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NASA NTRS1989

Euler and Navier-Stokes solutions for hypersonic flows

An upwind finite-element technique that uses cell-centered quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive unstructured grids in two and three dimensions. A perfect gas model as well as an equilibrium air model is implemented for solving high-speed flows. A first-order basic scheme and a higher-order flux-corrected transport (FCT) scheme have been implemented. This technique has been used to predict 'Type III and IV' shock interactions on a cylinder in two dimensions and a swept cylinder in three dimensions, with a view to determine the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are very distinctly captured with a sequence of adaptively-generated grids. Three-dimensional corner flow, typically encountered in engine inlets due to compression of the flow by ramps in the walls, is also modeled. This procedure is the first step in developing an integrated fluid, thermal, structural analysis capability for hypersonic flight vehicles like the National Aero-Space Plane.

Thareja, Rajiv R.↗

NASA NTRS1989

Solution techniques for incompressible flow problems

A three-step Petrov-Galerkin (PG)/operator spliting scheme for the time-dependent incompressible Navier-Stokes equations is proposed. Each time step is split into two Stokes problems and one nonlinear convection-diffusion problem. Using a PG technique on the two outer Stokes problems ensures a stable scheme despite equal-order interpolation, while using a streamline upwind PG scheme on the inner convection-diffusion problem ensures a numerically stable solution at high Reynolds numbers. Numerical tests of this method have been carried out.

Tezduyar, T. E.↗

NASA NTRS1990

Transonic Navier-Stokes solutions about a complex high-speed accelerator configuration

Three-dimensional transonic viscous flow computations are presented for a generic high-speed accelerator model which includes wing, body, fillets, and a no-flow through engine nacelle. Solutions are obtained from an algorithm for the compressible Navier-Stokes equations which incorporates an upwind-biased, flux-vector-splitting approach along with longitudinally-patched grids. Results are presented for fully turbulent flow assumptions and include correlations with wind tunnel data. A good quantitative agreement for the forebody surface pressure distribution is achieved between computations and the available wind-tunnel measurements at freestream Mach number equal to 0.9. Furthermore, it is demonstrated that the flow is stagnating around the boattail region due to separation from the aft-engine cowl lip.

Ghaffari, Farhad↗

NASA NTRS1990

Prediction of vortical flows on wings using incompressible Navier-Stokes equations

Numerical solutions to the incompressible Navier-Stokes equations are in greater demand than ever before as the field of computational fluid dynamics (CFD) increases its impact as an engineering tool. An implicit upwind-relation finite-difference scheme is developed for solving unsteady incompressible Navier-Stokes equations incorporating an artificial time derivative of the pressure to the continuity equation. The essential features observed in experiments for complicated vortical flows past three round-edged low-aspect-ratio wings at high angles of attack are reproduced both qualitatively and quantitatively.

Hsu, C.-H.↗

NASA NTRS1990

Vortical flows over delta wings and numerical prediction of vortex breakdown

Navier-Stokes solutions of subsonic vortical flow over a 75 deg sweep delta wing with a sharp leading edge are presented. The sensitivity of the solution to the numerical scheme is examined using both a partially upwind scheme and a scheme with central differencing in all directions. At moderate angles of attack, no vortex breakdown is observed, whereas the higher angle-of-attack cases exhibit breakdown. The effect of numerical grid density is investigated, and solutions that are obtained with various grid densities are compared with experimental data. An embedded grid approach is implemented to enable higher resolution in selected isolated flow regions, such as the leeward-side surface, the leading-edge vortical flow, and the vortex breakdown region.

Ekaterinaris, J. A.↗

NASA NTRS1990

Applications of an adaptive unstructured solution algorithm to the analysis of high speed flows

An upwind cell-centered scheme for the solution of steady laminar viscous high-speed flows is implemented on unstructured two-dimensional meshes. The first-order implementation employs Roe's (1981) approximate Riemann solver, and a higher-order extension is produced by using linear reconstruction with limiting. The procedure is applied to the solution of inviscid subsonic flow over an airfoil, inviscid supersonic flow past a cylinder, and viscous hypersonic flow past a double ellipse. A detailed study is then made of a hypersonic laminar viscous flow on a 24-deg compression corner. It is shown that good agreement is achieved with previous predictions using finite-difference and finite-volume schemes. However, these predictions do not agree with experimental observations. With refinement of the structured grid at the leading edge, good agreement with experimental observations for the distributions of wall pressure, heating rate and skin friction is obtained.

Thareja, R. R.↗

NASA NTRS1990

Shock interference studies on a circular cylinder at Mach 16

This paper presents the results of a computational study on the shock interference problems on a cylindrical body typical of an engine inlet cowl leading edge at a nominal Mach number of 16. The two-dimensional Navier-Stokes equations are solved assuming the flow to be in chemical and thermal equilibrium and using a finite element method. The algorithm employs a cell-centered fully implicit upwind scheme. Adaptively generated unstructured meshes of triangles and quadrilaterals are employed. Under certain conditions the finite element code resulted in oscillatory solutions for shock interference at Mach 16. Some of the causes of the unsteady behavior are identified, and to the extent possible, such situations are avoided in the present application. Two shock interference conditions involving a Type IV (supersonic jet) and a Type III (attaching shear layer) are solved. The results are compared with available experimental data and reasonable agreement is observed. A semi-empirical method is also used to estimate the maximum surface heat flux and static pressure.

Prabhu, Ramadas K.↗

NASA NTRS1990

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Slack, David C.↗

NASA NTRS1990

Efficient real gas Navier-Stokes computations of high speed flows using an LU scheme

An efficient method to account for the chemically frozen thermodynamic and transport properties of air in three dimensional Navier-Stokes calculations was demonstrated. This approach uses an explicitly specified equation of state (EOS) so that the fluid pressure, temperature and transport properties are directly related to the flow variables. Since the pressure is explicitly known as a general function of the flow variables no assumptions are made regarding the pressure derivatives in the construction of the flux Jacobians. The method is efficient since no sub-iterations are required to deduce the pressure and temperature from the flux variables and allows different equations of state to be easily supplied to the code. The flexibility of the EOS approach is demonstrated by implementing a high order TVD upwinding scheme based upon flux differencing and Van Leer's flux vector splitting. The EOS approach is demonstrated by computing the hypersonic flow through the corner region of two mutually perpendicular flat plates and through a simplified model of a scramjet module gap-seal configuration.

Coirier, William J.↗

NASA NTRS1990

Comparative study of computational efficiency of two LU schemes for non-equilibrium reacting flows

The systems of equations governing chemically nonequilibrium flows are solved numerically by two lower-upper(LU) algorithms, namely, LU-SSOR (Yoon and Jameson, 1987) and LU-SW (Steger and Warming, 1981). The methods of flux-Jacobian splitting differentiate the two LU algorithms. The LU-SSOR gives a simpler implicit operator with less temporal damping, while the LU-SW converges faster but requires more computation for each iteration. Relative efficiencies and mutual merits of these two LU algorithms are compared. The results show that LU-SW with upwind-differenced right-hand-side gives the best convergence.

Tsai, Y.-L. Peter↗

NASA NTRS1990

Boundary-layer heat and moisture budgets from FIFE

Aircraft stacks were flown upwind and downwind of the First International Satellite Land Surface Climatology Project Field Experiment site in Kansas to measure the heat and moisture budgets of the boundary layer under fairly clear skies for four daytime periods. The terms in the conservation equation are evaluated. The vertical flux divergence and advection do not account for the difference between surface and low-level aircraft flux estimates. Budget estimates of the surface fluxes using the aircraft data agree well with surface flux measurements, but extrapolation of the aircraft fluxes gives surface fluxes that are too low.

Desjardins, R. L.↗

NASA NTRS1990

Thermochemical nonequilibrium issues for earth reentry of Mars mission vehicles

The thermochemical environment about an axisymmetric 60-deg sphere-cone with a circular aft skirt is computed using the Langley Aerothermodynamic Upwind Relaxation Algorithm. Earth entry at 12 km/sec is examined at 70-km and 80-km altitude for two vehicle base radii of 2 m and 6 m. These four test cases bracket some proposed scenarios for earth reentry of a manned Mars mission aerobrake at this velocity. Thermochemical nonequilibrium results are examined for each case and compared with thermal equilibrium results produced by artificially accelerating vibrational relaxation rates and with equilibrium results produced by a viscous shock layer method.

Mitcheltree, R. A.↗

NASA NTRS1990

Comparison of three-dimensional nonequilibrium PNS codes

A comparison study has been conducted using four recently developed parabolized Navier-Stokes (PNS) codes which have the capability of predicting finite-rate, chemically reacting flows over three-dimensional bodies. These are the (1) UPS code, (2) the STUFF code, (3) the TONIC code, and (4) the VRA-PNS code. All of the codes use the same seven-species, single-temperature air chemistry model, but otherwise they are unique, with different capabilities and characteristics. The differences include upwinding vs central differencing, strongly-coupled vs weakly-coupled chemistry, shock capturing vs shock fitting, finite volume vs finite difference, and full PNS vs thin-layer PNS equations. Three test cases were utilized to compare the codes. The comparisons presented indicate a good agreement among the codes tested.

Buelow, Philip E.↗

NASA NTRS1990

Numerical methods for TVD transport and coupled relaxing processes in gases and plasmas

The construction of second-order upwind schemes for nonequilibrium plasmas, for both one- and two-fluid formulations is demonstrated. Coupled relaxation processes, including ionization kinetics and radiative processes and their algorithms for nonequilibrium, multiple temperature conditions are described as well. The paper applies the numerical techniques on some simple test cases, points out critical problems and their solutions, and makes qualitative comparisons with known results, whenever possible.

Cambier, Jean-Luc↗

NASA NTRS1990

Computational study for passive control of supersonic asymmetric vortical flows around cones

The unsteady, compressible, double and single thin-layer Navier-Stokes equations are used to numerically study for the passive control of steady and unsteady, supersonic asymmetric flows around circular and noncircular cones. The main computational scheme of the present study is the implicit upwind, flux-difference splitting, finite-volume scheme. Passive control of flow asymmetry is studied by using a vertical fin in the leeward plane of geometric symmetry and side strakes with and without thickness at different orientations. The study is focused on circular-section cones since they are the most potential section-shapes for strong flow asymmetry. Side-strakes passive control has been shown to be more efficient and practical than the vertical-fin passive control.

Liu, C. H.↗

NASA NTRS1990

Temporal-adaptive Euler/Navier-Stokes algorithm for unsteady aerodynamic analysis of airfoils using unstructured dynamic meshes

A temporal adaptive algorithm for the time-integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal adaptive algorithm is a time-accurate integration procedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.

Kleb, William L.↗

NASA NTRS1990

Predicted aerodynamics for a proposed personnel launch vehicle

The Langley Aerothermodynamic Upwind Relaxation Algorithm has been modified to compute equilibrium flows over shapes at hypersonic velocities. As an initial test of the modified code, solutions were obtained for a paraboloid at Mach 6 wind-tunnel test conditions in CF4 gas and at Mach 16.85 flight conditions in equilibrium air that approximated the normal shock density ratio for the experimental test. Solutions for a lifting-body concept that is proposed for a Personnel Launch System were compared with test results at Mach 6 in CF4 over an angle-of-attack range of 15 to 35 deg and with results for nominal entry flight conditions at Mach 15.

Greene, Francis A.↗

NASA NTRS1990

CFD propels NASP propulsion progress

The most complex aerothermodynamics encountered in the National Aerospace Plane (NASP) propulsion system are associated with the fuel-mixing and combustion-reaction flows of its combustor section; adequate CFD tools must be developed to model shock-wave systems, turbulent hydrogen/air mixing, flow separation, and combustion. Improvements to existing CFD codes have involved extension from two dimensions to three, as well as the addition of finite-rate hydrogen-air chemistry. A novel CFD code for the treatment of reacting flows throughout the NASP, designated GASP, uses the most advanced upwind-differencing technology.

Povinelli, Louis A.↗