Aerodynamics of an outgassing sphere in a rarefied gas flow

The flow of rarefied gas past a sphere with no-flow condition on the surface has been well studied both experimentally and numerically. In the presence of blowing on the sphere into the oncoming flow, the reflection of the main flow from the body introduces new features. This problem has been considered in the continuum regime [1–3] and, in a kinetic approach, in a regime close to the free-molecule regime [4, 5]. In the present paper, a study is made in the transition regime on the basis of a system of two model kinetic equations of Krook. The first equation determines the distribution function of the molecules of the oncoming flow; the second describes the distribution function of the molecules flowing from the surface of the body. The introduction of the two gas species makes it possible to follow the spatial distribution of the outgassing molecules and determine what fraction of them returns to the body as a result of collisions. The drag coefficient of the sphere and the energy flux to it are determined numerically as functions of the blowing intensity, and approximate similarity laws are found.     

Simulation of the rarefied gas flow around a perpendicular disk

The present work contributes to define the domain of validity of two continuum approaches, based on Navier–Stokes (NS) and quasi gas-dynamic (QGD) equations, respectively. Results obtained using each method are compared with those obtained using a direct simulation Monte Carlo (DSMC) method considered as a reference. QGD equations differ from NS ones by the presence of additional dissipative terms. The present paper includes a brief presentation of QGD equations and DSMC procedures used here. The rarefied flow around a perpendicular disk has been considered for a freestream Mach number varying from 2 to 20, a Knudsen number equal to 0.1 and two levels of wall temperature.     

Supersonic flow of a rarefied gas around a wire grid

The direct simulation Monte Carlo method is used to study a plane-parallel supersonic gas flow through a grid formed by a number of infinite parallel wires. Characteristic features of the shock disturbance formation of in the interaction of a supersonic flow with a permeable grid are revealed. Particular attention is paid to studying the influence of geometrical parameters of the wire target on the number of particles colliding with the surface of the wires.     

Heat transfer and equilibrium temperature of a sphere in a supersonic rarefied gas flow

Some results are presented of experimental studies of the equilibrium temperature and heat transfer of a sphere in a supersonic rarefied air flow.The notations D sphere diameter - u, , T,,l, freestream parameters (u is velocity, density, T the thermodynamic temperature,l the molecular mean free path, the viscosity coefficient, the thermal conductivity) - T₀ temperature of the adiabatically stagnated stream - T_e mean equilibrium temperature of the sphere - T_w surface temperature of the cold sphere (T_we) - mean heat transfer coefficient - _e air thermal conductivity at the temperature T_e - P Prandtl number - M Mach number     

Relaxation processes in hypersonic rarefied binary gas mixture flow around a cylinder

Using the direct simulation Monte Carlo method, the hypersonic flow of a binary gas mixture around a cylinder is investigated over a wide rarefaction range: from an almost continuum regime (at the Knudsen number Kn = 0.01) to free-molecular flow. The effect of a small admixture of heavy diatomic particles in a light gas flow on the relaxation processes near the cylinder and the heat flux is studied.     

Slow flow of gas around a strongly heated or cooled sphere

Problems similar to those considered in [1, 2] are studied, namely, slow flow over a uniformly heated (or cooled) spherical particle and flow past a weakly nonuniformly heated sphere in the absence of external body forces and with allowance for thermal stresses in the gas. The use of an improved method of numerical solution [3] has made it possible to advance into the region of large temperature differences. A new effect is found: allowance for the thermal stresses in the case of flow around a strongly heated sphere leads to the appearance of a suction force instead of a drag. In the case of flow around a nonuniformly heated sphere the influence of thermal stresses is unimportant. The problems are considered for two temperature dependences of the transport coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–175, October–December, 1981.     

Influence of nonequilibrium radiation on rarefied gas flow around blunt bodies

The hypersonic nonequilibrium rarefied gas flow is investigated in the neighborhood of the stagnation streamline ahead of a blunt body by taking into account nonequilibrium radiation due to electron excitation for air and carbon dioxide. The analysis is on the basis of a numerical solution of the Navier—Stokes equations simplified under the assumption of local self-similarity of the flow with the Shockwave structure taken into account. It is shown that at low densities, when the shock wave and shock layer thicknesses are of the same order of magnitudes, the two-layer Cheng model becomes inapplicable in the presence of radiation. In this case, the governing process is diffusion of the electronically excited molecules from the shock layer into the forward part of the shock front. The mechanism of the formation of a second luminous plateau on the diagram of the nonequilibrium radiation intensity density is discussed. The combined influence of the limit in collisions and the diffusion transport processes on the intensity of molecular band radiation is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 81–87, November–December, 1974.The author is grateful to V. V. Lunev for discussion and remarks during performance of the research.     

Investigation of the rarefied gas flow around a circular cylinder in stationary and oscillatory regimes

Numerically, on the basis of the Krook kinetic equation, the rarefied gas flow around a circular cylinder is investigated in stationary and oscillatory regimes. The flows around a rotating cylinder and a cylinder with a nonuniformly heated surface are considered. The Knudsen numbers at which the lift force acting on the rotating cylinder changes sign are calculated. It is shown that at low Knudsen numbers a lift force acts on the nonuniformly heated cylinder.     

Numerical study of the generalized cylindrical Couette flow of rarefied gas

We study the cylindrical Couette flow of a rarefied gas between two cylinders in the generalized setup in which the inner of which not only rotates but also slides along its axis. The analysis is based on the numerical solution of the S-model kinetic equation. The influence of ratio of cylinder radiuses, velocities of the inner cylinder and Knudsen number on shear stresses, mass-flow rates as well as macroscopic parameters is investigated in the broad range of Knudsen numbers.     

Heat transfer from a heated sphere in a rarefied gas at rest

We consider the problem of heat transfer from a slightly heated sphere in a resting rarefied gas. We assume that the Krook equation is valid in this case. Two forms of the basic equations are presented, and relations are given which are obtained as a result of calculations of the heat flux and the temperature jump at the sphere surface as a function of a parameter which is inversely proportional to the Knudsen number. The results obtained are compared with results given by the known approximate theories.In conclusion the author wishes to thank M. N. Kogan for proposing the problem and for numerous discussions.     

Heat transfer from a sphere in the intermediate dynamics region of a rarefied gas

The results are given of the experimental study of convective heat transfer from a sphere in a low-density subsonic stream. Generalizing the results obtained and earlier known data for sub-and supersonic velocities, we suggest approximate formulas for calculating heat transfer from a sphere under any streamline flow conditions of a rarefied gas.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 170-172, March-April, 1972.     

Analytical solution of the problem of sphere rotation in a rarefied molecular gas

A problem of sphere rotation in a rarefied molecular gas is solved in an isothermal approximation. The particle velocity profile in the rarefied molecular gas entrained by the rotating sphere is obtained with a second-order correction in terms of the Knudsen number. For a rarefied molecular gas, in contrast to a monatomic gas, the particle velocity is demonstrated to depend substantially on the Prandtl number if rotational degrees of freedom of molecules are taken into account.