Hypersonic Viscous Interaction Theory for Slender Axisymmetric Bodies

Hypersonic Viscous Interaction Theory for Slender Axisymmetric Bodies
Author: Harold Mirels
Publisher:
Total Pages: 76
Release: 1967
Genre: Aerodynamics, Hypersonic
ISBN:

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Effects of viscous interaction are investigated for hypersonic flow over slender axisymmetric bodies. The entire range of interaction, from weak to strong, is considered for nose bluntness not greater than a 3/4 power law. Extensive numerical results are given for the self-similar flow over a 3/4 power law body. These results are correlated and used in a local similarity procedure for finding viscous interaction over arbitrary body shapes. Analytical expressions are derived for weak interaction on a cone and strong interaction on power law bodies. Following Dewey's approach, the local similarity procedure is simplified to a series of algebraic equations. These are solved for flow of air over a cone. Numerical results are presented for cone surface pressure, shear, heat transfer, drag and displacement thickness in all interaction regimes. The drag is in good average agreement with available experimental cone drag data. The analytical development is a unified treatment of viscous interaction effects on two-dimensional as well as axisymmetric bodies. Numerical results for wedges are included. (Author).

Hypersonic Strong Interaction Similarity Solutions for Flow Past and Very Slender Axisymmetric Body

Hypersonic Strong Interaction Similarity Solutions for Flow Past and Very Slender Axisymmetric Body
Author: W. B. Bush
Publisher:
Total Pages: 46
Release: 1968
Genre:
ISBN:

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The Navier-Stokes hypersonic strong-interaction theory is presented for the flow of a viscous, heat-conducting, compressible fluid past a very slender axisymmetric body, when the ratio of the radius of the body to the radial thickness of the viscous layer(s) (which the body produces and supports), goes to zero. The self-similar leading approximations for the behavior of the flow in these four regions are analyzed, and it is found that an arbitrary body supports '3/4-power' viscous and shock layers. (Author).

Hypersonic Flow Theory

Hypersonic Flow Theory
Author: Wallace Hayes
Publisher: Elsevier
Total Pages: 481
Release: 2012-12-02
Genre: Technology & Engineering
ISBN: 032314876X

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Hypersonic Flow Theory presents the fundamentals of fluid mechanics, focusing on the hypersonic flow theory and approaches in theoretical aerodynamics. This book discusses the assumptions underlying hypersonic flow theory, unified supersonic-hypersonic similitude, two-dimensional and axisymmetric bodies, and circular cylinder. The constant-streamtube-area approximation, streamtube-continuity methods, and tangent-wedge and tangent-cone are also deliberated. This text likewise covers the similar laminar boundary layer solutions, bluntness induced interactions on slender bodies, and free molecule transfer theory. The dynamics of hypersonic flight or hypersonic wing theory, magnetohydrodynamic theory, or any developments involving treatment of the Boltzmann equation are not included. This publication is intended for hypersonic aerodynamicists, students, and researchers conducting work on the hypersonic flow phenomena.

Axisymmetric Hypersonic Flow with Strong Viscous Interaction

Axisymmetric Hypersonic Flow with Strong Viscous Interaction
Author: John Webster Ellinwood
Publisher:
Total Pages: 50
Release: 1967
Genre: Aerodynamics, Hypersonic
ISBN:

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Stewartson's theory for axisymmetric hypersonic flow of a model gas with strong viscous interaction and strong shock wave is extended to power-law viscosity variation, nonunit Prandtl number, and body shapes other than power laws. For power-law bodies, the generalized theory is obtained in closed form without recourse to numerical integration. In addition, numerical computations are presented for axisymmetric flow over a three-quarter power-law body with strong shock wave and viscous interactions that range from weak to strong. (Author).

A Pressure-interaction Theory for Axisymmetric, Hypersonic, Laminar, Unseparated Flows

A Pressure-interaction Theory for Axisymmetric, Hypersonic, Laminar, Unseparated Flows
Author: John W. Ellinwood
Publisher:
Total Pages: 65
Release: 1970
Genre: Aerodynamics, Hypersonic
ISBN:

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Theories for axisymmetric viscous interaction are extended to include arbitrary values of the ratios of both surface to free-stream pressure and boundary-layer to body thickness, by identification of a new measure of transverse curvature in the boundary layer. Methods for four limit flows are isolated. Two of the methods are existing solutions for cones with either a strong shock wave or very thin boundary layer. One is a new local solution for general, very thin bodies; it becomes exact when the pressure ratio approaches one or is unbounded. The fourth is a local similarity solution for power-law bodies with linearizable small-disturbance flow; it becomes exact when the ratio of boundary-layer to body thickness vanishes or is unbounded. These methods have provided interpolated estimates of pressure on a very slender cone-cylinder in hypersonic flow that compare well with original experimental data. Similar predictions of heat transfer rate compare poorly. (Author).

Strong Viscous Interaction with Mass Transfer in Axisymmetric Hypersonic Flow

Strong Viscous Interaction with Mass Transfer in Axisymmetric Hypersonic Flow
Author: John Webster Ellinwood
Publisher:
Total Pages: 16
Release: 1968
Genre: Aerodynamics, Hypersonic
ISBN:

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A theory is presented for the combined effects of mass transfer and viscous interaction on the hypersonic flow of a perfect gas in the limit where the body is vanishingly thin compared with an adjacent, single-species laminar boundary layer. The body temperature and a mass transfer parameter F must both be constant, but arbitrary body profiles are allowed. The results are applicable to porous bodies with nearly uniform mass transfer per unit length and to ablative bodies with a constant effective heat of ablation. The major boundary-layer properties are presented as analytic functions of Prandtl number, specific heat ratio, power-law viscosity power, body enthalpy ratio, and mass-transfer parameter. The theory is compared with numerical solutions for a thin body which grows as a three-quarter power law, and it is found to accurately predict the relative effects of mass transfer. (Author).

Hypersonic Viscous Interaction on a Slender Body of Revolution with Surface Mass Transfer

Hypersonic Viscous Interaction on a Slender Body of Revolution with Surface Mass Transfer
Author: Ting Yi Li
Publisher:
Total Pages: 44
Release: 1967
Genre: Aerodynamics, Supersonic
ISBN:

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An analytical formulation is presented of the problem of hypersonic viscous interaction on a very slender body of revolution with a thick boundary layer and mass transfer. Particular attention is directed to the establishment of the mathematical restrictions necessary to ensure the existence of similar solutions of the laminary boundary-layer equations for this class of problems. Yasuhara's analysis is extended to include surface mass transfer and binary mixture effects. It is shown that when the boundary-layer thickness is of the same order of magnitude as the characteristic body dimension, rigorous similarity is possible only for three-quarter-power-law bodies. This is in agreement with Yasuhara's earlier conclusions. Similar solutions to the boundary-layer growth equations exist when the transverse curvature expression is a function of the similarity variable. The criterion for the existence of similar solutions for the problem of hypersonic viscous interaction is that there must be a definite relationship between body surface shape and surface injection velocity. (Author).

Slender Bodies of Minimum Drag in Hypersonic Viscous Flow

Slender Bodies of Minimum Drag in Hypersonic Viscous Flow
Author: Harold Mirels
Publisher:
Total Pages: 30
Release: 1969
Genre:
ISBN:

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Hypersonic viscous flow about slender cones, wedges, and 3/4 power law bodies is considered. Body thickness ratios leading to minimum drag are determined subject to constraints of fixed base, fixed volume, or fixed surface area. It is assumed that the shocks are strong and that the fluid is ideal. It is found that minimum drag occurs in a flow region where viscous interaction and, for axisymmetric bodies, transverse curvature must be taken into account. Numerical results are given for optimum thickness ratio and minimum drag as a function of altitude. (Author).

Hypersonic Viscous Flow Over Slender Bodies Having Sharp Leading Edges

Hypersonic Viscous Flow Over Slender Bodies Having Sharp Leading Edges
Author: Stanley G. Rubin
Publisher:
Total Pages: 85
Release: 1967
Genre:
ISBN:

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The hypersonic viscous pressure interaction is treated by the development of a set of equations valid throughout the boundary layer, shock-wave structure and inviscid core. Primary interest is concerned with the nature of the leading edge continuum merged layer in which the shock wave and boundary layer are indistinguishable. Due to the parabolic nature of the equations, finite-difference solutions are attainable. The flow over a flat plate at zero incidence, as well as angle of attack, was considered. Velocity and state variable distributions across the viscous layer depict the formation of an outer shock wave and inner constant pressure boundary layer. The calculated values of surface pressure, heat transfer and shock jump conditions were at first significantly below the values predicted by strong interaction theory. Agreement was quite good downstream of the merged layer where Rankine-Hugoniot jump conditions were satisfied to within 8%. (Author).