Stuart E. Rogers

Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

The two-dimensional incompressible Navier-Stokes equations are solved in a time-accurate manner, using the method of pseudocompres sibility. Using this method, subiterations in pseudotime are required to satisfy the continuity equation at each time step. An upwind differencing scheme, based on flux-difference splitting, is used to compute the convective terms. The upwind differencing is biased, based on the sign of the local eigenvalue of the Jacobian matrix of the convective fluxes. Both third-order and fifth-order differencing schemes are used on the convective fluxes throughout the grids interior. The equations are solved using an implicit line relaxation scheme. This solution scheme is stable and is capable of running at large time steps in pseudo-time, leading to fast convergence for each physical time step. A variety of computed results are presented to validate the present scheme. Results for the flow over an oscillating plate are compared with the exact analytic solution, and good agreement is seen. Excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure. Flow solutions over a circular cylinder with vortex shedding are also presented. Finally, the flow past an airfoil at —90° angle of attack is computed.

Steady and Unsteady Solutions of the Incompressible Navier-Stokes Equations

An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The equations are solved with a line-relaxation scheme that allows the use of very large pseudotime steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. The steady-state solution of flow through a square duct with a 90-deg bend is computed, and the results are compared with experimental data. Good agreement is observed. Computations of unsteady flow over a circular cylinder are presented and compared to other experimental and computational results. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented. 28 refs.

Best Practices In Overset Grid Generation

Grid generation for overset grids on complex geometry can be divided into four main steps: geometry processing, surface grid generation, volume grid generation and domain connectivity. For each of these steps, the procedures currently practiced by experienced users are described. Typical problems encountered are also highlighted and discussed. Most of the guidelines are derived from experience on a variety of problems including space launch and return vehicles, subsonic transports with propulsion and high lift devices, supersonic vehicles, rotorcraft vehicles, and turbomachinery.

PEGASUS 5: An Automated Pre-Processor for Overset-Grid CFD

An all new, automated version of the PEGASUS software has been developed and tested. PEGASUS provides the hole-cutting and connectivity information between overlapping grids, and is used as the final part of the grid generation process for overset-grid computational fluid dynamics approaches. The new PEGASUS code (Version 5) has many new features: automated hole cutting; a projection scheme for fixing gaps in overset surfaces; more efficient interpolation search methods using an alternating digital tree; hole-size optimization based on adding additional layers of fringe points; and an automatic restart capability. The new code has also been parallelized using the Message Passing Interface standard. The parallelization performance provides efficient speed-up of the execution time by an order of magnitude, and up to a factor of 30 for very large problems. The results of three example cases are presented: a three-element high-lift airfoil, a generic business jet configuration, and a complete Boeing 777-200 aircraft in a high-lift landing configuration. Comparisons of the computed flow fields for the airfoil and 777 test cases between the old and new versions of the PEGASUS codes show excellent agreement with each other and with experimental results.

An upwind differencing scheme for the incompressible Navier-Stokes equations

Abstract The steady-state incompressible Navier–Stokes equations in two dimensions 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. The scheme is applicable to both steady-state and unsteady flow computations. In the current work steady-state applications are emphasized. Characteristic boundary conditions are formulated and used in the solution procedure. The overall scheme is capable of being run at extremely large pseudo-time steps, leading to fasr 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 two-dimensional circular cylinder.

PEGASUS 5: An Automated Preprocessor for Overset-Grid Computational Fluid Dynamics

An all new, automated version of the PEGASUS software has been developed and tested. PEGASUS provides the hole-cutting and connectivity information between overlapping grids and is used as the final part of the grid-generation process for overset-grid computational fluid dynamics approaches. The new PEGASUS code (Version 5) has many new features: automated hole cutting, a projection scheme for fixing small discretization errors in overset surfaces, more efficient interpolation search methods using an alternating digital tree and a stencil-jumping scheme, hole-size optimization based on adding additional layers of fringe points, and an automatic restart capability. The new code has also been parallelized using the message-passing interface standard. The parallelization performance provides efficient speedup of the execution time by an order of magnitude, and up to a factor of 30 for very large problems. The results of two example cases are presented: a three-element high-lift airfoil and a complete Boeing 777-200 aircraft in a high-lift landing configuration

Progress in high-lift aerodynamic calculations

The current work presents progress in the effort to numerically simulate the flow over high-lift aerodynamic components, namely, multi-element airfoils and wings in either a take-off or a landing configuration. The computational approach utilizes an incompressible flow solver and an overlaid chimera grid approach. A detailed grid resolution study is presented for flow over a three-element airfoil. Two turbulence models, a one-equation Baldwin-Barth model and a two equation k-omega model are compared. Excellent agreement with experiment is obtained for the lift coefficient at all angles of attack, including the prediction of maximum lift when using the two-equation model. Results for two other flap riggings are shown. Three-dimensional results are presented for a wing with a square wing-tip as a validation case. Grid generation and topology is discussed for computing the flow over a T-39 Sabreliner wing with flap deployed and the initial calculations for this geometry are presented.

Numerical solution of the incompressible Navier-Stokes equations for steady-state and time-dependent problems

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.An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a higher-order flux-difference splitting technique for the convective terms and a second-order central difference for the viscous terms. The steady-state solution of flow through a square duct with a 90 deg bend is computed and the results are compared with experimental data. Good agreement is observed. A comparison with an analytically known exact solution is then performed to verify the time accuracy of the algorithm. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented.

COMPUTATION OF VISCOUS FLOW FOR A BOEING 777 AIRCRAFT IN LANDING CONFIGURATION

A series of Navier-Stokes simulations of a complete Boeing 777-200 aircraft configured for landing is obtained using a structured overset grid process and the OVERFLOW CFD code. At approach conditions, the computed forces for the 777 computation are within 1.5% of experimental data for lift, and within 4% for drag. The computed lift is lower than the experiment at maximum-lift conditions, but shows closer agreement at post-stall conditions. The effect of sealing a span-wise gap between leading edge elements, and adding a chine onto the nacelle is computed at a high angle of attack. These additions make a significant difference in the flow over the wing near these elements. Detailed comparisons between computed and experimental surface pressures are shown. Good agreement is demonstrated at lower angles of attack, including a prediction of separated flow on the outboard flap.

Navier-Stokes Analysis of the Flow About a Flap Edge

The current study computationally examines one of the principal three-dimensional features of the e ow over a high-lift system, the e ow associated with a e ap edge. Structured, overset grids were used in conjunction with an incompressible Navier ‐Stokes solver to compute the e ow over a two-element highlift cone guration. The computations were run in a fully turbulent mode using the one-equation Baldwin‐Barth model. Specie c emphasis was given to the details of the e ow in the vicinity of the e ap edge, and so the geometry was simplie ed to isolate this region. The geometry consisted of an unswept wing, which spanned a wind-tunnel test section, equipped with a single-element e ap. Two e ap cone gurations were computed: a full-span and a half-span Fowler e ap. The chord-based Reynolds number was 3.7 3 10 6 for all cases. The results for the full-span e ap agreed with two-dimensional experimental results and verie ed the method. Grid topologies and related issues for the half-span e ap geometry are discussed. Results of the half-span e ap case are compared with three-dimensional experimental results, with emphasis on the e ow features associated with the e ap edge. The results show the effect of the vortex created by the e ap edge, including the impact on e ow separation and spanwise lift distribution.