Hypersonic Slender Body Aerodynamics

Chapter 1: Basics

• • 1.1 Introduction
• • 1.2 Supersonic Transport Aircraft
• • 1.3 Wings of Supersonic Aircraft
• • 1.3.1 Sharp Leading Edge
• • 1.3.2 Ground Effect
• • 1.3.3 Viscous Effect
• • 1.4 Basic Equations
• • 1.4.1 Velocity Potential Function in Slender Body Theory
• • 1.5 Pressure Distribution on the Surface
• • 1.5.1 General Solution
• • 1.5.2 Transverse Flow
• • 1.5.3 Longitudinal Flow
• • 1.6 Theoretical Methods – Inviscid Flow
• • 1.6.1 Complex Analytic (Holomorphic) Function
• • 1.6.2 Pitching Moment About a Reference Axis (Axis Through cg)
• • 1.7 Stability Derivatives for Delta Wings
• • 1.7.1 Dynamic Stability Derivatives
• • 1.7.2 Unsteady Slender Body Theory
• • 1.8 Method of Vortex (Source and Sink) Distribution
• • 1.8.1 Longitudinal Flow Problem
• • 1.8.2 For Cross Sections with Sharp Corners
• • 1.8.3 General Solutions for Slender Configurations
• • 1.8.4 Space Influence for g(x,M∞)
• • 1.8.4 Longitudinal flow:
• • 1.9 Cone in Supersonic Flow
• • 1.10 Optimization (Supersonic Flow)
• • 1.10.1 Zero‐Lift Case (α=0)
• • 1.10.2 Optimization for Total Drag to Be a Minimum
• • 1.11 Lift‐Case
• • 1.12 Nonlinear Theories
• • 1.12.1 Hürlimann Model
• • 1.12.1.1 Delta Wings
• • 1.12.1.2 Gerten's Model
• • 1.12.2 Breakdown of Vortices
• • 1.13 Summary
• • Exercise Problems

Chapter 2: Hypersonic Aerodynamics (Slender Bodies)

• • 2.1 Introduction
• • 2.2 Mach Number Independence Principle
• • 2.3 Atmospheric Properties
• • 2.3.1 Atmospheric Model
• • 2.4 Hypersonic Flow Characteristics
• • 2.5 Governing Equations
• • 2.6 Comparison of Supersonic and Hypersonic Flow
• • 2.7 Re‐entry Problem
• • 2.7.1 Slender Body Geometry
• • 2.8 Flow Past a Semi‐wedge
• • 2.8.1 Pressure Coefficient for Hypersonic Flow
• • 2.9 Hypersonic Limiting Case
• • 2.10 Newtonian Formula
• • 2.11 Surface Pressure Distribution
• • 2.12 Modified Newtonian Formula
• • 2.13 Tangent Wedge or Tangent Cone Method
• • 2.14 Busemann Correction for Centrifugal Force
• • 2.15 Shock‐Expansion Method
• • 2.15.1 For Similar Flow
• • 2.15.2 For Slender Bodies with Minimum Pressure‐Drag in Symmetrical Flow in the Hypersonic Flow Region
• • 2.16 Theory of Slender Hypersonic Bodies
• • 2.16.1 Basic Equations
• • 2.16.2 New Coordinate System
• • 2.16.3 Boundary Conditions
• • 2.17 Principle of Equivalence for Slender Hypersonic Bodies
• • 2.18 Design of Three‐Dimensional Hypersonic Slender Bodies
• • 2.18.1 Cone Flow Wave‐Rider
• • 2.19 Caret‐Wing or Nonweiler Wing or Wave‐Rider
• • 2.19.1 Volume Parameter
• • 2.19.1 Approximate Newtonian Formula
• • 2.20 Off‐design Conditions for Caret‐Wings
• • 2.20.1 Hypersonic Slender Body Theory
• • 2.21 Approximate Theories for Caret‐Wings
• • 2.21.1 Two‐Dimensional Wedge Theory for Caret‐Wings
• • 2.21.2 Wedge‐Type Analysis
• • 2.21.3 Newtonian Approximation
• • 2.21.4 Extended Newtonian Formula
• • 2.21.4 Design Condition
• • 2.21.4 Detachment Condition
• • 2.21.5 Measurements Made at Braunschweing
• • 2.22 Supersonic Test Facilities
• • 2.22.1 Blowdown Tunnel (without heating)
• • 2.22.2 Blowdown Tunnel (with heating)
• • 2.22.3 Helium Tunnel
• • 2.22.4 Hot‐Shot Tunnel
• • 2.22.5 Gun‐Tunnel
• • 2.22.6 Shock‐Tunnel
• • 2.22.7 Arc‐Heated Tunnel
• • 2.22.8 Low‐Density Tunnel
• • 2.22.9 Ballistic Range
• • 2.22.10 Wedge Theory
• • 2.22.11 (L/D)max Variation with Freestream Mach Number M∞
• • 2.23 Comparison of Theoretical and Experimental Results
• • 2.23.1 Pressure Distribution
• • 2.24 Stability Derivatives
• • 2.25 Summary
• • Exercise Problems

Chapter 3: Application of Slender‐body Theory

• • 3.1 Introduction
• • 3.2 Leading‐Edge Heat Transfer
• • 3.3 Stagnation‐Point Heat Transfer
• • 3.4 Heat Transfer Limitations for Slender‐body Vehicles
• • 3.5 Sublimation
• • 3.6 Aerodynamic Effects
• • 3.7 Nose Bluntness
• • 3.8 Blast‐wave Theory
• • 3.9 Thin Shock Layers
• • 3.10 Summary
• • Exercise Problems

Chapter 4: Experimental Approach

• • 4.1 Introduction
• • 4.2 Drag of Slender Bodies
• • 4.2.1 Flat Plate Analogy
• • 4.2.1.1 Flat Plate Solution for Skin Friction
• • 4.2.1.2 Slenderness Ratio
• • 4.2.2 Shape Factor
• • 4.2.3 Blunt Afterbody Correction
• • 4.3 Axisymmetric Slender Bodies
• • 4.3.1 Potential Flow Solution
• • 4.3.2 Pressure Distribution
• • 4.4 Summary
• • Exercise Problems