Supersonic transverse rarefied gas flow past a strip

The supersonic flow of a monatomic gas consisting of hard spherical particles past a flat strip normal to the flow is investigated using the direct simulation Monte-Carlo (DSMC) method. The calculations are performed over the Knudsen and Mach number ranges 0.015–5 and 1.8–15, respectively. The structure of the compressed layer and the aerodynamic characteristics are systematically studied for the Mach number 5 and various Knudsen numbers. The dependences of the compressed-layer thickness in molecular free paths are found. The nonequilibrium processes in the neighborhood of the strip are described on the basis of the data on the temperature anisotropy with respect to three coordinates.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 159–167. Original Russian Text Copyright © 2005 by Maltsev and Rebrov.     

Calculation of transverse flow of a stream of rarefied gas past a plate

We give the results of a calculation by the Monte Carlo method of the coefficient of resistance and the field of flow past a plate placed perpendicular to a stream of rarefied gas at Mach numbers M = 2–20 and Reynolds numbers Re₀27. The calculations were carried out for two forms of the law governing the variation of the coefficient of viscosity as a function of temperature (T, T). The results are compared with available calculated and experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 106–112, July–August, 1976.     

Low speed MHD Couette flow of a slightly rarefied and electrically conducting gas

The effects of an applied magnetic field on the steady, laminar, low speed plane Couette flow of a slightly rarefied and electrically conducting gas are studied. Consideration is given to the slip-flow regime, wherein the gas rarefaction begins to play its important role. The generally accepted method of analysis for slip flows is utilized, i.e. the continuum magnetohydrodynamic equations of motion are used throughout the gas, together with the first and the second order slip velocity and temperature jump boundary conditions. Considerations are further given to (1) the case of zero electric field and (2) the case of a nonconducting channel in which the net current across the channel is zero.     

Flow of rarefied gas past a sweptback cylinder

A numerical investigation has been made of the hypersonic flow of a rarefied monatomic gas past the windward part of the side surface of an infinite circular cylinder. The calculation was made by direct statistical Monte Carlo modeling for freestream Mach number M_t8=20, ratio of the surface temperature of the body to the stagnation temperature equal to t_tw =T _tw/T _t0 = 0.03, sweep angle 75°, and Reynolds number Re_t0 30.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 146–154, January–February, 1992.     

The problem of transonic flow past a convex body

The uniqueness of the asymptotic type of flow in the neighborhood of a corner point in transonic flow past a convex body is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 67–69, March–April, 1971.     

Investigation of hypersonic flow of rarefied gas past wings of infinite span

In the framework of the locally self-similar approximation of the Navier-Stokes equations an investigation is made of the flow of homogeneous gas in a hypersonic viscous shock layer, including the transition region through the shock wave, on wings of infinite span with rounded leading edge. The neighborhood of the stagnation line is considered. The boundary conditions, which take into account blowing or suction of gas, are specified on the surface of the body and in the undisturbed flow. A method of numerical solution of the problem proposed by Gershbein and Kolesnikov [1] and generalized to the case of flow past wings at different angles of slip is used. A solution to the problem is found in a wide range of variation of the Reynolds numbers, the blowing (suction) parameter, and the angle of slip. Flow past wings with rounded leading edge at different angles of slip has been investigated earlier only in the framework of the boundary layer equations (see, for example, [2], which gives a brief review of early studies) or a hypersonic viscous shock layer [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 150–154, May–June, 1984.     

Free convection effects on the oscillatory flow of an electrically conducting rarefied gas past an infinite, vertical plate with constant suction

An analysis of a two-dimensional, unsteady flow of an electrically conducting, viscous, incompressible rarefied gas past an infinite vertical porous plate is carried out under the following assumptions: (i) the suction velocity normal to the plate is constant (ii) the free stream velocity oscillates in time about a constant mean (iii) the plate temperature is constant (iv) the difference between the temperature of the plate and the free stream is moderately large causing the free convection currents (v) first order velocity-slip and the temperature jump boundary conditions (vi) transverse magnetic field (vii) induced magnetic field is negligible.Approximate solutions to the coupled, non-linear equations governing the flow are derived for the mean velocity, mean temperature, mean-skin-friction, mean rate of heat transfer, transient velocity and temperature, fluctuating parts of the velocity profiles, the amplitude and the phase of the skin-friction and the rate of heat-transfer. They are shown graphically followed by a discussion. The effects of ±G (Grashof number), ±E (Eckert number), M (Magnetic field parameter), h ₁ (rarefaction parameter), h ₂ (temperature jump coefficient), (frequency) are discussed for heating (G<0) or cooling (G>0) of the plate by the free convection currents.Nomenclature |B| amplitude of skin-friction - B ₀ applied magnetic field - c _p specified heat at constant pressure - E Eckert number - f ₁ Maxwell's reflection coefficient - f ₂ thermal accommodation coefficient - g _x acceleration due to gravity - G Grashof number - h ₁ rarefaction parameter (L ₁ v ₀/) - h ₂ non-dimensional temperature jump coefficient (L ₂ v ₀/) - k thermal conductivity - K _n Knudsen number - L mean free path - L ₁ (2–f ₁)L/f ₁ - L ₂ - l ₁ characteristic length - M magnetic field parameter - M _r, M _i fluctuating parts of velocity - m - P Prandtl number - p pressure - q rate of heat transfer - q _m mean rate of heat transfer - |Q| amplitude of rate of heat transfer - R suction Reynolds number - T temperature of fluid - T _w temperature of the plate - T temperature of the fluid in free stream - t time - t dimensionless time - U free stream velocity - U dimensionless free stream velocity - U mean of U(t) - u, v velocity components in x, y directions - u dimensionless velocity in x direction - u ₀ mean velocity - u ₁ fluctuating part of velocity - v ₀ suction velocity - x, y coordinate system - x, y dimensionless coordinates - frequency of the free stream oscillations - dimensionless frequency - dimensionless temperature - ₁ fluctuating part of temperature - phase angle of skin-friction - phase angle of rate of heat transfer - density of the fluid in the boundary layer - density of the fluid in the free stream - viscosity - kinematic viscosity - electrical conductivity of the fluid - small positive constant - skin-friction - _m mean skin-friction - specific heat ratio - ₁ coefficient of volume expansion     

Calculation of inviscid radiating gas flow past a blunt body

During hypersonic gas flow past a blunt body with a velocity on the order of the escape velocity or more, the gas radiation in the disturbed region behind the shock wave becomes the primary mechanism for aerodynamic heating and has a significant effect on the distribution of the gasdynamic parameters in the shock layer. This problem has been considered from different points of view by many authors. A rather complete review of these studies is presented in [1–4].In earlier studies [5, 6] the approximation of bulk emission was used. In this approximation, in order to account for the effect of radiative heat transfer a term is added in the energy equation which is equivalent to the body efflux, whose magnitude depends on the local thermodynamic state of the gas. However, the use of this assumption to solve the problem of inviscid flow past a blunt body leads to a singularity at the body [7, 8]. To eliminate the singularity, account is taken of the radiation absorption in a narrow wall layer [7], or the concept of a viscous and heat-conductive shock layer is used [8]. A further refinement was obtained by Rumynskii, who considered radiation selectivity and studied the flow of a radiating and absorbing gas in the vicinity of the forward stagnation point of a blunt body.In the present paper we study the distribution of the gasdynamic parameters in the shock layer over the entire frontal surface of a blunt body in a hypersonic flow of a radiating and absorbing gas with account for radiation selectivity.     

Laminar slip flow of an electrically conducting incompressible rarefied gas in a channel with a transverse magnetic field

Summary The effects of a constant external magnetic field on the laminar, fully developed flow of an electrically conducting incompressible rarefied gas in a nonconducting parallel-plate channel are studied. Consideration is given to the slip-flow regime, wherein a gas velocity discontinuity occurs at the channel walls. It is found that the magnitude of the slip velocity is unaffected by the magnetic-field strength for a given pressure drop, but that the mean gas velocity and wall friction coefficient are functions of both the velocity slip coefficient and the magnetic-field strength. The effect of a second-order slip-flow boundary condition is briefly discussed.     

Calculation of convective heat flux in the vicinity of the stagnation point for partially ionized gas flow past a body

From numerical solutions of the boundary layer equations for a four-component gas mixture (E, N⁺, N₂, and N) with gas injection, approximate formulas for the heat flux as a function of the variation of λρ/c_p and h^* across the boundary layer and the magnitude of the objection are obtained (λ is the thermal conductivity of the mixture,ρ is density, c_p is the specific heat, and h^* is the enthalpy of the ideal gas state of the mixture). An effective ambipolar diffusion coefficient D^(a)(i) is introduced, making possible finite formulas for the convective heat fluxes in the “frozen” boundary layer. We study the behavior of these coefficients within the boundary layer. A formula is obtained for convective heat flux to the wall from partially ionized air for a nine-component mixture (E, O⁺, N⁺, NO⁺, O, N, NO, O₂ N₂). Even for simpler four-component gas model three effective ambipolar diffusion coefficients are necessary: $$\begin{gathered} D^{(a)} (A) = D (A, M) D^{(a)} (I) = 2D (A, M), \hfill \\ D^{(a)} (M) = [ 1 + c_e (I)] D(A, M). \hfill \\ \end{gathered} $$ Here D(A, M) is the binary diffusion coefficient of the atoms into molecules, and c_e(I) is the ion concentration at the outer edge of the boundary layer. The assumption of an infinitely large charge-exchange cross section and the other simplifying assumptions used in [1] lead to overestimation of the magnitude of the dimensionless heat flux by 7–15% for the “frozen” boundary layer case.     

Analytical solution of the problem of heat transfer in rarefied gas between two coaxial cylinders

The method of characteristics was used within the framework of the kinetic approach to construct an analytical solution of the problem of heat transfer in a channel whose walls were formed by two coaxial cylinders. The main equation was the Williams kinetic equation, and the boundary condition on the channel walls was the diffusion reflection model. The vector field of the heat flux in the channel was determined, and the specific heat flux through the cross section of the channel was calculated. It was shown that the results obtained for a limiting case, in which the cylinder radii were significantly greater than the mean length of free path of gas molecules, were in good agreement with the results obtained for a plane channel with infinite parallel walls.