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At least 343 records · Page 19

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NASA NTRS1989

Navier-Stokes solutions for flows related to store separation

The objective is developing CFD capabilities to obtain solutions for viscous flows about generic configurations of internally and externally carried stores. The emphasis is placed on the supersonic flow regime with extensions being made to the transonic regime. The project is broken into four steps: (1) Cavity flows for internal carriage configurations; (2) High angle of attack flows, which may be experienced during the separation of the stores: (3) Flows about a body near a flat plate for external carriage configurations; and (4) Flows about a body inside or in the proximity of a cavity. Three-dimensional unsteady cavity flow solutions are obtained by an explicit, MacCormack algorithm, EMCAV3, for open, close, and transitional cavities. High angle of attack flows past cylinders are solved by an implicit, upwind algorithm. All the results compare favorably with the experimental data. For flows about multiple body configurations, the Chimera embedding scheme is modified for finite-volume and multigrid algorithms, MaGGiE. Then a finite volume, implicit, upwind, multigrid Navier-Stokes solver which uses on overlapped/embedded and zonal grids, VUMXZ3, is developed from the CFL3D code. Supersonic flows past a cylinder near a flat plate are computed using this code. The results are compared with the experimental data. Currently the VUMXZ3 code is being modified to accomplish step 4 of this project. Wind tunnel experiments are also being conducted for validation purposes.

Baysal, Oktay↗

NASA NTRS1989

A comparative study of Navier-Stokes codes for high-speed flows

A comparative study was made with four different codes for solving the compressible Navier-Stokes equations using three different test problems. The first of these cases was hypersonic flow through the P8 inlet, which represents inlet configurations typical of a hypersonic airbreathing vehicle. The free-stream Mach number in this case was 7.4. This 2-D inlet was designed to provide an internal compression ratio of 8. Initial calculations were made using two state-of-the-art finite-volume upwind codes, CFL3D and USA-PG2, as well as NASCRIN, a code which uses the unsplit finite-difference technique of MacCormack. All of these codes used the same algebraic eddy-viscosity turbulence model. In the experiment, the cowl lip was slightly blunted; however, for the computations, a sharp cowl leading edge was used to simplify the construction of the grid. The second test problem was the supersonic (Mach 3.0) flow in a three-dimensional corner formed by the intersection of two wedges with equal wedge angles of 9.48 degrees. The flow in such a corner is representative of the flow in the corners of a scramjet inlet. Calculations were made for both laminar and turbulent flow and compared with experimental data. The three-dimensional versions of the three codes used for the inlet study (CFL3D, USA-PG3, and SCRAMIN, respectively) were used for this case. For the laminar corner flow, a fourth code, LAURA, which also uses recently-developed upwind technology, was also utilized. The final test case is the two-dimensional hypersonic flow over a compression ramp. The flow is laminar with a free-stream Mach number of 14.1. In the experiment, the ramp angle was varied to change the strength of the ramp shock and the extent of the viscous-inviscid interaction. Calculations were made for the 24-degree ramp configuration which produces a large separated-flow region that extends upstream of the corner.

Rudy, David H.↗

NASA NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux difference splitting method was extended to treat 2-D viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-state Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Shuen, Jian-Shun↗

NASA NTRS1989

Conservation equations and physical models for hypersonic air flows over the aeroassist flight experiment vehicle

The code development and application program for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA), with emphasis directed toward support of the Aeroassist Flight Experiment (AFE) in the near term and Aeroassisted Space Transfer Vehicle (ASTV) design in the long term is reviewed. LAURA is an upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3-D, viscous, hypersonic flows in chemical and thermal nonequilibrium. The algorithm is derived using a finite volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large, block tri-diagonal systems. A single relaxation step depends only on information from nearest neighbors. Predictions for pressure distributions, surface heating, and aerodynamic coefficients compare well with experimental data for Mach 10 flow over an AFE wind tunnel model. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium over the full scale AFE configuration obtained on a multi-domain grid are discussed.

Gnoffo, Peter A.↗

NASA NTRS1990

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.

Rogers, Stuart E.↗

NASA NTRS1990

A multiblock multigrid three-dimensional Euler equation solver

Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit solvers (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.

Cannizzaro, Frank E.↗

NASA NTRS1990

Prediction of the Thrust Performance and the Flowfield of Liquid Rocket Engines

In an effort to improve the current solutions in the design and analysis of liquid propulsive engines, a computational fluid dynamics (CFD) model capable of calculating the reacting flows from the combustion chamber, through the nozzle to the external plume, was developed. The Space Shuttle Main Engine (SSME) fired at sea level, was investigated as a sample case. The CFD model, FDNS, is a pressure based, non-staggered grid, viscous/inviscid, ideal gas/real gas, reactive code. An adaptive upwinding differencing scheme is employed for the spatial discretization. The upwind scheme is based on fourth order central differencing with fourth order damping for smooth regions, and second order central differencing with second order damping for shock capturing. It is equipped with a CHMQGM equilibrium chemistry algorithm and a PARASOL finite rate chemistry algorithm using the point implicit method. The computed flow results and performance compared well with those of other standard codes and engine hot fire test data. In addition, the transient nozzle flowfield calculation was also performed to demonstrate the ability of FDNS in capturing the flow separation during the startup process.

Wang, T.-S.↗

NASA NTRS1991

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

A streamwise upwind algorithm for solving the unsteady 3-D Navier-Stokes equations was extended to handle the moving grid system. It is noted that the finite volume concept is essential to extend the algorithm. The resulting algorithm is conservative for any motion of the coordinate system. Two extensions to an implicit method were considered and the implicit extension that makes the algorithm computationally efficient is implemented into Ames's aeroelasticity code, ENSAERO. The new flow solver has been validated through the solution of test problems. Test cases include three-dimensional problems with fixed and moving grids. The first test case shown is an unsteady viscous flow over an F-5 wing, while the second test considers the motion of the leading edge vortex as well as the motion of the shock wave for a clipped delta wing. The resulting algorithm has been implemented into ENSAERO. The upwind version leads to higher accuracy in both steady and unsteady computations than the previously used central-difference method does, while the increase in the computational time is small.

Obayashi, Shigeru↗

NASA NTRS1991

Sharp monotonic resolution of discontinuities without clipping of narrow extrema

A strategy is presented for accurately simulating highly convective flows containing discontinuities such as density fronts or shock waves, without distorting smooth profiles or clipping narrow local extrema. The convection algorithm is based on non-artificially-diffusive third-order upwinding in smooth regions, with automatic adaptive stencil expansion to (in principle, arbitrarily) higher order upwinding locally, in regions of rapidly changing gradients. This is highly cost-effective because the wider stencil is used only where needed - in isolated narrow regions. A recently developed universal limiter assures sharp monotonic resolution of discontinuities without introducing artificial diffusion or numerical compression. An adaptive discriminator is constructed to distinguish between spurious overshoots and physical peaks; this automatically relaxes the limiter near local turning points, thereby avoiding loss of resolution in narrow extrema. Examples are given for one-dimensional pure convection of scalar profiles at constant velocity.

Leonard, B. P.↗

NASA NTRS1990

Flux-difference split scheme for turbulent transport equations

This paper describes a high accuracy upwind method to solve the mean compressible flow equations closed with two-equation turbulence models. A flux-difference splitting scheme is developed to compute the flowfield without introducing oscillations into the solution. A high-order accuracy scheme is used to predict both the mean flow variables and the turbulence variables. Results comparing two different two-equation turbulence models are presented for supersonic flow over a flat plate and a compressible, free shear-layer. The non-oscillatory behavior of the upwind scheme is demonstrated on the free shear-layer.

Morrison, J. H.↗

NASA NTRS1990

Computation and control of asymmetric vortex flow around circular cones using Navier-Stokes equations

The unsteady, compressible, thin-layer and full Navier-Stokes equations are used to numerically simulate steady and unsteady asymmetric, supersonic, locally conical flows around a 5-deg semiapex angle circular cone. The main computational scheme is the implicit, upwind, flux-difference splitting, finite-volume scheme. Comparison of asymmetric flow solutions using the thin-layer and full Navier-Stokes equations is presented and discussed. The implicit, upwind, flux-vector splitting, finite-volume scheme has also been used to solve for the unsteady asymmetric flow with vortex shedding. The unsteady-flow solution using the flux-vector splitting scheme perfectly agrees with the previously obtained solution using the flux-difference splitting scheme. Passive control of asymmetric flows has been demonstrated and studied using sharp- and round-edged, thick and thin strakes.

Kandil, Osama A.↗

NASA NTRS1991

Navier-Stokes solutions for an oscillating double-delta wing

An upwind-biased implicit scheme is used to investigate steady-state and unsteady Navier-Stokes solutions of the vortical flow over a double-delta wing configuration. The governing equations are solved numerically with a fully upwind, implicit, iterative, and factorized numerical scheme. Steady-state solutions for fixed angles of attack and unsteady solutions for a sinusoidal oscillatory motion are obtained. The steady-state solutions on the baseline grid are in agreement with the experiment, and grid refinements show some improvements of the predictions. The higher-order accuracy of the present scheme yields equivalent solutions on smaller grid densities compared to solutions obtained with a second-order accurate method on larger grids. As the angle of attack increases, the grid resolution requirements for adequate resolution of the leeward-side vortical flowfield become very severe. The unsteady solutions are in general agreement with the measurements and show a qualitative correlation with the experiment.

Ekaterinaris, John A.↗

NASA NTRS1991

Numerical analysis of a nuclear fuel element for nuclear thermal propulsion

A computational fluid dynamics model with porosity and permeability formulations in the transport equations has been developed to study the concept of nuclear thermal propulsion through the analysis of a pulsed irradiation of a particle bed element (PIPE). The numerical model is a time-accurate pressure-based formulation. An adaptive upwind scheme is employed for spatial discretization. The upwind scheme is based on second- and fourth-order central differencing with adaptive artificial dissipation. Multiblocked porosity regions have been formulated to model the cold frit, particle bed, and hot frit. Multiblocked permeability regions have been formulated to describe the flow shaping effect from the thickness-varying cold frit. Computational results for several zero-power density PIPEs and an elevated-particle-temperature PIPE are presented. The implications of the computational results are discussed.

Wang, Ten-See↗

NASA NTRS1991

A practical implementation of turbulence models for the computation of three-dimensional separated flows

An upwind MUSCL-type implicit scheme for the three-dimensional Navier-Stokes equations is presented and details on the implementation for three-dimensional flows of a 'diagonal' upwind implicit operator are developed. Turbulence models for separated flows are also described with an emphasis on the numerical specificities of the Johnson-King nonequilibrium model. Good predictions of separated two- and three-dimensional flows are demonstrated.

Marx, Yves P.↗

NASA NTRS1991

Development of new flux splitting schemes

Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for CFD. This is especially important for solution of complex three-dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for both their capability of resolving discontinuities and their sound theoretical basis in characteristic theory for hyperbolic systems. With this in mind, two new flux splitting techniques are presented for upwind differencing.

Liou, MENG-S.↗

NASA NTRS1992

An iterative implicit DDADI algorithm for solving the Navier-Stokes equation

An algorithm utilizing a first order upwind split flux technique and the diagonally dominant treatment is proposed to be the temporal operator for solving the Navier-Stokes equations. Given the limit of a five point stencil, the right hand side flux derivatives are formulated by several commonly used central and upwind schemes. Their performances are studied through a test case of free vortex convection in a uniform stream. From these results, a superior treatment for evaluating the flux term is proposed and compared with the rest. The application of the proposed algorithm to the full Navier-Stokes equations is demonstrated through a calculation of flow over a backward facing step. Results are compared against the calculation done by using the fourth order central differencing scheme with artificial damping.

Chen, S. C.↗

NASA NTRS1991

A video-aided study of sea spikes in radar backscatter at moderate incidence

Backscatter from a lake was measured at a 37-deg incidence angle using an FM-CW radar operating on X band and C band simultaneously. A limited amount of Ka-band data was also collected at 50 deg incidence. A video camera recorded the activity within the footprint looking upwind and crosswind. The video showed that breaking waves at all look directions and wedge-shaped waves when looking upwind consistently produced spikes in the radar time series. However, 62 percent to 90 percent of the spikes were not attributable to any surface structure visible on the video picture except wave crests. These spikes may be due to specular reflections or micro-scale breaking too small to be seen. Individual contributions to the backscattering coefficient were calculated for unattributed spikes, breaker spikes, and wedge spikes.

Bush, Daniel A.↗

NASA NTRS1991

Computational methods for shock waves in three-dimensional supersonic flow

A central artificial-viscosity and an upwind-biased difference method are contrived to solve the Euler equations for flowfields over typical spacecrafts. The spatial discretization is based on either nodal or cell-vertex formulation in the domain extending from free stream to the end of the vehicle. The outer boundary is treated as a bow shock in the first method but is placed in the free stream in the second, which captures both bow and internal shocks using an approximate Riemann solver based on high-order extrapolation to the cell face. These methods were tested for the Shuttle and Hermes orbiters at wind-tunnel conditions and angles of attack ranging from 0 to 60 deg. The artificial-viscosity method incorporated with a shock-fitting procedure shows smeared crossflow and wing-shock positions and required 15 percent more CPU per node than the upwind method. Greater flexibility and robustness is demonstrated by the latter on a fixed grid for all cases considered.

Li, Chien-Peng↗