Developing a Simple Solver for Transonic and Supersonic Aerodynamic Forces

by

Abstract

This paper discusses some of the areas in which our understanding of hypersonic flows has progressed in recent years with special reference to the hypersonic similarity concept and the hypersonic approximations; the interaction between the boundary layer over a slenderbody and the external inviscid flow; and the flow over blunt bodies, including the heat transfer problem.

When the inviscid pressure distributions predicted by the hypersonic approximations (Newtonian, shock expansion, tangent wedge, and cone) are compared with "exact" solutions and experimental data, it becomes evident that this problem is effectively solved for sharp nosed slender wings and bodies of revolution. The shock expansion and tangent wedge (or tangent cone) method may also be used to construct the flow field. An examination of the equations of motion shows that the simple tangent wedge (or cone) method, which is thought by some to be largely serniempirical, actually has a sound theoretical basis.

Table of Content

Chapter 1: Introduction4

Introduction And General Survey5

Chapter 2: Literature Review6

Aerodynamics6

Aerodynamic Force8

Resolution Of The Aerodynamic Force9

Aerodynamic sound11

Aircraft Design: Aerodynamics13

Biplane and Externally Braced Wings13

Streamlined Monoplanes17

Transonic Aircraft21

Supersonic and Hypersonic Aircraft25

Chapter 3: Research Methodology and theory29

Shock Expansion Method29

Hypersonic Viscous Flow Over Slender Bodies31

Fluid Mechanical Models32

Chapter 4: computational model development45

Hypersonic approximations for planar bodies and slender bodies of revolution46

Tangent Wedge and Tangent Cone Approximations46

Newtonian Approximation52

Chapter 5: Results & Discussion55

Strong and Weak Interactions55

Large heat transfer58

Weak Interaction59

Comparison Between Theory and Experiment: Influence of the Leading Edge at Hypersonic Speeds63

Hypersonic Flow Over Blunt Bodies66

Inviscid Flow66

Chapter 6: Conclusion69

References74

Chapter 1: Introduction

At hypersonic speeds the flow over sharp nosed slender shapes cannot be properly treated without considering boundary layer external flow interactions. Since the mass flux through the boundary layer is small, the streamlines entering the boundary layer are very nearly parallel to the outer edge. In other words, the flow inclination there is the sum of the body inclination and the slope of the boundary layer, and the local pressure is related to the boundary layer growth rate by means of the tangent wedge (or tangent cone) approximation. A second relation between these quantities is provided by the Prandtl boundary layer equations. For both strong and weak interactions over inclined wedges, for example, the governing viscous interaction parameter is .

The straightforward approach to this problem seems to be adequate when the Reynolds Number based on leading edge thickness, Ret, is a few hundred or less. For larger Ret the experimentally measured induced pressures on flat surfaces suggest that the strong bow shock decays surprisingly slowly at high Mach Numbers and that the expansion waves reflected from this shock and impinging on the surface may overwhelm the purely viscous effect (Allen, 2002).

For blunt bodies the modified Newtonian approximation in the form is highly accurate for Mach Numbers above 2.0, even for shapes with rapidly varying (convex) curvature. Current treatments of heat transfer over such bodies are limited to small temperature differences between gas and body surface. For this case the agreement between Sibulkin's theoretical result and experiments in the Mach Number ...