the rigor of the presented analysis, which, moreover, yields a natural generalization of the proposed mechanical picture of the transient growth to the well-established linear phenomenon of vortex-wave-mode coupling.
NASA Technical Reports Server (NTRS)
Weinan, E.; Shu, Chi-Wang
1992-01-01
High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.
An Implicit Immersed Boundary Method for Low Reynolds Number Incompressible Flows
NASA Astrophysics Data System (ADS)
Park, Hyun Wook; Lee, Changhoon; Choi, Jung-Il
2013-11-01
We develop a new formulation of immersed boundary (IB) method based on direct forcing for incompressible viscous flows. The new algorithm for the present IB method is derived using a block LU decomposition and Taylor series expansion, and the direct forcing for imposing no-slip condition on the IB surface is calculated in an iterative procedure. We perform simulations of two-dimensional flows around a circular cylinder and three-dimensional flows over a sphere for low and moderate Reynolds numbers. The result shows that present method yield a better imposition of no-slip condition on IB surface for low Reynolds number with a fairly larger time step than other IB methods based on direct forcing. Supported by EDISON (2011-0029561) program of NRF.
NASA Astrophysics Data System (ADS)
Ha, Sanghyun; You, Donghyun
2015-11-01
Utility of the computational power of Graphics Processing Units (GPUs) is elaborated for solutions of both incompressible and compressible Navier-Stokes equations. A semi-implicit ADI finite-volume method for integration of the incompressible and compressible Navier-Stokes equations, which are discretized on a structured arbitrary grid, is parallelized for GPU computations using CUDA (Compute Unified Device Architecture). In the semi-implicit ADI finite-volume method, the nonlinear convection terms and the linear diffusion terms are integrated in time using a combination of an explicit scheme and an ADI scheme. Inversion of multiple tri-diagonal matrices is found to be the major challenge in GPU computations of the present method. Some of the algorithms for solving tri-diagonal matrices on GPUs are evaluated and optimized for GPU-acceleration of the present semi-implicit ADI computations of incompressible and compressible Navier-Stokes equations. Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning Grant NRF-2014R1A2A1A11049599.
Viscid-inviscid interaction associated with incompressible flow past wedges at high Reynolds number
NASA Technical Reports Server (NTRS)
Warpinski, N. R.; Chow, W. L.
1977-01-01
An analytical method is suggested for the study of the viscid inviscid interaction associated with incompressible flow past wedges with arbitrary angles. It is shown that the determination of the nearly constant pressure (base pressure) prevailing within the near wake is really the heart of the problem, and the pressure can only be established from these interactive considerations. The basic free streamline flow field is established through two discrete parameters which adequately describe the inviscid flow around the body and the wake. The viscous flow processes such as the boundary layer buildup, turbulent jet mixing, and recompression are individually analyzed and attached to the inviscid flow in the sense of the boundary layer concept. The interaction between the viscous and inviscid streams is properly displayed by the fact that the aforementioned discrete parameters needed for the inviscid flow are determined by the viscous flow condition at the point of reattachment. It is found that the reattachment point behaves as a saddle point singularity for the system of equations describing the recompressive viscous flow processes, and this behavior is exploited for the establishment of the overall flow field. Detailed results such as the base pressure, pressure distributions on the wedge, and the geometry of the wake are determined as functions of the wedge angle.
NASA Astrophysics Data System (ADS)
Gelfgat, Alexander Yu.
2016-02-01
A visualization of three-dimensional incompressible flows by divergence-free quasi-two-dimensional projections of the velocity field onto three coordinate planes is revisited. An alternative and more general way to compute the projections is proposed. The approach is based on the Chorin projection combined with a SIMPLE-like iteration. Compared to the previous methodology based on divergence-free Galerkin-Chebyshev bases, this technique, formulated in general curvilinear coordinates, is applicable to any flow region and allows for faster computations. To illustrate this visualization method, examples in Cartesian and spherical coordinates, as well as post-processing of experimental 3D-PTV data, are presented.
NASA Technical Reports Server (NTRS)
Zahm, A. F.
1979-01-01
The pressure distribution and resistance found by theory and experiment for simple quadrics fixed in an infinite uniform stream of practically incompressible fluid are calculated. The experimental values pertain to air and some liquids, especially water; the theoretical refer sometimes to perfect, again to viscid fluids. Formulas for the velocity at all points of the flow field are given. Pressure and pressure drag are discussed for a sphere, a round cylinder, the elliptic cylinder, the prolate and oblate spheroid, and the circular disk. The velocity and pressure in an oblique flow are examined.
NASA Astrophysics Data System (ADS)
Gelfgat, Alexander Yu.
2016-08-01
A visualization of three-dimensional incompressible flows by divergence-free quasi-two-dimensional projections of the velocity field onto three coordinate planes is revisited. An alternative and more general way to compute the projections is proposed. The approach is based on the Chorin projection combined with a SIMPLE-like iteration. Compared to the previous methodology based on divergence-free Galerkin-Chebyshev bases, this technique, formulated in general curvilinear coordinates, is applicable to any flow region and allows for faster computations. To illustrate this visualization method, examples in Cartesian and spherical coordinates, as well as post-processing of experimental 3D-PTV data, are presented.
Efficient simulation of incompressible viscous flow over multi-element airfoils
NASA Technical Reports Server (NTRS)
Rogers, Stuart E.; Wiltberger, N. Lyn; Kwak, Dochan
1993-01-01
The incompressible, viscous, turbulent flow over single and multi-element airfoils is numerically simulated in an efficient manner by solving the incompressible Navier-Stokes equations. The solution algorithm employs the method of pseudo compressibility and utilizes an upwind differencing scheme for the convective fluxes, and an implicit line-relaxation scheme. The motivation for this work includes interest in studying high-lift take-off and landing configurations of various aircraft. In particular, accurate computation of lift and drag at various angles of attack up to stall is desired. Two different turbulence models are tested in computing the flow over an NACA 4412 airfoil; an accurate prediction of stall is obtained. The approach used for multi-element airfoils involves the use of multiple zones of structured grids fitted to each element. Two different approaches are compared; a patched system of grids, and an overlaid Chimera system of grids. Computational results are presented for two-element, three-element, and four-element airfoil configurations. Excellent agreement with experimental surface pressure coefficients is seen. The code converges in less than 200 iterations, requiring on the order of one minute of CPU time on a CRAY YMP per element in the airfoil configuration.
Efficient simulation of incompressible viscous flow over single and multi-element airfoils
NASA Technical Reports Server (NTRS)
Rogers, Stuart E.; Wiltberger, N. L.; Kwak, Dochan
1992-01-01
Incompressible viscous turbulent flows over single- and multiple-element airfoils are numerically simulated in an efficient manner by solving the incompressible Navier-Stokes equations. The solution algorithm uses the method of pseudocompressibility with an upwind-differencing scheme for the convective fluxes and an implicit line-relaxation scheme to study high-lift take-off and landing configurations and to compute lift and drag at various angles of attack up to stall. Two different turbulence models are tested in computing the flow over an NACA 4412 airfoil. The approach used for multiple-element airfoils involves the use of multiple zones of structured grids fitted to each element. Two different approaches are compared: a patched system of grids and an overlaid Chimera system of grids. Computational results are presented for two-element, three-element, and four-element airfoil configurations. Excellent agreement with experimental surface-pressure coefficients is seen. The code converges in less than 200 iterations, requiring on the order of one minute of CPU time on a CRAY YMP per element in the airfoil configuration.
Efficient simulation of incompressible viscous flow over multi-element airfoils
NASA Technical Reports Server (NTRS)
Rogers, Stuart E.; Wiltberger, N. Lyn; Kwak, Dochan
1992-01-01
The incompressible, viscous, turbulent flow over single and multi-element airfoils is numerically simulated in an efficient manner by solving the incompressible Navier-Stokes equations. The computer code uses the method of pseudo-compressibility with an upwind-differencing scheme for the convective fluxes and an implicit line-relaxation solution algorithm. The motivation for this work includes interest in studying the high-lift take-off and landing configurations of various aircraft. In particular, accurate computation of lift and drag at various angles of attack, up to stall, is desired. Two different turbulence models are tested in computing the flow over an NACA 4412 airfoil; an accurate prediction of stall is obtained. The approach used for multi-element airfoils involves the use of multiple zones of structured grids fitted to each element. Two different approaches are compared: a patched system of grids, and an overlaid Chimera system of grids. Computational results are presented for two-element, three-element, and four-element airfoil configurations. Excellent agreement with experimental surface pressure coefficients is seen. The code converges in less than 200 iterations, requiring on the order of one minute of CPU time (on a CRAY YMP) per element in the airfoil configuration.
Incompressible SPH Model for Simulating Violent Free-Surface Fluid Flows
NASA Astrophysics Data System (ADS)
Staroszczyk, Ryszard
2014-06-01
In this paper the problem of transient gravitational wave propagation in a viscous incompressible fluid is considered, with a focus on flows with fast-moving free surfaces. The governing equations of the problem are solved by the smoothed particle hydrodynamics method (SPH). In order to impose the incompressibility constraint on the fluid motion, the so-called projection method is applied in which the discrete SPH equations are integrated in time by using a fractional-step technique. Numerical performance of the proposed model has been assessed by comparing its results with experimental data and with results obtained by a standard (weakly compressible) version of the SPH approach. For this purpose, a plane dam-break flow problem is simulated, in order to investigate the formation and propagation of a wave generated by a sudden collapse of a water column initially contained in a rectangular tank, as well as the impact of such a wave on a rigid vertical wall. The results of simulations show the evolution of the free surface of water, the variation of velocity and pressure fields in the fluid, and the time history of pressures exerted by an impacting wave on a wall.
Large-scale computation of incompressible viscous flow by least-squares finite element method
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Lin, T. L.; Povinelli, Louis A.
1993-01-01
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of 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. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.
Gradient-augmented hybrid interface capturing method for incompressible two-phase flow
NASA Astrophysics Data System (ADS)
Zheng, Fu; Shi-Yu, Wu; Kai-Xin, Liu
2016-06-01
Motivated by inconveniences of present hybrid methods, a gradient-augmented hybrid interface capturing method (GAHM) is presented for incompressible two-phase flow. A front tracking method (FTM) is used as the skeleton of the GAHM for low mass loss and resources. Smooth eulerian level set values are calculated from the FTM interface, and are used for a local interface reconstruction. The reconstruction avoids marker particle redistribution and enables an automatic treatment of interfacial topology change. The cubic Hermit interpolation is employed in all steps of the GAHM to capture subgrid structures within a single spacial cell. The performance of the GAHM is carefully evaluated in a benchmark test. Results show significant improvements of mass loss, clear subgrid structures, highly accurate derivatives (normals and curvatures) and low cost. The GAHM is further coupled with an incompressible multiphase flow solver, Super CE/SE, for more complex and practical applications. The updated solver is evaluated through comparison with an early droplet research. Project supported by the National Natural Science Foundation of China (Grant Nos. 10972010, 11028206, 11371069, 11372052, 11402029, and 11472060), the Science and Technology Development Foundation of China Academy of Engineering Physics (CAEP), China (Grant No. 2014B0201030), and the Defense Industrial Technology Development Program of China (Grant No. B1520132012).
Identification of whistling ability of a single hole orifice from an incompressible flow simulation
Lacombe, Romain; Moussou, Pierre
2012-07-01
Pure tone noise from orifices in pipe result from vortex shedding with lock-in. Acoustic amplification at the orifice is coupled to resonant condition to create self-sustained oscillations. One key feature of this phenomenon is hence the ability of an orifice to amplify acoustic waves in a given range of frequencies. Here a numerical investigation of the linear response of an orifice is undertaken, with the support of experimental data for validation. The study deals with a sharp edge orifice. Its diameter equals to 0.015 m and its thickness to 0.005 m. The pipe diameter is 0.030 m. An air flow with a Mach number 0.026 and a Reynolds number 18000 in the main pipe is present. At such a low Mach number; the fluid behavior can reasonably be described as locally incompressible. The incompressible Unsteady Reynolds Averaged Navier-Stokes (URANS) equations are solved with the help of a finite volume fluid mechanics software. The orifice is submitted to an average flow velocity, with superimposed small harmonic perturbations. The harmonic response of the orifice is the difference between the upstream and downstream pressures, and a straightforward calculation brings out the acoustic impedance of the orifice. Comparison with experiments shows that the main physical features of the whistling phenomenon are reasonably reproduced. (authors)
An adaptive level set approach for incompressible two-phase flows
Sussman, M.; Almgren, A.S.; Bell, J.B.
1997-04-01
In Sussman, Smereka and Osher, a numerical method using the level set approach was formulated for solving incompressible two-phase flow with surface tension. In the level set approach, the interface is represented as the zero level set of a smooth function; this has the effect of replacing the advection of density, which has steep gradients at the interface, with the advection of the level set function, which is smooth. In addition, the interface can merge or break up with no special treatment. The authors maintain the level set function as the signed distance from the interface in order to robustly compute flows with high density ratios and stiff surface tension effects. In this work, they couple the level set scheme to an adaptive projection method for the incompressible Navier-Stokes equations, in order to achieve higher resolution of the interface with a minimum of additional expense. They present two-dimensional axisymmetric and fully three-dimensional results of air bubble and water drop computations.
Fischer, P.F.; Miller, N.I.; Tufo, H.M.
1998-10-29
As the sound speed is infinite for incompressible flows, computation of the pressure constitutes the stiffest component in the time advancement of unsteady simulations. For complex geometries, efficient solution is dependent upon the availability of fast solvers for sparse linear systems. In this paper we develop a Schwarz preconditioner for the spectral element method using overlapping subdomains for the pressure. These local subdomain problems are derived from tensor products of one-dimensional finite element discretizations and admit use of fast diagonalization methods based upon matrix-matrix products. In addition, we use a coarse grid projection operator whose solution is computed via a fast parallel direct solver. The combination of overlapping Schwarz preconditioning and fast coarse grid solver provides as much as a fourfold reduction in simulation time over previously employed methods based upon deflation for parallel solution of multi-million grid point flow problems.
Effect of shaft rotation on the incompressible flow in a labyrinth seal
NASA Technical Reports Server (NTRS)
Demko, J. A.; Morrison, G. L.; Rhode, D. L.
1987-01-01
The incompressible flow in a labyrinth seal at low leakage rates was computationally and experimentally investigated over a wide range of seal rotation rates. QUICK differencing was employed in the finite difference code to reduce the effects of false diffusion. The use of measured inlet boundary conditions for the axial and swirl velocity components and for the turbulent kinetic energy resulted in good agreement between velocity predictions and hot-film measurements. It was found that when the rotation rate is increased beyond a certain point, a second recirculation zone forms inside the seal cavity, altering the flow field in the cavity and resulting in a substantial increase in the pressure drop across it.
Instability of plane-parallel flow of incompressible liquid over a saturated porous medium
NASA Astrophysics Data System (ADS)
Lyubimova, T. P.; Lyubimov, D. V.; Baydina, D. T.; Kolchanova, E. A.; Tsiberkin, K. B.
2016-07-01
The linear stability of plane-parallel flow of an incompressible viscous fluid over a saturated porous layer is studied to model the instability of water flow in a river over aquatic plants. The saturated porous layer is bounded from below by a rigid plate and the pure fluid layer has a free, undeformable upper boundary. A small inclination of the layers is imposed to simulate the riverbed slope. The layers are inclined at a small angle to the horizon. The problem is studied within two models: the Brinkman model with the boundary conditions by Ochoa-Tapia and Whitaker at the interface, and the Darcy-Forchheimer model with the conditions by Beavers and Joseph. The neutral curves and critical Reynolds numbers are calculated for various porous layer permeabilities and relative thicknesses of the porous layer. The results obtained within the two models are compared and analyzed.
Instability of plane-parallel flow of incompressible liquid over a saturated porous medium.
Lyubimova, T P; Lyubimov, D V; Baydina, D T; Kolchanova, E A; Tsiberkin, K B
2016-07-01
The linear stability of plane-parallel flow of an incompressible viscous fluid over a saturated porous layer is studied to model the instability of water flow in a river over aquatic plants. The saturated porous layer is bounded from below by a rigid plate and the pure fluid layer has a free, undeformable upper boundary. A small inclination of the layers is imposed to simulate the riverbed slope. The layers are inclined at a small angle to the horizon. The problem is studied within two models: the Brinkman model with the boundary conditions by Ochoa-Tapia and Whitaker at the interface, and the Darcy-Forchheimer model with the conditions by Beavers and Joseph. The neutral curves and critical Reynolds numbers are calculated for various porous layer permeabilities and relative thicknesses of the porous layer. The results obtained within the two models are compared and analyzed. PMID:27575214
NASA Technical Reports Server (NTRS)
Chen, Y. S.
1986-01-01
In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.
A High Order Discontinuous Galerkin Method for 2D Incompressible Flows
NASA Technical Reports Server (NTRS)
Liu, Jia-Guo; Shu, Chi-Wang
1999-01-01
In this paper we introduce a high order discontinuous Galerkin method for two dimensional incompressible flow in vorticity streamfunction formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method The streamfunction is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability The method is suitable for inviscid or high Reynolds number flows. Optimal error estimates are proven and verified by numerical experiments.
Parallel solution of high-order numerical schemes for solving incompressible flows
NASA Technical Reports Server (NTRS)
Milner, Edward J.; Lin, Avi; Liou, May-Fun; Blech, Richard A.
1993-01-01
A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.
A Hybrid Nodal Method for Time-Dependent Incompressible Flow in Two-Dimensional Arbitrary Geometries
Toreja, A J; Uddin, R
2002-10-21
A hybrid nodal-integral/finite-analytic method (NI-FAM) is developed for time-dependent, incompressible flow in two-dimensional arbitrary geometries. In this hybrid approach, the computational domain is divided into parallelepiped and wedge-shaped space-time nodes (cells). The conventional nodal integral method (NIM) is applied to the interfaces between adjacent parallelepiped nodes (cells), while a finite analytic approach is applied to the interfaces between parallelepiped and wedge-shaped nodes (cells). In this paper, the hybrid method is formally developed and an application of the NI-FAM to fluid flow in an enclosed cavity is presented. Results are compared with those obtained using a commercial computational fluid dynamics code.
Flow accelerated organic coating degradation
NASA Astrophysics Data System (ADS)
Zhou, Qixin
Applying organic coatings is a common and the most cost effective way to protect metallic objects and structures from corrosion. Water entry into coating-metal interface is usually the main cause for the deterioration of organic coatings, which leads to coating delamination and underfilm corrosion. Recently, flowing fluids over sample surface have received attention due to their capability to accelerate material degradation. A plethora of works has focused on the flow induced metal corrosion, while few studies have investigated the flow accelerated organic coating degradation. Flowing fluids above coating surface affect corrosion by enhancing the water transport and abrading the surface due to fluid shear. Hence, it is of great importance to understand the influence of flowing fluids on the degradation of corrosion protective organic coatings. In this study, a pigmented marine coating and several clear coatings were exposed to the laminar flow and stationary immersion. The laminar flow was pressure driven and confined in a flow channel. A 3.5 wt% sodium chloride solution and pure water was employed as the working fluid with a variety of flow rates. The corrosion protective properties of organic coatings were monitored inline by Electrochemical Impedance Spectroscopy (EIS) measurement. Equivalent circuit models were employed to interpret the EIS spectra. The time evolution of coating resistance and capacitance obtained from the model was studied to demonstrate the coating degradation. Thickness, gloss, and other topography characterizations were conducted to facilitate the assessment of the corrosion. The working fluids were characterized by Fourier Transform Infrared Spectrometer (FTIR) and conductivity measurement. The influence of flow rate, fluid shear, fluid composition, and other effects in the coating degradation were investigated. We conclude that flowing fluid on the coating surface accelerates the transport of water, oxygen, and ions into the coating, as
NASA Astrophysics Data System (ADS)
Matsumoto, Yuko; Ueno, Kazuyuki
2006-11-01
A new numerical method to calculate an incompressible flow, a dipole method, is proposed. In the dipole method, a flow field is represented by superposition of many dipolar vortices, and these dipolar vortices are replaced ``dipole elements.'' The dipole elements move in fluid. Each dipole element is characterized by two variables, dipole moment and core radius. The dipole moment is a vector quantity whose direction is the same as the axis of the dipolar vortex. The core radius is an effective radius of rotational flow region of the dipolar vortex. These variables, changed with time, are determined by the momentum conservation law where the flow around the dipolar vortex is assumed to be irrotational. This dipole element has a self-induced velocity. Time evolutions of a dipolar vortex in two cases of background flows are simulated, the first case is a strain flow, and the second one is a rotational flow of the Rankin's vortex. The results of the dipole method are compared to numerical simulations using the vortex method with the same initial condition.
NASA Astrophysics Data System (ADS)
Yang, L. M.; Shu, C.; Wang, Y.; Sun, Y.
2016-08-01
The sphere function-based gas kinetic scheme (GKS), which was presented by Shu and his coworkers [23] for simulation of inviscid compressible flows, is extended to simulate 3D viscous incompressible and compressible flows in this work. Firstly, we use certain discrete points to represent the spherical surface in the phase velocity space. Then, integrals along the spherical surface for conservation forms of moments, which are needed to recover 3D Navier-Stokes equations, are approximated by integral quadrature. The basic requirement is that these conservation forms of moments can be exactly satisfied by weighted summation of distribution functions at discrete points. It was found that the integral quadrature by eight discrete points on the spherical surface, which forms the D3Q8 discrete velocity model, can exactly match the integral. In this way, the conservative variables and numerical fluxes can be computed by weighted summation of distribution functions at eight discrete points. That is, the application of complicated formulations resultant from integrals can be replaced by a simple solution process. Several numerical examples including laminar flat plate boundary layer, 3D lid-driven cavity flow, steady flow through a 90° bending square duct, transonic flow around DPW-W1 wing and supersonic flow around NACA0012 airfoil are chosen to validate the proposed scheme. Numerical results demonstrate that the present scheme can provide reasonable numerical results for 3D viscous flows.
New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows
Li, Zhilin; Lai, Ming-Chih
2012-01-01
In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension, which should be determined in such a way that the surface divergence of the velocity is zero along the interface. Thus, the area enclosed by the interface and the total length of the interface should be conserved during the evolution process. Because of the nonlinear and coupling nature of the problem, direct discretization by applying the immersed boundary or immersed interface method yields complex nonlinear systems to be solved. In our new methods, we treat the unknown surface tension as an augmented variable so that the augmented IIM can be applied. Since finding the unknown surface tension is essentially an inverse problem that is sensitive to perturbations, our regularization strategy is to introduce a controlled tangential force along the interface, which leads to a least squares problem. For Stokes equations, the forward solver at one time level involves solving three Poisson equations with an interface. For Navier-Stokes equations, we propose a modified projection method that can enforce the pressure jump condition corresponding directly to the unknown surface tension. Several numerical experiments show good agreement with other results in the literature and reveal some interesting phenomena. PMID:23795308
A new approach to wall modeling in LES of incompressible flow via function enrichment
NASA Astrophysics Data System (ADS)
Krank, Benjamin; Wall, Wolfgang A.
2016-07-01
A novel approach to wall modeling for the incompressible Navier-Stokes equations including flows of moderate and large Reynolds numbers is presented. The basic idea is that a problem-tailored function space allows prediction of turbulent boundary layer gradients with very coarse meshes. The proposed function space consists of a standard polynomial function space plus an enrichment, which is constructed using Spalding's law-of-the-wall. The enrichment function is not enforced but "allowed" in a consistent way and the overall methodology is much more general and also enables other enrichment functions. The proposed method is closely related to detached-eddy simulation as near-wall turbulence is modeled statistically and large eddies are resolved in the bulk flow. Interpreted in terms of a three-scale separation within the variational multiscale method, the standard scale resolves large eddies and the enrichment scale represents boundary layer turbulence in an averaged sense. The potential of the scheme is shown applying it to turbulent channel flow of friction Reynolds numbers from Reτ = 590 and up to 5,000, flow over periodic constrictions at the Reynolds numbers ReH = 10 , 595 and 19,000 as well as backward-facing step flow at Reh = 5 , 000, all with extremely coarse meshes. Excellent agreement with experimental and DNS data is observed with the first grid point located at up to y1+ = 500 and especially under adverse pressure gradients as well as in separated flows.
Instabilities of time-periodic, incompressible, inviscid flow in ellipsoidal domains.
NASA Astrophysics Data System (ADS)
Biello, Joseph A.; Saldanha, Kenneth I.; Lebovitz, Norman R.
1999-11-01
We consider the linear stability of exact, temporally periodic solutions of the Euler equations of incompressible, inviscid flow in an ellipsoidal domain. The problem of linear stability is reduced, without approximation, to a hierarchy of finite-dimensional Floquet problems governing fluid-dynamical perturbations of differing spatial scales and symmetries. We study two of these Floquet problems in detail, emphasizing parameter regimes of special physical significance. One of these regimes includes periodic flows differing only slightly from steady flows. Another includes long-period flows representing the nonlinear outcome of an instability of steady flows. In both cases much of the parameter space corresponds to instability, excepting a region adjacent to the spherical configuration. In the second case, even if the ellipsoid departs only moderately from a sphere, there are filamentary regions of instability in the parameter space. We relate this and other features of our results to properties of reversible and Hamiltonian systems, and compare our results with related studies of periodic flows.
NASA Technical Reports Server (NTRS)
Hobson, G. V.; Lakshminarayana, B.
1990-01-01
A new method is presented for the solution of incompressible flow in generalized coordinates. This method is based on the substitution of the pressure weighted form of the momentum equations into the continuity equation. The algorithm is rigorously derived and a Fourier analysis is used to assess its suitability to act as an error smoother. Linear stability analysis results indicate that the performance of the new pressure substitution method (PSM) and the pressure correction method (PCM) is about the same at low Reynolds numbers, with no significant pressure gradient. At high Reynolds numbers the PSM shows much faster convergence. Likewise prediction of various flows indicate that the PSM has better accuracy for high Reynolds number flows with significant pressure gradients. Since most practical aerodynamic flows have significant pressure gradients, the PSM seems to be attractive for such flows. Solutions for both laminar and turbulent flow are compared with the experimental data. A two-equation low Reynolds number turbulence model is used to resolve the turbulent flowfield.
NASA Technical Reports Server (NTRS)
Lawless, Patrick B.; Fleeter, Sanford
1991-01-01
A mathematical model is developed to analyze the suppression of rotating stall in an incompressible flow centrifugal compressor with a vaned diffuser, thereby addressing the important need for centrifugal compressor rotating stall and surge control. In this model, the precursor to to instability is a weak rotating potential velocity perturbation in the inlet flow field that eventually develops into a finite disturbance. To suppress the growth of this potential disturbance, a rotating control vortical velocity disturbance is introduced into the impeller inlet flow. The effectiveness of this control is analyzed by matching the perturbation pressure in the compressor inlet and exit flow fields with a model for the unsteady behavior of the compressor. To demonstrate instability control, this model is then used to predict the control effectiveness for centrifugal compressor geometries based on a low speed research centrifugal compressor. These results indicate that reductions of 10 to 15 percent in the mean inlet flow coefficient at instability are possible with control waveforms of half the magnitude of the total disturbance at the inlet.
MHD Couette flow of viscous incompressible fluid with Hall current and suction
NASA Astrophysics Data System (ADS)
Parvin, Afroja; Dola, Tanni Alam; Alam, Md. Mahmud
2016-07-01
An electrically conducting viscous incompressible fluid bounded by two parallel non-conducting plates has been investigated in the presence of Hall current. The fluid motion is uniform at the upper plate and the uniform magnetic field is applied perpendicular to the plate. The lower plate is stationary while upper plate moves with a constant velocity. The governing equations have been non-dimensionalzed by using usual transformations. The obtained governing non-linear coupled partial differential equations have been solved by using implicit finite difference technique. The numerical solutions are obtained for momentum and energy equations. The influence of various interesting parameters on the flow has been analyzed and discussed through graph in details. The values of Nusselt number and Skin-Friction for different physical parameters are also elucidated in the form of graph.
Effects of mistuning on bending-torsion flutter and response of a cascade in incompressible flow
Kaza, K.R.V.; Kielb, R.E.
1981-01-01
An investigation of the effects of blade mistuning on the aeroelastic stability and response of a cascade in incompressible flow is reported. The aerodynamic, inertial, and structural coupling between the bending and torsional motions of each blade and the aerodynamic coupling between the blades are included in the formulation. A digital computer program was developed to conduct parametric studies. Results indicate that the mistuning has a beneficial effect on the coupled bending-torsion and uncoupled torsion flutter. The effect of mistuning on forced response, however, may be either beneficial or adverse, depending on the engine order of the forcing function. Additionally, the results illustrate that it may be feasible to utilize mistuning as a passive control to increase flutter speed while maintaining forced response at an acceptable level.
A vortex point method for calculating inviscid incompressible flows around rotary wings
NASA Astrophysics Data System (ADS)
Canatloube, B.; Huberson, S.
1985-05-01
An integral method is presented for calculating incompressible inviscid unsteady flow around thin bodies in arbitrary motion, i.e., rotor blades in motion with respect to one another. Because an integral method is used, discretization is limited to the solid boundaries and the vortices. Boundary conditions are treated in terms of equation for the slipstream on the walls, the vorticity vector, a volume integral for the vorticity and a first-order Fredholm integral. The Helmholtz equation governs the evolution of vorticity, which forms a sheet of doublets. The pressure jumps on the blades are covered by the unsteady Bernoulli equation. Applications of the method to helicopter rotors, medium- and high-aspect ratio propellers and low-aspect ratio nautical propellers are demonstrated.
Simulation of three-dimensional incompressible flows with a vortex-in-cell method
NASA Technical Reports Server (NTRS)
Couet, B.; Buneman, O.; Leonard, A.
1981-01-01
A new method for the numerical simulation of three-dimensional incompressible flows is described. The vortex-in-cell (VIC) method presented traces the motion of the vortex filaments in the velocity field which these filaments create. The velocity field is not calculated directly by the Biot-Savart law of interaction but by creating a mesh-record of the vorticity field, then integrating a Poisson's equation via the fast Fourier transform to generate a mesh-record of the velocity field. The computed scales of motion are assumed to be essentially inviscid. Viscous of subgrid-scale effects are incorporated into a filtering procedure in wave vector space. Results of tracing a periodic array of single vortex rings are compared with a Green's function calculation. The agreement is very good.
Multiscale numerical methods for passive advection-diffusion in incompressible turbulent flow fields
NASA Astrophysics Data System (ADS)
Lee, Yoonsang; Engquist, Bjorn
2016-07-01
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the velocity fields in the Fourier space, which are similar to the decomposition in large eddy simulations. It also uses a hierarchy of local domains with different resolutions as in multigrid methods. The effective diffusivity from finer scale is used for the next coarser level computation and this process is repeated up to the coarsest scale of interest. The grids are only in local domains whose sizes decrease depending on the resolution level so that the overall computational complexity increases linearly as the number of different resolution grids increases. The method captures interactions between finer and coarser scales but has to sacrifice some of interactions between different scales. The proposed method is numerically tested with 2D examples including a successful approximation to a continuous spectrum flow.
The capturing of free surfaces in incompressible multi-fluid flows
NASA Astrophysics Data System (ADS)
Pan, Dartzi; Chang, Chih-Hao
2000-05-01
By treating it as a contact discontinuity in the density field, a free surface between two immiscible fluids can be automatically captured by the enforcement of conservation laws. A surface-capturing method of this kind requires no special tracking or fitting treatment for the free surface, thereby offering the advantage of algorithm simplicity over the surface-tracking or the surface-fitting method. A surface-capturing method based on a new multi-fluid incompressible Navier-Stokes formulation is developed. It is applied to a variety of free-surface flows, including the Rayleigh-Taylor instability problem, the ship waves around a Wigley hull and a model bubble-rising problem to demonstrate the validity and versatility of the present method. Copyright
Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method
NASA Technical Reports Server (NTRS)
Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.
1997-01-01
A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.
A fast pressure-correction method for incompressible two-fluid flows
NASA Astrophysics Data System (ADS)
Dodd, Michael S.; Ferrante, Antonino
2014-09-01
We have developed a new pressure-correction method for simulating incompressible two-fluid flows with large density and viscosity ratios. The method's main advantage is that the variable coefficient Poisson equation that arises in solving the incompressible Navier-Stokes equations for two-fluid flows is reduced to a constant coefficient equation, which can be solved with an FFT-based, fast Poisson solver. This reduction is achieved by splitting the variable density pressure gradient term in the governing equations. The validity of this splitting is demonstrated from our numerical tests, and it is explained from a physical viewpoint. In this paper, the new pressure-correction method is coupled with a mass-conserving volume-of-fluid method to capture the motion of the interface between the two fluids but, in general, it could be coupled with other interface advection methods such as level-set, phase-field, or front-tracking. First, we verified the new pressure-correction method using the capillary wave test-case up to density and viscosity ratios of 10,000. Then, we validated the method by simulating the motion of a falling water droplet in air and comparing the droplet terminal velocity with an experimental value. Next, the method is shown to be second-order accurate in space and time independent of the VoF method, and it conserves mass, momentum, and kinetic energy in the inviscid limit. Also, we show that for solving the two-fluid Navier-Stokes equations, the method is 10-40 times faster than the standard pressure-correction method, which uses multigrid to solve the variable coefficient Poisson equation. Finally, we show that the method is capable of performing fully-resolved direct numerical simulation (DNS) of droplet-laden isotropic turbulence with thousands of droplets using a computational mesh of 10243 points.
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.
1991-01-01
Downstream boundary conditions equivalent to the homogeneous form of the natural boundary conditions associated with the velocity-pressure formulation of the Navier-Stokes equations are derived for the vorticity-stream function formulation of two-dimensional incompressible flows. Of particular interest are the zero normal and shear stress conditions at a downstream boundary.
A spectral-element discontinuous Galerkin lattice Boltzmann method for incompressible flows.
Min, M.; Lee, T.; Mathematics and Computer Science; City Univ. of New York
2011-01-01
We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving nearly incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discontinuous Galerkin discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based on Gauss-Lobatto-Legendre grids. Our scheme is cost-effective with a fully diagonal mass matrix, advancing time integration with the fourth-order Runge-Kutta method. We present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous Galerkin approach. We show convergence studies for Couette flows and demonstrate two benchmark cases with lid-driven cavity flows for Re = 400-5000 and flows around an impulsively started cylinder for Re = 550-9500. Computational results are compared with those of other theoretical and computational work that used a multigrid method, a vortex method, and a spectral element model.
NASA Astrophysics Data System (ADS)
Crivellini, Andrea; D'Alessandro, Valerio; Bassi, Francesco
2013-05-01
In this paper the artificial compressibility flux Discontinuous Galerkin (DG) method for the solution of the incompressible Navier-Stokes equations has been extended to deal with the Reynolds-Averaged Navier-Stokes (RANS) equations coupled with the Spalart-Allmaras (SA) turbulence model. DG implementations of the RANS and SA equations for compressible flows have already been reported in the literature, including the description of limiting or stabilization techniques adopted in order to prevent the turbulent viscosity ν˜ from becoming negative. In this paper we introduce an SA model implementation that deals with negative ν˜ values by modifying the source and diffusion terms in the SA model equation only when the working variable or one of the model closure functions become negative. This results in an efficient high-order implementation where either stabilization terms or even additional equations are avoided. We remark that the proposed implementation is not DG specific and it is well suited for any numerical discretization of the RANS-SA governing equations. The reliability, robustness and accuracy of the proposed implementation have been assessed by computing several high Reynolds number turbulent test cases: the flow over a flat plate (Re=107), the flow past a backward-facing step (Re=37400) and the flow around a NACA 0012 airfoil at different angles of attack (α=0°, 10°, 15°) and Reynolds numbers (Re=2.88×106,6×106).
Parallel FEM LES with one-equation subgrid-scale model for incompressible flows
NASA Astrophysics Data System (ADS)
Li, Xian-Xiang; Liu, Chun-Ho; Leung, Dennis Y. C.
2010-01-01
This article develops a parallel large-eddy simulation (LES) with a one-equation subgrid-scale (SGS) model based on the Galerkin finite element method and three-dimensional (3D) brick elements. The governing filtered Navier-Stokes equations were solved by a second-order accurate fractional-step method, which decomposed the implicit velocity-pressure coupling in incompressible flow and segregated the solution to the advection and diffusion terms. The transport equation for the SGS turbulent kinetic energy was solved to calculate the SGS processes. This FEM LES model was applied to study the turbulence of the benchmark open channel flow at a Reynolds number Reτ = 180 (based on the friction velocity and channel height) using different model constants and grid resolutions. By comparing the turbulence statistics calculated by the current model with those obtained from direct numerical simulation (DNS) and experiments in literature, an optimum set of model constants for the current FEM LES model was established. The budgets of turbulent kinetic energy and vertical Reynolds stress were then analysed for the open channel flow. Finally, the flow structures were visualised to further reveal some important characteristics. It was demonstrated that the current model with the optimum model constants can predict well the organised structure near the wall and free surface, and can be further applied to other fundamental and engineering applications.
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
NASA Astrophysics Data System (ADS)
English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald
2013-12-01
We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.
A monolithic FEM-multigrid solver for non-isothermal incompressible flow on general meshes
NASA Astrophysics Data System (ADS)
Damanik, H.; Hron, J.; Ouazzi, A.; Turek, S.
2009-06-01
We present special numerical simulation methods for non-isothermal incompressible viscous fluids which are based on LBB-stable FEM discretization techniques together with monolithic multigrid solvers. For time discretization, we apply the fully implicit Crank-Nicolson scheme of 2nd order accuracy while we utilize the high order Q2P1 finite element pair for discretization in space which can be applied on general meshes together with local grid refinement strategies including hanging nodes. To treat the nonlinearities in each time step as well as for direct steady approaches, the resulting discrete systems are solved via a Newton method based on divided differences to calculate explicitly the Jacobian matrices. In each nonlinear step, the coupled linear subproblems are solved simultaneously for all quantities by means of a monolithic multigrid method with local multilevel pressure Schur complement smoothers of Vanka type. For validation and evaluation of the presented methodology, we perform the MIT benchmark 2001 [M.A. Christon, P.M. Gresho, S.B. Sutton, Computational predictability of natural convection flows in enclosures, in: First MIT Conference on Computational Fluid and Solid Mechanics, vol. 40, Elsevier, 2001, pp. 1465-1468] of natural convection flow in enclosures to compare our results with respect to accuracy and efficiency. Additionally, we simulate problems with temperature and shear dependent viscosity and analyze the effect of an additional dissipation term inside the energy equation. Moreover, we discuss how these FEM-multigrid techniques can be extended to monolithic approaches for viscoelastic flow problems.
An extended pressure finite element space for two-phase incompressible flows with surface tension
NASA Astrophysics Data System (ADS)
Groß, Sven; Reusken, Arnold
2007-05-01
We consider a standard model for incompressible two-phase flows in which a localized force at the interface describes the effect of surface tension. If a level set (or VOF) method is applied then the interface, which is implicitly given by the zero level of the level set function, is in general not aligned with the triangulation that is used in the discretization of the flow problem. This non-alignment causes severe difficulties w.r.t. the discretization of the localized surface tension force and the discretization of the flow variables. In cases with large surface tension forces the pressure has a large jump across the interface. In standard finite element spaces, due to the non-alignment, the functions are continuous across the interface and thus not appropriate for the approximation of the discontinuous pressure. In many simulations these effects cause large oscillations of the velocity close to the interface, so-called spurious velocities. In this paper, for a simplified model problem, we give an analysis that explains why known (standard) methods for discretization of the localized force term and for discretization of the pressure variable often yield large spurious velocities. In the paper [S. Groß, A. Reusken, Finite element discretization error analysis of a surface tension force in two-phase incompressible flows, Preprint 262, IGPM, RWTH Aachen, SIAM J. Numer. Anal. (accepted for publication)], we introduce a new and accurate method for approximation of the surface tension force. In the present paper, we use the extended finite element space (XFEM), presented in [N. Moes, J. Dolbow, T. Belytschko, A finite element method for crack growth without remeshing, Int. J. Numer. Meth. Eng. 46 (1999) 131-150; T. Belytschko, N. Moes, S. Usui, C. Parimi, Arbitrary discontinuities in finite elements, Int. J. Numer. Meth. Eng. 50 (2001) 993-1013], for the discretization of the pressure. We show that the size of spurious velocities is reduced substantially, provided we
NASA Technical Reports Server (NTRS)
Kuehn, Donald M.
1980-01-01
The turbulent, incompressible reattaching flow over a rearward-facing step has been studied by many researchers over the years. One of the principal quantities determined in these experiments has been the distance from the step to the point (or region) where the separated shear layer reattaches to the surface (x(r)). The values for x(r)/h, where h is the step height, have covered a wider range than can reasonably be attributed to experimental technique or inaccuracy. Often the reason for a largely different value of x(r)/h can be attributed to an incompletely developed turbulent layer, or a transitional or laminar boundary layer. However, for the majority of experiments where the boundary layer is believed to be fully developed and turbulent, x(r)/h still varies several step heights; generally, 5 1/2 approximately < x(r)/h approximately < 7 1/2. This observed variation has usually been attributed to such variables as l/h (step length to height, h/delta (step height to initial boundary-layer thickness), R(e)(theta)), or the experimental technique for determining reattachment location. However, there are so many different combinations of variables in the previous experiments that it was not possible to sort out the effects of particular conditions on the location of reattachment. In the present experiment velocity profiles have been measured in and around the region of separated flow. Results show a large influence of adverse pressure gradient on the reattaching flow over a rearward-facing step that has not been reported previously. Further, the many previous experiments for fully developed, turbulent flow in parallel-walled channels have shown a range of reattachment location that has not been explained by differences in initial flow conditions. Although these initial flow conditions might contribute to the observed variation of reattachment location, it appears that the pressure gradient effect can explain most of that variation.
Cochran, R.J.
1992-01-01
A study of the finite element method applied to two-dimensional incompressible fluid flow analysis with heat transfer is performed using a mixed Galerkin finite element method with the primitive variable form of the model equations. Four biquadratic, quadrilateral elements are compared in this study--the serendipity biquadratic element with bilinear continuous pressure interpolation (Q2(8)-Q1) and the Lagrangian biquadratic element with bilinear continuous pressure interpolation (Q2-Q1) of the Taylor-Hood form. A modified form of the Q2-Q1 element is also studied. The pressure interpolation is augmented by a discontinuous constant shape function for pressure (Q2-Q1+). The discontinuous pressure element formulation makes use of biquadratic shape functions and a discontinuous linear interpolation of the pressure (Q2-P1(3)). Laminar flow solutions, with heat transfer, are compared to analytical and computational benchmarks for flat channel, backward-facing step and buoyancy driven flow in a square cavity. It is shown that the discontinuous pressure elements provide superior solution characteristics over the continuous pressure elements. Highly accurate heat transfer solutions are obtained and the Q2-P1(3) element is chosen for extension to turbulent flow simulations. Turbulent flow solutions are presented for both low turbulence Reynolds number and high Reynolds number formulations of two-equation turbulence models. The following three forms of the length scale transport equation are studied; the turbulence energy dissipation rate ([var epsilon]), the turbulence frequency ([omega]) and the turbulence time scale (tau). It is shown that the low turbulence Reynolds number model consisting of the K - [tau] transport equations, coupled with the damping functions of Shih and Hsu, provides an optimal combination of numerical stability and solution accuracy for the flat channel flow.
NASA Technical Reports Server (NTRS)
Hafez, M.; Soliman, M.; White, S.
1992-01-01
A new formulation (including the choice of variables, their non-dimensionalization, and the form of the artificial viscosity) is proposed for the numerical solution of the full Navier-Stokes equations for compressible and incompressible flows with heat transfer. With the present approach, the same code can be used for constant as well as variable density flows. The changes of the density due to pressure and temperature variations are identified and it is shown that the low Mach number approximation is a special case. At zero Mach number, the density changes due to the temperature variation are accounted for, mainly through a body force term in the momentum equation. It is also shown that the Boussinesq approximation of the buoyancy effects in an incompressible flow is a special case. To demonstrate the new capability, three examples are tested. Flows in driven cavities with adiabatic and isothermal walls are simulated with the same code as well as incompressible and supersonic flows over a wall with and without a groove. Finally, viscous flow simulations of an oblique shock reflection from a flat plate are shown to be in good agreement with the solutions available in literature.
An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows
Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.
1997-06-01
A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.
Wave propagation in inhomogeneous media as turbulent mixing in six-dimensional incompressible flow
NASA Astrophysics Data System (ADS)
Kalda, Jaan; Kree, Mihkel
2015-11-01
Using the approximation of geometrical optics, light propagation in media with fluctuating coefficient of refraction can be described as Hamiltonian dynamics of wave vectors in 6-dimensional phase space where the spatial coordinates are complemented by the respective wave vector components. Hence, according to the Liouville's theorem, the dynamics of the wave front can be described as mixing in an incompressible 6D velocity field. As the wave energy is transferred along the ray trajectories, the energy density fluctuations follow the dilution of the wave front. We use the theory of turbulent mixing to show that the intensity-distribution of speckles (regions of high energy density) follows a power law, and to derive the scaling exponents. If the velocity field were isotropic, these exponents would be determined by the dimensionality of the flow. However, there is a strong anisotropy of the field due to the asymmetry between the spatial and wave vector coordinates. Also, the effective dimensionality of the flow is reduced by one due to the energy (wave frequency) conservation law: any ray trajectory is bound to a five-dimensional manifold within the 6D phase space. Implications of the anisotropy, and of the effective reduction of the dimensionality are studied numerically The research was supported by the European Union Regional Development Fund (Centre of Excellence TK124: ``Centre for Nonlinear Studies'').
Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows
NASA Astrophysics Data System (ADS)
Xia, Yidong; Wang, Chuanjin; Luo, Hong; Christon, Mark; Bakosi, Jozsef
2016-02-01
Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in the simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using the Hydra-TH code.
NASA Astrophysics Data System (ADS)
Rivera, Christian A.; Heniche, Mourad; Glowinski, Roland; Tanguy, Philippe A.
2010-07-01
A parallel approach to solve three-dimensional viscous incompressible fluid flow problems using discontinuous pressure finite elements and a Lagrange multiplier technique is presented. The strategy is based on non-overlapping domain decomposition methods, and Lagrange multipliers are used to enforce continuity at the boundaries between subdomains. The novelty of the work is the coupled approach for solving the velocity-pressure-Lagrange multiplier algebraic system of the discrete Navier-Stokes equations by a distributed memory parallel ILU (0) preconditioned Krylov method. A penalty function on the interface constraints equations is introduced to avoid the failure of the ILU factorization algorithm. To ensure portability of the code, a message based memory distributed model with MPI is employed. The method has been tested over different benchmark cases such as the lid-driven cavity and pipe flow with unstructured tetrahedral grids. It is found that the partition algorithm and the order of the physical variables are central to parallelization performance. A speed-up in the range of 5-13 is obtained with 16 processors. Finally, the algorithm is tested over an industrial case using up to 128 processors. In considering the literature, the obtained speed-ups on distributed and shared memory computers are found very competitive.
Detached Eddy Simulations of Incompressible Turbulent Flows Using the Finite Element Method
Laskowski, G M
2001-08-01
An explicit Galerkin finite-element formulation of the Spalart-Allmaras (SA) 1 - equation turbulent transport model was implemented into the incompressible flow module of a parallel, multi-domain, Galerkin finite-element, multi-physics code, using both a RANS formulation and a DES formulation. DES is a new technique for simulating/modeling turbulence using a hybrid RANSkES formulation. The turbulent viscosity is constructed from an intermediate viscosity obtained from the transport equation which is spatially discretized using Q1 elements and integrated in time via forward Euler time integration. Three simulations of plane channel flow on a RANS-type grid, using different turbulence models, were conducted in order to validate the implementation of the SA model: SA-RANS, SA-DES and Smagorinksy (without wall correction). Very good agreement was observed between the SA-RANS results and theory, namely the Log Law of the Wall (LLW), especially in the viscous sublayer region and, to a lesser extent, in the log-layer region. The results obtained using the SA-DES model did not agree as well with the LLW, and it is believed that this poor agreement can be attributed to using a DES model on a RANS grid, namely using an incorrect length-scale. It was observed that near the wall, the SA-DES model acted as an RANS model, and away from the wall it acted as an LES model.
Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows
Xia, Yidong; Wang, Chuanjin; Luo, Hong; Christon, Mark; Bakosi, Jozsef
2015-12-15
Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in the simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.
Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows
Xia, Yidong; Wang, Chuanjin; Luo, Hong; Christon, Mark; Bakosi, Jozsef
2015-12-15
Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.« less
NASA Technical Reports Server (NTRS)
Thompson, D. S.
1980-01-01
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 Astrophysics Data System (ADS)
Ding, Yan; Kawahara, Mutsuto
1999-09-01
The linear stability of incompressible flows is investigated on the basis of the finite element method. The two-dimensional base flows computed numerically over a range of Reynolds numbers are perturbed with three-dimensional disturbances. The three-dimensionality in the flow associated with the secondary instability is identified precisely. First, by using linear stability theory and normal mode analysis, the partial differential equations governing the evolution of perturbation are derived from the linearized Navier-Stokes equation with slight compressibility. In terms of the mixed finite element discretization, in which six-node quadratic Lagrange triangular elements with quadratic interpolation for velocities (P2) and three-node linear Lagrange triangular elements for pressure (P1) are employed, a non-singular generalized eigenproblem is formulated from these equations, whose solution gives the dispersion relation between complex growth rate and wave number. Then, the stabilities of two cases, i.e. the lid-driven cavity flow and flow past a circular cylinder, are examined. These studies determine accurately stability curves to identify the critical Reynolds number and the critical wavelength of the neutral mode by means of the Krylov subspace method and discuss the mechanism of instability. For the cavity flow, the estimated critical results are Rec=920.277+/-0.010 for the Reynolds number and kc=7.40+/-0.02 for the wave number. These results are in good agreement with the observation of Aidun et al. and are more accurate than those by the finite difference method. This instability in the cavity is associated with absolute instability [Huerre and Monkewitz, Annu. Rev. Fluid Mech., 22, 473-537 (1990)]. The Taylor-Göertler-like vortices in the cavity are verified by means of the reconstruction of three-dimensional flows. As for the flow past a circular cylinder, the primary instability result shows that the flow has only two-dimensional characteristics at the
A stable partitioned FSI algorithm for incompressible flow and deforming beams
NASA Astrophysics Data System (ADS)
Li, L.; Henshaw, W. D.; Banks, J. W.; Schwendeman, D. W.; Main, A.
2016-05-01
An added-mass partitioned (AMP) algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier-Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler-Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet-Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for one
Anti-diffusion method for interface steepening in two-phase incompressible flow
NASA Astrophysics Data System (ADS)
So, K. K.; Hu, X. Y.; Adams, N. A.
2011-06-01
In this paper, we present a method for obtaining sharp interfaces in two-phase incompressible flows by an anti-diffusion correction, that is applicable in a straight-forward fashion for the improvement of two-phase flow solution schemes typically employed in practical applications. The underlying discretization is based on the volume-of-fluid (VOF) interface-capturing method on unstructured meshes. The key idea is to steepen the interface, independently of the underlying volume-fraction transport equation, by solving a diffusion equation with reverse time, i.e. an anti-diffusion equation, after each advection time step of the volume fraction. As the solution of the anti-diffusion equation requires regularization, a limiter based on the directional derivative is developed for calculating the gradient of the volume fraction. This limiter ensures the boundedness of the volume fraction. In order to control the amount of anti-diffusion introduced by the correction algorithm we propose a suitable stopping criterion for interface steepening. The formulation of the limiter and the algorithm for solving the anti-diffusion equation are applicable to 3-dimensional unstructured meshes. Validation computations are performed for passive advection of an interface, for 2-dimensional and 3-dimensional rising-bubbles, and for a rising drop in a periodically constricted channel. The results demonstrate that sharp interfaces can be recovered reliably. They show that the accuracy is similar to or even better than that of level-set methods using comparable discretizations for the flow and the level-set evolution. Also, we observe a good agreement with experimental results for the rising drop where proper interface evolution requires accurate mass conservation.
A convective-like energy-stable open boundary condition for simulations of incompressible flows
NASA Astrophysics Data System (ADS)
Dong, S.
2015-12-01
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even when strong vortices or backflows occur at the outflow boundary. Under certain situations it can be reduced to a form that can be analogized to the usual convective boundary condition. One prominent feature of this boundary condition is that it provides a control over the velocity on the outflow/open boundary. This is not available with the other energy-stable open boundary conditions from previous works. Our numerical algorithm treats the proposed open boundary condition based on a rotational velocity-correction type strategy. It gives rise to a Robin-type condition for the discrete pressure and a Robin-type condition for the discrete velocity on the outflow/open boundary, respectively at the pressure and the velocity sub-steps. We present extensive numerical experiments on a canonical wake flow and a jet flow in open domain to test the effectiveness and performance of the method developed herein. Simulation results are compared with the experimental data as well as with other previous simulations to demonstrate the accuracy of the current method. Long-time simulations are performed for a range of Reynolds numbers, at which strong vortices and backflows occur at the outflow/open boundaries. The results show that our method is effective in overcoming the backflow instability, and that it allows for the vortices to discharge from the domain in a fairly natural fashion even at high Reynolds numbers.
Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows.
Li, Q; Luo, K H; Gao, Y J; He, Y L
2012-02-01
The existing lattice Boltzmann models for incompressible multiphase flows are mostly constructed with two distribution functions: one is the order parameter distribution function, which is used to track the interface between different phases, and the other is the pressure distribution function for solving the velocity field. In this paper, it is shown that in these models the recovered momentum equation is inconsistent with the target one: an additional force is included in the recovered momentum equation. The additional force has the following features. First, it is proportional to the macroscopic velocity. Second, it is zero in every single-phase region but is nonzero in the interface. Therefore it can be interpreted as an interfacial force. To investigate the effects of the additional interfacial force, numerical simulations are carried out for the problem of Rayleigh-Taylor instability, droplet splashing on a thin liquid film, and the evolution of a falling droplet under gravity. Numerical results demonstrate that, with the increase of the velocity or the Reynolds number, the additional interfacial force will gradually have an important influence on the interface and affect the numerical accuracy. PMID:22463354
A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.
Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J
2009-11-28
In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method. PMID:19840985
NASA Astrophysics Data System (ADS)
Dong, Suchuan
2015-11-01
This talk focuses on simulating the motion of a mixture of N (N>=2) immiscible incompressible fluids with given densities, dynamic viscosities and pairwise surface tensions. We present an N-phase formulation within the phase field framework that is thermodynamically consistent, in the sense that the formulation satisfies the conservations of mass/momentum, the second law of thermodynamics and Galilean invariance. We also present an efficient algorithm for numerically simulating the N-phase system. The algorithm has overcome the issues caused by the variable coefficient matrices associated with the variable mixture density/viscosity and the couplings among the (N-1) phase field variables and the flow variables. We compare simulation results with the Langmuir-de Gennes theory to demonstrate that the presented method produces physically accurate results for multiple fluid phases. Numerical experiments will be presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts to demonstrate the capabilities of the method for studying the interactions among multiple types of fluid interfaces. Support from NSF and ONR is gratefully acknowledged.
A Parallel Second-Order Adaptive Mesh Algorithm for Incompressible Flow in Porous Media
Pau, George Shu Heng; Almgren, Ann S.; Bell, John B.; Lijewski, Michael J.
2008-04-01
In this paper we present a second-order accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting the total velocity, defined to be the sum of the phase velocities, is divergence-free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids areadvanced multiple steps to reach the same time as the coarse grids and the data atdifferent levels are then synchronized. The single grid algorithm is described briefly,but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behavior of the method.
A velocity-correction projection method based immersed boundary method for incompressible flows
NASA Astrophysics Data System (ADS)
Cai, Shanggui
2014-11-01
In the present work we propose a novel direct forcing immersed boundary method based on the velocity-correction projection method of [J.L. Guermond, J. Shen, Velocity-correction projection methods for incompressible flows, SIAM J. Numer. Anal., 41 (1)(2003) 112]. The principal idea of immersed boundary method is to correct the velocity in the vicinity of the immersed object by using an artificial force to mimic the presence of the physical boundaries. Therefore, velocity-correction projection method is preferred to its pressure-correction counterpart in the present work. Since the velocity-correct projection method is considered as a dual class of pressure-correction method, the proposed method here can also be interpreted in the way that first the pressure is predicted by treating the viscous term explicitly without the consideration of the immersed boundary, and the solenoidal velocity is used to determine the volume force on the Lagrangian points, then the non-slip boundary condition is enforced by correcting the velocity with the implicit viscous term. To demonstrate the efficiency and accuracy of the proposed method, several numerical simulations are performed and compared with the results in the literature. China Scholarship Council.
NASA Astrophysics Data System (ADS)
Neustupa, T.
2016-06-01
This paper deals with the mathematical model of a steady flow of a heat-conductive incompressible viscous fluid through a spatially periodic plane profile cascade. The corresponding boundary value problem is reduced to one spatial period. We prove the existence of a weak solution of a coupled problem, with various boundary conditions on the parts of the boundary. Particularly, the condition on the outflow is a variant of the so called "do nothing" boundary condition.
NASA Technical Reports Server (NTRS)
Erwin, John R; Yacobi, Laura A
1953-01-01
A method was devised for estimating the incompressible-flow pressure distribution over compressor blade sections at design angle of attack. The theoretical incremental velocities due to camber and thickness of the section as an isolated airfoil are assumed proportional to the average passage velocity and are modified by empirically determined interference factors. Comparisons were made between estimated and test pressure distributions of NACA 65-series sections for typical conditions. Good agreement was obtained.
Turbulent Rayleigh-Taylor flow driven by time-varying accelerations
NASA Astrophysics Data System (ADS)
Ramaprabhu, Praveen; Lawrie, Andrew; Muthuraman, Karthik; UNC-LMFA Collaboration
2011-11-01
We report on numerical simulations of turbulent Rayleigh-Taylor flow subject to variable acceleration histories. The acceleration profiles were inspired by experiments and theoretical studies, and include an impulsive acceleration, accel-decel profiles, as well as a constant drive as the baseline case. The simulations were performed using the MOBILE software, a variable-density, incompressible fluid flow code. The advection algorithm employs a 3rd-order, monotonicity-preserving upwind scheme, allowing the definition of sharp interfaces in the flow, while pressure convergence is accelerated by the use of a multi-grid scheme. The simulations are initialized with two classes of perturbations: narrow-band, short-wavelength modes and broadband with long-wavelength modes. The effect of initial amplitudes on the perturbations is investigated under the variable drive conditions. The acceleration profiles are capable of producing stages of ``demixing,'' useful in validating turbulence models of RTI.
NASA Astrophysics Data System (ADS)
Rypina, Irina I.
The Lagrangian dynamics of two-dimensional incompressible fluid flows is considered, with emphasis on transport processes in atmospheric and oceanic flows. The dynamical-systems-based approach is adopted; the Lagrangian motion in such systems is studied with the aid of Kolmogorov-Arnold-Moser (KAM) theory, and results relating to stable and unstable manifolds and lobe dynamics. Some nontrivial extensions of well-known results are discussed, and some extensions of the theory are developed. In problems for which the flow field consists of a steady background on which a time-dependent perturbation is superimposed, it is shown that transport barriers arise naturally and play a critical role in transport processes. Theoretical results are applied to the study of transport in measured and simulated oceanographic and atmospheric flows. Two particular problems are considered. First, we study the Lagrangian dynamics of the zonal jet at the perimeter of the Antarctic Stratospheric Polar Vortex during late winter/early spring within which lies the "ozone hole". In this system, a robust transport barrier is found near the core of a zonal jet under typical conditions, which is responsible for trapping of the ozone-depleted air within the ozone hole. The existence of such a barrier is predicted theoretically and tested numerically with use of a dynamically-motivated analytically-prescribed model. The second, oceanographic, application considered is the study of the surface transport in the Adriatic Sea. The surface flow in the Adriatic is characterized by a robust three-gyre background circulation pattern. Motivated by this observation, the Lagrangian dynamics of a perturbed three-gyre system is studied, with emphasis on intergyre transport and the role of transport barriers. It is shown that a qualitative change in transport properties, accompanied by a qualitative change in the structure of stable and unstable manifolds occurs in the perturbed three-gyre system when the
NASA Astrophysics Data System (ADS)
Cochran, Robert James
A study of the finite element method applied to two-dimensional incompressible fluid flow analysis with heat transfer is performed using a mixed Galerkin finite element method with the primitive variable form of the model equations. Four biquadratic, quadrilateral elements are compared in this study--the serendipity biquadratic element with bilinear continuous pressure interpolation (Q2(8)-Q1) and the Lagrangian biquadratic element with bilinear continuous pressure interpolation (Q2-Q1) of the Taylor-Hood form. A modified form of the Q-2Q1 element is also studied. The pressure interpolation is augmented by a discontinuous constant shape function for pressure (Q2-Q1+). The discontinuous pressure element formulation makes use of biquadratic shape functions and a discontinuous linear interpolation of the pressure (Q2-P1(3)). Laminar flow solutions, with heat transfer, are compared to analytical and computational benchmarks for flat channel, backward-facing step and buoyancy driven flow in a square cavity. It is shown that the discontinuous pressure elements provide superior solution characteristics over the continuous pressure elements. Highly accurate heat transfer solutions are obtained and the Q2-P1(3) element is chosen for extension to turbulent flow simulations. Turbulent flow solutions are presented for both low turbulence Reynolds number and high Reynolds number formulations of two equation turbulence models. The following three forms of the length scale transport equation are studied: the turbulence energy dissipation rate (epsilon), the turbulence frequency (omega) and the turbulence time scale (tau). It is shown that the low turbulence Reynolds number model consisting of the k-tau transport equations, coupled with the damping functions of Shih and Hsu, provides an optimal combination of numerical stability and solution accuracy for the flat channel flow. Attempts to extend the formulation beyond the flat channel were not successful due to oscillatory
NASA Astrophysics Data System (ADS)
Lind, S. J.; Stansby, P. K.; Rogers, B. D.
2016-03-01
A new two-phase incompressible-compressible Smoothed Particle Hydrodynamics (SPH) method has been developed where the interface is discontinuous in density. This is applied to water-air problems with a large density difference. The incompressible phase requires surface pressure from the compressible phase and the compressible phase requires surface velocity from the incompressible phase. Compressible SPH is used for the air phase (with the isothermal stiffened ideal gas equation of state for low Mach numbers) and divergence-free (projection based) incompressible SPH is used for the water phase, with the addition of Fickian shifting to produce sufficiently homogeneous particle distributions to enable stable, accurate, converged solutions without noise in the pressure field. Shifting is a purely numerical particle regularisation device. The interface remains a true material discontinuity at a high density ratio with continuous pressure and velocity at the interface. This approach with the physics of compressibility and incompressibility represented is novel within SPH and is validated against semi-analytical results for a two-phase elongating and oscillating water drop, analytical results for low amplitude inviscid standing waves, the Kelvin-Helmholtz instability, and a dam break problem with high interface distortion and impact on a vertical wall where experimental and other numerical results are available.
NASA Astrophysics Data System (ADS)
Robertson, Eric D.
A comprehensive survey of available numerical methods and models was performed on the open source computational fluid dynamics solver OpenFOAM version 2.0 for incompressible turbulent bluff body flows. Numerical methods are illuminated using source code for side-by-side comparison. For validation, the accuracy of flow predictions over a sphere in the subcritical regime and delta wing with sharp leading edge is assessed. Solutions show mostly good agreement with experimental data and data obtained from commercial software. A demonstration of the numerical implementation of a dynamic hybrid RANS/LES framework is also presented, including results from test studies.
NASA Technical Reports Server (NTRS)
Johnson, F. T.
1980-01-01
A method for solving the linear integral equations of incompressible potential flow in three dimensions is presented. Both analysis (Neumann) and design (Dirichlet) boundary conditions are treated in a unified approach to the general flow problem. The method is an influence coefficient scheme which employs source and doublet panels as boundary surfaces. Curved panels possessing singularity strengths, which vary as polynomials are used, and all influence coefficients are derived in closed form. These and other features combine to produce an efficient scheme which is not only versatile but eminently suited to the practical realities of a user-oriented environment. A wide variety of numerical results demonstrating the method is presented.
A survey of grid-free methods for the simulation of 3-D incompressible flows in bounded domains
Gharakhani, A.
1997-09-01
The state-of-the-art in Lagrangian methods for the grid-free simulation of three-dimensional, incompressible, high Reynolds number, internal and/or external flows is surveyed. Specifically, vortex and velicity (or impulse) element methods are introduced. The relative merits of various available techniques and the outstanding challenges in simulating the processes of convection and diffusion, as well as in satisfying the wall boundary conditions are discussed individually. Issues regarding the stretch and solenoidality of vorticity are also discussed. A potentially successful algorithm for simulating the flow around a parachute is proposed as well.
Incompressible laminar flow through hollow fibers: a general study by means of a two-scale approach
NASA Astrophysics Data System (ADS)
Borsi, Iacopo; Farina, Angiolo; Fasano, Antonio
2011-08-01
We study the laminar flow of an incompressible Newtonian fluid in a hollow fiber, whose walls are porous. We write the Navier-Stokes equations for the flow in the inner channel and Darcy's law for the flow in the fiber, coupling them by means of the Beavers-Joseph condition which accounts for the (possible) slip at the membrane surface. Then, we introduce a small parameter {\\varepsilon ≪ 1} (the ratio between the radius and the length of the fiber) and expand all relevant quantities in powers of ɛ. Averaging over the fiber cross section, we find the velocity profiles for the longitudinal flow and for the cross-flow, and eventually, we determine the explicit expression of the permeability of the system. This work is also preliminary to the study of more complex systems comprising a large number of identical fibers (e.g., ultrafiltration modules and dialysis).
Richard C. Martineau; Ray A. Berry; Aurélia Esteve; Kurt D. Hamman; Dana A. Knoll; Ryosuke Park; William Taitano
2009-01-01
This report illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially-heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated body force, velocity, and divergence of velocity distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present. The results show that the use of
Ohkitani, Koji
2015-09-01
We consider incompressible Euler flows in terms of the stream function in two dimensions and the vector potential in three dimensions. We pay special attention to the case with singular distributions of the vorticity, e.g., point vortices in two dimensions. An explicit equation governing the velocity potentials is derived in two steps. (i) Starting from the equation for the stream function [Ohkitani, Nonlinearity 21, T255 (2009)NONLE50951-771510.1088/0951-7715/21/12/T02], which is valid for smooth flows as well, we derive an equation for the complex velocity potential. (ii) Taking a real part of this equation, we find a dynamical equation for the velocity potential, which may be regarded as a refinement of Bernoulli theorem. In three-dimensional incompressible flows, we first derive dynamical equations for the vector potentials which are valid for smooth fields and then recast them in hypercomplex form. The equation for the velocity potential is identified as its real part and is valid, for example, flows with vortex layers. As an application, the Kelvin-Helmholtz problem has been worked out on the basis the current formalism. A connection to the Navier-Stokes regularity problem is addressed as a physical application of the equations for the vector potentials for smooth fields. PMID:26465559
NASA Astrophysics Data System (ADS)
Guilmineau, E.; Piquet, J.; Queutey, P.
The incompressible viscous turbulent flow past airfoils is numerically simulated by solving the incompressible Reynolds-Averaged-Navier-Stokes equations (RANSE). We use a physical method, for the reconstruction of fluxes in the mass and momentum balance discrete equations. Different turbulent models are tested over several cases; namely, the flow past the popular NACA 4412 airfoil, near maximum lift conditions, the flow past an AS-240 airfoil, at two incidences. The numerical simulation of the flow around a NACA 0012 airfoil in high amplitude pitching oscillation is finally considered.
NASA Astrophysics Data System (ADS)
Quaini, A.; Glowinski, R.; Čanić, S.
2016-01-01
This computational study shows, for the first time, a clear transition to two-dimensional Hopf bifurcation for laminar incompressible flows in symmetric plane expansion channels. Due to the well-known extreme sensitivity of this study on computational mesh, the critical Reynolds numbers for both the known symmetry-breaking (pitchfork) bifurcation and Hopf bifurcation were investigated for several layers of mesh refinement. It is found that under-refined meshes lead to an overestimation of the critical Reynolds number for the symmetry breaking and an underestimation of the critical Reynolds number for the Hopf bifurcation.
Yang, L M; Shu, C; Wang, Y
2016-03-01
In this work, a discrete gas-kinetic scheme (DGKS) is presented for simulation of two-dimensional viscous incompressible and compressible flows. This scheme is developed from the circular function-based GKS, which was recently proposed by Shu and his co-workers [L. M. Yang, C. Shu, and J. Wu, J. Comput. Phys. 274, 611 (2014)]. For the circular function-based GKS, the integrals for conservation forms of moments in the infinity domain for the Maxwellian function-based GKS are simplified to those integrals along the circle. As a result, the explicit formulations of conservative variables and fluxes are derived. However, these explicit formulations of circular function-based GKS for viscous flows are still complicated, which may not be easy for the application by new users. By using certain discrete points to represent the circle in the phase velocity space, the complicated formulations can be replaced by a simple solution process. The basic requirement is that the conservation forms of moments for the circular function-based GKS can be accurately satisfied by weighted summation of distribution functions at discrete points. In this work, it is shown that integral quadrature by four discrete points on the circle, which forms the D2Q4 discrete velocity model, can exactly match the integrals. Numerical results showed that the present scheme can provide accurate numerical results for incompressible and compressible viscous flows with roughly the same computational cost as that needed by the Roe scheme. PMID:27078488
A Priori Estimates for Free Boundary Problem of Incompressible Inviscid Magnetohydrodynamic Flows
NASA Astrophysics Data System (ADS)
Hao, Chengchun; Luo, Tao
2014-06-01
In the present paper, we prove the a priori estimates of Sobolev norms for a free boundary problem of the incompressible inviscid magnetohydrodynamics equations in all physical spatial dimensions n = 2 and 3 by adopting a geometrical point of view used in Christodoulou and Lindblad (Commun Pure Appl Math 53:1536-1602, 2000), and estimating quantities such as the second fundamental form and the velocity of the free surface. We identify the well-posedness condition that the outer normal derivative of the total pressure including the fluid and magnetic pressures is negative on the free boundary, which is similar to the physical condition (Taylor sign condition) for the incompressible Euler equations of fluids.
On an Inviscid Model for Incompressible Two-Phase Flows with Nonlocal Interaction
NASA Astrophysics Data System (ADS)
Gal, Ciprian G.
2016-03-01
We consider a diffuse interface model which describes the motion of an ideal incompressible mixture of two immiscible fluids with nonlocal interaction in two-dimensional bounded domains. This model consists of the Euler equation coupled with a convective nonlocal Cahn-Hilliard equation. We establish the existence of globally defined weak solutions as well as well-posedness results for strong/classical solutions.
Multigrid solution of incompressible turbulent flows by using two-equation turbulence models
Zheng, X.; Liu, C.; Sung, C.H.
1996-12-31
Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.
Sussman, M. . Dept. of Mathematics); Fatemi, E.
1999-04-01
In Sussman, Smereka, and Osher, a numerical scheme was presented for computing incompressible air-water flows using the level set method. Crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set. In this paper the authors implement a constraint along with higher order difference schemes in order to make the iteration method more accurate and efficient. Accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set. The authors apply the redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost. They validate the results with experiment and theory. They show that the distance level set scheme with the added constraint competes well with available interface tracking schemes for basic advection of an interface. They perform basic accuracy checks and more stringent tests involving complicated interfacial structures. As with all level set schemes, the method is easy to implement.
NASA Technical Reports Server (NTRS)
Hansen, Arthur G.
1958-01-01
Analysis is presented on the possible similarity solutions of the three-dimensional, laminar, incompressible, boundary-layer equations referred to orthogonal, curvilinear coordinate systems. Requirements of the existence of similarity solutions are obtained for the following: flow over developable surface and flow over non-developable surfaces with proportional mainstream velocity components.
NASA Astrophysics Data System (ADS)
Liao, Xian; Zhang, Ping
2016-06-01
Regarding P.-L. Lions' open question in Oxford Lecture Series in Mathematics and its Applications, Vol. 3 (1996) concerning the propagation of regularity for the density patch, we establish the global existence of solutions to the two-dimensional inhomogeneous incompressible Navier-Stokes system with initial density given by {(1 - η){1}_{{Ω}0} + {1}_{{Ω}0c}} for some small enough constant {η} and some {W^{k+2,p}} domain {Ω0}, with initial vorticity belonging to {L1 \\cap Lp} and with appropriate tangential regularities. Furthermore, we prove that the regularity of the domain {Ω_0} is preserved by time evolution.
Combustion accelerated swirling flows in high confinements
NASA Astrophysics Data System (ADS)
Weber, Roman; Dugue, Jacques
Nine cold flows, 15 well-mixed flames, and eight type II diffusion flames of coke-oven gas are measured in the present study of the effect of combustion on the properties of swirl-induced internal recirculation zones (IRZ) formed in the vicinity of swirl-stabilized burners. Formulae for calculating the effective swirl number are presented. Attention is given to experiments in which initial swirling cold flows are combustion-accelerated; the position and degree of acceleration are systematically varied. The experimental results obtained deepen current understanding of the effects of combustion on swirling flows.
NASA Astrophysics Data System (ADS)
Hoarau, Y.; Braza, M.; Ventikos, Y.; Faghani, D.; Tzabiras, G.
2003-12-01
The transition to turbulence in the incompressible flow around a NACA0012 wing at high incidence is studied by DNS in the Reynolds number range 800 10000. Two main routes are identified for the two-dimensional transition mechanisms: that to aperiodicity beyond the von Kármán mode via a period-doubling scenario and the development of a shear-layer instability, forced by the fundamental oscillation of the separation point downstream of the leading edge. The evolution of the global parameters as well as the variation law of the shear-layer instability wavelength are quantified. The history of the three-dimensional transition mechanisms from a nominally two-dimensional flow structure is identified beyond the first bifurcation, as well as the preferred spanwise wavelengths.
Treelike networks accelerating capillary flow
NASA Astrophysics Data System (ADS)
Shou, Dahua; Ye, Lin; Fan, Jintu
2014-05-01
Transport in treelike networks has received wide attention in natural systems, oil recovery, microelectronic cooling systems, and textiles. Existing studies are focused on transport behaviors under a constant potential difference (including pressure, temperature, and voltage) in a steady state [B. Yu and B. Li, Phys. Rev. E 73, 066302 (2006), 10.1103/PhysRevE.73.066302; J. Chen, B. Yu, P. Xu, and Y. Li, Phys. Rev. E 75, 056301 (2007), 10.1103/PhysRevE.75.056301]. However, dynamic (time-dependent) transport in such systems has rarely been concerned. In this work, we theoretically investigate the dynamics of capillary flow in treelike networks and design the distribution of radius and length of local branches for the fastest capillary flow. It is demonstrated that capillary flow in the optimized tree networks is faster than in traditional parallel tube nets under fixed constraints. As well, the flow time of the liquid is found to increase approximately linearly with penetration distance, which differs from Washburn's classic description that flow time increases as the square of penetration distance in a uniform tube.
Treelike networks accelerating capillary flow.
Shou, Dahua; Ye, Lin; Fan, Jintu
2014-05-01
Transport in treelike networks has received wide attention in natural systems, oil recovery, microelectronic cooling systems, and textiles. Existing studies are focused on transport behaviors under a constant potential difference (including pressure, temperature, and voltage) in a steady state [B. Yu and B. Li, Phys. Rev. E 73, 066302 (2006); J. Chen, B. Yu, P. Xu, and Y. Li, Phys. Rev. E 75, 056301 (2007)]. However, dynamic (time-dependent) transport in such systems has rarely been concerned. In this work, we theoretically investigate the dynamics of capillary flow in treelike networks and design the distribution of radius and length of local branches for the fastest capillary flow. It is demonstrated that capillary flow in the optimized tree networks is faster than in traditional parallel tube nets under fixed constraints. As well, the flow time of the liquid is found to increase approximately linearly with penetration distance, which differs from Washburn's classic description that flow time increases as the square of penetration distance in a uniform tube. PMID:25353880
Richard C. Martineau; Ray A. Berry; Aur´elia Esteve; Kurt D. Hamman; Dana A. Knoll; Ryosuke Park; William Taitano
2010-06-01
This manuscript illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially-heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated specific force quantities and velocity and temperature distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present.
NASA Astrophysics Data System (ADS)
Margairaz, Fabien; Giometto, Marco; Parlange, Marc; Calaf, Marc
2015-11-01
The performance of dealiasing schemes and their computational cost on a pseudo-spectral code are analyzed. Dealiasing is required to limit the error that occurs when two discretized variables are multiplied, polluting the accuracy of the result. In this work three different dealiasing methods are explored: the 2/3 rule, the 3/2 rule, and a high order Fourier smoothing based method. We compare the cost of the traditionally accepted 3/2 rule (Canuto et al., 1988), where an expansion of the computational domain to a larger grid is required, to the cost of the other two techniques that do not require this expansion. This analysis is performed in the framework of Large-Eddy Simulations (LES) of incompressible flows using the constant Smagorinsky sub-grid model with a wall damping function and a wall model based on the log-law. A highly efficient LES code parallelized using a 2D pencil decomposition has been developed. The code employs the traditional pseudo-spectral approach to integrate the incompressible Navier-Stokes equations. Several simulations of a neutral atmospheric boundary layer using different degrees of numerical resolution are considered. Results show a net difference in computational cost between the different techniques without relevant changes in statistics.
NASA Astrophysics Data System (ADS)
Yang, L. M.; Shu, C.; Wang, Y.
2016-03-01
In this work, a discrete gas-kinetic scheme (DGKS) is presented for simulation of two-dimensional viscous incompressible and compressible flows. This scheme is developed from the circular function-based GKS, which was recently proposed by Shu and his co-workers [L. M. Yang, C. Shu, and J. Wu, J. Comput. Phys. 274, 611 (2014), 10.1016/j.jcp.2014.06.033]. For the circular function-based GKS, the integrals for conservation forms of moments in the infinity domain for the Maxwellian function-based GKS are simplified to those integrals along the circle. As a result, the explicit formulations of conservative variables and fluxes are derived. However, these explicit formulations of circular function-based GKS for viscous flows are still complicated, which may not be easy for the application by new users. By using certain discrete points to represent the circle in the phase velocity space, the complicated formulations can be replaced by a simple solution process. The basic requirement is that the conservation forms of moments for the circular function-based GKS can be accurately satisfied by weighted summation of distribution functions at discrete points. In this work, it is shown that integral quadrature by four discrete points on the circle, which forms the D2Q4 discrete velocity model, can exactly match the integrals. Numerical results showed that the present scheme can provide accurate numerical results for incompressible and compressible viscous flows with roughly the same computational cost as that needed by the Roe scheme.
NASA Astrophysics Data System (ADS)
Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.
2014-07-01
Stable partitioned algorithms for fluid-structure interaction (FSI) problems are developed and analyzed in this two-part paper. Part I describes an algorithm for incompressible flow coupled with compressible elastic solids, while Part II discusses an algorithm for incompressible flow coupled with structural shells. Importantly, these new added-mass partitioned (AMP) schemes are stable and retain full accuracy with no sub-iterations per time step, even in the presence of strong added-mass effects (e.g. for light solids). The numerical approach described here for bulk compressible solids extends the scheme of Banks et al. [1,2] for inviscid compressible flow, and uses Robin (mixed) boundary conditions with the fluid and solid solvers at the interface. The basic AMP Robin conditions, involving a linear combination of velocity and stress, are determined from the outgoing solid characteristic relation normal to the fluid-solid interface combined with the matching conditions on the velocity and traction. Two alternative forms of the AMP conditions are then derived depending on whether the fluid equations are advanced with a fractional-step method or not. The stability and accuracy of the AMP algorithm is evaluated for linearized FSI model problems; the full nonlinear case being left for future consideration. A normal mode analysis is performed to show that the new AMP algorithm is stable for any ratio of the solid and fluid densities, including the case of very light solids when added-mass effects are large. In contrast, it is shown that a traditional partitioned algorithm involving a Dirichlet-Neumann coupling for the same FSI problem is formally unconditionally unstable for any ratio of densities. Exact traveling wave solutions are derived for the FSI model problems, and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the AMP algorithm for the cases of light, medium and heavy solids.
Convergence acceleration of viscous flow computations
NASA Technical Reports Server (NTRS)
Johnson, G. M.
1982-01-01
A multiple-grid convergence acceleration technique introduced for application to the solution of the Euler equations by means of Lax-Wendroff algorithms is extended to treat compressible viscous flow. Computational results are presented for the solution of the thin-layer version of the Navier-Stokes equations using the explicit MacCormack algorithm, accelerated by a convective coarse-grid scheme. Extensions and generalizations are mentioned.
A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries
Dong, S.; Wang, X.
2016-01-01
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries. PMID:27163909
An efficient second-order projection method for viscous incompressible flow
NASA Astrophysics Data System (ADS)
Bell, J. B.; Howell, L. H.; Colella, P.
1991-04-01
In this paper we describe a second-order projection method for the time-dependent, incompressible Navier-Stokes equations. The method is a second-order fractional step scheme in which one first solves diffusion-convection equations to determine intermediate velocities which are then projected onto the space of divergence-free vector fields. The diffusion-convection step uses a specialized second-order Godunov method for differencing the nonlinear convective terms that is conservative and free-stream preserving and provides a robust treatment of the nonlinearities at high Reynolds number. The projection is based on cell-centered centered difference approximations to divergence and gradient operators with the resulting linear system solved using a multigrid relaxation scheme. We apply the method to vortex spindown in a box to validate the numerical convergence of the method and to measure its overall performance.
A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries.
Dong, S; Wang, X
2016-01-01
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries. PMID:27163909
NASA Technical Reports Server (NTRS)
Mhuiris, N. M. G.
1986-01-01
For incompressible fluids the law of mass conservation reduces to a constraint on the velocity vector, namely that it be divergence free. This constraint has long been a source of great difficulty to the numericist seeking to discretize the Navier-Stokes and Euler equations. A spectral method is discussed which overcomes this difficulty. Its efficacy is demonstrated on some simple problems. The velocity is approximated by a finite sum of divergence free vectors, each of which satisfies the same boundary conditions as the velocity. Projecting the governing equation onto the space of inviscid vector fields eliminates the pressure term and produces a set of ordinary differential equations that must be solved for the coefficents in the velocity. The pressure can then be recovered if it is needed.
NASA Technical Reports Server (NTRS)
Sheng, Chunhua; Hyams, Daniel G.; Sreenivas, Kidambi; Gaither, J. Adam; Marcum, David L.; Whitfield, David L.
2000-01-01
A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.
NASA Technical Reports Server (NTRS)
Queijo, M J
1956-01-01
A method of computing span loads and the resulting rolling moments for sideslipping wings of arbitrary plan form in incompressible flow is derived. The method requires that the span load at zero sideslip be known for the wing under consideration. Because this information is available for a variety of wings, this requirement should not seriously restrict the application of the present method. The basic method derived herein requires a mechanical differentiation and integration to obtain the rolling moment for the general wing in sideslip. For wings having straight leading and trailing edges over each semispan, the rolling moment due to sideslip is given by a simple equation in terms of plan-form parameters and the lateral center of pressure of the lift due to angle of attack. Calculated span loads and rolling-moment parameters are compared with experimental values. The comparison indicates good agreement between calculations and available experimental data.
NASA Astrophysics Data System (ADS)
Chen, Mufeng; Niu, Xiaodong
2016-06-01
An improved momentum-exchanged immersed boundary-based lattice Boltzmann method (MEIB-LBM) for incompressible viscous thermal flows is presented here. MEIB-LBM was first proposed by Niu et al, which has been shown later that the non-slip boundary condition is not satisfied. Wang. et al. and Hu. et al overcome this drawback by iterative method. But it needs to give an appropriate relaxation parameter. In this work, we come back to the intrinsic feature of LBM, which uses the density distribution function as a dependent variable to evolve the flow field, and uses the density distribution function correction at the neighboring Euler mesh points to satisfy the non-slip boundary condition on the immersed boundary. The same idea can also be applied to the thermal flows with fluid-structure interference. The merits of present improvements for the original MEIB-LBM are that the intrinsic feature of LBM is kept and the flow penetration across the immersed boundaries is avoided. To validate the present method, examples, including forced convection over a stationary heated circular cylinder for heat flux condition, and natural convection with a suspended circle particle in viscous fluid, are simulated. The streamlines, isothermal contours, the drag coefficients and Nusselt numbers are calculated and compared to the benchmark results to demonstrate the effective of the present method.
Approximate factorization for incompressible flow. Ph.D. Thesis; [Navier-Stokes equation
NASA Technical Reports Server (NTRS)
Bernard, R. S.
1981-01-01
For computational solution of the incompressible Navier-Stokes equations, the approximate factorization (AF) algorithm is used to solve the vectorized momentum equation in delta form based on the pressure calculated in the previous time step. The newly calculated velocities are substituted into the pressure equation (obtained from a linear combination of the continuity and momentum equation), which is then solved by means of line SOR. Computational results are presented for the NACA 66 sub 3 018 airfoil at Reynolds numbers of 1000 and 40,000 and attack angles of 0 and 6 degrees. Comparison with wind tunnel data for Re = 40,000 indicates good qualitative agreement between measured and calculated pressure distributions. Quantitative agreement is only fair, however, with the calculations somewhat displaced from the measurements. Furthermore, the computed velocity profiles are unrealistically thick around the airfoil, due to the excessive amount of artificial viscosity needed for stability. Based on the performance of the algorithm with regard to stability, it is concluded that AF/SOR is suitable for calculations at Reynolds numbers less than 10,000. Speedwise, the method is faster than point SOR by at least a factor of two.
Turbulent jet patterns in accelerating flows
NASA Technical Reports Server (NTRS)
Lipshitz, A.; Greber, I.
1981-01-01
Results of flow visualization experiments, and a semi-empirical model of a single turbulent jet injected perpendicularly to a different density cross flow are presented. The model is based on integral conservation equations, including the pressure terms appropriate to accelerating flow. It uses an entrainment correlation obtained from previous experiments of a jet in a cross stream. The results show trajectories and spreading rates, and are typified by a set of three parameters: momentum ratio, Froude number and density ratio. Agreement between test and calculated results is encouraging, but tend to be poorer with increasing momentum ratio.
NASA Astrophysics Data System (ADS)
Chen, Yu; Xie, Xilin
2016-05-01
E and Liu [J. Comput. Phys. 138 (1997) 57-82] put forward a finite difference method for 3D viscous incompressible flows in the vorticity-vector potential formulation on non-staggered grids. In this paper, we will extend this method to the case of flows in the presence of a deformable surface. By use of two kinds of surface differential operators, the implementation of boundary conditions on a plane is generalized to a curved smooth surface with given velocity distribution, whether this be an inflow/outflow interface or a curved wall. To deal with the irregular and varying physical domain, time-dependent curvilinear coordinates are constructed and the corresponding tensor analysis is adopted in deriving the component form of the governing equations. Therefore, the equations can be discretized and solved in a regular and fixed parametric domain. Numerical results are presented for a 3D lid-driven cavity with a deforming surface and a 3D duct flow with a deforming boundary. A new way to validate numerical simulations is proposed based on an expression for the rate-of-strain tensor on a deformable surface.
NASA Astrophysics Data System (ADS)
Zhou, J. X.; Shen, X.; Yin, Y. J.; Guo, Z.; Wang, H.
2015-06-01
In this paper, Gas-liquid two phase flow mathematic models of incompressible fluid were proposed to explore the feature of fluid under certain centrifugal force in vertical centrifugal casting (VCC). Modified projection-level-set method was introduced to solve the mathematic models. To validate the simulation results, two methods were used in this study. In the first method, the simulation result of basic VCC flow process was compared with its analytic solution. The relationship between the numerical solution and deterministic analytic solution was presented to verify the correctness of numerical algorithms. In the second method, systematic water simulation experiments were developed. In this initial experiment, special experimental vertical centrifugal device and casting shapes were designed to describe typical mold-filling processes in VCC. High speed camera system and data collection devices were used to capture flow shape during the mold-filling process. Moreover, fluid characteristic at different rotation speed (from 40rpm, 60rpmand 80rpm) was discussed to provide comparative resource for simulation results. As compared with the simulation results, the proposed mathematical models could be proven and the experimental design could help us advance the accuracy of simulation and further studies for VCC.
NASA Astrophysics Data System (ADS)
Berdanier, Reid A.; Key, Nicole L.
2016-03-01
The single slanted hot-wire technique has been used extensively as a method for measuring three velocity components in turbomachinery applications. The cross-flow orientation of probes with respect to the mean flow in rotating machinery results in detrimental prong interference effects when using multi-wire probes. As a result, the single slanted hot-wire technique is often preferred. Typical data reduction techniques solve a set of nonlinear equations determined by curve fits to calibration data. A new method is proposed which utilizes a look-up table method applied to a simulated triple-wire sensor with application to turbomachinery environments having subsonic, incompressible flows. Specific discussion regarding corrections for temperature and density changes present in a multistage compressor application is included, and additional consideration is given to the experimental error which accompanies each data reduction process. Hot-wire data collected from a three-stage research compressor with two rotor tip clearances are used to compare the look-up table technique with the traditional nonlinear equation method. The look-up table approach yields velocity errors of less than 5 % for test conditions deviating by more than 20 °C from calibration conditions (on par with the nonlinear solver method), while requiring less than 10 % of the computational processing time.
Software Design for Particles in Incompressible flow, non-subcycled case
Martin, Daniel; Martin, Dan; Colella, Phil
2005-02-08
To implement an AMR incompressible Navier-Stokes with particles algorithm, we have decided to use a non-subcycled algorithm to simplify the implementation of the particle drag forcing term. This requires a fairly broad redesign of the software from what was presented in [1], since we will no longer be using the AMR/AMR Level base classes to manage the AMR hierarchy. The new classes map on to the functionality of the classes in the original design in a fairly straightforward way, as illustrated in Table 1. The new PAmrNS class takes on the functionality of the Particle AMRNS class in the earlier implementation, along with the functionality of the AMR and Amr Level classes in the Chombo AMR Time Dependent library. The new Amr Projector class replaces the original CC Projector class, while the new AMR Particle Projector class replaces the original Particle Projector class. A basic diagram of the class relationships between the AMRINS-particles classes is depicted in Figure 1. The PAmrNS class will manage the AMR hierarchy and the non-subcycled advance. The non-subcycled advance is much simpler than the subcycled case, both in terms of algorithmic complexity (no need for synchronization projections, etc) and in terms of software implementation. The AMR Particle Projector will do the particle projection originally implemented in the Particle Projector class on an AMR hierarchy, including all image particle effects. The rest of the implementation (Drag Particle, etc) will be the same as in the original software design. Since much of the functionality and internal storage in the CC Projector class in the original AMRINS code is devoted to subcycling-related functionality, the Amr CC Projector is a stripped-down version of the CC Projector which only contains the functionality needed to do the multilevel cell-centered and face-centered projections.