Interaction of a supersonic flow with a transverse jet injected through a circular aperture in a plate

A flow pattern created by the interaction of a supersonic flow with a transverse sonic or supersonic jet injected normally to the direction of the main flow through a circular aperture in a plate is considered. The pressure rises in front of the jet owing to the retarding action of the incident flow. The boundary layer building up on the wall in front of the injection nozzle is accordingly detached. The flow pattern in the region of interaction between the jet and the external flow is illustrated in Fig. 1. The three-dimensional zone of detachment thus formed deflects the incident flow from the wall, and in front of the jet a complicated system of sharp jumps in contraction develops. A three-dimensional system of jumps also develops in the jet itself.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 5, pp. 193–197, September–October, 1970.     

Interaction of a blown gas jet with a supersonic oncoming stream without formation of a three-dimensional region of boundary layer separation

A study is made of the flow resulting from the interaction of a supersonic stream with a transverse sonic or supersonic jet blown at right angles to the direction of the main stream through a nozzle whose exit section is situated on a flat wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 137–139, May–June, 1981.     

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.     

Computation of base flow characteristics with uniform blowing

Blowing at bluff body base was considered under different conditions and for small amount of blowing this problem was solved using dividing streamline model [1]. The effect of supersonic blowing on the flow characteristics of the external supersonic stream was studied in [2–4]. The procedure and results of the solution to the problem of subsonic blowing of a homogeneous fluid at the base of a body in supersonic flow are discussed in this paper. Analysis of experimental results (see, e.g., [5]) shows that within a certain range of blowing rate the pressure distribution along the viscous region differs very little from the pressure in the free stream ahead of the base section. In this range the flow in the blown subsonic jet and in the mixing zones can be described approximately by slender channel flow. This approximation is used in the computation of nozzle flows with smooth wall inclination [6, 7]. On the other hand, boundary layer equations are used to compute separated stationary flows with developed recirculation regions [8] in order to describe the flow at the throat of the wake. The presence of blowing has significant effect on the flow structure in the base region. An increasing blowing rate reduces the size of the recirculation region [9] and increases base pressure. This leads to a widening of the flow region at the throat, usually described by boundary-layer approximations. At a certain blowing rate the recirculation region completely disappears which makes it possible to use boundary-layer equations to describe the flow in the entire viscous region in the immediate neighborhood of the base section.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 76–81, January–February, 1984.     

The effect of the arrangement of the openings on the amplification factor during asymmetric gas blowing into a laval nozzle

In asymmetric blowing of a gas into the supersonic part of a nozzle the main flow is perturbed by the jet which is being blown. Two interaction regimes are distinguished. In the first the perturbation of the main flow does not extend to the side of the nozzle opposite to the blast: the central angle subtended by the perturbation of the exit section of the nozzle is 2_a < 180 ° (Fig. 1). This regime is characterized by the fact that the curvature of the nozzle has no effect on the magnitude of the lateral force. In the second regime the zone of the perturbed flow extends to the side of the nozzle opposite to the blast (2_a > 180 °), and this leads to a decrease in the gradient of the lateral force with respect to the flow rate of the gas which is being blown. The first regime has been studied in the most detail.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 136–141, November–December, 1984.     

Flow investigation in separation zones ahead of supersonic jets in a subsonic stream

The flow in the three-dimensional separation zone of a turbulent boundary layer on a plate in front of a supersonic jet injected perpendicularly to the subsonic drifing flow is considered. The purpose of the investigation is to establish the physical singularities of subsonic flow around a supersonic jet obstacle and to obtain dependences of the geometric flow characteristics on the free-stream and injected-jet parameters. Results of an experimental investigation permitted proposing approximate dependences of the geometric three-dimensional separation-zone characteristics which appear in the subsonic stream ahead of a jet obstacle.     

Flowfield characteristics of a transverse jet into supersonic flow with pseudo-shock wave

We performed an experimental investigation of the flowfield of a transverse jet into supersonic flow with a pseudo-shock wave (PSW). In this study, we injected compressed air as the injectant, simulating hydrocarbon fuel. A back pressure control valve generated PSW into Mach 2.5 supersonic flow and controlled its position. The positions of PSW were set at nondimensional distance from the injector by the duct height (x/H) of ?1.0, ?2.5, and ?4.0. Particle image velocimetry (PIV) gave us the velocity of the flowfield. Mie scattering of oil mist only with the jet was used to measure the spread of the injectant. Furthermore, gas sampling measurements at the exit of the test section were carried out to determine the injectant mole fraction distributions. Gas sampling data qualitatively matched the intensity of Mie scattering. PIV measurements indicated that far-upstream PSW decelerated the flow speed of the main stream and developed the boundary layer on the wall of the test section. The flow speed deceleration at the corner of the test section was remarkable. The PSW produced nonuniformity in the main stream and reduced the momentum flux of the main stream in front of the injector. The blowing ratio, defined as the square root of the momentum flux ratio, of the jet and the main stream considering the effect of the boundary layer thickness was shown to be a useful parameter to explain the jet behavior.     

Flow in the zones of separation of a turbulent boundary layer in front of a subsonic jet injected through a circular nozzle

Flow taking place in the three-dimensional region of separation formed by the interaction of a subsonic stream with a single subsonic jet emerging from a circular hole in a plate perpendicular to the stream is considered. The aim of the investigation is to discover the physical characteristics of the flow in the three-dimensional separation zone in front of a subsonic jet obstacle and to determine the principal laws governing the geometrical and hydrodynamic characteristics of the flow as functions of the parameters of the driving stream and jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 34–41, May–June, 1973.     

Study of heat transfer in the separation zones formed in front of supersonic jets in a subsonic carrier flow

The heat transfer taking place between the gas and the surface of the plate in the zone of three-dimensional separation of the turbulent boundary layer in front of a set of supersonic jets injected perpendicularly to a subsonic carrier flow is considered. The aim of this investigation is to establish the main physical characteristics of heat transfer in the separation zones in front of jet obstacles and to obtain the distributions of the local heat-transfer coefficients and the temperature of the thermally insulating wall as functions of the parameters of the carrier flow and the injected jets. Analysis of the experimental results yields certain approximating relationships for the distribution of the local heat-transfer coefficients as functions of the Mach number of the carrier flow M, the Mach number of the jet M_j, the relative boundary-layer displacement thickness _s= _s ^* /d, and the degree of jet superheating T_ojT_o relative to the separation zones in front of supersonic jet obstacles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–72, July–August, 1975.     

Laminar boundary layer on swept-back wings of infinite span at an angle of attack

A study is made of the flow of a compressible gas in a laminar boundary layer on swept-back wings of infinite span in a supersonic gas flow at different angles of attack. The surface is assumed to be either impermeable or that gas is blown or sucked through it. For this flow and an axisymmetric flow an analytic solution to the problem is obtained in the first approximation of an integral method of successive approximation. For large values of the blowing or suction parameters, asymptotic solutions are found for the boundary layer equations. Some results of numerical solution of the problem obtained by the finite-difference method are given for wings of various shapes in a wide range of angles characterizing the amount by which the wings are swept back and also the blowing or suction parameters. A numerical solution is obtained for the equations of the three-dimensional mixing layer formed in the case of strong blowing of gas from the surface of the body. The analytic and numerical solutions are compared and the regions of applicability of the analytic expressions are estimated. On the basis of the solutions obtained in the present paper and studies of other authors a formula is proposed for the calculation of the heat fluxes to a perfectly catalytic surface of swept-back wings in a supersonic flow of dissociated and ionized air at different angles of attack. Flow over swept-back wings at zero angle of attack has been considered earlier (see, for example, [1–4]) in the theory of a laminar boundary layer. In [5], a study was made of flow over swept-back wings at nonzero angle of attack at small and moderate Reynolds numbers in the framework of the theory of a hypersonic viscous shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 27–39, May–June, 1980.We thank G. A. Tirskii for a helpful discussion of the results.     

Use of flows with straight sonic line in nozzles with corners

The optimal scheme of a Laval nozzle is discussed. In the case of a profiled nozzle with a corner it is possible to use in the region of mixed flow both flows of general form with curvilinear sonic line as well as the special case when the sonic line is straight. It is shown that the latter alternative is preferable: when the supersonic part of the profile is determined by the simple wave method, the velocity at the wall increases monotonically and the flow does not contain shock waves. In contrast, in nozzles with curvilinear sonic line, a section in which the velocity decreases is formed immediately behind the corner, which can lead to boundary layer separation. In addition, for values of the supersonic velocity at the nozzle exit near the velocity of sound it is proved that the characteristics of the simple wave intersect in the flow region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 168–170, January–February, 1981.     

Three-dimensional laminar boundary layer on a permeable surface in the neighborhood of a symmetry plane

Analytical and numerical methods are used to investigate a three-dimensional laminar boundary layer near symmetry planes of blunt bodies in supersonic gas flows. In the first approximation of an integral method of successive approximation an analytic solution to the problem is obtained that is valid for an impermeable surface, for small values of the blowing parameter, and arbitrary values of the suction parameter. An asymptotic solution is obtained for large values of the blowing or suction parameters in the case when the velocity vector of the blown gas makes an acute angle with the velocity vector of the external flow on the surface of the body. Some results are given of the numerical solution of the problem for bodies of different shapes and a wide range of angles of attack and blowing and suction parameters. The analytic and numerical solutions are compared and the region of applicability of the analytic expressions is estimated. On the basis of the solutions obtained in the present work and that of other authors, a formula is proposed for calculating the heat fluxes to a perfectly catalytic surface at a symmetry plane of blunt bodies in a supersonic flow of dissociated and ionized air at different angles of attack. Flow near symmetry planes on an impermeable surface or for weak blowing was considered earlier in the framework of the theory of a laminar boundary layer in [1–4]. An asymptotic solution to the equations of a three-dimensional boundary layer in the case of strong normal blowing or suction is given in [5, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 37–48, September–October, 1980.     

Change in the parameters of a supersonic flow in the presence of transverse blowing

A study has been made of the flow formed in a supersonic nozzle when gas is blown in a transverse jet into an expanding supersonic flow. Measurements were made of the total and static pressures of the flow at several sections of the nozzle. It was established that, depending on the relative flow rate = m_j/(m_j+ m₀) of the blown gas (m_jand m₀ are the flow rates of the blown gas and the main flow, respectively), there exist two flow regimes with different dependences of the Mach number of the flow. At small , the experimental flow parameters correspond satisfactorily to the parameters calculated in a one-dimensional model with a narrow mixing layer near the blowing section. Agreement was observed at flow rates less than a certain ^*, this critical value being determined in the model as the flow rate at which the flow after mixing becomes sonic. In the experiments at large flow rates of the blown gas, ^* < < 1, the value of M for the flow hardly depends on and corresponds to the calculated value of M for a supersonic flow having the velocity of sound near the blowing section. A scheme is proposed for calculating the flow in a nozzle with transverse blowing in the supersonic part; it describes satisfactorily the experimental results in the complete range of blown-gas-main-flow flow rate ratios (0 1) over the complete length of the nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 188–192, May–June, 1984.     

Experimental flow analysis of three-dimensional separation zones in front of weirs

Some results of experimental studies are shown concerning subsonic flow in separation zones of three-dimensional turbulent boundary layers formed in front of cylindrical weirs and rectangular parallelepipeds or dashboards. The width to height ratio of the weirs was varied from 0.25 to 24, and the boundary layer thickness to weir height ratio at separation was varied from 0.2 to 2.0. Flow patterns are shown along with the effects of the setup ge-ometry, of the weir width to height ratio, of the boundary layer parameters, and of the Euler and Reynolds numbers on the flow pattern and on the coordinates of characteristic points in the separation zone. Data are furnished for determining the dimensions of three-dimensional separation zones in front of weirs. The flow and the heat transfer in three-dimensional separation zones at subsonic velocities have not yet been explored adequately. The separation data published in [1, 2, 3] are not sufficient for determining the flow pattern, the static pressure distribution, and the characteristic dimensions of a separation zone — all of which are needed for calculating the heat transfer in the separation zone [4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 50–54, January–February, 1972.The authors thank V. S. Avduevskii for reviewing the results.     

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.     

Calculation of spatial flow past an inclined flat plate with a detached shock wave

The results of a numerical analysis of a supersonic underexpanded jet impinging on an inclined flat plate are presented. The effects of the angle between the plate and the jet symmetry axis, the distance from the nozzle exit section, the exit Mach number, and the off-design conditions on the distribution of the gasdynamic parameters in the jet flowfield and on the plate surface are demonstrated. Specific features of the compressed layer and obstacle surface flows are revealed. The three-dimensional flow is simulated using the large particle method on the basis of the nonstationary Euler equations written in the cylindrical coordinate system. The calculated results are compared with experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 31–35, January–February, 1997.     

Investigation of the propagation of a two-dimensional wall jet over a step

The propagation of an underexpanded sonic jet over a flat end face has been experimentally investigated. As distinct from previous studies, the object of investigation is not a free jet, but a jet flowing from a nozzle along a horizontal surface. The total separation of the jet from the surface and its attachment to the end wall are related to the propagation characteristics of underexpanded wall jets. The effect of the total pressure in the jet and the height of the step on the separation of the jet and its attachment to the wall and, moreover, on the principal characteristics of the flow — the pressure in the base region, the extent of the circulation zone, the jet trajectory — is examined. The associated hysteresis effects are studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 61–66, July–August, 1991.     

Experimental investigation of the flow in the mixing layer in the initial section of an underexpanded jet in a parallel stream

The results are given of an experimental investigation of the flow in the initial section of a turbulent underexpanded jet exhausting from a profiled nozzle with Mach number M _a = 2.56 at the exit into a parallel stream with Mach number M = 3.1. Analysis of the results of measurement of the fields of the total head p₀ and the stagnation temperature T₀ in conjunction with results of calculation of a jet of an ideal gas make it possible to construct the velocity profile in the mixing layer of the underexpanded jet in the parallel supersonic flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 161–163, January–February, 1981.     

Shock structure in separated nozzle flows

In the case of high overexpansion, the exhaust jet of the supersonic nozzle of rocket engines separates from nozzle wall because of the large adverse pressure gradient. Correspondingly, to match the pressure of the separated flow region, an oblique shock is generated which evolves through the supersonic jet starting approximately at the separation point. This shock reflects on the nozzle axis with a Mach reflection. Thus, a peculiar Mach reflection takes place whose features depend on the upstream flow conditions, which are usually not uniform. The expected features of Mach reflection may become much difficult to predict, depending on the nozzle shape and the position of the separation point along the divergent section of the nozzle.      

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.