1. Introduction

A problem of non-equilibrium thermochemical processes in carbon dioxide (CO2) mixture flows has been studied in a great number of experimental and theoretical works owing to

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needs of Mars planet investigations. These works started in the 1960s. Further studies were stimulated by development of Pathfinder and other Martian entry vehicles [1–6].

Calculations of the convective heat flux and the non-equilibrium radiation were carried out of

Numerical Modeling of Hypersonic Aerodynamics and Heat Transfer Problems of the Martian Descent Modules

The part of results have been obtained in the framework of the INTAS Project 03-51-5204 "Numerical, Analytical and Experimental Investigation of Convective and Radiative Heating of Martian Descent Module". This Project was elaborated jointly between institutes-

The Martian atmosphere is composed mostly of carbon dioxide (96%), nitrogen (1.9%), argon (1.9%), and others. Small admixtures of nitrogen (N2) and argon (Ar) in the Mars atmosphere do not play a significant role in the process of heat transfer to descent vehicles (at least, at moderate velocities of flight till the convective heat transfer prevails). It is possible to restrict ourselves by consideration of model atmosphere as the pure carbon dioxide. The pressure on the planet surface is taken equal to 6.0 mbar. It is 0.6% of Earth's mean sea level pressure. The

The conditions of a flow corresponding to the last stage of flight of space vehicles in an

process at such velocities is a process of dissociation. Up to 75% of full gas flow energy can be

The region where non-equilibrium physical and chemical processes realized is a significant part from all considered regions (Figure 2). Velocity of physical and chemical processes, as a rule, grows together with density of gas. For considered flow conditions, the degree of gas ionization is small and does not bring the appreciable contribution to internal gas energy. The translational degrees freedom becomes equilibrium on distances of several free path lengths of molecules behind front of a shock wave for considered altitude. The distribution of rotation energy also is established slightly later. Therefore, it is usually supposed that translational and vibration degrees of freedom of particles are in equilibrium. At high temperatures that observed in a shock layer, the characteristic times of a vibration energy relaxation of molecules and characteristic times of dissociation become one order. Thus the account of non-equilibrium excitation of vibration degrees of freedom of carbon dioxide molecules is necessary. The region of relaxation behind the bow shock wave has a specific structure that consists of sequential relaxation zones. The flow in shock and boundary layers are being especially non-equilibrium.

Since the Martian atmosphere is strongly rarefied, non-equilibrium processes affect heat transfer at the more significant part of the descent trajectory. The most thermal-loaded part of the typical descent trajectory is the region of frozen chemical reactions and equilibrium-excited

, H < 60 km) were studied. Determining

http://dx.doi.org/10.5772/intechopen.71666

43

2. Governing equations of hypersonic non-equilibrium polyatomic

the MSRO vehicle entering into the Martian atmosphere [7–19].

participants from Russian side and European Collaborators [5].

gas flows

spent on it.

atmosphere is quite dusty.

atmosphere of Mars (V<sup>∞</sup> ≤ 6 km/s, r<sup>∞</sup> > 10<sup>5</sup> kg/m<sup>3</sup>

It causes the energy redistribution of the internal energy.

vibration degrees of freedom.

There are two ways of derivation of the gas dynamics equations for a multi-component mixture: kinetic and phenomenological. The first approach is based on the kinetic theory of gases. The zero-order and the first-order distribution functions are known and expressed by means of different gradients, the diffusive driving forces, etc. [7, 8]. If potentials of interaction between particles are defined, then the equations in terms of species densities, macroscopic velocity, and gas temperature can be carried out by methods of the kinetic theory of gases [9–12]. The transport theory of polyatomic gas mixtures taking into of account internal molecular structure, different rates of vibration, and non-harmonic transitions has been developed for a five component CO2/O2/CO/O/C mixture taking vibration excitation of molecules into account. The algorithm for transport coefficients calculation has been realized as a program module.

The phenomenological approach is based on application of the basic theorems of mechanics and laws of thermodynamics for macroscopic volume of the continuous media and leads to unclosed system of the equations. For closure of this system, the additional definition of mass, momentum, and energy fluxes is necessary. Unknown values of transfer coefficients within the framework of the phenomenological approach can be defined from approximation either from experiment. The kinetic and phenomenological approaches give the same result as structure of gas dynamic equations system.

The governing equations with rigorous kinetic schemes for transport coefficients are solved numerically for a flow in a viscous shock layer near the blunt body imitating the form of the spacecraft Mars Sample Return Orbiter (MSRO) and MARS EXPRESS vehicles descending in an atmosphere of Mars for the conditions typical for the re-entering regime [9–12]. The form of considered vehicles represents spherically blunted cone with aт angle 120 and radius R = 1.0 m (MSRO) and R = 0.38 m (MARS EXPRESS) joined with the cylinder (Figure 1).

Figure 1. Martian vehicle.

Calculations of the convective heat flux and the non-equilibrium radiation were carried out of the MSRO vehicle entering into the Martian atmosphere [7–19].

needs of Mars planet investigations. These works started in the 1960s. Further studies were

There are two ways of derivation of the gas dynamics equations for a multi-component mixture: kinetic and phenomenological. The first approach is based on the kinetic theory of gases. The zero-order and the first-order distribution functions are known and expressed by means of different gradients, the diffusive driving forces, etc. [7, 8]. If potentials of interaction between particles are defined, then the equations in terms of species densities, macroscopic velocity, and gas temperature can be carried out by methods of the kinetic theory of gases [9–12]. The transport theory of polyatomic gas mixtures taking into of account internal molecular structure, different rates of vibration, and non-harmonic transitions has been developed for a five component CO2/O2/CO/O/C mixture taking vibration excitation of molecules into account. The algorithm for transport coefficients calculation has been realized as a pro-

The phenomenological approach is based on application of the basic theorems of mechanics and laws of thermodynamics for macroscopic volume of the continuous media and leads to unclosed system of the equations. For closure of this system, the additional definition of mass, momentum, and energy fluxes is necessary. Unknown values of transfer coefficients within the framework of the phenomenological approach can be defined from approximation either from experiment. The kinetic and phenomenological approaches give the same result as structure of

The governing equations with rigorous kinetic schemes for transport coefficients are solved numerically for a flow in a viscous shock layer near the blunt body imitating the form of the spacecraft Mars Sample Return Orbiter (MSRO) and MARS EXPRESS vehicles descending in an atmosphere of Mars for the conditions typical for the re-entering regime [9–12]. The form of considered vehicles represents spherically blunted cone with aт angle 120 and radius R = 1.0 m

(MSRO) and R = 0.38 m (MARS EXPRESS) joined with the cylinder (Figure 1).

stimulated by development of Pathfinder and other Martian entry vehicles [1–6].

gram module.

gas dynamic equations system.

42 Advances in Some Hypersonic Vehicles Technologies

Figure 1. Martian vehicle.

The part of results have been obtained in the framework of the INTAS Project 03-51-5204 "Numerical, Analytical and Experimental Investigation of Convective and Radiative Heating of Martian Descent Module". This Project was elaborated jointly between institutesparticipants from Russian side and European Collaborators [5].
