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Hypersonic Aerodynamics and Heat Transfer

978-1-56700-309-3 (Print)
978-1-56700-287-4 (Online)

Hypersonic Aerodynamics and Heat Transfer

Sergey Vladimirovich Utyuzhnikov
The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

G. A. Tirskiy
Moscow Institute for Physics and Technology, Moscow, Russia


Results of theoretical and experimental studies of the problems concerned super/hypersonic flows around the models of real space vehicle configurations such as "Buran"-orbiter, winged cone (airplane-like body), Clipper space vehicle, Martian planetary probe are presented. Theoretical analysis is based on solution 2/3D Navier- Stokes equations and their simplified asymptotic models with account for equilibrium and nonequilibrium chemical reactions taking place at the background of relaxation of excited internal energy modes of the particles in the shock layer and on the vehicle surface.
Exact and simple relationships for the transport of species mass and heat are derived from rigorous kinetic theory for multicomponent mixtures of gases and plasma with different diffusion characteristics of the species (governing relations - thermodynamic parameter gradients expressed through the fluxes) as well as velocity slip, temperature and species concentration jumps boundary conditions for the surfaces of finite catalycity in multicomponent chemically and thermally nonequilibrium gas flow.
Phenomenological and kinetic models are developed for heterogeneous catalytic reactions on the thermal protection materials of the space vehicles entering Earth and Mars atmospheres along gliding trajectories.
The problem of multicomponent thermally and chemically nonequilibrium air flow in inductively coupled plasma torch and jet flow around the models installed in the facility work section in considered. The possibility to specify catalytic properties of real heat shield coatings are demonstrated using numerical and test values of heat fluxes or surface equilibrium radiation temperatures.
Original iterative/marching method to solve viscous shock layer equations is presented. The method is based on splitting of marching component of the pressure gradient onto hyperbolic part and a part that minimizes the elliptic part to a maximum degree that are then subjected to the global iterations procedure. Using the splitting of this kind allows numerical obtaining the drug and heat transfer coefficients within single or couple global iterations with reasonable for practical purposes accuracy.
The knowledge area connected to development of large computer software for conjugate problem of ballistics, aerodynamics, vehicle heat transfer and thermal strength of constructions of variable mass and shape is developed for all stages of the modern rocket-space vehicles designing.

383 pages, © 2013

Table of Contents:

Chapter 1: Asymptotically Simplified Gas-Dynamic Models of Supersonic and Hypersonic Aerodynamics and Heat Transfer
1.1: Introduction
1.2: Theory of the Boundary Layer in the Second Approximation
1.3: Composite Systems of Equations for a Viscous Fluid: Equations of the Viscous Shock Layer, and Parabolized Navier-Stokes Equations
1.4: Approximation of the Thin Viscous Shock Layer (TVSL)
1.5: Equations of the Viscous Shock Layer
1.6: Parabolized Navier-Stokes Equations
1.7: General Comments
1.8: Navier-Stokes Equations
1.9: Numerical Solution of the Simplified NS Equations
Chapter 2: Generalized Equations of the Viscous Shock Layer with Slip Conditions on the Surface and Bow Shock Wave
2.1: Introduction
2.2: Two-Dimensional Navier-Stokes Equations in the Natural Coordinate System Fitted to the Body Surface
2.3: Boundary Conditions
2.4: Drag and Heat-Transfer Coefficients
2.5: Generalized Viscous Shock Layer Equations at Low, Moderate, and High Reynolds Numbers
2.6: Generalized Boundary Conditions on the Bow Shock Wave
2.7: Navier-Stokes Equations and Boundary Conditions in Dorodnitsyn-Lees Variables
2.8: Boundary Conditions in the Variables ξ and η
2.9: Estimation of the Order of the Coefficients of the NS Equations in the Variables ξ and η
2.10: Drag and Heat-Transfer Coefficients in the Variables ξ and η
2.11: Generalized Viscous Shock Layer Equations with Slip and Temperature Jump Conditions on the Body Surface and with Generalized Rankine-Hugoniot Conditions on the Bow Shock Wave
2.12: Conclusions
Chapter 3: New Form of 'Forces via Fluxes' Transport Relations for Multicomponent Gas and Plasma Mixtures with Exact Transport Coefficients and Applications
3.1: Introduction
3.2: Classical (Old) Form of Transport Relations in the Form of “Fluxes via Thermodynamic Forces”
3.3: New Exact Form of the Transport Relations for the Component Mass and Heat in the Mixture, Resolved with Respect to the Gradients of Hydrodynamic Variables via Fluxes (Force via Fluxes): Exact Stefan–Maxwell Relations
3.4: Applications
3.4.1 Hydrodynamic Equations for Thermochemically Equilibrium Flows of a Multicomponent Plasma
3.4.2 Effect of Separation of Chemical Elements
3.4.3 Further Applications of the New Form of the Transport Equations
3.5: Conclusions
Chapter 4: Slip Boundary Conditions on a CatalyticWall in a Chemically Reacting Multicomponent Many-Temperature Gas Flow with Excited Internal Degrees of Freedom of Particles
4.1: Introduction
4.2: Kinetic Justification of Gas-Dynamic Equations in the Case of Relaxation of Internal Degrees of Freedom for Chemically Reacting Multicomponent Mixtures of Gases
4.2.1 Kinetic Equations and Zeroth Approximation
4.2.2 Hydrodynamic Equations in the Zeroth Approximation
4.2.3 First Approximation
4.2.4 Navier–Stokes Equations and Transport Coefficients
4.3: Boundary Conditions for a Chemically Reacting Gas with Different Vibrational Temperatures of the Components
4.3.1 Kinetic Boundary Conditions
4.3.2 Asymptotic Equation and Zeroth Approximation of the Internal Problem
4.3.3 Formulation of the Problem for the First Approximation
4.3.4 Maxwell–Loyalka Method and Boundary Conditions
4.3.5 Application of the Slip Boundary Conditions
4.4: Conclusions
Appendix 4.A
Appendix 4.B
Chapter 5: Physicochemical Models of Hypersonic Flows
5.1: Introduction
5.2: Equations of Conservation (Balance) of Mass, Momentum, and Energy for Gas Mixtures
5.3: Internal Energy of the Species
5.4: Equation of Conservation (Balance) of the Energy of Internal Degrees of Freedom of Particles
5.5: Equation of Conservation (Balance) of the Energy of the Electron Component
5.6: Molecular Transport Relations and Transport Coefficients
5.7: Fluxes of the Energy of Internal Degrees of Freedom
5.8: Kinetics of Dissociation and Ionization Reactions for a One-Temperature Mixture of Gases and Plasma
5.9: Thermally and Chemically Nonequilibrium Regimes of Hypersonic Flow
5.10: Exchange Terms in Equations of Energy Balance of Internal Degrees of Freedom: Effect of Vibrational-Dissociation-Vibrational Interaction (VDVI)
5.11: Heterogeneous Recombination and Heterogeneous Deactivation of Internal Degrees of Freedom of Particles
5.12: Interrelation of Gas-Phase Exchange Reactions and Heterogeneous Recombination Reactions of Atoms in Dissociated Air
5.13: Formation of Excited Particles in the Flow and on the Body Surface
5.14: Effect of Electron-Excited Particles on Gas-Phase Kinetics
5.15: Locally Thermochemically Equilibrium Flows of Gas Mixtures with Different Diffusion Properties of the Species
5.16: Conclusions
Chapter 6: Modeling of Catalytic Properties of Thermal Protection Coatings of Space Vehicles
6.1: Introduction
6.2: Experimental Methods and Facilities
6.3: Laboratory and In-Flight Data
6.4: Theoretical Models of Heterogeneous Catalysis during Reentry into the Earth’s Atmosphere
6.5: Heterogeneous Catalytic Processes in Entering the Martian Atmosphere
6.6: Modeling of Catalytic Properties of Thermal Protection Coatings on Space Vehicles on the Basis of Quantum Mechanics and Molecular Dynamics
6.7: Conclusions
Chapter 7: Navier–Stokes-Based Numerical Simulation of Flows of a Chemically and Thermally Nonequilibrium Air Plasma in the Discharge Channel and Underexpanded Jets of the IPG-4 Induction Plasmatron
7.1: Introduction
7.2: IPG-4 Plasmatron
7.3: Thermochemical Model
7.4: Navier–Stokes Equations in the Integral Form
7.5: Calculation of the Induction Plasma Flow in the Discharge Channel and in Underexpanded Jets Escaping from the Sonic Nozzle of the Plasmatron
7.6: Conclusions
Chapter 8: Numerical Study of Specific Features of Heat Transfer in a Hypersonic Flow Around a Blunted Cone Lying on a Triangular Plate with Blunted Edges
8.1: Introduction
8.2: Thermodynamic Properties
8.3: Chemical and Transport Models of the Gas Medium
8.4: Geometry of the Body Surface
8.5: Method of the Solution
8.6: Construction of the Computational Grid
8.7: Free-Stream Parameters and Data for Computations
8.8: Calculation Results
8.9: Conclusions
Chapter 9: Model of Partial Chemical Equilibrium for Solving Problems of a Hypersonic Viscous Gas Flow around Bodies
9.1: Introduction
9.2: Formulation of the Problem
9.3: Model of Partial Chemical Equilibrium
9.4: Comparative Analysis of the Problem Solutions within the Framework of NS and FVSL Equations
9.5: Results of Solving the Problem by Using the Partial Chemical Equilibrium Model
9.6: Application of the Partial Chemical Equilibrium Model in the Martian Atmosphere
9.7: Conclusions
Chapter 10: Numerical Modeling of Heat Transfer of Hypersonic Flying Vehicles Flying in the Earth’s Atmosphere
10.1: Introduction
10.2: Calculation Methods
10.3: Physicochemical Model of Air
10.4: Boundary Conditions
10.5: Thin Triangular Plate with a Blunted Nose in a Viscous Hypersonic Flow
10.6: Experimental Study of Heat Transfer on a Model of a Reentry Vehicle
10.7: Flow Around a Midwing Hypersonic Vehicle
10.8: Flow around a Low-Wing Hypersonic Vehicle
10.9: Conclusions
Chapter 11: Heat Transfer and Flow Structure near the Planetary Probe Surface
11.1: Introduction
11.2: Examined Configurations
11.3: Wind Tunnels and Flow Parameters
11.4: Heat Flux Probes
11.5: Method of Numerical Simulation of Laminar and Turbulent Flows
11.5.1 Formulation of the Problem Differential Navier–Stokes Equations Boundary and Initial Conditions
11.5.2 Reynolds-Averaged Navier–Stokes Equations
11.5.3 Modeling of Real Gas Flows
11.5.4 Approximation of Equations
11.5.5 Solution of Nonlinear Grid Equations
11.5.6 Solution of Systems of Linear Algebraic Equations Direct Method of Solving a System of Linear Algebraic Equations Iterative Method of Solving a System of Linear Algebraic Equations Convergence Acceleration by Means of Preconditioning
11.5.7 Efficiency of the Numerical Solution of Grid Equations
11.5.8 Construction of the Computational Grid
11.5.9 Development of a Set of Universal Codes
11.5.10 Study of Convergence of the Calculated Data
11.6: Flow Structure and Heat Transfer near the Surface of Model No. 1
11.6.1 Laminar Flow
11.6.2 Transitional and Turbulent Flows
11.7: Flow Structure and Heat Transfer near the Surface of Model No. 2
11.7.1 Heat Transfer
11.7.2 Separation Region Length
11.8: Comparison of Models No. 1 and No. 2
11.9: Conclusions
Chapter 12: Methodology of Formation of the Windward Surface of a Winged Reentry Vehicle with Reduced Thermal Intensity
Chapter 13: Numerical Modeling of Hypersonic Heat Transfer on the Windward Side of the Buran Reentry Vehicle
13.1: Introduction
13.2: Model of the Medium
13.2.1 Basic Parameters of the Medium: Equation of State
13.2.2 Chemical Reactions in the Gas Phase
13.2.3 Thermodynamic Functions
13.2.4 Model of Molecular Transport Processes
13.2.5 Model of Heterogeneous Processes
13.3: Constitutive Equations and Method of Solving the Problem
13.3.1 Coordinate System
13.3.2 Constitutive Equations
13.3.3 Boundary Conditions
13.3.4 Discretization of the Computational Domain
13.3.5 System of Difference Equations
13.3.6 Metric Coefficients
13.3.7 Regularization of Difference Equations
13.3.8 Organization of Flow Field Calculation
13.3.9 Solution of Block Equations
13.4: Calculation of the Flow around the Buran Reentry Vehicle
13.4.1 Description of the Windward Side of the Buran Reentry Vehicle
13.4.2 Coordinate System and Difference Grid
13.4.3 Presentation of Calculated Data
13.4.4 Analysis of Heat Transfer Calculations on the Windward Surface of the Buran Reentry Vehicle
13.5: Conclusions
Chapter 14: Mathematical Modeling of Heat and Mass Transfer during Aerothermochemical Destruction of Thermal Protection Materials
14.1: Introduction
14.2: Object of Research: Thermal Destruction of the Binder
14.3: Heterogeneous Chemical Interaction between Silica and Carbon in Internal Layers of the Material
14.4: Melting Ablation of Silica
14.5: Mechanical Ablation of Carbon and Gaseous Products of Material Destruction
14.6: Energy Conservation Equation
14.7: Sublimation of Condensed Components of the Material from the Wall
14.8: Heterogeneous Chemical Reactions Proceeding on the Wall
14.9: Ablation of Silica from the Wall
14.10: Ablation of Condensed Carbon from the Wall
14.11: Correlation Dependence between Rates of Destruction of Solid Species of the Material
14.12: System of Boundary Conditions on the Wall
14.13: System of Boundary Conditions on the Front of Primary Pyrolysis of the Binder
Chapter 15: Modeling of Turbulent Compressible Near-Wall Flows
15.1: Introduction
15.2: Specific Features of the Structure of Turbulent Compressible Near-Wall Flows. Algebraic Models
15.2.1 Structure of the Turbulent Boundary Layer
15.2.2 Variants of the Prandtl Model
15.2.3 Models of Effective Transport Coefficients
15.3: One-Equation Differential Turbulence Models
15.3.1 Models with an Equation for Turbulent Viscosity
15.3.2 Model with the Equation for the Turbulent Kinetic Energy
15.4: Two-Equation Models
15.4.1 Two-Equation K–L Models
15.4.2 Two-Equation K–ε Models
15.4.3 Relations for Linear K–ε Models
15.4.4 Two-Equation K–ω Models
15.5: Three-Equation K–F–R Models
15.6: Models Based on Equations for the Reynolds Stress
15.6.1 Differential Models for the Reynolds Stress
15.6.2 Models Based on Algebraic Relations for the Reynolds Stress
15.6.3 Allowance for Compressibility Effects in High-Order Closure Models
15.7: Conclusions
Chapter 16: Numerical Method of Solving Viscous Shock Layer Equations in a Wide Range of Reynolds Numbers
16.1: Introduction
16.2: Formulation of the Problem
16.3: Characteristic Analysis of the System of VSL Equations and the Model of a Parabolic-Hyperbolic Viscous Shock Layer
16.4: Splitting of the Streamwise Pressure Gradient and Method of Global Iterations
16.5: Marching Method of Solving the Cauchy Problem with a Transonic Bifurcation
16.5.1 Numerical Solution of a Model Problem of the One-Dimensional Theory of the Laval Nozzle
16.5.2 Marching Method of Solving the System of PHVSL Equations
16.6: Convergence of Global Iterations
16.6.1 Inviscid Shock Layer
16.6.2 Viscous Shock Layer
16.7: Conclusions
Chapter 17: Analytical Method of Solving Thin Viscous Shock Layer Equations at Low Reynolds Numbers
17.1: Introduction
17.2: Thin Viscous Shock Layer Model at Low Reynolds Numbers Re. Two-Dimensional Flows
17.3: TVSL Model in the Vicinity of the Stagnation Line in a Three-Dimensional Flow
17.4: TVSL Model in the Vicinity of the Plane of Symmetry in a Three-Dimensional Flow
17.5: Regimes and Parameters of the Hypersonic Rarefied Gas Flows
17.6: Asymptotic Solution of TVSL Equations
17.7: Estimation of the Accuracy and Applicability Area of the Analytical Solution
17.8: Conclusion
Chapter 18: Near-Wall Domain Decomposition in Turbulence Modeling
18.1: Introduction
18.2: Non-Overlapping Linear Domain Decomposition
18.3: Nonoverlapping Nonlinear Domain Decomposition
18.4: Interface Boundary Conditions for RANS Equations
18.4.1 One-Dimensional Domain Decomposition Exact Domain Decomposition Approximate Domain Decomposition
18.5: Interface Boundary Conditions for LR RANS Equations
18.5.1 Test Cases
18.5.2 Comparison Against Analytical and Numerical Wall Functions
18.5.3 Extension to Multidimensional Problems
18.5.4 Preconditioning Technique Based on Domain Decomposition