Slender axisymmetric cavities in a supersonic flow

Slender axisymmetric cavities in a subsonic flow of compressible fluid were investigated in [1–4]. In [5] a finite-difference method was used to calculate the drag coefficient of a circular cone, near which the shape of the cavity was determined for subsonic, transonic, and supersonic water flows; however, in the supersonic case the entire shape of the cavity was not determined. Here, on the basis of slender body theory an integrodifferential equation is obtained for the profile of the cavity in a supersonic flow. The dependence of the cavity elongation on the cavitation number and the Mach number is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–181, January–February, 1989.     

Thin axisymmetric cavities in a subsonic compressible flow

The investigation of subsonic compressible flow past thin axisymmetric cavities carried out in [1–3] is continued by the method of asymptotic expansions. The dependence of the elongation of the cavity on the cavitation number and the Mach number is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–177, September–October, 1987.The author is grateful to Yu. L. Yakimov for discussing his results.     

Heat transfer and supersonic flow structure in surface cavities

The characteristics of the flow and heat transfer in two- and three-dimensional open cavities on plane and cylindrical surfaces in a supersonic stream in the presence of a turbulent boundary layer have been investigated experimentally. The effects of the Mach number, boundary layer thickness, the shape of the cavity, and its angle of inclination to the free-stream direction on the flow parameters in the mixing layer above the cavity and the heat flux and pressure distribution on the surface of the cavity and its bottom are descirbed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 74–80, July–August, 1998.     

Fluctuations in cavities in a supersonic gas flow

Numerical calculations are carried out within the framework of the ideal compressible gas model for the unsteady flows in rectangular cavities exposed to a supersonic external stream. The Euler equations are integrated by means of Godunov's finite-difference method [6]. On the basis of an analysis of the calculation results an expression is proposed for determining the possible frequencies of the flow rate oscillations in the cavity as a function of the free-stream Mach number M and the geometry of the cavity. The results obtained are compared with the experimental data and calculations of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 121–127, March–April, 1990.     

Computational and experimental investigation of flow over a transient pitching hydrofoil

The present study is developed within the framework of marine structure design operating in transient regimes. It deals with an experimental and numerical investigation of the time–space distribution of the wall-pressure field on a NACA66 hydrofoil undergoing a transient up-and-down pitching motion from 0° to 15° at four pitching velocities and a Reynolds number Re = 0.75 × 10⁶. The experimental investigation is performed using an array of wall-pressure transducers located on the suction side and by means of time–frequency analysis and Empirical Modal Decomposition method. The numerical study is conducted for the same flow conditions. It is based on a 2D RANS code including mesh reconstruction and an ALE formulation in order to take into account the foil rotation and the tunnel walls. Due to the moderate Reynolds number, a laminar to turbulent transition model was also activated. For the operating flow conditions of the study, experimental and numerical flow analysis revealed that the flow experiences complex boundary layer events as leading-edge laminar separation bubble, laminar to turbulent transition, trailing-edge separation and flow detachment at stall. Although the flow is relatively complex, the calculated wall pressure shows a quite good agreement with the experiment provided that the mesh resolution and the temporal discretization are carefully selected depending on the pitching velocity. It is particularly shown that the general trend of the wall pressure (low frequency) is rather well predicted for the four pitching velocities with for instance a net inflection of the wall pressure when transition occurs. The inflection zone is reduced as the pitching velocity increases and tends to disappear for the highest pitching velocity. Conversely, high frequency wall-pressure fluctuations observed experimentally are not captured by the RANS model. Based on the good agreement with experiment, the model is then used to investigate the effects of the pitching velocity on boundary layer events and on hydrodynamic loadings. It is shown that increasing the pitching velocity tends to delay the laminar-to-turbulence transition and even to suppress it for the highest pitching velocity during the pitch-up motion. It induces also an increase of the stall angle (compared to quasi-static one) and an increase of the hysteresis effect during pitch-down motion resulting to a significant increase of the hydrodynamic loading.     

Investigation of supersonic three-dimensional flow past pointed axisymmetric bodies

The flow pattern near bodies of revolution with very long cylindrical and pointed nose sections is studied in the framework of an ideal gas model by means of a numerical method based on MacCormack's difference scheme. The existence of internal shock waves, oriented in both the longitudinal and the transverse directions, in the shock layer is established. The variation of the aerodynamic coefficients of the configuration with its length, angle of attack, and free stream Mach number is investigated. The calculated and experimental data are compared, and the connection between the flow parameters on the body surface and the position of the separation line of the boundary layer on its lateral face is established. A method of calculating the influence of the boundary layer on the values of the aerodynamic coefficients of bodies of revolution of large aspect ratio at small angles of attack is proposed. Axisymmetric flow near blunt bodies has been studied in detail in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 127–133, September–October, 1986.The author expresses his gratitude to A. N. Pokrovskii for his help in calculating the boundary layer parameters on the surfaces of the considered configurations.     

Experimental investigation of nonstationary flow in cavities in a supersonic flow

An experimental investigation was made into the flow and pressure pulsations in cylindrical cavities open toward a supersonic flow and set up at zero angle of attack (i.e., the cavity axis and the direction of the flow coincide).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 180–183, September–October, 1979.     

Study of supersonic flow past axisymmetric bodies of different form

A method is proposed in [1] for calculating supersonic flow past smooth bodies. The present article presents a computational scheme and calculational formulas for determining the gasdynamic functions at the nodes of the lines=const. A comparison is made of certain of the results obtained with the results of other studies [2, 3]. Results are also presented of the calculation of the flow of a perfect gas past ellipsoids of revolution (=2.3) and inverted cones with spherical and ellipsoidal blunting.The author wishes to thank G. F. Telenin for his guidance in the present study.     

Distribution of radiant heat fluxes over the surface of three-dimensional and axisymmetric bodies in a supersonic ideal-gas flow

Numerous studies have been devoted to the calculation of supersonic radiating flow past bodies (see the bibliography in [1, 2]). In almost all these studies the gas flows investigated are plane or axisymmetric. Three-dimensional flows, however, have received little attention. The flow of air past three-dimensional bodies was considered in [3], where the chief object was to investigate the accuracy with which a real radiating volume can be simulated by the widely used plane-layer approximation. In [4] the flow of a hydrogen-helium mixture past three-dimensional bodies was investigated in the hypersonic approximation in the neighborhood of the stagnation point and in two planes of symmetry with allowance for the screening of the radiation of vaporized material.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 92–97, January–February, 1986.The authors wish to thank V. V. Lunev for his useful observations and advice.     

Aerodynamics of axisymmetric bodies in supersonic flow with local blowing

Journal of Applied Mechanics and Technical Physics -     

Experimental flow study over a blunt-nosed axisymmetric body at incidence

The flowfield over a blunt-nosed cylinder was examined experimentally at a low subsonic speed for Re=1.88×10⁵ and angles of attack up to 40°. Velocity measurements were carried out (employing a seven-hole Pitot tube) as well as wall static pressure and wall shear-stress measurements. Surface flow visualization was applied using liquid crystals and a mixture of oil–TiO₂. For all the examined cases no flow asymmetries were found. For high angles of attack (20° and above) a separation “bubble” appears at the leeside of the nose area (streamwise flow separation). The basic feature of the circumferential pressure distribution at the after body area for these angles of attack is a plateau close to the suction peak and a fast recovery next to it. One streamwise vortex on each side of the symmetry plane is formed as well as a separation bubble about 90° far from this plane, where the cross-flow primary separation line is located. Each cross-flow primary separation line starts at the leeside nose area and moves towards the windward side along the cylindrical after body. The space between the two primary separation lines close to the wall is characterized by high flow fluctuations on the leeside, compared to the low fluctuations of the windward side.     

Numerical and analytical study of transverse supersonic flow over a flat cone

Quasisteady supersonic flow over a flat cone on a plane surface is studied. A formula is derived for the angle through which the flow lines turn at the cone. The results are used to justify the use of two-dimensional simulations of the flow. Peak pressures and total impulses are obtained numerically for various cone angles.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Nonsteady supersonic flow over spiked bodies

In longitudinal supersonic flow over spiked cylinders nonsteady regimes can occur in which a separation zone is periodically generated at the spike, grows vigorously in size, and then vanishes. Several authors [1–6] have investigated the physical pattern of flow with separation zone fluctuations (using shadowgraphs) and have determined the boundaries of existence of the nonsteady regime as a function of the ratio between the spike length and diameter of the cylinder. The authors, however, did not systematically study the dependence of the pulsation frequency on the freestream Mach and Reynolds numbers or on the relative diameter and tip angle of the spike. We have undertaken such an investigation. We are concerned primarily with the influence of the dimensionless parameters on the Strouhal number Sh of the separation zone pulsations at a spike attached to the front of a flat-ended cylinder. Earlier investigations [4–6] have been carried out using motion pictures with film speeds up to 32·10³ frames/sec. In the present study we used high-speed motion pictures with a speed of 6.25· 10⁵ frames/sec. This speed allowed us to determine the precise sequence of phases of the pulsations and their relative durations, as well as the speed at which the boundaries of the separation zone move.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 118–124, September–October, 1976.     

Numerical analysis of supersonic viscous gas flow past axisymmetric nonpointed bodies

Supersonic viscous homogeneous gas flow past axisymmetric smooth nonpointed bodies is analyzed numerically for widely varying Mach and Reynolds numbers and flow geometry. The initial equations of a viscous shock layer are solved by the stabilization method. The effect of the determining parameters on the flow character and the heat transfer distribution along the surface is analyzed. The accuracy and domain of applicability of several approximate approaches to the solution of the problem are estimated. Tomsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–117, January–February, 1999. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00298).     

Influence of injection on stabilization of flow over an axisymmetric body with a recess facing into a supersonic oncoming stream

Numerical modeling of supersonic flow over a body with an annular step formed by two coaxial cylinders is performed by the Godunov method within the framework of the model of an ideal gas. Regimes of nonsteady streamline flow and peculiarities of the flow associated with the presence of a cylindrical recess in the nose part of the body are analyzed. The influence of the intensity of injection of an annular wall jet from the bottom of the recess on flow stabilization and the body drag is investigated. The domain of the existence of steady streamline flow is established. Khar'kov Aviation Institute, Khar'kov 310070. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 84–90, July–August, 1998.     

Passage of a supersonic flow over intersecting surfaces

Using the linear formulation, the problem of passage of a supersonic flow over slightly curved intersecting surfaces whose tangent planes form small dihedral angles with the incident flow velocity at every point is considered. Conditions on the surfaces are referred to planes parallel to the incident flow forming angles 0≤γ≤2π at their intersection [1]. The problem reduces to finding the solution of the wave equation for the velocity potential with boundary conditions set on the surfaces flowed over and the leading characteristic surface. The Volterra method is used to find the solution [2]. This method has been applied to the problem of flow over a nonplanar wing [3] and flow around intersecting nonplanar wings forming an angle γ=π/n (n=1, 2, 3, ...) with consideration of the end effect on the wings forming the angle [4]. In [5] the end effect was considered for nonplanar wings with dihedral angle γ=m/nπ. In the general case of an arbitrary angle 0≤γ≤2π the problem of finding the velocity potential reduces to solution of Volterra type integrodifferential equations whose integrands contain singularities [1]. It was shown in [6] that the integrodifferential equations may be solved by the method of successive approximation, and approximate solutions were found differing slightly from the exact solution over the entire range of interaction with the surface and coinciding with the exact solution on the characteristic lines (the boundary of the interaction region, the edge of the dihedral angle). The solution of the problem of flow over intersecting plane wings (the conic case) for an arbitrary angle γ was obtained in terms of elementary functions in [7], which also considered the effect of boundary conditions set on a portion of the leading wave diffraction. In [8, 9] the nonstationary problem of wave diffraction at a plane angle π≤γ≤2π was considered. On the basis of the wave equation solution found in [8], this present study will derive a solution which permits solving the problem of supersonic flow over nonplanar wings forming an arbitrary angle π≤γ≤2π in quadratures. The solutions for flow over nonplanar intersecting surfaces for the cases 0≤γ≤π [6] and π≤γ≤2π, found in the present study, permit calculation of gasdynamic parameters near a wing with a prismatic appendage (fuselage or air intake). The study presents a method for construction of solutions in various zones of wing-air intake interaction.