Effect of Gas Injection from the Surface of a Body on Its Interaction with a Temperature Inhomogeneity in a Supersonic Flow

The flow pattern in the shock layer and the aerodynamic characteristics of a hemisphere in unsteady axisymmetric interaction with a closed spherical hot-gas region embedded in the oncoming supersonic flow in the presence of intense injection of gas from the body surface into the shock layer are studied on the basis of the inviscid perfect gas model. Two cases are considered, namely, (1) when the radius of the permeable surface is greater than that of the temperature inhomogeneity and (2) when the injection is localized in the vicinity of the forward stagnation point and the permeable region is smaller the inhomogeneity.     

Distribution of the concentration in a diffusion wake with stokes flow around a particle

The problem of steady-state convective diffusion to a solid spherical particle located in a Stokes flow was discussed in [1] in the approximation of a diffusion boundary layer. The region of the rear critical point at which the boundarylayer solution is inacceptable was investigated in [2, 3]. With the investigation of the diffusional interaction of several particles in a stream of liquid (for example, two spheres with a common axis, directed along the flow), we must know the distribution of the concentration in a region of small angles behind the body, giving the flow for the following particle. In the present work a solution is given to the problem of the distribution of the concentration in the diffusional wake of a spherical particle. It is shown that the concentration rises proportionally to the square root of the distance to its surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 176–179, January–February, 1977.The author thanks Yu. P. Gupalo and Yu. S. Ryazantsev for their useful observations.     

Heat transfer characteristics in flow around a spherically blunted cone at incidence and gas injection from a blunted surface

New methods of controlling thermal regimes in a high-enthalpy spatial flow around a body are considered. They are related to gas injection from the blunted surface and heat overflow in the material of the shell. The effect of injection is analyzed for different thermal conductivities. It is shown that highly heat-conducting materials can be successfully used to decrease the maximum temperatures at the windward side due to intense heat removal to the region of a porous spherical bluntness. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 162–169, July–August, 1999.     

Model of a gas of solid particles with allowance for inelastic collisions

A study is made of the structure of the interaction region of a flow of solid particles with a surface (or another flow) in the case when the width of this region is much greater than the mean free path of the particles between collisions. The disperse phase is described by means of a model of an ideal non-heat-conducting gas of imperfectly elastic spherical particles. For simplicity, the influence of the carrier medium on the motion of the particles is ignored.     

Unsteady flow of an incompressible viscous fluid around a deformable spherical body

An unsteady flow of a viscous incompressible fluid around a deformable spherical body is considered in the approximation of low Reynolds numbers with a predetermined flow velocity. The hydrodynamic impact of the flow incoming onto the body is determined with allowance for small radial displacements of the body surface. The effect of spherical body surface deformation on the magnitude of the incoming flow impact force is taken into account, in particular, the dependence of small radial displacements of the body surface on the time is found, which makes it possible to minimize the physical impact of the incident flow.     

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.     

On the center of pressure of a body

It is shown that under conditions of local interaction of a flow with the surface of a body the position of the center of pressure does not depend on the angle of attack or the form of the model of the flow past the body for a large class of configurations including conical, cylindrical, spherical, and flat elements. The problem of finding the shape of conical bodies with unchanged position of the center of pressure in a supersonic flow without slip was formulated by Ostapenko [1], who also found the shape of some such bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 129–133, September–October, 1982.     

Asymptotic solution of the euler equations in the shock layer on a blunt body in nonuniform flow with gas injection from the body surface

Supersonic nonuniform gas flow over blunt bodies without surface injection has previously been investigated by both numerical [1–3] and experimental [3] methods. The processes of surface vaporization under the influence of an intense heat flux, artificial gas injection and surface combustion [4] are all worthy of study. The problem of the interaction between a nonuniform supersonic flow and a body in the presence of intense gas injection from the surface is examined and an analytical solution is constructed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 126–134, November–December, 1989.     

Specific Features of the Flow in the Supercritical Boundary Layer Near a Break Point on a Cold Surface

The interaction between a boundary layer and a supersonic flow past a plate with a flap deflected at a small angle in the presence of strong cooling of the body surface is considered. For supercritical regimes, the entire interaction region is located behind the leading edge of the flap and the pressure distribution has a discontinuity of the derivative near the corner point. The flow in a break-point neighborhood with a characteristic length x of the order of the boundary layer thickness is studied. It is shown that in this region a substantial pressure difference arises. The pressure distribution along the surface is found. The viscous sublayer in this region develops under the action of the given pressure gradient.     

Characteristics of unsteady type IV shock/shock interaction

Characteristics of the unsteady type IV shock/shock interaction of hypersonic blunt body flows are investigated by solving the Navier–Stokes equations with high-order numerical methods. The intrinsic relations of flow structures to shear, compression, and heating processes are studied and the physical mechanisms of the unsteady flow evolution are revealed. It is found that the instantaneous surface-heating peak is caused by the fluid in the “hot spot” generated by an oscillating and deforming jet bow shock (JBS) just ahead of the body surface. The features of local shock/boundary layer interaction and vortex/boundary layer interaction are clarified. Based on the analysis of flow evolution, it is identified that the upstream-propagating compression waves are associated with the interaction of the JBS and the shear layers formed by a supersonic impinging jet, and then the interaction of the freestream bow shocks and the compression waves results in entropy and vortical waves propagating to the body surface. Further, the feedback mechanism of the inherent unsteadiness of the flow field is revealed to be related to the impinging jet. A feedback model is proposed to reliably predict the dominant frequency of flow evolution. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.     

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.     

Reflection of a spherical blast wave from a planar surface

Numerous authors have carried out rather extensive studies in the last twenty to thirty years of the problem of the interaction of shock and blast waves with obstacles in their paths. Owing to the complexity of the problem, they assumed certain limiting cases for the shock wave interactions in which the parameters behind the shock wave were usually taken to be constants. The first wave diffraction studies involving variable parameters behind the front were presented in [1, 2], wherein a development of the theory of “short waves” (blast waves at a substantial distance from the center of an explosion) and their reflection from a planar surface was given. The theory of short waves assumes that the jump in pressure at the wave front and the region over which the parameters vary are small. The problem concerning reflection of a blast wave from a surface was also considered in [3, 4], wherein a solution in the region behind the reflected wave was obtained at initial times. The initial stage in the reflection of a blast wave from a planar, cylindrical, or spherical surface (the one-dimensional case) was studied in [5]. In this paper we investigate the interaction of a spherical blast wave, resulting from a point explosion, with a planar surface; we consider both regular and non-regular reflection stages. In solving this problem we use S. L. Godunov's finite-difference method. We obtain numerical solutions for various values of the shock strength at the instant of its encounter with the surface. We present the pressure fields in the flow regions, the pressure distribution over the surface at various instants of time, and the trajectories of the triple point. The parameter values at the front of the reflected wave are compared with results obtained from the theory of regular reflection of shock waves.     

Controlling the level of the sonic boom generated by a flying vehicle by means of cryogenic forcing. 2. Distributed injection of a supercooled gas from the vehicle surface

The possibility of improving the efficiency of cryogenic forcing on the parameters of the hanging shock determining the length of the region of minimization of the sonic boom (middle zone) generated by a modified power-law body is studied. The effect of distributed injection of the coolant from the body surface on the formation of a perturbed flow near the body and at large distances from the body is considered. The scheme of distributed injection and the regime of coolant exhaustion are demonstrated to exert a significant effect on the length of the middle zone of the sonic boom. A scheme of cryogenic forcing is determined, which ensures reduction of bow shock wave intensity by more than 40% at distances corresponding to 7000 body diameters. The mechanism of cryogenic forcing on the flow structure near the body is discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 136–144, March–April, 2009.     

Interaction of a three-dimensional boundary layer with an extensive obstacle

A special variant is considered of the theory of longitudinal—transverse interaction in which the pressure field in the perturbed region of flow forms under the influence of centrifugal forces which lead to a change in the pressure across the boundary layer. This regime of flow is realized in flow of an incompressible fluid, when the two-dimensional boundary layer developing along the smooth section of the contour of a solid body enters into interaction with a three-dimensional irregularity on the surface around which flow is taking place, a projection or a depression. On the assumption that the height of the irregularity is not great, a solution is constructed for the linearized problem of interaction. It is shown that the properties of the flow of fluid in the region of interaction, in particular the possibility of penetration of perturbations into the boundary layer in front of an irregularity, depend on the sign of the curvature exhibited by the contour of the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 39–48, January–February, 1988.     

Development of slow disturbances in a hypersonic boundary layer

The mechanisms of development of slow time-dependent disturbances in the wall region of a hypersonic boundary layer are established and a diagram of the disturbed flow patterns is plotted; the corresponding nonlinear boundary value problem is formulated for each of these regimes. It is shown that the main factors that form the disturbed flow are the gas enthalpy near the body surface, the local viscous-inviscid interaction level, and the type, either subsonic or supersonic, of the boundary layer as a whole. Numerical and analytical solutions are obtained in the linear approximation. It is established that enhancement of the local viscous-inviscid interaction or an increased role for the main supersonic region of the boundary layer makes the disturbed flow by and large “supersonic”: the upstream propagation of the disturbances becomes weaker, while their downstream growth is amplified. Contrariwise, local viscous-inviscid interaction attenuation or an increased role for the main subsonic region of the boundary layer has the opposite effect. Surface cooling favors an increased effect of the main region of the boundary layer while heating favors an increased wall region effect. It is also found that in the regimes considered disturbances travel from the turbulent flow region downstream of the disturbed region under consideration counter to the oncoming flow, which may be of considerable significance in constructing the nonlinear stability theory.     

Diffraction of a plane acoustic wave by a rigid sphere in a cylindrical cavity: An axisymmetric problem

The paper studies the interaction of a rigid spherical body and a cylindrical cavity filled with an ideal compressible fluid in which a plane acoustic wave of unit amplitude propagates. The solution is based on the possibility of transforming partial solutions of the Helmholtz equation between cylindrical and spherical coordinates. Satisfying the interface conditions between the cavity and the acoustic medium and the boundary conditions on the spherical surface yields an infinite system of algebraic equations with indefinite integrals of cylindrical functions as coefficients. This system of equations is solved by reduction. The behavior of the system is studied depending on the frequency of the plane wave     

Rarefied gas flow past a sphere with injection

Hypersonic rarefied gas flow over the windward face of a sphere is considered in the presence of distributed injection from the surface of the body. A similar problem was previously solved in [1–3] within the framework of continuum mechanics and in [4] on the basis of model kinetic equations. In the present study the calculations were carried out using the Monte Carlo method of direct statistical modeling [5, 6]. The injected gas was the same as the free-stream gas. A simple monatomic gas model with a rigid sphere interaction potential was employed. The reflection of the molecules from the surface of the body was assumed to be diffuse with total energy accommodation. The calculation procedure using weighting factors is described in [7]. The influence of injection on the mechanical and thermal effect of the gas flow on the body is investigated for various degrees of rarefaction of the medium and injection rates.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 175–179, July–August, 1990.     

Temperature force of interaction between spherical particles

The force of interaction between small particles in a gas induced by a temperature difference between the particle surface and the gas far away from the particle is considered. The particle dimensions correspond to the free-molecular, transitional, and continuum heat transfer regimes. A Monte-Carlo numerical method of direct statistical simulation of the solution of the nonlinear Boltzmann equation and the results of asymptotic solutions are used. The force of interaction between two hot or cold spherical particles is investigated. The dependence of the temperature force on the particle size, i.e. on the flow regime (Knudsen number), and the distance between the particles is examined. Approximations for these dependences are constructed.     

Method of mean-mass parameters for a three-dimensional boundary layer in a flow with vorticity

When a gas flows with hypersonic velocity over a slender blunt body, the bow shock induces large entropy gradients and vorticity near the wall in the disturbed flow region (in the high-entropy layer) [1]. The boundary layer on the body develops in an essentially inhomogeneous inviscid flow, so that it is necessary to take into account the difference between the values of the gas parameters on the outer edge of the boundary layer and their values on the wall in the inviscid flow. This vortex interaction is usually accompanied by a growth in the frictional stress and heat flux at the wall [2, 3]. In three-dimensional flows in which the spreading of the gas on the windward sections of the body causes the high-entropy layer to become narrower, the vortex interaction can be expected to be particularly important. The first investigations in this direction [4–6] studied the attachment lines of a three-dimensional boundary layer. The method proposed in the present paper for calculating the heat transfer generalizes the approach realized in [5] for the attachment lines and makes it possible to take into account this effect on the complete surface of a blunt body for three-dimensional laminar, transition, or turbulent flow regime in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 80–87, January–February, 1981.     

Interaction of a supersonic jet exhausting into vacuum with an obstacle

A study is made of the interaction between an axisymmetric supersonic jet exhausting into vacuum and an obstacle of a fairly complicated configuration and positioned relative to the nozzle in such a way that in the interaction region behind the detached shock wave there is a three-dimensional flow possessing a symmetry plane. The flow in the interaction region is described by the system of equations of motion of an inviscid perfect gas with boundary conditions on the shock wave (Rankine-Hugoniot relation) and on the surface of the obstacle (no-flow condition). The other boundaries of the region are the symmetry plane of the flow and an arbitrarily chosen surface in the supersonic part of the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti Gaza, No. 1, pp. 156–161, January–February, 1981.