Scott L. Lawrence

Upwind Algorithm for the Parabolized Navier-Stokes Equations

A new upwind algorithm based on Roes scheme has been developed to solve the two-dimensional parabolized Navier-Stokes equations. This method does not require the addition of user-specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming (1978) scheme in terms of accuracy, stability, computer time and storage requirements, and programming effort. The new algorithm has been validated by applying it to three laminar test cases, including flat-plate boundary-layer flow, hypersonic flow past a 15-deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with results obtained using the conventional Beam-Warming algorithm.

Application of an upwind algorithm to the three-dimensional parabolized Navier-Stokes equations

A new computer code for the solution of the three-dimensional parabolized Navier-Stokes equations has been developed. The code employs a state-of-the-art upwind algorithm to capture strong shock waves. The algorithm is implicit, uses finite volumes, and is second-order accurate in the crossflow directions. The new code is validated through application to laminar hypersonic flows past two simple body shapes: a circular cone of 10 deg half-angle, and a generic all-body hypersonic vehicle. Cone flow solutions were computed at angles of attack of 12, 20, and 24 deg and results are in agreement with experimental data. Results are also presented for the flow past the all-body vehicle at angles of incidence of 0 and 10 deg.

Upwind parabolized Navier-Stokes code for chemically reacting flows

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous, chemically reacting flow around two-dimensional or axisymmetric bodies. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence, Tannehill, and Chaussee. The upwind algorithm is based on Roes flux-difference splitting scheme, which has been modified to account for real gas effects. The algorithm solves the gasdynamic and species continuity equations in a loosely coupled manner. The new code has been validated by computing the Moo = 25 laminar flow of chemically reacting air over a wedge and a cone. The results of these computations are compared with the results from a centrally differenced, fully coupled, nonequilibrium PNS code. The agreement is excellent, except in the vicinity of the shock wave, where the present code exhibits superior shock-capturing capabilities.

Generation of Aerodynamic Data using a Design of Experiment and Data Fusion Approach

‡As one component of an expert system to generate aerodynamic data using Computational Fluid Dynamics (CFD) tools, a new approach utilizing Design of Experiment (DOE) and data fusion is outlined in the following paper. The goal of combining data fusion (merging of various fidelity solutions into a single, coherent database) with an adaptive DOE design is to improve the efficiency of the data generation process. A comparison between databases created using this novel approach and a more conventional full-factorial design shows that the new process can dramatically reduce the computational times required to generate data.

Three-dimensional upwind parabolized Navier-Stokes code for real gasflows

A real gas, upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional hypersonic flow of equilibrium air around various body shapes. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence et al. (1986). The upwind algorithm is based on Roes (1981) flux-difference splitting scheme which has been modified to account for real gas effects using the nearly exact approach of Vinokur and Liu (1988). Simplified curve fits are employed to obtain the thermodynamic and transport properties of equilibrium air. The new code has been validated by computing the M-infinity = 25 laminar flow of air over cones at various angles of attack. The results of these computations are compared with the results from a conventional centrally-differenced, real gas PNS code and the previous axisymmetric, upwind, real gas code. The agreement is excellent in all cases.

Development of an iterative PNS code for separated flows

A new iterative parabolized Navier-Stokes (PNS) algorithm is being developed to efficiently compute supersonic viscous flowfields with embedded separated regions. In the vicinity of these embedded regions, the PNS equations are solved iteratively in order to duplicate the results that would be obtained with the complete Navier-Stokes equations. The algorithmsplits the streamwise flux vector using either the Vigneron or the Steger-Warming methods. Once a separated flow region is computed, the algorithm returns to the usual PNS space-marching mode until, the next embedded region is encountered. The algorithm has been successfully incorporated into NASA’s upwind PNS (UPS) code. The new algorithm has been validated by applying it to three separated flow test cases consisting of flow over a compression ramp, a shock impingement flow and flow over a cone-flare geometry. The present numerical re&lts are in excellent agreement with other NavierStokes computations and experimentaldata.

Application of computational fluid dynamics to sonic boom near- and mid-field prediction

A technique combining a quasilinear extrapolation theory and a three-dimensional parabolized Navier-Stokes (PNS) code has been used to calculate the supersonic overpressure from three different geometries at near- and mid-fields. Wind-tunnel data is used for code validation. Comparison of the computed results with different grid refinements, and different extrapolation distances, are shown in this article. It is observed that a large number of grid points is needed to resolve the tail shock/expansion fan interaction. Therefore, an adaptive grid approach is employed to calculate the flowfield. The effects of a thin, attached boundary layer and the sting of the wind-tunnel model to the sonic boom have also been studied in this article. The agreement between the results and the wind-tunnel data confirms that this technique can be applied to the problem of sonic-boom prediction.

Three-dimensional upwind parabolized Navier-Stokes code for supersonic combustion flowfields

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional chemically reacting flow in scramjet (supersonic combustion ramjet) engines. The code is a modification of the three-dimensional upwind PNS (UPS) airflow code which has been extended in the present study to permit internal flow calculations with hydrogen-air chemistry. With these additions, the new code has the capability of computing both aerodynamic and propulsive flowfields. The algorithm solves the PNS equations using a finite-volume, upwind TVD method based on Roes approximate Riemann solver that has been modified to account for nonequilibrium effects. The fluid medium is assumed to be a chemically reacting mixture of thermally perfect (but calorically imperfect) gases in thermal equilibrium. The new code has been applied to two test cases. These include the Burrows-Kurkov supersonic combustion experiment and a three-dimensional shockinduced combustion flowfleld. The computed results compare favorably with the available experimental data.

Application of CFD to sonic boom near and mid flow-field prediction

A three-dimensional parabolized Navier-Stokes (PNS) code has been used to calculate the supersonic overpressures from three different geometries at near- and mid-flow fields. Wind-tunnel data is used for code validation. Comparison of the computed results with different grid refinements is shown in this paper. It is observed that a large number of grid points is needed to resolve the tail shock/expansion fan interaction. Therefore, an adaptive grid approach is employed to calculate the flow field. The agreement between the numerical results and the wind-tunnel data confirms that computational fluid dynamics can be applied to the problem of sonic boom prediction.

Flow over an All-Body Hypersonic Aircraft: Experiment and Computation

The objective of the present investigation is to establish a benchmark experimental data base for a generic hypersonic vehicle shape for validation and/or calibration of advanced computational fluid dynamics computer codes. This paper includes results from the comprehensive test program conducted in the NASA Ames 3.5-ft Hypersonic Wind Tunnel for a generic all-body hypersonic aircraft model. Experimental and computational results on flow visualization, surface pressures, surface convective heat transfer, and pilot-pressure flowfield surveys are presented. Comparisons of the experimental results with computational results from an upwind parabolized Navier-Stokes code developed at NASA Ames demonstrate the capabilities of this code. HE advanced computational fluid dynamics (CFD) com- puter codes being developed for use in the design of such hypersonic aircraft as the National Aero-Space Plane (NASP) and other hypersonic vehicles require comparisons of the com- putational results with a broad spectrum of experimental data to fully assess the validity of the codes and to develop confi- dence in the numerical simulation procedures. This is particu- larly true for complex flowfields with such features as bound- ary-layer transition and turbulence, rapid flow expansions, and leeside flow with the attendant flow separation and vor- tices. Validated codes for such flowfields will be critical to the development of the NASP and other hypersonic vehicles. Therefore, the objective of the present investigation is to es- tablish a benchmark experimental data base for a generic hy- personic vehicle shape for validation and/or calibration of advanced CFD computer codes. This is being done by con- ducting a comprehensive test program for a generic all-body hypersonic aircraft model in the NASA Ames 3.5-ft Hyper- sonic Wind Tunnel to obtain pertinent surface and flowfield data over a broad range of test conditions. Experimental and computational results on flow visualization, surface pressures, surface convective heat transfer, and pitot-pressure flowfield surveys will be presented in this, paper. Of particular signifi- cance, comparisons of the experimental results with computa- tional results from the NASA Ames UPS code (an upwind parabolized Navier-Stokes solver) will be shown to demon- strate the capabilities of this code. Some comparisons of the data with computations from approximate inviscid methods will also be given.