Numerical investigation of supersonic flow past blunt bodies with protruding spikes

A procedure for the calculation of a supersonic flow of ideal gas near axisymmetric blunt bodies with protruding spikes is developed. The flow past a frustum of a cone with a protruding spherically blunt cylindrical spike as a dependence on the ratio K of the spike length1 to the diameter D of the flat end of the body and the Mach number M of the oncoming flow is studied. Several steady flow regimes are obtained, including the formation of circulation zones and internal shock waves in the shock layer. It is shown that mounting a spike in front of the frustum of a cone can lead to a 40–50% reduction in its drag. A full investigation of the variation of the drag coefficient as a dependence on K is carried out for M = 3.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 119–127, May–June, 1986.The authors express their gratitude to V. A. Levin for the formulation of the problem and his constant attention to the work.     

Effect of angle of attack on supersonic flow past axisymmetric blunt bodies with surface injection

The effect of angles of attack in the interval 0 40° on the flow pattern and the aerodynamic characteristics of a body of power-law shape (equation of the generator in the cylindrical coordinate system r=zⁿ, n=0.125) is investigated for supersonic flow without injection and with intense subsonic localized injection from the surface. As a result of numerical calculations it is established that the use of Newton's theory for determining the coordinates of the gas stagnation point behind the shock in flow past an impermeable body of the shape in question leads to serious errors, and an expression for determining the location of this point is given. It is shown that for three-dimensional flow the flow pattern and the surface pressure distribution are sharply different from the case=0. It is established that on the parameter interval in question intense injection considerably reduces the aerodynamic drag without loss of static stability, which is important in connection with the solution of the problem of gas-stable aircraft control.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 95–101, September–October, 1987.     

Numerical investigation of the flow past axisymmetric bodies with surface injection

Incompressible viscous gas flow past axisymmetric bodies with surface injection is numerically investigated on the range of Reynolds numbers from 10 to 2·10⁵.Izhevsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 162–166, July–August, 1996.     

Numerical investigation of flow of a viscous reacting gas past blunt bodies

Numerical solution of the Navier—Stokes equations is used to estimate the limits of applicability of simplified models used to describe the laminar nonequillbrium flow of a viscous multicomponent reacting gas past blunt bodies moving at hypersonic velocity in air.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 19–23, September–October, 1982.     

Computation of unsteady flow past blunt bodies

In accordance with the recent experimental research for flow visualization,theunsteady behavior of the starting period is investigated numerically for flow past bluntbodies.Finite difference methods are employed to solve the unsteady two-dimensionalincompressible Navier-Stokes equations.A short discussion is presented of explicit,implicit and ADI methods.Finally,the explicit and ADI schemes are used to study the flowfield in the starting period for flow past mountain-shaped and rectangular bodies.     

Unsteady supersonic flow around blunt bodies with detached shock wave

The numerical method of calculating the supersonic three-dimensional flow about blunt bodies with detached shock wave presented in [1–3] is applied to the case of unsteady flow. The formulation of the unsteady problem is analogous to that of [4], which assumes smallness of the unsteady disturbances.The paper presents some results of a study of the unsteady flow about blunt bodies over a wide range of variation of the Mach number M=1.50– and dimensionless oscillation frequency l/V=0–1.0. A comparison is made with the results obtained from the Newton theory.     

Numerical investigation of the structure of nonequilibrium three-dimensional hypersonic flow past blunt bodies

Three-dimensional dissociating air flow past blunt bodies is investigated within the framework of the parabolized Navier-Stokes equations in the thin layer approximation. Multicomponent diffusion, barodiffusion and homogeneous chemical reactions, including dissociation-recombination and exchange reactions, are taken into account. The boundary conditions are assigned in the free stream and at the surface of the body with allowance for heterogeneous catalytic reactions and slip effects. The problem of flow at zero angle of attack past blunt bodies possessing two planes of symmetry is investigated numerically for flow patterns varying from smeared layer structure to almost ideal flow (Re=50-10⁵). The flow conditions corresponded to the motion of a body with lift along a re-entry trajectory [1]. The contribution of the chemical reactions in the shock wave as compared to the diffusion flux at the edge of the shock wave was estimated. The edge of the shock wave is assumed to correspond to the point at which the density profile has the greatest slope. The influence of slip effects and barodiffusion on the flow characteristics is demonstrated. The results of the calculations are compared with calculations based on the thin viscous shock layer model [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 143–150, September–October, 1987.The author wishes to express his thanks to G. A. Tirskii and V. V. Lunev for useful discussions and valuable advice.     

Investigation of unsteady supersonic flow past conical bodies

A study is made of the three-dimensional supersonic flow of ideal gas past conical bodies executing harmonic oscillations in the plane of the angle of attack about some angle β₀ in accordance with the law α = α₀ cos ωt, so that the total angle of attack is β = β₀ + α₀ cos ωt.     

Flow past blunt bodies with nose spikes and surface injection

Axisymmetric supersonic ideal-gas flow past a blunt body with a forward-projecting spike is numerically investigated with allowance for injection from the surface. The effect of the length and shape of the spike, the parameters of the injected gas and the position of the permeable zone on the flow pattern and drag is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 128–133, July–August, 1987.     

Hypersonic flow past ducted blunt bodies of revolution

Chernyi [1, 2] has examined the problem of hypersonic flow past a ducted cone with sharp leading edge. In the following we present an analysis of the characteristic features of this problem in the case of a blunt leading edge. We use hypersonic theory for flow past slender bodies with nose blunting of relatively small dimensions [1, 3, 4], based on replacing the nose by a concentrated force and use of the nonsteady analogy. It has been shown in [4, 5] that within the framework of this theory the effect of the violation of the law of plane sections and also the effect of the chemical and physical transformations of the gas in the high-entropy layer is qualitatively equivalent to a change in the drag coefficient of the nose. This approach makes it possible to establish useful similarity laws. The development of these ideas in the direction of the study of the flow structure behind the bow shock wave and analysis of the parameters defining this structure is given in [6–8] in which, in particular, the role of the entropy distribution with respect to the streamlines in the transitional section between the nose and the side surface was clarified and the important practical empirical result was established that this distribution is universal for noses of any form for given flow conditions. In the following these results are extended to blunt bodies of revolution with a duct in the nose. We examine the flow region which is external to the duct under the assumption that the external flow regime corresponds to maximum flow rate through the duct. A characteristic feature of the problem is associated with the additional characteristic linear dimension r₀, which determines the gas mass lost through the duct.     

Experimental investigation of three-dimensional supersonic flow past an axisymmetric body with an annular cavity

The results of an experimental investigation of supersonic Mach 2.5 flow past an axisymmetric cylindrical model body with a rectangular annular cut-out on its lateral surface are presented. The evolution of the structure of the flow over the cavity with continuous variation in the angle of attack is studied on the basis of the data of flow visualization and balance measurements on the range of the relative cavity lengths L/h from 8 to 16. Hysteresis phenomena are revealed and analyzed.