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Vortex flows caused by a swept wing are described in some detail. The thin-shear-layer Navier-Stokes equations with an algebraic eddy-viscosity turbulence model are solved. An implicit, factored numerical scheme is used. On the upper surface of the wing, flow is primarily along the free-stream and spanwise direction, respectively, at small and large angles of attack.
Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions.
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.
Scramjet simulant-gas exhaust flows are computed using two-dimensional Navier-Stokes (NS) equations. The NS equations are solved using an implicit, upwind, finite-volume scheme, and the Reynolds stresses are modeled algebraically. The solutions are compared with experimental data where the freestream and the nozzle exhaust fluids are air. The NS equations for the flow, where the scramjet exhaust simulant gas is a mixture of Freon-12 and argon, are solved by an explicit, finite difference scheme. The results are compared with experimental data, and certain discrepancies are explained.
Full three-dimensional Navier-Stokes computational results are compared with new experimental measurements for the flowfield within a round diffusing S-duct. The present study extends previous computational and experimental results for a similar smaller scale S-duct. Predicted results are compared with the experimental static and total pressure fields, and velocity vectors. Additionally, wall pressures, velocity profiles in wall coordinates, and skin friction values are presented. The CFD results employ algebraic and k-epsilon turbulence models. The CFD computed and experimentally determined separated flowfield is carefully examined.
A lattice Boltzmann model is presented which gives the complete Navier-Stokes equation and may provide an efficient parallel numerical method for solving various fluid problems. The model uses the single-time relaxation approximation and a particular Maxwell-type distribution. The model eliminates exactly (1) the non-Galilean invariance caused by a density-dependent coefficient in the convection term and (2) a velocity-dependent equation of state.
Full three-dimensional Navier-Stokes computational results are compared with new experimental measurements for the flowfield within a round diffusing S-duct. The present study extends previous computational and experimental results for a similar smaller scale S-duct. Predicted results are compared with the experimental static and total pressure fields, and velocity vectors. Additionally, wall pressures, velocity profiles in wall coordinates, and skin friction values are presented. The CFD results employ algebraic and k-epsilon turbulence models. The CFD computed and experimentally determined separated flowfield is carefully examined.
A multi-dimensional upwind scheme for solving the Euler equations has been extended to solve the Navier-Stokes equations. These methods share the property of not requiring body-fitted computational grids. A time advance scheme which is second-order accurate in time and space has been developed for use in conjunction with state-vector splitting to accurately resolve regions with significant gradients in flow quantities. The scheme has been tested on several simple viscous flow problems for which analytic solutions are known; the agreement of computation with theory is excellent.
A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.
A full Navier-Stokes analysis was performed to evaluate the performance of the subsonic diffuser of a NASA Lewis Research Center 70/30 mixed-compression bifurcated supersonic inlet for high speed civil transport application. The PARC3D code was used in the present study. The computations were also performed when approximately 2.5 percent of the engine mass flow was allowed to bypass through the engine bypass doors. The computational results were compared with the available experimental data which consisted of detailed Mach number and total pressure distribution along the entire length of the subsonic diffuser. The total pressure recovery, flow distortion, and crossflow velocity at the engine face were also calculated. The computed surface ramp and cowl pressure distributions were compared with experiments. Overall, the computational results compared well with experimental data. The present CFD analysis demonstrated that the bypass flow improves the total pressure recovery and lessens flow distortions at the engine face.
A method for generating high quality unstructured triangular grids for high Reynolds number Navier-Stokes calculations about complex geometries is described. Careful attention is paid in the mesh generation process to resolving efficiently the disparate length scales which arise in these flows. First the surface mesh is constructed in a way which ensures that the geometry is faithfully represented. The volume mesh generation then proceeds in two phases thus allowing the viscous and inviscid regions of the flow to be meshed optimally. A solution-adaptive remeshing procedure which allows the mesh to adapt itself to flow features is also described. The procedure for tracking wakes and refinement criteria appropriate for shock detection are described. Although at present it has only been implemented in two dimensions, the grid generation process has been designed with the extension to three dimensions in mind. An implicit, higher-order, upwind method is also presented for computing compressible turbulent flows on these meshes. Two recently developed one-equation turbulence models have been implemented to simulate the effects of the fluid turbulence. Results for flow about a RAE 2822 airfoil and a Douglas three-element airfoil are presented which clearly show the improved resolution obtainable.
We present details and performance of a pressure based multigrid solution procedure for the Navier-Stokes equations discretized on triangular grids. The discretization uses a control volume methodology, with linear inter-nodal variation of the flow variables. The use of the multigrid technique provides rapid and grid-independent rates of convergence. Three model driven cavity flows are computed, and the performance of the method at several grid densities and Reynolds numbers is reported. Representative flow fields characterizing the viscous eddies are also presented.
An algebraic multigrid scheme is presented for solving the discrete Navier-Stokes equations to second-order accuracy using the defect-correction method. Solutions have been obtained for problems involving both structured and unstructured meshes, with the resolution and resolution grading controlled by global and local mesh refinements. The solver is efficient and robust to the extent that no underrelaxation of variables has been required to ensure convergence, but rates of convergence can be improved with small amounts of underrelaxation of the velocity-pressure coupling. Provided that the computational mesh can resolve the flow field, convergence characteristics are almost mesh independent. Rates of convergence actually improve with refinement, asymptotically approaching mesh independent values. For extremely coarse meshes where dispersive truncation errors would be expected to prevent convergence (or even induce divergence), solutions can still be obtained by using explicit underrelaxation in the iterative cycle.
Under the Advanced Subsonic Technology (AST) Program, an aeroelastic analysis code (TURBO-AE) based on Navier-Stokes equations is currently under development at NASA Lewis Research Center s Machine Dynamics Branch. For a blade row, aeroelastic instability can occur in any of the possible interblade phase angles (IBPA s). Analyzing small IBPA s is very computationally expensive because a large number of blade passages must be simulated. To reduce the computational cost of these analyses, we used time shifted, or phase-lagged, boundary conditions in the TURBO-AE code. These conditions can be used to reduce the computational domain to a single blade passage by requiring the boundary conditions across the passage to be lagged depending on the IBPA being analyzed. The time-shifted boundary conditions currently implemented are based on the direct-store method. This method requires large amounts of data to be stored over a period of the oscillation cycle. On CRAY computers this is not a major problem because solid-state devices can be used for fast input and output to read and write the data onto a disk instead of storing it in core memory.
This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.
Numerical simulations are performed using a Reynolds-averaged Navier-Stokes (RANS) flow solver for a circulation control airfoil. 2D and 3D simulation results are compared to a circulation control wind tunnel test conducted at the NASA Langley Basic Aerodynamics Research Tunnel (BART). The RANS simulations are compared to a low blowing case with a jet momentum coefficient, C(sub u), of 0:047 and a higher blowing case of 0.115. Three dimensional simulations of the model and tunnel walls show wall effects on the lift and airfoil surface pressures. These wall effects include a 4% decrease of the midspan sectional lift for the C(sub u) 0.115 blowing condition. Simulations comparing the performance of the Spalart Allmaras (SA) and Shear Stress Transport (SST) turbulence models are also made, showing the SST model compares best to the experimental data. A Rotational/Curvature Correction (RCC) to the turbulence model is also evaluated demonstrating an improvement in the CFD predictions.
A fully implicit set of boundary conditions is developed for the solution of the parabolized Navier-Stokes equations for supersonic flow in two dimensions. Shock fitting is employed at the shock and the body has no-slip and specified temperature conditions. A specified heat transfer condition at the wall can be handled in a similar manner. In addition, the shock location is advanced in space in a fully implicit manner by utilizing the Rankine-Hugoniot conditions along with global conservation of mass.
To study the nonlinear physics of inhomogeneous turbulent shear flow, the unaveraged Navier-Stokes equations are solved numerically. For initial conditions a three-dimensional cosine velocity fluctuation and a mean-velocity profile with a step are used. Although the initial conditions are nonrandom. The flow soon becomes turbulent. Concentrated turbulent energy develops near the plane where the mean velocity gradient is initially infinite. The terms in the one-point correlation equation for turbulent energy, including those for the diffusion and production of turbulence, are calculated, the diffusion terms tend to make the turbulence more homogeneous.