Singularities of supersonic flows around pointed bodies with a detached shock

Results are presented of a numerical investigation of the axisymmetric flow around a family of bodies with a pointing angle for which the shock is detached. It is shown that the supersonic part of the stream remains the same for all bodies of the family for a fixed value of M despite the fact that the shaper of the subsonic zone is related quite strongly to the pointing angle _*. The dependence of the shock standoff and its radius of curvature on the spreading line on the body shape is studied. Effects inherent in flows around sharply pointing bodies are discussed. A dimensionless parameter characterizing each body of the family under consideration is introduced and used to establish general flow regularities. Data illustrating the possibility of applying such parametrization are analyzed for a wider class of pointing bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 111–115, July–August, 1975.     

Evaluation of the energy efficiency of heat addition upstream of the body in a supersonic flow

Criteria for evaluating the energy efficiency of heat addition upstream of the body in a supersonic gas flow are obtained. Based on the functional objectives of flying vehicles and the thermodynamic model of the process, estimates are obtained for missile and aircrafttype vehicles. The minimum Mach numbers at which heat addition upstream of the body is reasonable are evaluated. The increase in the flight range in the cruising regime for an aircrafttype vehicle and on the active trajectory for a missiletype vehicle is evaluated. Estimates for fuel economy in launching an aerospace plane into an Earth orbit are given. It is shown that a significant part of the fuel should be spent on producing energy for gas heating in order to obtain a noticeable effect. The minimum necessary efficiency" of conversion of the fuel energy into the gasheating energy is evaluated.     

Three-dimensional supersonic flow of ideal gas past a body with tail fins

The results are given of numerical and experimental investigations of the steady supersonic flow of an ideal gas past a model of a body with + and X fins. The angle of attack varied from 0 to 20 °. A study is made of the physical structure of the flow, and the pressure distributions, the coefficients of the normal force and the pitching moment of the complete body and the individual fins, and also the increment of the coefficient of the normal force acting on the body due to the influence of the fins are found. A comparison with linear theory and the experimental data is made. The agreement between the calculated results and the experimental data is satisfactory.     

Investigation of the supersonic flow around a pointed elliptical cone at an angle of attack

The picture of ideal gas flow around cones at zero and low angles of attack has been well studied by using approximate methods [1], and results for high angles of attack have been obtained mainly numerically [2–7]. At high angles of attack it is sensible to examine inviscid flow only up to some generator on the downwind side of the cone at which boundary-layer separation occurs. Hence, the domain where the flow can be considered inviscid yields the main contribution to the magnitude of the aerodynamic forces and the heat fluxes [5, 9]. A picture of the supersonic flow around a pointed elliptical cone is obtained in this paper by the numerical solution of the gasdynamics equations. The whole flow domain is computed at low angles of attack while the solution at high angles is obtained in a domain bounded by some surface of three-dimensional type [10]. The dependence of the flow parameters on the angle of attack is studied when the shock is attached to the cone apex. In contrast to a circular cone, at low angles of attack two spreading lines occur on the surface of an elliptical cone, to which the maximum pressure corresponds. As the angle of attack increases, these lines come together and merge at a certain time. At high angles of attack the flow picture is analogous to a circular cone with a pressure maximum in the plane of symmetry.     

Investigation of supersonic flow around a blunt body with injection for high Reynolds numbers

The paper discusses the supersonic flow around a blunt smooth body by a stream of viscous gas with subsonic injection from the surface of the body. The effect of various injection cycles on the physical flow characteristics ahead of the body are studied in [1, 2]; the problem is considered in the approximation of a boundary layer. The nonuniform composition of the gas ahead of the body, chemical reactions between the various components, and the effect of radiation are taken into account. For a number of flow cycles, which are of practical importance, it will be of interest to consider higher approximations in powers of [=1/Re, see Eq. (1.1) below] in the shock layer ahead of the body and, in particular, to explain the action of the displacement effect and also the limits of applicability of the boundary-layer approximation assumed in [1, 2]. Extensive literature has been devoted to the asymptotics of the problem of flow around a blunt body of a viscous gas at high Reynolds numbers (see, for example, Van Dyke's book [3]). An investigation of the problem, based on the method of M. I. Vishik and L. A. Lyusternik, is contained in [4–6]. (The advantage of the use of Vishlik and Lyusternik's method in comparison with the method of internal and external expansion is discussed in [4].) The effect of injection on the flow has not been considered in the papers listed. In this paper, approximate solutions are constructed with an error of order and ² which take into account the effect of the injectionf on the flow . The approximate solutions are compiled from a more accurate nonviscous flow (external solution) and boundary-layer corrections. The boundary-layer corrections are constructed on a shock wave and a contact boundary in such a way that the solution would be continuous and quite smooth. For the external solution at the contact boundary, conditions are obtained which take into account the effect of viscosity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 69–77, January–February, 1974.     

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.     

Resonant phenomena in a transonic flow around an airfoil with pulsed periodic energy supply

Interaction of a pulsed periodic source of energy with a closing shock wave arising near airfoils in transonic flight is studied. The evolution of the shock-wave structure of the flow around a symmetric airfoil is examined by solving two-dimensional unsteady gas-dynamic equations, and a resonant mechanism of interaction is found, which leads to considerable (by an order of magnitude) reduction of the wave drag of the airfoil.     

Three-dimensional PIV measurement of flow around an arbitrarily moving body

A three-dimensional (3D) particle image velocimetry measurement technique capable of simultaneously monitoring 3D fluid flows and the structure of an arbitrarily moving surface embedded in the flow was proposed with a heavy emphasis on image processing methods. The costs associated with the experimental apparatus were reduced by recording the surface and the trace particles at one image plane without the use of additional cameras or illumination devices. An optimal exposure time for surface and particle imaging was identified using red fluorescent tracer particles in conjunction with a long-pass glass filter. The particle image and surface image were then separated using an image separation process that relied on the feature scaling differences between the particles and the surface texture. A feature detection process and a matching process facilitated estimation of the 3D surface points, and the 3D surface structure was modeled by Delaunay triangulation. The particle volume reconstruction algorithm constrained the voxels inside the surface structure to zero values to minimize ghost particle generation. Volume self-calibration was employed to improve the reconstruction quality and the triangulation accuracy. To conserve computing resources in the presence of numerous zero voxels, the MLOS-SMART reconstruction and the direct non-zero voxel cross-correlation method were applied. Three-dimensional experiments that modeled the flows around an eccentric rotating cylinder and a flapping flag were conducted to validate the present technique.     

Three-dimensional structure of flow in a supersonic underexpanded jet

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 42–47, July–August, 1991.     

Conditions of supersonic flow around multiwedge bodies

An experimental study was made of some schemes for flow around multiwedge bodies at supersonic flow velocities. On the basis of data on the distribution of the pressure, on visualization of the flow, and on optical measurements, an analysis was made of the structure of the flow. Zones of breakaway of the flow were observed at the lateral surfaces of the lobes. In the nose part of a multiwedge body there is a three-dimensional configuration of attached plane shock waves, going over into a combined detached nonaxisymmetric wave directed toward the base of the body.     

Pressure oscillation on a plane upstream of an obstacle in a supersonic flow

The levels and spectra of pressure oscillation on a plane upstream of a vertical cylinder and a step in an M=3 supersonic flow are measured in the presence of a turbulent boundary layer. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 69–74, January–February, 1998.     

Structure of supersonic inviscid nonsymmetric conical flow around a V-wing

The shock wave structure of flow around a V-wing and its properties determining the conical flow topology are numerically investigated within the framework of the inviscid gas model on a wide range of the angles of attack and yaw when in the disturbed supersonic flow either nonsymmetric Mach interaction between the shocks attached to the leading edges of the wing or a shockless flow in the compressed layer on the windward cantilever is realized. The subranges of the angles of attack and yaw with the disturbed flow properties characteristic of the wing of the given geometry are determined. It is found that at high angles of attack, when the branching point of the bow shock beneath the leeward cantilever generates an intense contact discontinuity, the structure of the conical flow in the shock layer on the windward cantilever involves a singularity of a new type which can be characterized as a “vortical” Ferri singularity. It is located above the point of convergence of the streamlines proceeding from the leading edges of the wing, at the vertex of the corresponding contact discontinuity. Flow patterns with the point of convergence of the streamlines proceeding from the leading edges located in the elliptical flow region, which is placed at a local maximum of the pressure distribution over the surface are also found. The range of the angles of attack and yaw on which this new property of supersonic conical flows is realized in the presence of a branched shock system is determined.     

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.     

Physical and mathematical modeling of a supersonic flow around a cylinder with a porous insert

Results of numerical and experimental modeling of a supersonic flow (M_∞ = 4.85) around a model of a streamwise-aligned cylinder with a cellular-porous insert permeable for the gas on the frontal face of the cylinder are described. Experimental data on the influence of the pore structure and the length of the porous cylindrical insert on the model drag, pressure on the frontal face of the cylinder, and flow pattern are obtained. Numerical modeling includes solving Favre-averaged Navier-Stokes equations, which describe the motion of a viscous compressible heat-conducting gas. The system is supplemented with a source term taking into account the drag of the porous body within the framework of the continuum model of filtration. Data on pressure and velocity fields inside the porous body are obtained in calculations, and the shape of an effective pointed body whose drag is equal to the drag of the model considered is determined. The calculated results are compared with the measured data and schlieren visualization of the flow field.     

Three-dimensional steady supersonic duct flow using Lagrangian formulation

In this paper, numerical simulation of three-dimensional supersonic flow in a duct is presented. The flow field in the duct is complex and can find its applications in the inlet of air-breathing engines. A unique streamwise marching Lagrangian method is employed for solving the steady Euler equations. The method was first initiated by Loh and Hui (1990) for 2-D steady supersonic flow computations and then extended to 3-D computation by the present authors Loh and Liou (1992). The new scheme is shown to be capable of accurately resolving complicated shock or contact discontinuities and their interactions. In all the computations, a free stream of Mach numberM=4 is considered.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Numerical analysis of the effect of local energy supply on the aerodynamic drag and heat transfer of a spherically blunted body in a supersonic air flow

The effect of local source of energy in a supersonic flow on the aerodynamic drag and heat transfer of a spherically blunted body is studied numerically. Calculations are performed on the basis of the Navier-Stokes equations for a thermally equilibrium model of air. Data on the effect of the intensity and size of the energy source on the wave drag, friction, and heat transfer are obtained. Particular attention is given to studying the effect of drag reduction by means of a focused heat source. The gas-dynamic nature of this effect is studied. The limits of drag reduction are estimated, and optimal conditions of heat supply are determined. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 171–179, September–October, 2000.