Experimental modeling of three-dimensional modes of hypersonic flow past cylindrically-blunted bodies

Several sets of experimental studies of the structure of transverse hypersonic flow past blunt bodies (cylinder and truncated wedge) and heat transfer on them are performed in the UT-1M shock tube of the Central Aerohydrodynamics Institute. The purpose of the investigation was to obtain three-dimensional modes of hypersonic flow past the nose surfaces of blunt bodies in an artificially disturbed and nominally uniform flows. The controlled disturbances in the freestream were produced by thin threads pulled over the nozzle exit. In the experiment the flow was visualized using the Töpler method and the heat flux distribution over the cylinder was measured using luminescent temperature transformers. The experiments show that both the flow and the heat transfer in the vicinity of the cylinder nose are very sensitive to vortex disturbances in the oncoming hypersonic flow. In a nominally uniform flow (M_∞ = 8 and Re_∞ = 3160–11670) a steady three-dimensional mode of flow past the nose surface of a blunt wedge could be obtained in the form of a single vortex pair.     

Hypersonic flow past a wing at large angles of attack with detached shock wave

The thin shock layer method [1–3] has been used to solve the problem of hypersonic flow past the windward surface of a delta wing at large angles of attack, when the shock wave is detached from the leading edge (but attached to the apex of the wing) and the velocity of the gas in the shock layer is of the same order as the speed of sound. A classification of the regimes of flow past a delta wing at large angles of attack has been made. A general solution has been obtained for the problem of three-dimensional hypersonic flow past the wing allowing for nonequilibrium physicochemical processes of thermal radiation of the gas at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 149–157, May–June, 1985.     

Hypersonic similarity in the flow of an imperfect gas around slender blunt bodies of complex shape

The hypersonic similarity laws for flow around slender blunt bodies [1–3] are generalized to bodies with nonsmooth lateral surface, in particular, those having corners (under the condition of unseparated supersonic flow). The similarity conditions are considered for a gas which is imperfect throughout the entire disturbed region.     

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.     

A method for calculating intense injection from surfaces of blunt bodies entering planetary atmospheres at hypersonic velocities

Flow past blunt bodies entering planetary atmospheres at hypersonic velocities is studied. A method for calculating the flowfield near the body nose is developed which allows for radiative heat transfer in the P ₁ approximation of the spherical harmonics method but does not take gas viscosity and heat conduction into account. The solution is constructed on the basis of a two-layer flow model, with account for intense injection of ablation products from the body nose due to radiative heat fluxes from the shock layer. The advantages of the method are that the multi-dimensional character of the radiation field is taken into account and the general problem of radiation gasdynamics is solved on the basis of a unified algorithm. The flow past a spherical segment and a spherically-blunted cone re-entering the Earth’s atmosphere at a velocity of 20 km/s and an entry angle of ?10° is calculated.     

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.     

Hypersonic flow-past of plane blunt bodies by a nonviscous radiating gas

An analytic solution is obtained in the work in a Newtonian approximation [1] for the flow-past problem for a plane blunt body by a steady-state uniform hypersonic inviscous space-radiating gas flow. The hypersonic flow-past problem for axisymmetrical blunt bodies by a nonviscous space-radiating gas has been previously considered [2–4]. In this case a satisfactory solution of the problem was obtained even in a zero-th approximation by decomposing the unknown values in terms of a parameter equal to the ratio of gas densities before and after passage of the shock wave. The solution of the problem in a zero-th approximation with respect to in the case of flow-past of plane blunt bodies does not turn out to be satisfactory, since the departure of the shock and the radiant flux to the body as gas flows into the shock layer turns out to be strongly overstated under nearly adiabatic conditions. Freeman [5] demonstrated that results may be significantly improved for flow-past of a plane blunt body by a nonradiating gas if a more precise expression is used for the tangential velocity component expressed in a new approximation with respect to the parameter . This refinement is applied in this work for solving the flow-past problem for a plane blunt body by a space-radiating gas. The distribution of the gasdynamic parameters in the shock layer, the departure of the shock wave, and the radiant heat flux to the surface of the body are found. The solution obtained is analyzed in detail for the example of flow-past regarding a circular cylinder.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 3, 68–73, May–June, 1975.     

Heat transfer peaks on a blunt-nosed triangular plate in hypersonic flow

An experimental investigation [1] of hypersonic flow over a blunt-nosed triangular plate revealed anomalies — the presence on the windward side of narrow bands of intensified heat transfer. Below, this effect is related to the appearance in the flow near the surface of regions of gas spreading induced, in its turn, by the interference between the bow shock (due to the blunt nose) and the leading edges of the plate. This spreading is called inertial, since it takes place at almost constant pressure. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 131–137, March–April, 1994.     

Nonequilibrium hypersonic flow of gas past a wing of small aspect ratio

It is well known [1] that nonequilibrium physicochemical processes taking place in gases at high temperature influence the gas-dynamic parameters and aerodynamic characteristics of bodies in hypersonic flight. In the present paper, the thin shock layer method [2–4] is used to consider the problem of nonequilibrium hypersonic flow of gas past a wing of small aspect ratio at an angle of attack. It is shown that the flow component of the vorticity is conserved along the streamlines, and this property is exploited to obtain an analytic solution of the equations of the three-dimensional nonequilibrium shock layer. The influence of the disequilibrium on the thickness of the shock layer and the pressure distribution is investigated.     

Magnetohydrodynamic control of supersonic flow past bodies: Possibilities and undesirable effects

Basic problems of super-and hypersonic magnetohydrodynamics (MHD) associated with the determination of the integral characteristics of bodies and vehicles inside which there are systems generating a uniform magnetic field are considered. Three classes of flows, namely, flow in a hypersonic multimode fixed-geometry air-intake; internal and external flow in a model of a hypersonic vehicle containing an air-intake with an MHD generator, a combustion chamber, and a supersonic nozzle; and hypersonic flow past a blunt cone are studied using numerical simulation and theoretical analysis (on the basis of the complete averaged system of Navier-Stokes equations and the electrodynamic equations). Attention is concentrated on the presence of an additionalmagnetic force acting on the system generating themagnetic field and, consequently, on the body and initiating an additional drag (in the case of a vehicle-reducing its thrust). Attractive possibilities for MHD flow control, namely, an increase in the degree of flow compression in the air-intake, a reduction in the ignition length in the combustion chamber, and a decrease in the heat flux to the nose of the body, are noted, as well as negative effects associated with the action of the magnetic force on the bodies considered.     

高超声速飞行器气动防热新概念研究

传统乘波构型的高超声速飞行器尖锐的前缘存在严重的气动加热问题,而简单的前缘钝化气动防热方法由于造成很大的升阻比损失,难以发挥实质性作用. 引入``人工钝前缘(ABLE)'概念,拟以一种新的思路解决这一矛盾. 通过定义ABLE构型的外形参数,并采用CFD数值计算方法研究了各参数对气动力和气动热特性的影响规律,在流场分析的基础上进行了外形优化,最终得到令人满意的新型高超声速飞行器头部外形,总结了运用ABLE概念进行气动防热的相关设计原则和规律.      

Asymptotic solutions of the two-dimensional equations for a thin viscous shock layer in a rarefied gas

Two-dimensional hypersonic rarefied gas flow around blunt bodies is investigated for the continuum to free-molecular transition regime. In [1], as a result of an asymptotic analysis, three rarefied gas flow regimes, depending on the relationship between the problem parameters, were detected and one of these regimes was investigated. In the present study, asymptotic solutions of the thin viscous shock layer equations at small Reynolds numbers are obtained for the other two flow regimes. Analytical expressions for the heat transfer, friction and pressure coefficients are obtained as functions of the incident flow parameters and the body geometry and temperature. As the Reynolds number tends to zero, the values of these coefficients approach their values in free-molecular flow. The scaling parameters of hypersonic rarefied gas flow around bodies are determined for different regimes. The asymptotic solutions are compared with the results of direct Monte Carlo simulation.     

The value of the entropy at the surface of paraboloids

The author studies the magnitude of the entropy at paraboloid surfaces in supersonic perfect gas flow using the numerical results of the solution to the problem of three-dimensional flow past a blunt nose [1]. We first discuss briefly the state of the problem and information on the method of [1] and then present the main conclusions of the study and some data confirming these conclusions.In conclusion, the author thanks V. V. Rusanov for valuable comments and discussion and E. I. Nazhestkin for performing the computer computations and participating in the analysis of the computational results.     

Asymptotic solution of the two-dimensional equations for a thin viscous rarefied shock layer on a cold surface

Hypersonic rarefied flow past blunt bodies is studied in the continuum-free-molecular transition regime. On the basis of an asymptotic analysis three rarefied gas flow patterns are established depending on the relation between the relevant parameters of the problem. In the first regime corresponding to a cold surface asymptotic solutions of the equations of a thin viscous shock layer are derived at low Reynolds numbers in the axisymmetric and plane cases. Simple analytical expressions for the pressure and the heat transfer and friction coefficients are obtained as functions of the freestream parameters and the body geometry. With decrease in the Reynolds number the coefficients approach the values corresponding to free-molecular flow. In this regime a similarity parameter for the hypersonic rarefied flow past bodies is determined. The asymptotic solutions are compared with numerical solutions and the results of direct statistical simulation by the Monte Carlo method.     

Asymptotic Investigation of the Thin Viscous Shock Layer Equations in the Neighborhood of the Stagnation Point for Low Reynolds Numbers

Hypersonic three-dimensional viscous rarefied gas flow past blunt bodies is investigated in the neighborhood of the stagnation point. The problem of applicability of the model of a thin viscous shock layer to the regime of transition from continuum to free-molecular flow is considered. In [1], it was shown that at low Reynolds numbers three hypersonic flow regimes can be distinguished and one of those regimes was investigated. In the present study an asymptotic solution of the thin viscous shock layer equations is obtained for another flow regime. With decrease in the Reynolds number the heat transfer coefficient determined by the solution obtained approaches its free-molecular value and the friction coefficient approaches its free-molecular limit, provided that the shock layer thickness is small. The analytical solution is compared with a numerical solution and the results of calculations based on direct Monte Carlo simulation.     

Effect of the shape of a blunt nose on the drag coefficient of a body in a hypersonic rarefied gas flow

The effect of the shape of a blunt nose of a body located in a hypersonic rarefied gas flow on the field of flow and on the aerodynamic characteristics is studied in the example of flow round ellipsoids of revolution at a zero angle of attack. The problem of the flow in the transition regime is solved on the basis of numerical analysis of the model kinetic Bhatnagar—Gross—Krook (BGK) equation for a monatomic gas. The good agreement of the results of the numerical calculations with the experimental data in a broad range of Mach numbers has shown [1, 2] that the numerical solution of the model kinetic equations is a reliable and effective means for studying flow problems. In the case when the problem is posed of determining the laws of the purely force interaction of a flow with the body, sufficiently good accuracy is given by the use of the model BGK equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 190–192, March–April, 1985.     

Lifting bodies using the flow behind axisymmetric conical shock waves

One of the methods of designing aircraft with supersonic flight speeds involves solving an inverse problem by means of the well-known flow schemes and the substitution of rigid surfaces for the flow surfaces. Lifting bodies using the flows behind axisymmetric shock waves belong to these configurations. All lifting bodies using the flow behind a conical shock wave can be divided into two types [1]. Bodies whose leading edge passes through the apex of the conical shock wave pertain to the first type and those whose leading edge lies below the apex of the conical shock wave, to the second. For small apex angles of the basic cone at hypersonic flow velocities an approximate solution of the variation problem was obtained, which showed that the lift-drag ratio of lifting bodies of the second type is higher than that of the first [2]. The present paper gives a numerical solution of the problem for flow past lifting bodies of the second type using the flow behind axisymmetric conical shock waves with half-angles of the basic cone _S=9.5 and 18° The upper surfaces of the bodies are formed by intersecting planes parallel to the velocity vector of the oncoming flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 135–138, March–April, 1986.     

Strong mass injection at the surface of a blunt body in a supersonic flow

The case of supersonic flow over a blunt body when another gas is injected through the surface of the body in accordance with a given law is theoretically investigated. If molecular transport processes are neglected, the flow between the shock wave and the surface of the body should be regarded as two-layer, that is, as consisting of the flow in the shock layer between the shock wave and the contact surface and the flow in the layer of injected gas. A numerical solution of the problem is obtained near the front of the body and its accuracy is estimated. Approximate analytic solutions are obtained in the injected-gas layer: a constant-density solution and a solution of the boundary-layer type in the local similarity approximation. Near the flow axis the numerical and analytic solutions are fairly close, but at a distance from the axis the assumptions made reduce the accuracy of the approximate solutions. The flow in question can serve as a gas-dynamic model of a series of problems describing the radiant heating of blunt bodies in a hypersonic flow. In the presence of intense radiative heat transfer, vaporization is so great that the thickness of the vapor layer is comparable with the thickness of the shock layer. Moreover, the thermal shielding of various kinds of obstacles in channels through which a radiating plasma flows can be organized by means of the forced injection of a strong absorber. The formulation of a similar problem was reported in [1], but the results of the solution were not given. A two-layer model of the flow of an ideal gas over a blunt body was used in [2, 3] for the analysis of radiative heat transfer. In [2] the neighborhood of the stagnation point is considered. In [3] preliminary results relating to two-layer flow over blunt cones are presented. The solution is obtained by Maslen's approximate method.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 89–97, March–April, 1972.     

Influence of the hall effect on hypersonic flow past a wedge

This paper deals with the problem of the steady-state hypersonic flow of an inviscid compressible gas past a wedge. Inside the wedge a magnetic field is excited in a direction perpendicular to the generator. The flow in the region of perturbation is investigated on the basis of the ordinary equations of magnetohydrodynamics and Ohm's law, written for the case where the Hall effect is taken into account. The system of equations obtained has been solved numerically on a computer by the method of finite differences. The results show that for the given problem the Hall effect intensifies the magnetohydrodynamic action of the magnetic field on the flow. M. D. Ladyzhenskii [1] has also studied hypersonic flow past bodies from inside which a magnetic field is excited. He has investigated the influence of a strong magnetic field on the flow for the case where the Hall effect is neglected. The object of the present study is to determine the importance of the Hall effect.The author wishes to thank M. D. Ladyzhenskii for formulating the problem and discussing the progress of the work.