Influence of second-order boundary layer effects in hypersonic flow over slender blunt cones

The aim of this study is to determine the influence of second-order effects in the aggregate on supersonic axisymmetric flow over slender blunt cones and also to determine the region of applicability of approximate methods of taking into account the strongest of these second-order effects — entropy layer absorption. A system of complete viscous shock layer equations containing all the terms of the gas dynamic Euler equations and all the second-order terms of asymptotic boundary layer theory is chosen as the gas-dynamic model. Within the calculation domain the problem is solved in a unified manner.Translated from Izvestiya Rossiiskoi Akademii Nauk, Meknanika Zhidkosti i Gaza, No.4, pp. 129–134, July–August, 1992.     

Calculation of heat transfer accompanying hypersonic three-dimensional flow of air over slender blunt-nosed cones

The effective length method [1, 2] has been used to make systematic calculations of the heat transfer for laminar and turbulent boundary layers on slender blunt-nosed cones at small angles of attack ( + 5° in a separationless hypersonic air stream dissociating in equilibrium (half-angles of the cones 0 20°, angles of attack 0 15°, Mach numbers 5 M 25). The parameters of the gas at the outer edge of the boundary layer were taken equal to the inviscid parameters on the surface of the cones. Analysis of the results leads to simple approximate dependences for the heat transfer coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 173–177, September–October, 1981.     

Effect of nose shape on hypersonic flow past slender blunt bodies at an angle of attack

We examine some characteristics of hypersonic flow past slender blunt bodies of revolution at a small angle of attack 1, where is the relative body thickness. It is shown that, within the framework of hypersonic theory, for a correct-consideration of the effect of the conditions in the transitional section between the nose and the lateral surface it is necessary, in the general case, to specify the circumferential distribution of the force effect for the nose and the mass of the gas. For small , the effect of the nose, just as in two-dimensional flows [1–4], shows up only through its drag coefficient c_x, for =0. On this basis, the similarity law [1–4] for flow past such bodies, with arbitrary form of the lateral surface and differing in the shape of the nose blunting, which is valid over the entire disturbed region, with the exception of a small vicinity of the nose, is extended to the case in question.The notation r₀ and L maximum nose radius and characteristic body length - V, M, and density, velocity, Mach number, and adiabatic exponent of the gas in the approaching stream - , V²i, and V²p density, enthalpy, and pressure - x, r, and coordinate system of the cylindrical body with its center at the transitional section between the nose and the side surface - Vu, Vv, and Vw corresponding velocity components     

Asymptotic theory of the flow near the rear end of a slender axisymmetric body

Steady high-Reynolds-number flow of a viscous incompressible fluid past a slender axisymmetric body is considered. The structure of the near wake and the boundary layer in the vicinity of the rear end of the body is studied. The relationship between the maximum relative body thickness and the rearend shape giving a local boundary layer — potential flow interaction zone in a small neighborhood of the rear end is found. The boundary value problem for this region is solved numerically.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 68–77, September–October, 1993.     

Supersonic flow over a slender wing with subsonic edges

The method of integral equations is generalized to calculate steady flow past wings with an arbitrary shape in plan with subsonic leading and trailing edges. The determination of the velocity potential in the leading part of the wing, where there is no influence of the vortex sheet, is reduced to the solution of a two-dimensional integral equation of the second kind. The trailing part, which is subject to the influence of the vortex sheet, is divided into a number of subregions, in which the calculation of the acceleration potential reduces to the solution of one-dimensional equations of the type of Fredholm equations of the second kind and to quadrature. The unique solvability of the obtained integral equations is investigated; it is shown that they can be solved by successive approximation. As an example, the solution to the problem of flow past a flat delta-shaped wing is found and compared with the exact solution to the problem found by the method of conic flows [4, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 119–127, September–October, 1981.I thank G. Yu. Stepanov for discussing the paper.     

The hydromagnetic flow over an oscillating flat plate with arbitrary periodic oscillation

In this paper, the hydromagnetic flow over a flat plate with arbitrary periodic oscillation is solved exactly. The solution is also applicable for common incompressible viscous flow over a flat plate with arbitrary oscillation. It is found that the penetration of hydromagnetic flow will decrease with increasing non-dimensional magnetic parameter M. The transient part will die away after a certain time for a specific M. The solution will collapse into the steady-state case after a long time. However, for non-hydromagnetic flow, there will be no steady-state solution if the coefficient of the zero-frequency component is not zero.     

Rarefied gas flow near the forward stagnation point of a blunt body at hypersonic speeds

With reduction of the density in a hypersonic stream the transition of the flow from continuum to free molecule takes place gradually. The transition region may be divided into several regimes, in each of which a definite physical phenomenon is most significant. For the case of the flow in the vicinity of the forward stagnation point of a blunt body these phenomena include increase of the thickness of the detached shock wave and of the boundary layer, the presence of viscous flow in the entire disturbed layer ahead of the blunt body, reduction of the number of collisions between molecules and the associated relaxation effects, the increasing role of the interaction of the stream molecules with the surface, and the phenomena of slip and temperature jump.     

Calculation of hypersonic flow over a body with a discontinuity,allowing for two-dimensional radiative transfer

It is shown that the degree of the integrals appearing in the general expressions for radiative flux and its divergence can be reduced to one in the two-dimensional case by analytical integration with respect to one of the angular variables. The resulting formulas contain some special functions whose role is analogous to that of the integral exponents E_n(x) in the one-dimensional case. The authors postulate and numerically solve the problem of flow in a radiative absorbing shock layer near the downstream of a discontinuity of shape. It is shown that at high hypersonic speed the two-dimensional radiation near the discontinuity can appreciably affect the pressure distribution downstream. It is shown that the radiative flux to the lateral surface directly behind the discontinuity is comparable to the flux on the forward surface and can be calculated by using appropriate two-dimensional formulas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 114–121, March–April, 1976.The author thanks V. V. Lunev for formulating the problem and for technical advice.     

Asymmetric vortices flow over slender body and its active control at high angle of attack

The studies of asymmetric vortices flow over slender body and its active control at high angles of attack have significant importance for both academic field and engineering area. This paper attempts to provide an update state of art to the investigations on the fields of forebody asymmetric vortices. This review emphasizes the correlation between micro-perturbation on the model nose and its response and evolution behaviors of the asymmetric vortices. The critical issues are discussed, which include the formation and evolution mechanism of asymmetric multi-vortices; main behaviors of asymmetric vortices flow including its deterministic feature and vortices flow structure; the evolution and development of asymmetric vortices under the perturbation on the model nose; forebody vortex active control especially discussed micro-perturbation active control concept and technique in more detail. However present understanding in this area is still very limited and this paper tries to identify the key unknown problems in the concluding remarks. The project supported by the National Natural Science Foundation of China (10172017), Aeronautical Science Foundation of China (02A51048) and Foundation of National Key Laboratory of Aerodynamic Design and Research (51462020504HK0101)     

Boundary-layer separation on a cooled body and interaction with a hypersonic flow

In previous papers, e.g., [1, 2], boundary-layer separation was investigated by analyzing solutions of the boundary-layer equations with a given external pressure distribution. In general, this kind of solution cannot be continued after the separation point. Study of the asymptotic behavior of solutions of the Navier-Stokes equations [3–5] shows that, in boundarylayer separation in supersonic flow over a smooth surface, the main effect on the flow in the immediate vicinity of the separation point is a large local pressure gradient induced by interaction with the external flow. The solution can be continued beyond the separation point and linked to the solutions in the other regions, located downstream [5]. Similar results for incompressible flow were recently obtained in [6]. We can assume that in general there is always a small region near the separation point in which separation is self-induced, and where the limiting solution of the Navier-Stokes equations does not contain unattainable singular points. However, this limiting slope picture can be more complex and can contain more regions where the behavior of the functions differed from that found in [3–6]. The present paper investigates separation on a body moving at hypersonic speed, where the ratio of the stagnation temperature to the body temperature is large. It is shown that both. for hypersonic and supersonic speeds the flow near the separation point is appreciably affected by the distribution of parameters over the entire unperturbed boundary layer, and not only in a narrow layer near the body, as was true in the flows studied earlier [3–6]. Regions may appear with appreciable transverse pressure drops within the zone occupied by layers of the unperturbed boundary layer. Similarity parameters are given, the boundary problems are formulated, and the results of computer calculation are presented. The concept of subcritical and supercritical boundary layers is refined, and the dependence of pressure coefficients responsible for separation on the temperature factor is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 99–109, November–December 1973.     

An analytic solution of dense two-phase flow in a vertical pipeline

According to a mathematical model for dense two-phase flows presented in theprevious paper,a dense two-phase flow in a vertical pipeline is analytically solved,and theanalytic expressions of velocity of each continuous phase and dispersed phase arerespectively derived The results show that when the drag force between two phases dependslinearly on their relative velocity,the relative velocity profile in the pipeline coincides withDarcy’s law except for the thin layer region near the pipeline wall,and that the theoreticalassumptions in the dense two-phase flow theory mentioned are reasonable.     

Calculation of the viscosity effect on the aerodynamic characteristics of slender bodies at hypersonic flow velocities

Approximating dependences of the local coefficients of friction, heat transfer, and pressure induced by a boundary layer on the generalized similarity parameters, including the inviscid flow characteristics, are obtained on the basis of the results of a numerical calculation of hypersonic flow past a number of plane and axisymmetric bodies. If the inviscid flow characteristics are known, these relations can be used to take the viscosity approximately into account under conditions of interaction between the laminar boundary layer and the hypersonic inviscid stream [1].Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 142–150, July–August, 1995.     

Influence of nose perturbations on behaviors of asymmetric vortices over slender body

The influence of nose perturbations on the behaviors of asymmetric vortices over a slender body with a three-caliber ogive nose is studied in this paper. The tests of a nose-disturbed slender body with surface pressure measurement were conducted at a low speed wind tunnel with subcritical Reynolds number of 1×10⁵ at angle of attack α=50°. The experiment results show that the behaviors and structure of asymmetric vortices over the slender body are mainly controlled by manual perturbation on the nose of body as compared with geometrical minute irregularities on the test model from the machining tolerances. The effect of the perturbation axial location on asymmetric vortices is the strongest if its location is near the model apex. There are four sensitive circumferential locations of manual perturbation at which bistable vortices over the slender body are switched by the perturbation. The flowfield near the reattachment line of lee side is more sensitive to the perturbation, because the saddle point to saddle point topological structure in this reattachment flowfield is unstable. Various types of perturbation do not change the perturbation effect on the behaviors of bistable asymmetric vortices. The project supported by the National Natural Science Foundation of China (10172017) and the Foundation of National Key Laboratory of Aerodynamic Design and Research (00JS51.3.2 HK01)     

The stokes flow of an arbitrary prolate axisymmetric body towards an infinite plane wall

By distributing continuously the image Sampsonlets with respect to the plane and by applying the constant density, the linear and the parabolic approximation, the analytic expressions in closed form for flow field are obtained. The drag factor of the prolate spheroid and the Cassini oval are calculated for different slender ratios and different distances between the body and the plane. It is demonstrated that the proposed method is satisfactory both in convergence and accuracy. Comparison with existing results in the case of prolate spheroid shows that the coincidence is quite good.