An upwind-differencing scheme for the incompressible Navier-Stokes equations

The steady state incompressible Navier-Stokes equations in 2-D are solved numerically using the artificial compressibility formulation. The convective terms are upwind-differenced using a flux difference split approach that has uniformly high accuracy throughout the interior grid points. The viscous fluxes are differenced using second order accurate central differences. The numerical system of equations is solved using an implicit line relaxation scheme. Although the current study is limited to steady state problems, it is shown that this entire formulation can be used for solving unsteady problems. Characteristic boundary conditions are formulated and used in the solution procedure. The overall scheme is capable of being run at extremely large pseudotime steps, leading to fast convergence. Three test cases are presented to demonstrate the accuracy and robustness of the code. These are the flow in a square-driven cavity, flow over a backward facing step, and flow around a 2-D circular cylinder

Efficient simulation of incompressible viscous flow over multi-element airfoils

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

Numerical solution of the incompressible Navier-Stokes equations

The current work is initiated in an effort to obtain an efficient, accurate, and robust algorithm for the numerical solution of the incompressible Navier-Stokes equations in two- and three-dimensional generalized curvilinear coordinates for both steady-state and time-dependent flow problems. This is accomplished with the use of the method of artificial compressibility and a high-order flux-difference splitting technique for the differencing of the convective terms. Time accuracy is obtained in the numerical solutions by subiterating the equations in psuedo-time for each physical time step. The system of equations is solved with a line-relaxation scheme which allows the use of very large pseudo-time steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. Numerous laminar test flow problems are computed and presented with a comparison against analytically known solutions or experimental results. These include the flow in a driven cavity, the flow over a backward-facing step, the steady and unsteady flow over a circular cylinder, flow over an oscillating plate, flow through a one-dimensional inviscid channel with oscillating back pressure, the steady-state flow through a square duct with a 90 degree bend, and the flow through an artificial heart configuration with moving boundaries. An adequate comparison with the analytical or experimental results is obtained in all cases. Numerical comparisons of the upwind differencing with central differencing plus artificial dissipation indicates that the upwind differencing provides a much more robust algorithm, which requires significantly less computing time. The time-dependent problems require on the order of 10 to 20 subiterations, indicating that the elliptical nature of the problem does require a substantial amount of computing effort

Comparison of Implicit Schemes for the Incompressible Navier-Stokes Equations

For a computational flow simulation tool to be useful in a design environment, it must be very robust and efficient. To develop such a tool for incompressible flow applications, a number of different implicit schemes are compared for several two-dimensional flow problems in the current study. The schemes include Point-Jacobi relaxation, Gauss-Seidel line relaxation, incomplete lower-upper decomposition, and the generalized minimum residual method preconditioned with each of the three other schemes. The efficiency of the schemes is measured in terms of the computing time required to obtain a steady-state solution for the laminar flow over a backward-facing step, the flow over a NACA 4412 airfoil, and the flow over a three-element airfoil using overset grids. The flow solver used in the study is the INS2D code that solves the incompressible Navier-Stokes equations using the method of artificial compressibility and upwind differencing of the convective terms. The results show that the generalized minimum residual method preconditioned with the incomplete lower-upper factorization outperforms all other methods by at least a factor of 2

Tracking Debris Shed by a Space-Shuttle Launch Vehicle

The DEBRIS software predicts the trajectories of debris particles shed by a space-shuttle launch vehicle during ascent, to aid in assessing potential harm to the space-shuttle orbiter and crew. The user specifies the location of release and other initial conditions for a debris particle. DEBRIS tracks the particle within an overset grid system by means of a computational fluid dynamics (CFD) simulation of the local flow field and a ballistic simulation that takes account of the mass of the particle and its aerodynamic properties in the flow field. The computed particle trajectory is stored in a file to be post-processed by other software for viewing and analyzing the trajectory. DEBRIS supplants a prior debris tracking code that took .15 minutes to calculate a single particle trajectory: DEBRIS can calculate 1,000 trajectories in .20 seconds on a desktop computer. Other improvements over the prior code include adaptive time-stepping to ensure accuracy, forcing at least one step per grid cell to ensure resolution of all CFD-resolved flow features, ability to simulate rebound of debris from surfaces, extensive error checking, a builtin suite of test cases, and dynamic allocation of memory

Numerical Simulation of Flow Through an Artificial Heart

A solution procedure was developed that solves the unsteady, incompressible Navier-Stokes equations, and was used to numerically simulate viscous incompressible flow through a model of the Pennsylvania State artificial heart. The solution algorithm is based on the artificial compressibility method, and uses flux-difference splitting to upwind the convective terms; a line-relaxation scheme is used to solve the equations. The time-accuracy of the method is obtained by iteratively solving the equations at each physical time step. The artificial heart geometry involves a piston-type action with a moving solid wall. A single H-grid is fit inside the heart chamber. The grid is continuously compressed and expanded with a constant number of grid points to accommodate the moving piston. The computational domain ends at the valve openings where nonreflective boundary conditions based on the method of characteristics are applied. Although a number of simplifing assumptions were made regarding the geometry, the computational results agreed reasonably well with an experimental picture. The computer time requirements for this flow simulation, however, are quite extensive. Computational study of this type of geometry would benefit greatly from improvements in computer hardware speed and algorithm efficiency enhancements

CFD Assessment of Forward Booster Separation Motor Ignition Overpressure on ET XT 718 Ice/Frost Ramp

Computational fluid dynamics assessment of the forward booster separation motor ignition over-pressure was performed on the space shuttle external tank X(sub T) 718 ice/frost ramp using the flow solver OVERFLOW. The main objective of this study was the investigation of the over-pressure during solid rocket booster separation and its affect on the local pressure and air-load environments. Delta pressure and plume impingement were investigated as a possible contributing factor to the cause of the debris loss on shuttle missions STS-125 and STS-127. A simplified computational model of the Space Shuttle Launch Vehicle was developed consisting of just the external tank and the solid rocket boosters with separation motor nozzles and plumes. The simplified model was validated by comparison to full fidelity computational model of the Space Shuttle without the separation motors. Quasi steady-state plume solutions were used to calibrate the thrust of the separation motors. Time-accurate simulations of the firing of the booster-separation motors were performed. Parametric studies of the time-step size and the number of sub-iterations were used to find the best converged solution. The computed solutions were compared to previous OVERFLOW steady-state runs of the separation motors with reaction control system jets and to ground test data. The results indicated that delta pressure from the overpressure was small and within design limits, and thus was unlikely to have contributed to the foam losses

Simulation of blood flow through an artificial heart

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 state and unsteady flow calculations are done by solving the incompressible Navier-Stokes equations in 3-D 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

Paper Session III-A - Dual-Use Applications of a Computational Fluid Dynamics Code for Viscous Incompressible Flow

An efficient incompressible flow analysis code, INS3D, has been developed at NASA Ames Research Center and applied successfully to numerous aerospace applications. The INS3D code has also been applied to non-aerospace applications, such as biofluid problems, with great success. This paper presents a computational flow simulation capability originally developed for liquid rocket engine analysis and subsequently applied to analyze the left ventricular assist device being developed jointly by NASA Johnson Space Center and the Baylor College of Medicine

Aerodynamics and Debris Transport for the Space Shuttle Launch Vehicle

No abstract availabl