Supersonic flow past axisymmetric flared cones

Systematic data on the determination of the aerodynamic characteristics of axisymmetric bodies with a break in the generating line (Fig. 1a, b) in supersonic flow at zero angle of attack are presented in [1, 2, and others]. A characteristic feature of the flow past such bodies is the appearance of an extensive separation zone dec in the region of the break in the generator when the break angle exceeds some minimum value _min, which for a turbulent boundary layer depends basically on the Mach number M at the body surface ahead of the separation zone. In this case, compression waves which change into the oblique compression shocks dc and cc, emanate both from the beginning of the separation zone (point c) and from the end of it (point d). These shocks, intersecting at the point c, form the triple shock configuration acd and acc for which we introduce the notationac[c, d]. The maximum value (_max) of the generator break angle is limited by the possibility of the existence of an attached compression shock, dc. According to these data a change in the generator break angle for the range _minmax of the angle does not disrupt the nature of the flow in the separation zone, but only alters the size of this zone.We shall examine the flow past cones with values of the generator break angles (_max) for which the attached shock dc cannot exist.     

Negative wake in the uniform flow past a cylinder

The upstream/downstream streamline shift and the associated negative wake generation (streamwise velocity overshoot in the wake) in a viscoelastic flow past a cylinder are studied in this paper, for the Oldroyd-B, UCM, PTT, and FENE-CR fluids, using the Discrete Elastic Viscous Split Stress Vorticity (DEVSS-ω) scheme (Dou HS, Phan-Thien N (1999). The flow of an Oldroyd-B fluid past a cylinder in a channel: adaptive viscosity vorticity (DAVSS-ω) formulation. J Non-Newtonian Fluid Mech 87:47–73). The numerical algorithm is a parallelized unstructured Finite Volume Method (FVM), running under a distributed computing environment through the Parallel Virtual Machine (PVM) library. It is demonstrated that both the normal stress and its gradient are responsible for the negative wake generation and streamline shifting. Fluid extensional rheology plays an important role in the generation of the negative wake. The negative wake can occur in flows where the fluid extensional viscosity does not increase rapidly with strain rate. The formation of the negative wake does not depend on whether the streamlines undergo an upstream or a downstream shift. Shear-thinning viscosity weakens the velocity overshoot and while shear-thinning first normal stress coefficient enhances the velocity overshoot. Wall proximity is not necessary for the velocity overshoot; however, it enhances the strength of the negative wake. For the Oldroyd-B fluid, the ratio of the solvent viscosity to the zero-shear viscosity plays an important role in the streamline shift. In addition, mesh dependent behaviour of normal stresses along the centreline at high De in most cylinder/sphere simulations is due to the convection of normal stress from the cylinder to the wake, which results in the maximum of the normal stress being located off the centreline by a short distance at high De.     

Supersonic flow past a cylinder with a fluid flare

The aerodynamic parameters and the pressure distribution over the surface of a cylinder in a steady axisymmetric supersonic flow is studied within the framework of the inviscid perfect gas model in the absence and the presence of combined intense air injection fromthe flat face and the lateral surface into the shock layer. The purpose of the study is to investigate the effect of gas blowing from different regions of the cylindrical surface on the supersonic axisymmetric flow past the body.     

Supersonic viscous perfect gas flow past a circular cylinder

The complete Navier-Stokes equations are used to calculate supersonic perfect gas flow past a circular isothermal cylinder by the method described in [1]. The effects of the Mach number M=2.5–10 and the Reynolds number Re=30-10⁵ on the flowfield structure and heat transfer to the cylinder wall are investigated. Special attention is paid to the study of the near wake and the local characteristics on the leeward side of the cylinder.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 107–115, November–December, 1993.     

Supersonic axisymmetric flow past a blunt cone executing longitudinal low-frequency oscillations

The aerodynamic parameters of an oscillating cone in unsteady axisymmetric supersonic flow are investigated on the basis of the inviscid perfect gas model both in the absence and in the presence of strong air injection from its flat end into the shock layer.     

Supersonic flow past blunt bodies screened by a permeable surface

A study is made of a steady flow of supersonic gas past the front part of blunt bodies with allowance for the screening effect of a thin perforated surface, whose presence is simulated by the introduction of a supplementary hydrodynamic discontinuity (an active surface [1, 2]).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 139–144, March–April, 1986.     

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.     

Supersonic flow past blunt bodies involving fast nonequilibrium processes

In the numerical integration of the system of equations of relaxation gasdynamics the solution may become unstable. Instability arises in those cases when the characteristic time for the nonequilibrium process becomes less than the characteristic flow time. To ensure stability it is necessary to reduce the integration step. With approach to equilibrium conditions, when the process rate increases, the step reduction may lead to excessive computational time. Preceding studies have overcome the difficulty in solving the one-dimensional [1–3] and two dimensional [4] problems by various techniques, the basic idea being the use of implicit difference schemes for approximating the relaxation equations.In the present paper analogous considerations are used to develop a scheme for calculating supersonic flow past blunt bodies with fast non-equilibrium processes within the framework of [5]. The basic coordinate system , is used to approximate the equations, just as in [5]. However the relaxation equation is solved along a streamline element. Calculations are presented for the air flow past a sphere with account for the oxygen dissociation reaction. The validity of the binary similarity law for this model is verified. As an example of the applicability of the technique, a calculation is made of the flow of a chemically reacting mixture with heat release about a sphere.     

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.     

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.     

Supersonic nonequilibrium flow past segmental bodies of a mixture simulating the atmosphere of venus

Calculations of the flow of the mixture 0.94 CO₂+0.05 N₂+0.01 Ar past the forward portion of segmentai bodies are presented. The temperature, pressure, and concentration distributions are given as a function of the pressure ahead of the shock wave and the body velocity. Analysis of the concentration distribution makes it possible to formulate a simplified model for the chemical reaction kinetics in the shock layer that reflects the primary flow characteristics. The density distributions are used to verify the validity of the binary similarity law throughout the shock layer region calculated.The flow of a CO₂+N₂+Ar gas mixture of varying composition past a spherical nose was examined in [1]. The basic flow properties in the shock layer were studied, particularly flow dependence on the free-stream CO₂ and N₂ concentration.New revised data on the properties of the Venusian atmosphere have appeared in the literature [2, 3] One is the dominant CO₂ concentration. This finding permits more rigorous formulation of the problem of blunt body motion in the Venus atmosphere, and attention can be concentrated on revising the CO₂ thermodynamic and kinetic properties that must be used in the calculation.The problem of supersonic nonequilibrium flow past a blunt body is solved within the framework of the problem formulation of [4].Notation V body velocity - shock wave standoff - universal gas constant - ratio of frozen specific heats - hRt/m enthalpy per unit mass undisturbed stream P pressure - density - T temperature - m molecular weight - c_p specific heat at constant pressure - (X) concentration of component X (number of particles in unit mass) - R body radius of curvature at the stagnation point - _j rate of j-th chemical reaction shock layer P V ² pressure - density - TT temperature - mm molecular weight Translated from Izv. AN SSSR. Mekhanika Zhidkosti i Gaza, Vol. 5, No. 2, pp. 67–72, March–April, 1970.The author thanks V. P. Stulov for guidance in this study.     

Supersonic flow over elongated blunt bodies with a cross section of elliptical shape

Up to now computational algorithms have been developed for, and systematic studies have been made of, supersonic flow over axisymmetric bodies both by a stream of ideal gas and by an air stream with equilibrium and nonequilibrium physicochemical transformations [1–6]. Conical flows around bodies having cross sections of different shapes and in a wide range of angles of attack have been studied in detail [7–11]. With the further development of numerical methods the next problem has become the analysis of supersonic flow over blunt bodies of large elongation having cross sections of sufficiently arbitrary shape. The effects of essentially three-dimensional flow (without planes of symmetry) over bodies whose cross sections represent ellipses with a constant or variable ratio of axes along the length of the body are discussed in the present paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 155–159, November–December, 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).     

Supersonic flow past a blunt wedge

A study is made of the asymptotic solution of the problem of flow past a blunt wedge by a uniform supersonic stream of perfect gas. By separation of variables it is shown that at large distances the disturbance of the flow is damped exponentially. In the case of subsonic flow behind the shock wave the exponent of the leading correction term in the expansion of the shock front is calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–140, July–August, 1984.     

Supersonic swirling flow past a blunt body

The problem of supersonic swirling flow past a blunt body is studied numerically on the basis of the complete Navier-Stokes equations.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 158–160, November–December, 1994.