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.     

Viscous instability of hypersonic flow past a wedge

Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 55–60, March–April, 1992.     

Damping characteristics of a reentry vehicle at hypersonic velocities

The experimental equipment, model, test conditions, and methods used for determining the streamwise damping on a setup with free oscillations on rolling bearings are described. Characteristics of aerodynamic damping of the model with two positions of the rotation axis and Mach numbers M_∞ = 2, 4, and 6 are measured. Irregular oscillations of the model with a greater displacement of the rotation axis with respect to the longitudinal axis are found to arise at M_∞ = 2.     

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.     

The effect of initial acceleration on the waves produced by a moving oscillatory surface pressure

Summary This paper studies the effect of variation of velocity of the oscillatory surface pressure distribution over a finite time interval t₀ on the wave generated from rest. The result of such an acceleration is found to produce the same steady state wave system as it would be if the pressure started impulsively with the uniform velocity at t=t₀. The effect of initial acceleration is felt in the transient part of the wave system.

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Sommario Questa memoria studia l'effetto della variazione di velocità di una distribuzione oscillatoria di pressione superficiale in un intervallo di tempo finito t₀, sull'onda generata a partire dalla quiete. Si trova che questa accelerazione produce lo stesso sistema di onde di regime che si avrebbe se la pressione iniziasse complessivamente con velocità uniforme al tempo t=t₀. L'effetto dell'accelerazione iniziale è sentito nella parte transitoria del sistema di onde.

     

Instability of a hypersonic flow over a wedge in the Newtonian approximation

At the present time, there are a number of works in the literature that treat unsteady hypersonic flows in the Newtonian approximation [1–4]. Since the angle of incidence of the shock wave _s coincides in the zero-order approximation with the angle of inclination of the bodys [1], the latter is usually used in the boundary conditions on the shock. However, in the zero-order approximation _b can be used with the same justification. Both approaches are equally justified and give similar results for a steady flow. For unsteady flows the results can differ radically. It will be shown below that for an investigation of a flow over a fixed wedge with constant conditions in the free stream a steady-state pattern is obtained in the first case and a solution growing in time, in the second case.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 158–160, July–August, 1976.     

Laminar near wake of a sharp wedge in hypersonic perfect-gas flow

The laminar near wake behind a sharp wedge with the semi-vertex angle of 10° and a flat base section placed at zero incidence in a Mach 6 uniform perfect-gas flow with the specific heat ratio 1.4 at Reynolds numbers ranging from 3 × 10² to 10⁵ is considered. The study is carried out on the basis of the numerical solution of the Navier-Stokes equations. The results on the base pressure and the pressure and local stagnation temperature distributions along the plane of symmetry and in several cross-sections in the near wake are compared in detail with the data [1].     

A new analytical model for pressure estimation of symmetrical water impact of a rigid wedge at variable velocities

In this paper we present an analytical solution to symmetrical water impact problems of a two-dimensional wedge. Unlike previous studies, we have taken into account the effect of velocity reduction of the solid body upon impact in order to determine impact pressure as well as the overall force acting on the body. This feature of our study provides a better estimate of the transitory nature of the phenomenon and leads to a more precise evaluation of the true dynamic load borne by the body. We obtained the solution to this problem through a generalization of the Wagner formulation and the use of an existing analytical prediction model of the entry velocity of the wedge. This approach allows us to obtain an original analytical equation for pressure in terms of the kinetics and geometrical parameters of the impact. The validity of the proposed model is demonstrated by a favourable comparison between the analytical results and the physical experiments carried out on several wedge models.     

Simulation of the aerodynamic drag of three-dimensional star-shaped bodies at hypersonic velocities

The domain of the parameters in which the aerodynamic drag of hypersonic pyramidal bodies, whose wave component is calculated within the framework of conical flows with the boundary layer displacement thickness taken into account, agrees satisfactorily with the experimental data is found. The calculation model is also applicable in the region of minimum aerodynamic drag of star-shaped bodies in the class of conical bodies equivalent in length and mid-sectional area.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 69–79, September–October, 1996.     

Flow past a thin wedge in a wind tunnel with partially perforated walls at high subsonic velocities

The problem of flow past a thin two-dimensional wedge at high subsonic velocity in a wind tunnel with partially perforated walls is considered for low suction flow rates. The solution of this model problem may be used in determining the optimal parameters of the suction system for which the aerodynamic characteristics in the tunnel are closest to those in an unbounded stream.In conclusion the author wishes to thank E. M. Kalinin for suggesting the study of this problem.     

Statistical laws of the pressure fluctuations in a hypersonic turbulent boundary layer

The results of measuring the pressure fluctuations on the wall of the nozzle of a hypersonic wind tunnel beneath a developed turbulent boundary layer are presented for the Mach number M_∞ = 7.5. On the basis of a statistical analysis, it is shown that the action of the turbulent flow is dynamically similar to the propagation of a random sequence of wave packets with continuously distributed temporal and spatial scales. Low-frequency disturbances are associated with large-scale structures of long duration that propagate at a mean-statistical velocity similar in value to the outer flow velocity. The continuous generation of weakly-correlated small-scale disturbances ensuring the maintenance and development of turbulence occurs chiefly in the inner region of the boundary layer. Spectral estimates of the power generated by the turbulent flow in the wall region of the boundary layer are presented.     

Oblique water entry of a wedge into waves with gravity effect

The hydrodynamic problem of a two dimensional wedge entering waves with gravity effect is analysed based on the incompressible velocity potential theory. The problem is solved through the boundary element method in the time domain. The stretched coordinate system in the spatial domain, which is based on the ratio of the Cartesian system in the physic space to the vertical distance the wedge has travelled into the water, is adopted based on the consideration that the decay of the effect of the impact away from the body is proportional to this ratio. The solution is sought for the total potential which includes both the incident and disturbed potentials, and decays towards the incident potential away from the body. A separate treatment at initial stage is used, in which the solution for the disturbed potential is sought to avoid the very large incident potential amplified by dividing the small travelled vertical distance of the wedge. The auxiliary function method is used to calculate the pressure on the body surface. Detailed results through the free surface elevation and the pressure distribution are provided to show the effect of the gravity and the wave, and their physical implications are discussed.     

Influence of convective acceleration in the stokes equation on the pressure in a fluid

High rates of slip at points of friction, and also the use of water as a lubricant lead one to consider the problem of the influence of inertial forces on the development of the load capacity of a film of lubricant. A number of authors [1–6] have taken into account the convective terms in the Navier-Stokes equation in determining the pressure in a fluid film of lubricant in a bearing. An increase in the load capacity of the lubricant film by 20% at Re = 5000 was noted in [6]. In the present paper, we show that the convective inertia terms in the Navier-Stokes equation are equivalent to the square of the pressure, the tangential stresses, and the vorticity. The derived equation is used to determine in the first approximation the contribution of the inertial forces to the load capacity of the lubricant film of a high-speed bearing.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 148–152, September–October, 1979.I thank A. K. D'yachkov for supervising the work, M. V. Korovchinskii for helpful comments, and also E. I. Poddubnaya for her computer calculations.     

Study of effect of a smooth hump on hypersonic boundary layer instability

Effect of a two-dimensional smooth hump on linear instability of hypersonic boundary layer is studied by using parabolized stability equations. Linear evolution of mode S over a hump is analyzed for Mach 4.5 and 5.92 flat plate and Mach 7.1 sharp cone boundary layers. Mean flow for stability analysis is obtained by solving the parabolized Navier–Stokes equations. Hump with height smaller than local boundary layer thickness is considered. The case of flat plate and sharp cone without the hump are also studied to provide comparable data. For flat plate boundary layers, destabilization and stabilization effect is confirmed for hump located at upstream and downstream of synchronization point, respectively. Results of parametric studies to examine the effect of hump height, location, etc., are also given. For sharp cone boundary layer, stabilization influence of hump is also identified for a specific range of frequency. Stabilization influence of hump on convective instability of mode S is found to be a possible cause of previous experimental observations of delaying transition in hypersonic boundary layers.