Thermal Protection Modeling

By A.S. Yakimov

Thermal Protection Modeling presents the fundamental knowledge, applications, and methods of heat transfer augmentation techniques for current and future thermal protection systems. This book covers common challenges and their most appropriate solutions, presenting boundary conditions for the simulations of heat transfer and design of combined and active thermal protection. Important application aspects of heat transfer augmentation techniques in a single-phase system are compared in a practical way with a strong modeling approach. This book will provide a strong understanding of the current and future state of thermal protection systems and assist the reader in their own problem solving and modeling approaches.

• Provides a clear understanding of heat and mass transfer, as well as modeling and thermal protection concepts
• Offers a mathematically and practically balanced approach to provide readers with various problems and solutions
• Covers active, thermionic, and combined thermal protection

• Language: English
• Publisher: Academic Press
• Release date: Feb 11, 2023
• ISBN: 9780323998390

A.S. Yakimov

AS. Yakimov (the Department of Physical and Computational Mechanics, Tomsk State University, Tomsk, Russia). Anatoly Stepanovich Yakimov is a Senior Fellow and Professor of the Department of Physical and Computational Mechanics of Tomsk State University, Russia. He is the author of text-books, monographs and 70 scientific publications devoted to the mathematical modeling of the thermal protection and the development of mathematical technology solution of mathematical physics equations.

Book preview

Thermal Protection Modeling

Anatoly S. Yakimov

Chair, Physical and Computational Mechanics, Tomsk State University, Tomsk, Russia

Table of Contents

Cover image

Title page

Copyright

About the author

Preface

Introduction

Chapter 1. Active thermal protection

1.1. Mathematical modeling of heat and mass exchange process in heat shielding material

1.2. Modeling heat and mass exchange process in transpiration cooling system with gas flow pulsation

1.3. Modeling heat and mass transfer process of transpiration cooling systems under exposure to small energy perturbations

1.4. Modeling heat and mass transfer of porous cooling system processes with phase transitions

1.5. Modeling two-phase porous cooling processes at exposure to low-energy perturbations

Chapter 2. Thermionic thermal protection

2.1. Mathematical Modeling of Active Thermionic Thermal Protection with High-enthalpy Flow Around a Composite Shell

2.2. Thermionic thermal protection system of spherical blunted cone in high-enthalpy airflow

Chapter 3. Combined thermal protection

3.1. Mathematical modeling of rotation on conjugate heat and mass transfer in high-enthalpy flow around a spherically blunted cone at an angle of attack

3.2. Numerical analysis of heat and mass transfer characteristics in radiative and convective heating of a spherically blunted cone

3.3. Effect of oscillations of blunt body on heat

3.4. Conclusion

Bibliography

Index

Copyright

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About the author

Anatoly Stepanovich Yakimov is a Doctor of Engineering Sciences, Senior Research Officer, and Professor at the Department of Physical and Computational Mechanics, National Research Tomsk State University.

E-mail: [e-mail]

He graduated in 1970 from the Faculty of Mechanics and Mathematics, Kuibyshev Tomsk State University.

In 1981, he defended his thesis for the degree of Candidate of Physical and Mathematical Sciences at the Research Institute of Applied Mathematics and Mechanics, Tomsk State University (specialization 01.02.05—fluid, gas, and plasma mechanics).

In 1999, he defended his thesis for the degree of Doctor of Engineering Sciences (specialization 05.13.16—application of computers, mathematical modeling, and mathematical methods in research—and specialization 01.02.05) at Tomsk State University.

He is the coauthor of a textbook and the author of 1 monograph and 84 publications (not including theses) devoted to mathematical modeling of thermal protection issues, as well as to environmental protection and mathematical solutions to equations in mathematical physics. The latter subject is addressed in the following publications:

[1] Grishin AM, Zinchenko VI, Efimov KN, Subbotin AN, Yakimov, AS. The Iterated interpolation method and its applications. Tomsk: Tomsk University Publishing House, 2004, 320 pp.

[2] Grishin AM, Golovanov AN, Zinchenko VI, Efimov KN, Yakimov AS. Mathematical and physical modeling of thermal protection. Tomsk: Tomsk University Publishing House, 2011, 357 pp.

[3] Yakimov AS. Analytical solution methods for boundary value problems. Tomsk: Tomsk University Publishing House, 2011, 199 pp.

[4] Yakimov AS. Analytical solution methods for boundary value problems. Tomsk: Tomsk University Publishing House, 2014, 214 pp.

[5] Yakimov AS. Mathematical modeling of thermal protection and some problems of heat and mass transfer. Tomsk: Tomsk University Publishing House, 2015, 216 pp.

[6] Yakimov AS. Analytical solution methods for boundary value problems. Boston: Academic Press, an imprint of Elsevier, 2016, 189 pp.

[7] Yakimov AS. Thermal protection modeling of hypersonic flying apparatus. Switzerland: Springer, 2018, 114 pp.

Preface

This monograph is devoted to the study of transpiration cooling systems, the thermal protection of composite materials exposed to low-energy disturbances, and the numerical solutions of conjugate heat and mass transfer problems. The author offers several mathematical models of active and combined thermal protection systems, accounting for such complicating factors as ablation from the surface, the phase transition of liquid in porous materials, vibration, and rotation of the body around the longitudinal axis. A mathematical model of a new thermionic thermal protection system for high-enthalpy heating of a composite shell is developed. How electron evaporation from the emitter surface affects decreases in temperature in a multielement thermionic thermal protection system is shown. A numerical analysis of the heat and mass exchange process for carbon plastic under multiple impulse actions is presented. Numerical solutions of boundary value problems are compared with known experimental data. This book is intended for specialists in the fields of thermal protection and heat and mass transfer, as well as graduate students and students of senior courses in physical and mathematical specialties.

Introduction

At the end of the last century and the beginning of this millennium, much attention was paid to developing and designing hypersonic flight vehicles in Russia and worldwide. When hypersonic flight vehicles enter the atmosphere of the Earth or other planets at a cosmic velocity, their impressive kinetic energy [1] transforms into heat. This necessitates the development of various thermal protection methods: ablative thermal protective coatings, forced feed of a coolant into the near-wall gas layer, reradiation of heat to the environment, etc.

With this in mind, a thermophysical calculation accounting for the capabilities of advanced materials should be considered an integral part of hypersonic flight vehicle design.

During the 20th century, mathematical modeling of heat and mass transfer processes became essential for thermal protection and the development of advanced structural materials for flight vehicles. In many cases, mathematical modeling is more cost-effective, and it is often the only possible research method. This is largely associated with experimental conditions, such as the high temperatures and pressures that arise when a flight vehicle enters the atmosphere at high velocity.

Another important issue is expanding the operating temperature range. This makes it possible to approach real operational conditions of thermal protective materials when the levels of convective heat flows from the gas phase reach ∼ W/ or more.

Aerospace engineering uses various active and passive thermal protection methods associated with a variety of flight vehicle designs and their specific atmospheric flight conditions [2 − 19]. Passive thermal protection methods based on ablative thermal protective coatings have been and remain the most popular solutions [2 − 15]. However, these methods have one disadvantage—they change the initial geometric shape of flight vehicles and, therefore, their aerodynamic flight characteristics, negatively affecting the accuracy of ballistic parameters.

Numerous studies [15 − 25], including recent ones [2,6,10,18,19,23,26 − 31], suggest that active thermal protection systems of flight vehicles based on forced injection of a coolant into the boundary layer are quite effective and promising. An important advantage of these systems is that they do not change the geometric shape and, therefore, the aerodynamic characteristics of flight vehicles up to the end point of their flight path.

Under high heat loads, structural materials are often stressed to the limit of their performance capability. The development of combined thermal protection seems to be an alternative solution [25,26,28,29,32,33]. Some studies [28,29,32] focus on the effects of heat-conductive materials that decrease the surface temperature in the air heat curtain area. Materials with high thermal conductivity and the injection of a coolant gas from the surface of the porous blunted area have decreased maximum surface temperatures. As shown in Ref. [31], the increased thermal conductivity of materials leads to a lower temperature of the thermal protective coating. Increased porosity ensures a more uniform distribution of the coolant over the surface and decreases heat loads on the protected structure.

In real conditions, thermal protective materials are exposed to low-energy perturbations: acoustic vibrations, wall vibrations, and pulsations of gas flows [34–41]. Thermochemical destruction characteristics in such systems may vary widely. Stimulation of heat and mass transfer processes in continuous and permeable media is considered in Ref. [34 − 41]. A study [35] demonstrates that pulsating flows improve fuel–air mixing and reduce the extent of the combustion zone. The primary advantage of the method proposed in Ref. [35] is the high effectiveness of the process in terms of minimum pressure losses and the maximum increase in temperature. As shown in Ref. [36], both stimulation and suppression of heat transfer are possible in the pulse impact jet compared with a steady flow. An increased Reynolds number suppresses heat transfer, with all frequencies tending toward a steady flow.

It is important to note that the energy cost of excitation is much less than the total energy of processes in the mechanics of reactive media [30,31,37 − 41].

A promising direction in thermal protection is based on the thermionic method [42–45]. In this case, the evaporation of thermal electrons from the emitter is accompanied by a decrease in the temperature of the latter [44–46]. This physical effect allows heat energy received from convective heating to be directly converted into electrical energy.

In conclusion, let us briefly consider one of the trends in the development of promising thermal protection methods associated with body rotation and oscillation. Rotation may ensure good stability in flight, and when combined with injection from the surface of thermal protective materials, change flow conditions and body-flow heat transfer [47–49]. In contrast to axially symmetric heating [32], for flow around the body at the angle of attack [27], the difference in heat flows on the leeward and windward sides may be significant, which leads to uneven heating. To reduce the influence of this effect, hypersonic aircraft impart rotational or oscillational movement around the longitudinal axis.

The possibility of attenuating moderate-intensity laser radiation by combustion products of carbon-graphite materials has been investigated [50].

Some results of numerical solutions to boundary value problems are compared with known experimental data [2,51].

To accomplish this objective, effective mathematical techniques and software systems must be developed to solve spatial problems in reactive media mechanics. The proposed mathematical models and numerical solutions to spatial problems [52] are new. Using the method proposed in Ref. [52], some problems associated