Numerical solution of the hypersonic viscous shock-layer equations
Viscous shock layer equations of laminar hypersonic flow past blunt body at moderate to high Reynolds numbers
Davis, R. T.↗
SEARCH · Search NASA
Results for “EQUATIONS - BOUNDARY LAYER”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Fundamental equations of the theory of shells consisting of an arbitrary number of anisotropic layers
Equations of theory of shells consisting of several anisotropic layers
ANISOTROPIC SHELL↗
Aerothermodynamic Analysis of Stardust Sample Return Capsule with Coupled Radiation and Ablation
An aerothermodynamic analysis of the forebody aeroshell of the Stardust Sample Return Capsule is carried out by using the axisymmetric viscous shock-layer equations with and without fully coupled radiation and ablation. Formulation of the viscous shock-layer equations with shoulder radius as the length scale and implementation of the Vigneron pressure condition allow resolution of the flowfield over the shoulder. With a predominantly supersonic outflow over the shoulder, a globally iterated solution or viscous shock-layer equations can be obtained. The stagnation-point results are obtained along a specified trajectory, whereas detailed calculations along the body are provided at the peak-heating point. The equilibrium calculations with ablation injection are the focus of the present study because of the lack of a general chemical nonequilibrium analysis that accounts for both surface and flowfield effect. The equilibrium calculations also provide a simple way to conserve surface (and flowfield) elemental composition for the current small ablation injection rates, where the surface elemental composition is a mixture of freestream and ablator elements. Therefore, the coupled laminar and turbulent flow solutions with radiation and ablation are obtained by using the equilibrium flow chemistry, whereas a nonequilibrium chemistry model is used for solutions without ablation and turbulence. Various computed results are compared with those obtained by the other researchers.
Gupta, Roop N.↗
Reacting viscous-shock-layer solutions with multicomponent diffusion and mass injection
Numerical solutions of the viscous-shock-layer equation where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium are presented. Also the effects of the diffusion model, surface catalysis, and mass injection on surface transport and flow parameters are considered. The flow is treated as a mixture of five inert and thermally perfect species. The viscous-shock-layer equations are solved by using an implicit-difference scheme. All calculations are for hyperboloids with included angles of 20 and 45. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented to show the effects of the chemical models; diffusion models; surface catalysis; and mass injection of air on heat transfer; skin friction; shock standoff distance; wall pressure distribution; and tangential velocity, temperature, and species profiles. The results show that an equilibrium analysis can substantially overpredict the heat-transfer rates for flow conditions experienced by earth-orbital entry vehicles. Moreover, at such conditions surface catalysis significantly influences heat-transfer and flow-field properties. If a binary rather than a multicomponent diffusion model is assumed, negligible errors in most flow properties result. Quantitative results are presented that show the effect of mass injection on flow properties within and downstream of the injection region.
Moss, J. N.↗
Wrinkling phenomenon in structures. I - Model formulations
Those structural element models which can suffer the wrinkling phenomenon are analyzed. A laminated elastic material, defined as a one-parametrical family of surfaces whose in-plane strains are negligible in comparison to the strains in the transverse direction, is analyzed in terms of its geometry, geometrical compatibility equations, layer geometry, kinematics, kinematical compatibility equations, and governing dynamical equations. These aspects are also examined for the case of a soft shell, defined as a shell for which the in-plane strains of the middle surface are negligible compared to the strains in the transverse direction, and for the case of a soft rod, defined as a rod for which the strains along the axis are negligible compared to the strains in the transverse direction. The influence of internal fluid flow on the wrinkling phenomenon for layers of laminated material and for a flexible pipe containing an inviscid and incompressible fluid is also analyzed.
Zak, M.↗
Ablation and radiation coupled viscous hypersonic shock layers.
Coupled ablator shock layer solutions for the stagnation point are presented for typical hyperbolic entry atmospheric flight conditions. These solutions were obtained by numerically solving the stagnation line shock layer equations and quasi-steady ablator equations. These equations included ablation and radiation coupling within the viscous shock layer, line and continuum radiation for both air and phenolic-nylon ablation species and local thermodynamic equilibrium throughout. The results presented provide a sound basis for understanding many of the processes characteristic of hypersonic shock layer heating.-
Engel, C. D.↗
Linear stability of the reacting mixing layer
This work is aimed at understanding the stability of reacting mixing layers. Linear instability is analyzed for a wide variety of mixing layers to study the effects of the heat release. Analytic functions as well as laminar solutions of thin shear layer equations are used as the base flows. Both temporal and spatial developing layers are investigated. The laminar solutions are more consistent than the analytic functions. The stability properties are sensitive to the mean profiles. Including variable transport properties changes the mean profiles considerably. Chemical reaction during the instability is not very important; its primary effect is to change the laminar profiles. New modes are found in the outer part of the layer when the heat release is significant, and become dominant for large heat release. In general, heat release stabilizes the center mode but the outer mode is less affected.
Shin, D. S.↗
The location of the dip equator at E-layer altitude.
Magnetic dip equator position at E layer and gradient with time and altitude, using geomagnetic field models
Cain, J. C.↗
User's guide for the computer code COLTS for calculating the coupled laminar and turbulent flow over a Jovian entry probe
A user's guide for a computer code 'COLTS' (Coupled Laminar and Turbulent Solutions) is provided which calculates the laminar and turbulent hypersonic flows with radiation and coupled ablation injection past a Jovian entry probe. Time-dependent viscous-shock-layer equations are used to describe the flow field. These equations are solved by an explicit, two-step, time-asymptotic finite-difference method. Eddy viscosity in the turbulent flow is approximated by a two-layer model. In all, 19 chemical species are used to describe the injection of carbon-phenolic ablator in the hydrogen-helium gas mixture. The equilibrium composition of the mixture is determined by a free-energy minimization technique. A detailed frequency dependence of the absorption coefficient for various species is considered to obtain the radiative flux. The code is written for a CDC-CYBER-203 computer and is capable of providing solutions for ablated probe shapes also.
Kumar, A.↗
Entry into outer planet environments. I - The radiating shock layer with coupled ablation for carbon and silica
Fully coupled solutions of shock layer equations for the stagnation region are obtained, comprising a set of converged benchmark flowfield solutions for silica and carbon heat shields entering modeled atmospheres of Saturn and Uranus. Model atmospheres and entry trajectories providing significant radiative heating to the entry probes so that the heating environment and effects of mass addition on the heating environment are clearly defined are emphasized. Results referable to the carbon heat shield are questioned because of the high (sublimation) wall temperature assumed and the relatively low shock layer temperature.
Liu, C.-H.↗
Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium
The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.
Anderson, E. C.↗
Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium
The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.
Anderson, E. C.↗
Numerical solution of the viscous hypersonic flow past blunted cones at angle of attack
Hypersonic viscous flow over spherically blunted cones of large half angle is computed at small angles of attack in the plane of symmetry of the flow field. Time-dependent viscous shock-layer equations in body-oriented coordinates are used to describe the flow field. The shock wave is treated as a discontinuity, across which the Rankine-Hugoniot relations are used to compute the flow conditions behind the shock. A time-marching second-order finite-difference method is used to solve the equations for a perfect gas. The local CFL (Courant-Friedrich-Lewy) time increment is used to advance the solution in time at each grid point. A fourth-order damping is used to damp the oscillations in the flow quantities. The numerical results of the present analysis for quantities such as shock standoff distance, surface-pressure distribution, and heating rates compare well with the existing theoretical and experimental results.
Kumar, A.↗
Low Reynolds number flow past a blunt axisymmetric body at angle of attack
Low Reynolds number flow of an ideal gas over a blunt axisymmetric body of large half-angle at small angles of attack is investigated, for the case of laminar hypersonic flow. Time-varying viscous shock layer equations describing the flowfield are obtained from the full Navier-Stokes system by keeping terms to second order in the inverse square root of Re in both viscous and inviscid regions; the equations are valid for moderate to high Re. Drag, skin friction, and heating rates were obtained at small (or zero) angles of attack. Conditions experienced by planetary entry probes during the high-altitude (early) legs of an atmospheric entry trajectory are pertinent to the problem.
Kumar, A.↗
Aerothermodynamic environment for Jovian entry with silica heat shield
Solutions are presented for the stagnation-region shock-layer equations, including radiative transfer with spectral lines and silica ablation during Jovian entry. Results for variations of entry angle, sphere-cone configuration, and atmospheric model are given. The effect of silica ablation on the radiative and convective surface heating is correlated with the ratio of the wall to free-stream mass flux. Correlations are also given for spectral distributions. The effect of newly obtained SiO radiation properties on the surface heating is examined.
Green, M. J.↗
Viscous shock-layer analysis of hypersonic flows over long slender bodies
Numerical solutions from the time-steady viscous shock-layer equations are presented for the hypersonic laminar and turbulent flow of a perfect gas over long slender bodies. These results are obtained from a spatial-marching implicit finite-difference technique. Detailed comparisons have been made with other predictions and experimental data to assess the accuracy of the present numerical technique, especially for slender-body flows. Results from the present method show that coupling the normal momentum and continuity equations and the use of the Vigneron pressure condition in the subsonic nose region give quite accurate and stable results. These results compare (with some exceptions) favorably with those obtained using PNS and other VSL methods.
Gupta, R. N.↗
Stagnation flow field analysis for an aeroassist flight experiment vehicle
Continuum methods are used to analyze the stagnation flow field of the aeroassist flight experiment (AFE) vehicle. For the lower altitude portion of an AFE trajectory, the viscous shock-layer equations are employed. At higher altitudes, the full Navier-Stokes equations with chemical nonequilibrium and surface slip are used. Particular attention is given to the effect of surface catalyticity on surface heating, electron number density, and flow field structure.
Gupta, Roop N.↗
A thin-layer solution of the flow about a prolate spheroid
Computational results are presented for the transitional or turbulent flow about a prolate spheroid, at alpha = 10 deg or 30 deg, correspondingly, using an implicit, approximately factored, partially flux-split algorithm, based on the thin-layer equations. The computed flow field is in good agreement with available experimental data.
Panaras, A. G.↗