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NASA NTRS1997

An Adaptive Flow Solver for Air-Borne Vehicles Undergoing Time-Dependent Motions/Deformations

This report describes a concurrent Euler flow solver for flows around complex 3-D bodies. The solver is based on a cell-centered finite volume methodology on 3-D unstructured tetrahedral grids. In this algorithm, spatial discretization for the inviscid convective term is accomplished using an upwind scheme. A localized reconstruction is done for flow variables which is second order accurate. Evolution in time is accomplished using an explicit three-stage Runge-Kutta method which has second order temporal accuracy. This is adapted for concurrent execution using another proven methodology based on concurrent graph abstraction. This solver operates on heterogeneous network architectures. These architectures may include a broad variety of UNIX workstations and PCs running Windows NT, symmetric multiprocessors and distributed-memory multi-computers. The unstructured grid is generated using commercial grid generation tools. The grid is automatically partitioned using a concurrent algorithm based on heat diffusion. This results in memory requirements that are inversely proportional to the number of processors. The solver uses automatic granularity control and resource management techniques both to balance load and communication requirements, and deal with differing memory constraints. These ideas are again based on heat diffusion. Results are subsequently combined for visualization and analysis using commercial CFD tools. Flow simulation results are demonstrated for a constant section wing at subsonic, transonic, and a supersonic case. These results are compared with experimental data and numerical results of other researchers. Performance results are under way for a variety of network topologies.

Singh, Jatinder↗

NASA NTRS1997

Some Approaches Towards Constructing Optimally Efficient Multigrid Solvers for the Inviscid Flow Equations

Some important advances took place during the last several years in the development of genuinely multidimensional upwind schemes for the compressible Euler equations. In particular, a robust, high-resolution genuinely multidimensional scheme which can be used for any of the flow regimes computations was constructed. This paper summarizes briefly these developments and outlines the fundamental advantages of this approach.

Sidilkover, David↗

NASA NTRS1997

Comparison of Several Dissipation Algorithms for Central Difference Schemes

Several algorithms for introducing artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical results are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme.

Swanson, R. C.↗

NASA NTRS1998

Aeroheating Predictions for X-34 Using an Inviscid-Boundary Layer Method

Radiative equilibrium surface temperatures and surface heating rates from a combined inviscid-boundary layer method are presented for the X-34 Reusable Launch Vehicle for several points along the hypersonic descent portion of its trajectory. Inviscid, perfect-gas solutions are generated with the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) and the Data-Parallel Lower-Upper Relaxation (DPLUR) code. Surface temperatures and heating rates are then computed using the Langley Approximate Three-Dimensional Convective Heating (LATCH) engineering code employing both laminar and turbulent flow models. The combined inviscid-boundary layer method provides accurate predictions of surface temperatures over most of the vehicle and requires much less computational effort than a Navier-Stokes code. This enables the generation of a more thorough aerothermal database which is necessary to design the thermal protection system and specify the vehicle's flight limits.

Riley, Christropher J.↗

NASA NTRS1998

Flow and Turbulence Modeling and Computation of Shock Buffet Onset for Conventional and Supercritical Airfoils

Flow and turbulence models applied to the problem of shock buffet onset are studied. The accuracy of the interactive boundary layer and the thin-layer Navier-Stokes equations solved with recent upwind techniques using similar transport field equation turbulence models is assessed for standard steady test cases, including conditions having significant shock separation. The two methods are found to compare well in the shock buffet onset region of a supercritical airfoil that involves strong trailing-edge separation. A computational analysis using the interactive-boundary layer has revealed a Reynolds scaling effect in the shock buffet onset of the supercritical airfoil, which compares well with experiment. The methods are next applied to a conventional airfoil. Steady shock-separated computations of the conventional airfoil with the two methods compare well with experiment. Although the interactive boundary layer computations in the shock buffet region compare well with experiment for the conventional airfoil, the thin-layer Navier-Stokes computations do not. These findings are discussed in connection with possible mechanisms important in the onset of shock buffet and the constraints imposed by current numerical modeling techniques.

Bartels, Robert E.↗

NASA NTRS1996

Dependence of the Normalized Radar Cross Section of Water Waves on Bragg Wavelength-Wind Speed Sensitivity

Measurements of the normalized radar cross section (sigma(sup o)) made by the YSCAT ultrawideband scatterometer during an extended deployment on the Canada Centre for Inland Waters(CCIW) Research Tower located at Lake Ontario are analyzed and compared with anemometer wind measurements to study the sensitivity of (sigma(sup o)) to the wind speed as a function of the Bragg wavelength. This paper concentrates on upwind and downwind azimuth angles in the wind speed range of 4.5-12 m/s. While YSCAT collected measurements of sigma(sup o) at a variety of frequencies and incidence angles, this paper focuses on frequencies of 2.0, 3.05, 5.30, 10.02, and 14.0 GHz and incidence angles within the Bragg regime, 30-50 deg. Adopting a power law model to describe the relationship between sigma(sup o) and wind speed, both wind speed exponents and upwind/downwind (u/d) ratios of sigma(sup o) are found using least squares linear regression. The analysis of the wind speed exponents and u/d ratios show that shorter Bragg wavelengths (Lambda less than 4 cm) are the most sensitive to wind speed and direction. Additionally, vertical polarization (V-pol) sigma(sup o) is shown to be more sensitive to wind speed than horizontal polarization (H-pol) sigma(sup o), while the H-pol u/d ratio is larger than the V-pol u/d ratio.

Long, David G.↗

NASA NTRS1995

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.

Rogers, Stuart E.↗

NASA NTRS1998

Aeroheating Predictions for X-34 Using an Inviscid-Boundary Layer Method

Riley, Christopher J.↗

NASA NTRS1998

Computational Aeroheating Predictions for X-34

Radiative equilibrium surface temperatures, heating rates, streamlines, surface pressures, and flow-field features as predicted by the Langley Aerothermodynamic Upwind Relaxation Algorithm (Laura) are presented for the X-34 Technology Demonstrator. Results for two trajectory points corresponding to entry peak heating and two control surface deflections are discussed. This data is also discussed in context of Thermal Protection System (TPS) design issues. The work presented in this report is part of a larger effort to define the X-34 aerothermal environment, including the application of engineering codes and wind-tunnel studies.

Kelb, William L.↗

NASA NTRS1993

A Grid-resolved Analysis of Base Flowfield for a Four-Engine Clustered Nozzle Configuration

The objective of this study is to propose a computational methodology that can effectively anchor the base flowfield of a four-engine clustered nozzle configuration. This computational methodology is based on a three-dimensional, viscous flow, pressure-based computational fluid dynamics (CFD) formulation. For efficient CFD calculation, a Prandtl-Meyer solution treatment is applied to the algebraic grid lines for initial plume expansion resolution. As the solution evolves, the computational grid is adapted to the pertinent flow gradients. The CFD model employs an upwind scheme in which second- and fourth-order central differencing schemes with artificial dissipation are used. The computed quantitative base flow properties such as the radial base pressure distributions, model centerline static pressure, Mach number and impact pressure variations, and base pressure characteristic curve agreed reasonably well with those of the measurement.

Wang, Ten-See↗

NASA NTRS1998

Computational Aeroheating Predictions for X-34

Radiative equilibrium surface temperatures, heating rates, streamlines, surface pressures, and flow-field features as predicted by the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) are presented for the X-34 Technology Demonstrator. Results for two trajectory points corresponding to entry peak heating and two control surface deflections are discussed. This data is also discussed in the context of Thermal Protection System (TPS) design issues. The work presented in this report is part of a larger effort to define the X-34 aerothermal environment, including the application of engineering codes and wind-tunnel studies.

Kleb,William H.↗

NASA NTRS1998

The Local ISM and its Interaction with the Winds of Nearby Late-type Stars

We present new Goddard High-Resolution Spectrograph (GHRS) observations of the Ly-alpha and Mg II absorption lines seen toward the nearby stars 61 Cyg A and 40 Eri A. We use these data to measure interstellar properties along these lines of sight and to search for evidence of circumstellar hydrogen walls, which are produced by collisions between the stellar winds and the Local InterStellar Medium (LISM). We were able to model the Ly-alpha lines of both stars without hydrogen-wall absorption components, but for 61 Cyg A the fit required a stellar Ly-alpha, line profile with an improbably deep self-reversal, and for 40 Eri A the fit required a very low deuterium-to-hydrogen ratio that is inconsistent with previous GHRS measurements. Since these problems could be rectified simply by including stellar hydrogen-wall components with reasonable attributes, our preferred fits to the data include these components. We have explored several ways in which the hydrogen-wall properties measured here and in previous work can be used to study stellar winds and the LISM. We argue that the existence of a hydrogen wall around 40 Eri A and a low H I column density along that line of sight imply that either the interstellar density must decrease toward 40 Eri A or the hydrogen ionization fraction (chi) must increase. We find that hydrogen-wall temperatures are larger for stars with faster velocities through the LISM. The observed temperature-velocity relation is consistent with the predictions of hydromagnetic shock jump conditions. More precise comparison of the data and the jump conditions suggests crude upper limits for both chi and the ratio of magnetic to thermal pressure in the LISM (alpha): chi less than 0.6 and alpha less than 2. The latter upper limit corresponds to a limit on the LISM magnetic field of B less than 5 micro G. These results imply that the plasma Mach number of the interstellar wind flowing into the heliosphere is M(sub A) greater than 1.3, which indicates that the collision is supersonic and that there should therefore be a bow shock outside the heliopause in the upwind direction. Finally, we estimate stellar wind pressures (P sub wind) from the measured hydrogen-wall column densities. These estimates represent the first empirical measurements of wind properties for late-type main-sequence stars. The wind pressures appear to be correlated with stellar X-ray surface fluxes, F(x), in a manner consistent with the relation P(wind) varies as F(x)(exp -1/2), a relation that is also consistent with the variations of P(sub wind) and F(sub x) observed during the solar activity cycle. If this relation can in fact be generalized to solar-like stars, as is suggested by our data, then it is possible to estimate stellar wind properties simply by measuring stellar X-rays. One implication of this is that stellar wind pressures and mass-loss rates are then predicted to increase with time, since F(sub x) is known to decrease with stellar age.

Wood, Brian E.↗

NASA NTRS1996

Computational Modeling of Multi-Phase/Multi-Species Flows with Applications to Liquid Rocket Engines

Accurate prediction of all physical phenomena in a combustion chamber is essential for better understanding of the system performance. Atomization, evaporation, combustion, chemical kinetics, and turbulence are those processes of great importance that need to be well understood. Processes involving the liquid phase in a combustion chamber will be further complicated under supercritical conditions. More advanced and accurate numerical techniques are required to extend our understanding of the above phenomena. A computer program for multi-species/multi-phase flow was developed for NASA/MSFC in 1992. This code, called Liquid Thrust Chamber Performance (LTCP) program takes an Eulerian- Eulerian approach and is based on the Total Variation Diminishing (TVD) technique with Lax-Friedrichs upwind method. Under the NASA/ASEE SFFP the LTCP code was used to predict the performance characteristics of several engines that were of particular interest to NASA. This code was also successful in a combustion detonation study. Converting the program to the PC platform was accomplished which extends usability and makes it available to a wider range of users. The Eulerian formulation of the liquid phase provides a suitable model that can be extended to include combustion modeling under supercritical conditions. The results have been compared against the ones of other codes and available measured data. The algorithm proved to be robust and efficient for problems with stiff source terms.

Navaz, Homayun K.↗

NASA NTRS1960

Effects of Control-Response Characteristics on the Capability of Helicopter for Use as a Gun Platform

An investigation with a variable-stability helicopter was undertaken to ascertain the steadiness and ability to "hold on" to the target of a helicopter employed as a gun platform. Simulated tasks were per formed under differing flight conditions with the control-response characteristics of the helicopter varied for each task. The simulated gun-platform mission included: Variations of headings with respect to wind, constant altitude and "swing around" to a wind heading of 0 deg, and increases in altitude while performing a swing around to a wind heading of 0 deg. The results showed that increases in control power and damping increased pilot ability to hold on to the target with fewer yawing oscillations and in a shorter time. The results also indicated that wind direction must be considered in accuracy assessment. Greatest accuracy throughout these tests was achieved by aiming upwind.

Pegg, Robert J.↗

NASA NTRS1998

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

Frink, Neal T.↗

NASA NTRS1999

A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

Bui, Trong T.↗

NASA NTRS1998

Flow Applications of the Least Squares Finite Element Method

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Jiang, Bo-Nan↗

NASA NTRS1998

Effect of Reduced Frequency on Super Maneuver Delta Wing

The unsteady, three-dimensional, Reynolds averaged Navier Stokes equations (NS) are used to simulate and study the flow response around a delta wing undergoing a pitch-up motion up to 90 degrees amplitude. The governing equations are solved time-accurately using the upwind. Roe flux-difference splitting, finite volume scheme. The primary model under consideration consists of a 76 degree swept, sharp-edged delta wing of zero thickness. The Reynolds number and Mach number are 0.45 X 10(exp 6) and .03 respectively. The wing is forced to pitch-up through a ramp function, using a wide range of reduced frequency to provide a good understanding of reduced frequency effect on high amplitude pitch maneuvers. Three reduced frequency values of .0834, 0.134 and 0.04, are used in this study. The computed results are compared with each other as well as the existing experimental data.

Abdelhamid, Yahia A.↗