Viscous Shock-layer Flows Research Articles

Two- and three-dimensional analysis of hypersonic nonequilibrium low-density flows

Flowfield results have been obtained for hypersonic, low-density, twoand three-dimensional, nonequilibrium viscous shock-layer flows. Three-dimensional calculations are performed for sphere-coneshaped bodies at various angles of attack. Recently obtained surface and shock-slip boundary conditions are implemented to account for the low-density effects. These boundary conditions may also be employed with the Navier-Stokes equations with or without a shock-fitting solution technique. A method is suggested for obtaining the input shock shape for the three-dimensional nonequilibrium viscous flow. This approach gives superior convergence of results, especially under low-density flow conditions, and makes the VSL method self-starting. The analytic algebraic grid implemented with the equations does not add any numerical dissipation. Obtained results show the effect of low density on the surrounding flowfield and surface quantities for a hypervelocity vehicle. Good agreement is obtained with the available numerical results (including the direct simulation Monte Carlo predictions) and experimental data for the low-density flight conditions.

Numerical solution of a free-boundary problem in hypersonic flow theory: Nonequilibrium viscous shock layers

Non equilibrium viscous shock layer flows produced near the stagnation point of a blunt body constitute a standard problem in hypersonic flow theory. This flow configuration is usually modeled with the viscous shock layer (VSL) equations derived by writing the full Navier-Stokes equations in boundary-layer coordinates and performing an order of magnitude analysis. The terms retained in this process assure that for moderate Reynolds numbers the resulting equations are uniformly valid between the body surface and the shock, which may be treated as a thin discontinuity. The VSL equations are generally solved by starting with the thin layer approximation (TVSL). Boundary conditions are specified at the body surface and the Rankine-Hugoniot relations are imposed at the shock. Because the position of the shock is not known, one has to solve a free boundary problem. This paper presents a novel solution procedure for this situation. A reduced coordinate is introduced and the free boundary problem is transformed into a nonlinear eigenvalue problem. The new problem for an augmented set of variables is then solved with Newton iterations and adaptive gridding. The method is illustrated in the paper with a solution of the thin shock layer equations at the stagnation streamline. The solution obtained on this line is then used as an initial condition for a two-dimensional marching procedure. The complete axisymmetric problem is solved by performing fully coupled Newton iterations; moreover, we consider a new enlarged unknown function including the shock location. The model includes detailed transport properties and complex kinetics for air dissociation and ionization. However, in order to focus on the numerical method and for the sake of simplicity, thermodynamic equilibrium is assumed.

High-altitude effects on three-dimensional nonequilibrium viscous shock-layer flows

Three-dimensional finite-rate chemically reacting viscous shock-layer flows over complex geometries have been analyzed using a two-temperature model (electron and heavy particle temperature). For the cases under consideration, the results from the two-temperature model without shock slip agree with those from the onetemperature model. Almost negligible difference in electron concentration across the shock layer was observed between oneand two-temperature models.

Effects of slip and chemical reaction models on three-dimensional nonequilibrium viscous shock-layer flows

Three-dimensional finite rate chemically reacting viscous shock-layer flows over complex geometries have been analyzed using seven- and eleven-species air models. The viscous shock-layer code for analyzing nonequilibrium flow over multiconics using a seven-species air model has been modified to include an elevenspecies air model. The viscous shock-layer code with seven-species model has been modified to include wall-slip conditions, and the results for fully catalytic and noncatalytic surfaces with slip are presented. For the cases under consideration, the surface-measurable quantities computed using the two models agree well with each other. Wall slip had negligible effect on electron number density, whereas with shock slip, an order of magnitude increase in electron density was predicted.

Three-Dimensional Nonequilibrium Viscous Shock-Layer Flows over Complex Geometries

RESULTS of numerical analyses of three-dimensi onal, nonequilibrium, viscous shock-layer flows over complex geometries are presented in this paper.1 The viscous shocklayer code (VSLNEQ)2 for analyzing nonequilibrium, multicomponent, ionizing airflow over sphere-cones has been extended to analyze multiconic geometries. The geometries considered for the analysis include straight and bent biconics and a sphere-cone-cy linder-flare with a moderate flare angle. This code is capable of analyzing shock-slip or no-shock-slip boundary conditions and fully catalytic or noncatalytic wall boundary conditions. The results from the nonequilibrium code have been compared with perfect gas and equilibrium air results. In general, the surface pressure distributions are in good agreement, whereas the nonequilibrium heat transfer is about 15% higher than the perfect-gas results. The aerodynamic forces and moments at the base of the bent biconic for various flow conditions are presented and they agree reasonably well with each other.

Nonequilibrium viscous shock-layer flows over blunt sphere-cones at angle of attack

A computer program for predicting the three-dimensional nonequilibrium viscous shock-layer flows over blunt sphere-cones at angle of attack has been developed. The method used is the viscous shock-layer approach for nonequilibrium, multicomponent ionizing air. Analysis of flowfields over a sphere-cone has been performed for both shock-slip and no-shock-slip conditions and the results are compared. This code is capable of analyzing equilibrium and noncatalytic wall boundary conditions, whereas the diffusion model is limited to binary diffusion. Results from this code have been compared with those from another code for the axisymmetric case, while the three-dimensional results are presented around the entire body at 10 deg angle of attack.

Hypersonic viscous shock-layer flows including leeside separation

The three-dimensional, laminar, viscous hypersonic flowfield over blunted cones at large angles of attack, including crossflow separation, has been solved using both viscous shock-layer and parabolized Navier-Stokes equations. A computer code has been developed using this technique, and calculations were made for two test cases, which typically encompass laminar re-entry flow conditions. Case 1 considered low Mach number (10) and high Reynolds number (2x 10/ft) at moderate angle of attack (10 deg). Case 2 considered high Mach number (25) and low Reynolds number (7256/ft) at large angle of attack (35 deg). The results have been compared with a complete parabolized Navier-Stokes solution, and for case 1, the aerodynamic coefficients have been compared with available experimental data. The comparisons indicate good agreement for wall pressure, both longitudinal and crossflow skin-friction coefficients and aerodynamic coefficients. A fast implicit iterative technique known as the Pseudo Elimination Method has been used to solve the parabolized Navier-Stokes equations, and the computing time has been reduced by 35%. The computing times required indicate that the present code obtains complete flowfield solutions in the shortest possible time, thus making it an ideal tool for design analysis of lifting re-entry vehicles.

Hypersonic viscous shock-layer flow over a highly cooled sphere

Hypersonic viscous shock-layer flow over a highly cooled sphere

Viscous Shock-Layer Flows for the Space Shuttle Windward Plane of Symmetry

Viscous Shock-Layer Flows for the Space Shuttle Windward Plane of Symmetry

Hypersonic Ionizing Air Viscous Shock-Layer Flows over Sphere Cones

Hypersonic, nonequilibrium viscous flow with ionization over nonanalv tic blunt bodies is considered. The equations which govern the viscous shock-layer flow are presented and the method by which the equations are solved is discussed. The predictions of the present finite-difference method are compared with other numerical predictions as well as with experimental data. Flows over two sphere cones are considered, the RAM C re-entry body (a 9° sphere cone at 233,000 ft and 25,000 fps) and a 7.5° sphere cone at the experimental wind-tunnel conditions of Pappas and Lee. The predictions of the present method agreed well with the experimental data and with the other numerical predictions except those of Kang and Dunn for the 9° sphere cone. Substantial differences were found between the present predictions and the more approximate predictions of Kang and Dunn for heattransfer distributions and temperature profiles.

Viscous Shock Layer Flow in the Windward Plane of Cones at Angle of Attack

Viscous Shock Layer Flow in the Windward Plane of Cones at Angle of Attack