Shock Layer Flow Research Articles

Rotational and vibrational temperaturemeasurementsusing CARS in a hypervelocity shock layer flow and comparisons with CFD calculations

Rotational and vibrational temperaturemeasurementsusing CARS in a hypervelocity shock layer flow and comparisons with CFD calculations

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.

Comparison of planar fluorescence measurements and computational modeling of shock-layer flow

Planar laser-induced fluorescence is used to image transient and quasisteady flow phenomena associated with an impulsively started supersonic jet incident on a circular cylinder. The transient phenomena observed are consistent with established theoretical work on the development of nozzle flows in a shock tunnel and with well-understood shock reflection processes. The technique is also used to measure the rotational temperature in the jet and in the shock layer on the cylinder after the establishment of quasisteady flow conditions. The inviscid flow between the bow shock and the edge of the boundary layer and the viscous flow within the boundary layer are modeled numerically using an iterative scheme. Good agreement is achieved between the computational and experimental results for most of the imaged field, except for the region near the shock vertex, where flow nonuniformities near the centerline perturb the shock from the shape expected for a uniform incident flow.

Computation of nonequilibrium radiating shock layers

A computational technique of coupling radiative transfer to fluid motion is developed for axisymmetric blunt body shock layer flows in a thermochemical nonequilibrium environment. The coupled formulation of radiation and flowfield leads to a governing set of integro-diffe rential equations. This equation set is solved using a modified Gauss-Seidel line relaxation technique that incorporates the inversion of full block matrix associated with radiative transfer using a block iteration method. The thermodynamic state of the gas is described by three temperatures: 1) translational, 2) rotational, and 3) vibrational-e lectronic. Radiation phenomenon is assumed to be governed by the vibrational-electronic temperature. The radiative properties are described by a spectrally detailed model. The computations are presented for two cases, including the Fire II flight experiment. It is shown that the method converges and the calculated spectra qualitatively agree with the experimental data for the two test cases. The calculated total radiative flux underestimates the measured values owing to the low vibrational-electronic temperature predicted in the flowfield calculation.

Accuracy and Efficiency Assessments for a Weak Statement CFD Algorithm for High-Speed Aerodynamics

A bilinear finite element, implicit Runge-Kutta space-time discretization has been established for an aerodynamics weak statement CFD algorithm. The algorithm admits real-gas effect simulation, for reliable hypersonic flow characterization, via an equilibrium reacting air model. The terminal algebraic system is solved using an efficient block-tridiagonal quasi-Newton linear algebra procedure that employs tensor matrix product factorizations within a lexicographic mesh-sweeping protocol. A block solution-adaptive remeshing, for totally arbitrary convex elements, is also utilized to facilitate accurate shock and/or boundary layer flow resolution. Numerical validations are presented for representative benchmark supersonic-hypersonic aerodynamics problem statements.

Vibrational temperature measurements in a shock layer using laser induced predissociation fluorescence

The feasibility of applying laser induced predissociation fluorescence (LIPF) to the measurement of vibrational temperatures in a shock layer flow around a cylinder in a pulsed supersonic free stream is examined. Single shot spatially and spectrally resolved LIPF measurements are presented and a comparison with theoretical predictions is made.

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.

Calculation of the flow field past spherically blunted cones near the plane of symmetry for various shock layer flow regimes with insufflation of gas from the surface

Calculation of the flow field past spherically blunted cones near the plane of symmetry for various shock layer flow regimes with insufflation of gas from the surface

Flow structure on the windward side of V-wings with separation of the turbulent boundary layer

The qualitative characteristics of shock-layer flow associated with separation of the turbulent boundary layer under the influence of one or several successive shock waves are explored with reference to a number of examples typical of conical flows.

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.

A Numerical Study of Gas-Particle Supersonic Flow Past Blunt Bodies : The Case of Two-Dimensional Flow

A numerical method (inverse method) was developed for a gas-particle supersonic flow past two-dimensional blunt bodies. This method is based on two transformations (von Mises and additional one), which are convenient for determining the shock layer flow field and the body shape. Using the present method, the pure gas flow field around a circular cylinder was first solved numerically for freestream Mach numbers M∞=3.0, with particle diameter dp=2, 5, 10μm and freestream loading ratios αα=0, 0.2, 0.5 and 1.0, respectively. The effects of dp and α on the shock stand-off distance, the body surface pressure and flow quantities along the stagnation streamline are discussed, and flow patterns in the shock layers are shown.

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.

A Numerical Study of Gas-Particle Supersonic Flow Past Blunt Bodies : The Case of Axisymmetric Flow

A numerical method (inverse method) was developed for a gas-particle supersonic flow past axisymmetric blunt bodies. This method is based on a stream function coordinate system, which makes it convenient to determine the shock layer flow fields and body shapes. Using the present method, the gas-solid particle flows in the shock layers around blunt bodies (nearly spheres) were solved for freestream Mach number M∞=2. The effects of freestream loading ratio and particle diameter on the shock layer thickness, the body surface pressure and the flow quantities along the stagnation streamline are shown, and the flow patterns (gas streamlines and particles streamlines) in the shock layers are also shown.

A Numerical Study of Gas-Particle Supersonic Flow Past Blunt Bodies : The Case of Two-Dimensional Flow

A numerical method (inverse method) was developed for a gas-particle supersonic flow past two-dimensional blunt bodies. This method is based on two transformations (von Mises and additional one), which are convenient for determining the shock layer flow fields and the body shapes. Using the present method, the pure gas flow field around a circular cylinder was first solved numerically for the freestream Mach numbers M∞=2.0 and 3.0. Then the gas-particle flow in the shock layer around blunt bodies (nearly circular cylinders) was solved for freestream Mach number M∞=3.0, with particle diameter dp 2, 5, 10 μm and freestream loading ratios α=0, 0.2, 0.5 and 1.0, respectively. The effects of dp and α on the shock stand-off distance, the body surface pressure and flow quantities along the stagnation streamline are discussed, and the flow patterns in the shock layers are also shown.

Chemical equilibrium laminar or turbulent three-dimensional viscous shock-layer flows

A computational method has been developed to predict three-dimensional hypersonic laminar or turbulent shock-layer flows for perfect gas or equilibrium air. A two-layer eddy-viscosity model is used for the turbulent regime. The thermodynamic and transport properties for air are obtained by interpolation within a twodimensional table or from curve-fit data. Comparisons are made for air in chemical equilibrium and perfect gas for laminar and turbulent flow over a 7-deg half-angle spherically blunted cone at various flight altitudes with a cold, moderately cool, and an adiabatic wall for angles of attack up to 20 deg. Surface pressure and wall heattransfer distributions, force and moment coefficients, and execution times are compared for some sample cases. This method can be used to predict viscous flowfields in chemical equilibrium over axisymmetric re-entry vehicles at angles of attack up to 25 deg.

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.

Implicit Solution for the Shock-Layer Flow around General Bodies

The simplified forms of the Navier-Stokes equations are solved by an iterative implicit scheme along the body axis for angles of incidence up to 30 deg. The method of solution yields both the inviscid and viscous flows simultaneously and predicts bow shock at stations normal to the axis. The technique is developed from a comparatively simple linearization procedure and has an option to iterate between body stations for higher accuracy. Reliable procedures have been introduced to account for the effect of the axial pressure gradient and to adjust the step increment for a given convergence requirement. A blunt cone and a Shuttle Orbiter-like configuration were studied and good agreement is obtained with available laminar boundary-layer solutions and experimental data. ISCOUS flowfield solutions around a re-entry vehicle are needed for the prediction of heating distributions as well as for the interpretation of aerodynamic data to support the design and flight test processes. The traditional boundary- layer (BL) approach that decouples the viscous flow from the outer inviscid flow has been valuable in the past; however, for the problems of current interest, such as the Space Shuttle Orbiter and the maneuverable re-entry vehicle, a more ac- curate solution is being obtained from the coupled fluid dynamics equations. This paper presents a method suitable for complex configurations that may be described by a lofting technique used by the aerospace industry. The method is devised to solve the Euler equations for the inviscid region and the parabolic Navier-Stokes (PNS) equations for the viscous region along an identifiable main-flow direction. The PNS equations are obtained from the full NS equation by omitting the second-order and the mixed derivatives and by approximating the exact pressure gradient in the designated direction. The flowfield of interest is bounded between the shock, the body, an initial-data plane normal to the specified direction, and a downstream station parallel to the initial plane. Although the length scales associated with the flow phenomena differ greatly on that plane, highly nonuniform grid spacings near the wall are not desirable in practice, as the shock must be calculated accurately. Hence, a detailed shock- layer solution requires a large number of grid points and consequently long computation time. In return for its cost, this method does not have any of the known shortcomings associated with the BL analyses and offers new capabilities for predicting leeside flow and crossflow separation. For this reason, there has been an intensive research effort in this decade to solve for the viscous flow as an integral part of the flowfield.

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.

Effects of probe shape change on flow phenomena during Jovian entry

The effects of probe shape change on the flow phenomena around a Jovian entry body is investigated. The initial body shapes considered are: 45° sphere cone, 35° hyperboloid, and 45° ellipsoid. The radiating shock-layer flow is assumed to be axisymmetric, inviscid, and in chemical and local thermodynamic equilibrium. The radiative transfer is calculated with an existing nongray radiation model that accounts for molecular band, atomic line and continuum transitions. The results indicate that the shock-standoff distance, shock temperature and density, wall pressure distribution and radiative heating to the body are influenced significantly because of the probe shape change. The effect of shape change on radiative heating of the afterbody was considerably larger for the sphere cone and ellipsoid that for the hyperboloid. For the peak heating conditions, the net radiative heating to the body was found to be highest for the ellipsoid.