Some Preliminary Thoughts * Part I: Inviscid Hypersonic Flow * Hypersonic Shock and Expansion-Wave Relations * Local Surface Inclination Methods * Hypersonic Inviscid Flowfields: Approximate Methods * Hypersonic Inviscid Flowfields: Exact Methods * Part II: Viscous Hypersonic Flow * Viscous Flow: Basic Aspects, Boundary Layer Results, and Aerodynamic Heating * Hypersonic Viscous Interactions * Computational Fluid Dynamic Solutions of Hypersonic Viscous Flows * Part III: High-Temperature Gas Dynamics * High-Temperature Gas Dynamics: Some Introductory Considerations * Some Aspects of the Thermodynamics of Chemically Reacting Gases (Classical Physical Chemistry) * Elements of Statistical Thermodynamics * Elements of Kinetic Theory * Chemical Vibrational Nonequilibrium * Inviscid High-Temperature Equilibrium Flows * Inviscid High-Temperature Nonequilibrium Flows * Kinetic Theory Revisited: Transport Properties in High-Temperature Gases * Viscous High-Temperature Flows * Introduction to Radiative Gas Dynamics.

Hypersonic and high temperature gas dynamics

multi component diffusion coefficient, ft/sec binary diffusion coefficient, ft/sec thermal diffusion coefficient, Ib sec/ft enthalpy, z^ h^Ci, ft/sec i enthalpy of species i, ft/sec thermal conductivity of mixture, lb/(sec° R) density-viscosity product, piJL/(pn)r multi component Lewis-Semenov number, Cpp binary Lewis-Semenov number Cpp^a/k thermal Lewis-Semenov number, cpDi/k molecular weight of the mixture, 1 / ( Z-j Ci/

Finite difference methods of solution of the boundary-layer equations

Hypersonic and High-Temperature Gas Dynamics, Second Edition

The field of aerothermoelasticity plays an important role in the analysis and optimization of airbreathing hypersonic vehicles, impacting the design of the aerodynamic, structural, control, and propulsion systems at both the component and multi-disciplinary levels. This study aims to expand the fundamental understanding of hypersonic aerothermoelasticity by performing systematic investigations into fluid-thermal-structural coupling, and also to develop frameworks, using innovative modeling strategies, for reducing the computational effort associated with aerothermoelastic analysis. Due to the fundamental nature of this work, the analysis is limited to cylindrical bending of a simply-supported, von K arm an panel. Multiple important effects are included in the analysis, namely: 1) arbitrary, nonuniform, in-plane and through-thickness temperature distributions, 2) material property degradation at elevated temperature, and 3) the effect of elastic deformation on aerodynamic heating. It is found that including elastic deformations in the aerodynamic heating computations results in non-uniform heat flux, which produces non-uniform temperature distributions and non-uniform material property degradations. This results in reduced flight time to the onset of flutter and localized regions in which the material temperature limits may be exceeded. Additionally, the trade-off between computational cost and accuracy is evaluated for aerothermoelastic analysis based on either quasi-static or time-averaged dynamic fluid-thermal-structural coupling, as well as computational fluid dynamics based reduced-order modeling of the aerodynamic heat flux. It is determined that these approaches offer the potential for significant improvements in aerothermoelastic modeling in terms of efficiency and/or accuracy.

Studies on Fluid-Thermal-Structural Coupling for Aerothermoelasticity in Hypersonic Flow

The symmetric and asymmetric leeward-side flow fields on an inclined ogive-cylinder have been investigated using a number of experimental techniques. Naturally occurring and perturbed flow fields were studied at a moderate Reynolds number and at many incidence angles. By close examination of the steady side force behavior at different roll orientations of the tip, it has been established that micro-variations in the tip geometry of the model have a large influence on the downstream development of the flow field. Under certain conditions, a bistable flow field was observed.

Asymmetric Vortices on a Slender Body of Revolution

It is pointed out that preliminary design and optimization studies for new aerospace vehicles require techniques which can calculate aerodynamic heating rates accurately and efficiently. The method employed to calculate the flow field depends to a large extent on the shape of the vehicle, Mach number, Reynolds number, and Knudsen number. In the case of the aero-assisted orbital transfer vehicle (AOTV), a substantial portion of the flight will be in the transitional regime between continuum and free molecule flow. The present paper discusses some approximate methods which have been used to calculate heating rates on high-speed vehicles. Attention is given to the stagnation point and leading edges, the downstream region, the axisymmetric analog, laminar and turbulent heating rates, transition heating rates, gas models, and three-dimensional applications.

A review of some approximate methods used in aerodynamic heating analyses

An approximate method for calculating heating rates on three-dimensional vehicles at angle of attack is presented. The method is based on the axisymmetric analog for three-dimensional boundary layers and uses a generalized body-fitted coordinate system. Edge conditions for the boundary-layer solution are obtained from an inviscid flowfield solution, and because of the coordinate system used, the method is applicable to any blunt body geometry for which an inviscid flowfield solution can be obtained. The method is validated by comparing with experimental heating data and with thin-layer Navier-Stokes calculations on the shuttle orbiter at both wind-tunnel and flight conditions and with thin-layer Navier-Stokes calculations on the HL-20 at wind-tunnel conditions.

Approximate method for calculating heating rates on three-dimensional vehicles

The effects of such geometric perturbations as variations of model-tip sharpness and roughness, as well as discrete surface perturbations, on the asymmetric flow past slender bodies is experimentally investigated for the cases of a cone/cylinder model having a 10-deg semiapex angle and a 3.0-caliber tangent ogive model. Both models have base diameters of 3.5 inches, and were tested in laminar flow conditions at angles-of-attack in the 30-60 deg range. Single, discrete roughness elements were represented by beads; bead effectiveness was judged on the basis of the extent to which they affected the flowfield in various conditions.

Effects of nose bluntness, roughness, and surface perturbations on the asymmetric flow past slender bodies at large angles of attack

A rapid, approximate method has been developed for calculating the heating rates on three-dimensional vehicles such as the Space Shuttle Orbiter and other advanced reentry configurations. The method is based on the axisymmetric analogue for three-dimensional boundary layers. It uses information obtained from a three-dimensional inviscid flowfield solution, such as HALIS, to calculate inviscid surface streamlines along which approximate heating rates are calculated independent of what happens along other streamlines. Three-dimensional effects are included through the metric coefficient that describes the divergence or convergence of streamlines. Boundary-layer edge properties are obtained from the inviscid flowfield solution by interpolating in the inviscid flowfield at a distance equal to the boundary-layer thickness away from the wall. This accounts, approximately, for the variable boundary-layer edge entropy. Using this method, heating calculations can be made along a typical streamline in a few seconds. This method has been used to accurately predict heating rates for simple shapes such as a spherically blunted cone and more complex shapes such as the Shuttle Orbiter for a variety of wind-tunnel and flight conditions. A unique feature of the method is its ability to accurately predict heating rates on the Shuttle Orbiter wing.

Application of axisymmetric analog for calculating heating in three-dimensional flows

A relatively simple method is presented to include the effects of entropy-layer swallowing in a method developed previously for calculating laminar, transitional, and turbulent heating rates on three-dimensional bodies in hypersonic flows. The boundary layer swallows the entropy layer when the boundary layer downstream of the nose region has entrained those streamlines which passed through the nearly normal part of the bow shock wave. The entropy at the edge of the boundary layer is then determined by equating the mass flow inside the boundary layer to that entering part of the bow shock wave. A new inviscid flowfield solution, which is an extension of Maslen's axisymmetric method, is developed to calculate the three-dimensional shock shape and couple the inviscid solution with the viscous solution. The calculated heating rates compare favorably with Mayne's theory and experimental data for blunted circular and elliptical cones at angles of attack. The effects of entropy layer swallowing on the calculated heating rates were small for laminar heating but large increases were noted for the turbulent heating rates. The computer program developed to calculate the results presented herein required only about 7 sec per streamline on the IM 370/165 computer.

Fred R. Dejarnette

Papers

A review of some approximate methods used in aerodynamic heating analyses

Approximate method for calculating heating rates on three-dimensional vehicles

Effects of nose bluntness, roughness, and surface perturbations on the asymmetric flow past slender bodies at large angles of attack

Application of axisymmetric analog for calculating heating in three-dimensional flows

Aerodynamic Heating on 3-D Bodies Including the Effects of Entropy-Layer Swallowing