Some effects of strong blowing of gas into a supersonic flow

The intense evaporation of bodies moving in the atmospheres of planets at high supersonic velocities has been partly simulated both theoretically [1–5] (numerical calculations of strong blowing in the framework of the Navier-Stokes equations were also made at the Scientific-Research Institute of Mechanics at the Moscow State University by É. A. Gershbein and A. F. Kolesnikov [6]) as well as experimentally [7–9]. Below, the results are given of investigations of strong blowing of gas from the flat end of a cylinder into a supersonic flow at Reynolds numbers such that the mixing layer separating the blown and the oncoming gas is fairly thin. In this case, the mixing layer can be regarded as a contact surface, so that the problem of blowing can be solved in the framework of Euler's equations. The results of a numerical solution are compared with the results of experiments on the separation and profile of the shock wave, the thickness of the blowing layer on the axis, and also on the pressure distribution on the end of the cylinder. It was established experimentally, and then confirmed numerically that there is a downwash of the blown gas on the periphery of a porous end. It is shown that for the same blowing parameter K, which is equal to the ratio of the dynamic head of the blown gas to the dynamic head of the oncoming gas, and for a given distribution of K over the surface of the body the contact surface tends to a certain limiting position with increasing Mach number of the oncoming flow, i.e., the profile of the contact surface is stabilized. The influence of the adiabatic exponent on the thickness of the blowing layer is estimated. The present investigations continue earlier experimental studies, the main results of which have been presented in [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–98, January–February, 1980.     

Effect of micro-blowing of a gas from the surface of a flat plate on its drag

Low-velocity gas flows past a flat plate are numerically simulated. The influence of gas micro-blowing from some part of the surface and its distribution on the local and integral friction coefficients is studied. It is demonstrated that the integral value of friction is almost independent of the distribution of blowing domains over the plate surface if the total blowing intensity stays unchanged. The calculated decrease in the friction drag is in both qualitative and quantitative agreement with experimental results.     

Blowing of a foreign gas in a hypersonic viscous shock layer

We consider the problem of a hypersonic viscous flow of a nonreactive mixture of ideal gases around smooth thick bodies in the framework of a two-layer model of a thin shock layer for moderately small Reynolds numbers. We investigate the effect of blowing of a foreign gas through a permeable surface in the bow region of a spherical blunt body. We introduce a transformation of variables that gives a number of important advantages in the numerical solution of the problem under consideration. The problem of mass blowing from the surface of a body into a boundary layer has an extensive literature. The effect of blowing for moderately small Reynolds numbers has been considerably less studied [1–5], and in the majority of papers on this question either the critical point of a blunt body or the blowing of a gas homogeneous with the gas in the incoming flow is investigated.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 110–116, July–August, 1972.     

Experimental investigation of the efficiency of gas screens at a burning-out surface with the blowing of a foreign gas

The article gives the results of a systematic experimental investigation of the efficiency of a gas screen at a burning-out graphite surface organized in different manners and with the blowing of a foreign gas into the boundary layer. In the experiments, the Reynolds number was varied within the limits R_Δ ≈ 1.2·10⁵ = 1.6·10⁶, R* ≈ 100–2000, R_Z = 2.3·10²–1.5·10⁴; the enthalpy factor of the nonisothermicity in the initial cross section varied from i_s/i₀ = 1 with the tangential blowing of nitrogen to i_s/i₀ ≈ 34 with the blowing of helium through the heated porous section.     

Hypersonic flow past a rectangular profile through which gas is blown strongly

In the present paper, we consider the hypersonic flow past a rectangular profile and the end of a cylinder when there is strong distributed blowing of gas through their flat front parts. The injected gas is assumed to be inviscid, and the pressure on the contact surface which separates the exterior flow and the blowing layer is determined in accordance with Newton's formula. The use of perturbation theory in the case of a thin blowing layer has made it possible to obtain limit problems for different flow regions, and the analytic solution and subsequent asymptotic matching of these problems yield the form of the contact surface and the distribution of the pressure on the body. It is shown that the drag of the body depends nonmonotonically on the flow rate of the blown gas. The optimal blowing parameters and the corresponding minimal drag are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 154–166, January–February, 1982.I thank V. A. Levin for interest in the work and valuable discussions.     

Numerical study of flows of a viscous compressible gas and of an equilibrium gas mixture in a flat nozzle in the presence of strong blowing

The problem of the interaction of a viscous supersonic stream in a flat nozzle with a transverse gas jet of the same composition blown through a slot in one wall of the nozzle is examined. The complete Navier-Stokes equations are used as the initial equations. The statement of the problem in the case of the absence of blowing coincides with [1]. The conditions at the blowing cut are obtained on the assumption that the flow of the blown jet up to the blowing cut is described by one-dimensional equations of ideal gasdynamics. The proposed model of the interaction is generalized to the case of flow of a multicomponent gas mixture in chemical equilibrium. The exact solutions found in [2] are used as the boundary conditions at the entrance to the section of the nozzle under consideration. The results of numerical calculations of the flows of a homogeneous nonreacting gas and of an equilibrium mixture of gases consisting of four components (H₂, H₂O, CO, CO₂) are given for different values of the parameters of the main stream and of the blown jet. In the latter case it is assumed that the effect of thermo- and barodiffusion can be neglected.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 55–63, July–August, 1974.     

Numerical simulation of transpiration cooling through porous material

Transpiration cooling using ceramic matrix composite materials is an innovative concept for cooling rocket thrust chambers. The coolant (air) is driven through the porous material by a pressure difference between the coolant reservoir and the turbulent hot gas flow. The effectiveness of such cooling strategies relies on a proper choice of the involved process parameters such as injection pressure, blowing ratios, and material structure parameters, to name only a few. In view of the limited experimental access to the subtle processes occurring at the interface between hot gas flow and porous medium, reliable and accurate simulations become an increasingly important design tool. In order to facilitate such numerical simulations for a carbon/carbon material mounted in the side wall of a hot gas channel that are able to capture a spatially varying interplay between the hot gas flow and the coolant at the interface, we formulate a model for the porous medium flow of Darcy–Forchheimer type. A finite‐element solver for the corresponding porous medium flow is presented and coupled with a finite‐volume solver for the compressible Reynolds‐averaged Navier–Stokes equations. The two‐dimensional and three‐dimensional results at Mach number Ma = 0.5 and hot gas temperature T_HG=540 K for different blowing ratios are compared with experimental data. Copyright © 2014 John Wiley & Sons, Ltd.     

Strong blowing on the surfaces of a body immersed in a supersonic gas stream

This article considers the problem of strong blowing on the surface of a body immersed in a supersonic gas flow. It is not difficult to show that for intense blowing the motion of the blown gas can be described by the Euler equations, and viscosity and transport effects appear only in the neighborhood of the contact surface separating the oncoming flow and the blown gas. It is shown that to a first approximation the pressure is constant across the layer and equal to the pressure at the contact surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, pp. 97–104, No. 5, September–October, 1973.     

On the possibility of blowing a gas jet into a supersonic flow without formation of a three-dimensional boundary-layer separation zone

We consider the flow formed by the interaction of a supersonic flow and a transverse sonic or supersonic jet blown at right angles to the direction of the main flow through a nozzle whose exit section is in a flat wall. When a gas jet is blown through a circular opening [1] the pressure rises in front of the jet because of the stagnation of the oncoming flow. This leads to separation of the boundary layer formed on the wall in front of the blowing nozzle. The resulting three-dimensional separation zone leads to a sharp increase in the pressure and the heat fluxes to the wall in front of the blowing nozzle, which is undesirable in many modern applications. The aim of the present investigation was to find a shape of the exit section of the blowing nozzle for which there is no three-dimensional separation zone of the boundary layer in front of the blowing nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–165, May–June, 1979.     

复杂微通道气体流动的格子Boltzmann模拟

构建了一个模拟复杂微通道内气体流动的多松弛格子Boltzmann模型。该模型采用动力学曲面滑移边界,考虑了微尺度效应和努森层影响。此外,为了更准确地描述微通道内气体的滑移速度,在模型中引入孔隙局部Kn数来代替平均Kn数。之后采用Poiseuille流对模型进行验证,模拟结果与用直接模拟蒙特卡洛方法和分子模拟结果吻合较好,证明了该模型模拟微通道内处于滑移区和过渡区气体流动的有效性。最后,采用该模型模拟多孔介质内气体渗流过程。结果表明,随着孔隙平均Kn数的增加,多孔介质内的高渗区域增加,且优先从小孔隙中开始增加,这是由于小孔隙中微尺度效应更加明显,相对大孔隙流动阻力更小所致。     

Viscoelastic fluid flow impinging on a wall with suction or blowing

The oblique flow of a viscoelastic fluid impinging on a porous wall with suction or blowing is studied. It is found that when suction is applied the fluid penetrates the wall while blowing causes the shifting of the stagnation point. It is also found that this shifting depends upon the magnitude of the blowing and upon the Weissenberg number.     

地下爆炸气体输运的一种双孔隙度数学模型

考虑气体在压力驱动下的渗透、气体和岩体的热传导以及气体的扩散,建立了用于模拟地下爆炸气体输运的二维轴对称双孔隙度双渗透率数学模型,并编制了数值模拟程序;研究了参数在取值范围内变化对计算结果的影响。结果显示：泄漏到地表的气体随着裂隙区域圆心角的增大而先增大后减小,随裂隙渗透率的增大而增大,随介质孔隙度和孔隙渗透率的增大而减小。用该模型对一次砂砾岩中地下爆炸实验气体的泄漏行为进行了数值模拟。将数值模拟结果与气体泄漏实测结果进行对比,反推出当地介质的裂隙渗透率在4×10^-11 m2～5×10^-11 m2之间。利用反推得到的介质参数,可以对同类介质中地下爆炸气体泄漏行为进行预测。     

Effect of distributed gas injection on aerodynamic characteristics of a body of revolution in a supersonic flow

Results of experimental and numerical investigations of the effect of gas injection through a permeable porous surface on the drag coefficient of a cone-cylinder body of revolution in a supersonic flow with the Mach number range M _h = 3–6 are presented. It is demonstrated that gas injection through a porous nose cone with gas flow rates being 6–8% of the free-stream flow rate in the mid-section leads to a decrease in the drag coefficient approximately by 5–7%. The contributions of the decrease in the drag force acting on the model forebody and of the increase in the base pressure to the total drag reduction are approximately identical. Gas injection through a porous base surface with the flow rate approximately equal to 1% leads to a threefold increase in the base pressure and to a decrease in the drag coefficient. Gas injection through a porous base surface with the flow rate approximately equal to 5% gives rise to a supersonic flow zone in the base region.     

Influence of blowing on the anisotropy of the Reynolds stress tensor in a turbulent channel flow

The effects of localized wall blowing through a porous strip are investigated using hot-wire anemometry in a turbulent channel flow. Three blowing magnitudes are studied: σ=0.22, 0.36 and 0.58, where σ is the momentum flux gain ratio and that of the incoming channel flow at three different positions from the spanwise porous strip. The main emphasis of this work was the departure from isotropy of the turbulent flow with localized blowing. The anisotropic invariant map (AIM) for the Reynolds stress tensor revealed that blowing decreased the anisotropy of the turbulent structure in the near-wall region, and a decrease in the longitudinal integral length scale was observed when the blowing rate increased.     

Turbulent boundary layers on porous surfaces in the case of blowing at different angles to the wall

The results are given of an experimental investigation of turbulent boundary layers on porous plates in the case of homogeneous blowing at various angles to the wall. It is shown that the intensity and angle of the blowing influence the profiles of the averaged and pulsating components of the velocities, the characteristic thicknesses, the surface friction, and the turbulent tangential stresses in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 59–64, May–June, 1982.We thank V. I. Kondrat'ev and V. S. Senterov for participating in the work.     

Conjugate model for heat and mass transfer of porous wall in the high temperature gas flow

Heat and mass transfer of a porous permeable wall in a high temperature gas dynamical flow is considered. Numerical simulation is conducted on the ground of the conjugate mathematical model which includes filtration and heat transfer equations in a porous body and boundary layer equations on its surface. Such an approach enables one to take into account complex interaction between heat and mass transfer in the gasdynamical flow and in the structure subjected to this flow. The main attention is given to the impact of the intraporous heat transfer intensity on the transpiration cooling efficiency. The project supported by the National Natural Science Foundation of China (19889209) and Russian Foundation for Basic Research (97-02-16943)     

Flow of rarefied gas past a sphere in the presence of blowing from its surface

Flow of a rarefied gas past a sphere with various conditions of blowing on the surface is considered. The investigation is based on numerical solution of model kinetic equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 182–185, September–October, 1982.     

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.     

Effect of blowing various gases into the boundary layer on the friction,heat, and mass transfer for a power-law variation of the external flow velocity

Formulas are derived which make it possible to determine the effect of various physical characteristics of the injected and external gases on the blowing coefficient for zero Mach number and a temperature factor of unity. Considering that the blowing coefficients for heat transfer depend very weakly on the Mach number and the temperature ratio [1], it may be recommended that the formulas obtained for these values be used for other values of these parameters as well.The present method is based on obtaining corrections to the solution of the boundary layer equations for a homogeneous gas for the case of injection through the wall with a low flowrate of the second gas. In this case a linear correction yields the blowing coefficients; the quadratic correction yields a second-order improvement and the limits of applicability of the linear correction.     

Calculation of two-dimensional dispersion in a gas in unsteady flow in a porous medium

A two-dimensional problem of the flow of a gas containing an impurity through a porous medium is considered. At the initial time, the gas containing a uniformly distributed impurity is at a high pressure in a spherical cavity in a porous medium at a certain distance from a flat surface. It is assumed that for t > the motion of the carrier gas is described by the system of equations for flow in a porous medium and the dispersion of the impurity is described by the equations of convective diffusion and nonequilibrium adsorption. A numerical method for solving the problem is discussed. Some results of calculations are given. The influence of the flat surface on the flow of the gas and the dispersion of the impurity is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–67, September–October, 1982.We thank V. N. Nikolaevskii for comments which permitted a significant improvement in the paper.