Minimum-drag cascade design for supersonic flow with subsonic normal velocity component

The variational problem of designing the slender profile of a plane cascade in a supersonic ideal (inviscid and nonheat-conducting) gas flow with a subsonic normal velocity component is solved in the linear approximation. The optimum profiles constructed differ fundamentally from the closest analog — the supersonic single profile creating minimum wave drag for given lift. Following [1], it is easy to show that in this case the optimum profile is a plate at an angle of attack determined by the given lift.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 137–146, January–February, 1995.     

Interaction of an external supersonic flow with the subsonic layer near a wavy wall

A solution of the problem of supersonic flow past a wavy wall with an adjacent subsonic layer is obtained. The solution is a generalization of the well-known solutions [1] of the linear problem of purely subsonic and purely supersonic flow past a wavy wall and goes over into these solutions in the limiting cases of infinite and zero wall-layer thickness, respectively. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 97–103, January–February, 1997.     

Aerodynamics of axisymmetric bodies in supersonic flow with local blowing

Journal of Applied Mechanics and Technical Physics -     

Discrete vortices in the wake of various profiles in subsonic and supersonic two-dimensional gas flow

The Mach number dependence of the Strouhal number, the frequency of discrete vortices, the vortex velocity, and other parameters are determined in the wake of wedges and flat plates for low angles of attack. The studies were made using high-speed motion-picture photography through a Schlieren system and with photomultipliers. The results are presented in tabular and graphical form.Notation h transverse distance - l longitudinal distance between vortices - V freestream velocity in m/sec - n_v vortex frequency for one row of vortex street in sec - M freestream Mach number - S₁ Strouhal number based on projection of the model onto the plane perpendicular to the freestream direction - S₂ Strouhal number calculated from the wake neck width d₂ for M>1 - R Reynolds number calculated from d - R_* critical Reynolds number - model apex angle - angle of attack - L length in flow direction in mm The author wishes to thank G. I. Petrov for his interest in the study and his advice.     

Local subsonic zones in supersonic jet flows

The results of the experimental investigation of supersonic turbulent jets with local subsonic zones of forward and reverse flow exhausting into the ambient atmosphere or an outer stream, either parallel or transverse to the jet, are presented. Some gasdynamic features of the flows containing these zones, which have not been adequately addressed in the literature, are analyzed. Thus, supersonic flows with back pressure, e.g., highly overexpanded and underexpanded jet flows, and those upstream and downstream of a jet on the leeward side of a cone in a supersonic gas stream, are studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–150, January–February, 1998.     

Calculation of the diffusion combustion of a subsonic jet in a co-current supersonic flow

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 91–95, January–February, 1988.     

Investigation of supersonic viscous flow past a sphere in the presence of subsonic and sonic injection

Supersonic flow past a sphere with a given rate of gas injection along the generator is investigated numerically on the range Re=10²–10⁴. Calculations have been made on the interval 0 90°, where is the angle between the axis of symmetry and the normal to the surface. It is shown that for high subsonic and sonic injection rates it is possible to observe qualitatively new features in the flow structure and in the distribution of the local supersonic flow characteristics around the perimeter of the sphere not previously noted in [9]. In the case of sonic injection the changes in flow structure occur only in the supersonic zone. In the neighborhood of the transition from a subsonic to sonic injection velocity the heat flux has a local maximum, which in absolute value does not exceed the heat flux in the absence of injection. It is shown that there may be qualitative differences in the pressure distribution over the surface of the body with increase in the injection parameter depending on the distribution and value of the injected gas flow rate and, moreover, the number Re.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 83–89, January–February, 1988.     

Effect of energy release in shock layer on supersonic flight

The problem of supersonic flow past an elongated axisymmetric body in the presence of an energy release zone between the surface of the body and the shock wave is considered. By means of such zones it is possible to modify the aerodynamic characteristics of the body and influence its flight by decreasing or increasing the drag coefficient (see, for example, [1, 2]) or by creating an additional lift force or aerodynamic moment [3]. A simple model of steady-state flow past a body with an energy source is used to determine what parameters the source should have to permit the maximization of the controlling force (in the present case the lift) for a given energy consumption per unit time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 142–151, July–August, 1990.In conclusion, the author wishes to thank V. P. Stulov for his interest in the work.     

Three-dimensional supersonic flow around a pointed body with upstream energy supply

The effect of a local source of energy on a three-dimensional supersonic flow and the aerodynamic characteristics of a pointed ogival body is numerically studied. The results obtained show that the position of the local source of energy upstream of the body on the axis or its deviation from the axis can affect significantly the aerodynamic characteristics of the body (drag, lift, and pitching moment) and the flight trajectory of the vehicle. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translanted from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 116–121, September–October, 1998.     

Effect of energy release in the shock layer on supersonic flight

The presence of an energy release zone in a supersonic stream leads to the formation of perturbations propagated from the source of energy release [1, 2]. The action of such a stream on a body past which it flows is determined by the strength of the source and the configuration and location of the energy release zone. The dependence of the aerodynamic characteristics of a blunt cone on the parameters of the source of energy release is analyzed on the basis of the results of a numerical integration of the equations of motion of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 178–182, July–August, 1987.The author wishes to thank V. P. Stulov for his interest in the work and useful suggestions.     

Nonlinear dynamics analysis of a two-dimensional thin panel with an external forcing in incompressible subsonic flow

Based on the potential theory of incompressible flow and the energy method, a two-dimensional simply supported thin panel subjected to external forcing and uniform incompressible subsonic flow is theoretically modeled. The nonlinear cubic stiffness and viscous damper in the middle of the panel is considered. Transformation of the governing partial differential equation to a set of ordinary differential equations is performed through the Galerkin method. The stability of the fixed points of the panel system is analyzed. The regions of different motion types of the panel system are investigated in different parameter spaces. The rich dynamic behaviors are presented as bifurcation diagrams, phase-plane portraits, Poincaré maps and maximum Lyapunov exponents based on carefully numerical simulations.     

Study of heat transfer in the separation zones formed in front of supersonic jets in a subsonic carrier flow

The heat transfer taking place between the gas and the surface of the plate in the zone of three-dimensional separation of the turbulent boundary layer in front of a set of supersonic jets injected perpendicularly to a subsonic carrier flow is considered. The aim of this investigation is to establish the main physical characteristics of heat transfer in the separation zones in front of jet obstacles and to obtain the distributions of the local heat-transfer coefficients and the temperature of the thermally insulating wall as functions of the parameters of the carrier flow and the injected jets. Analysis of the experimental results yields certain approximating relationships for the distribution of the local heat-transfer coefficients as functions of the Mach number of the carrier flow M, the Mach number of the jet M_j, the relative boundary-layer displacement thickness _s= _s ^* /d, and the degree of jet superheating T_ojT_o relative to the separation zones in front of supersonic jet obstacles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–72, July–August, 1975.     

Small amplitude pressure wave in subsonic and supersonic bubble flows in convergent-divergent nozzles

This paper makes a theoretical analysis of the propagation phenomena of the small amplitude pressure wave in the subsonic and supersonic bubble flow with a velocity slip between bubble and liquid in the convergent-divergent nozzle. From an analysis of the time-mean flow, the nondimensional parameter $\text{m = {u}\text{2}\text{G}\text{·α(1 ? α)ρ}\text{l}\text{β(2 ? 1/S)/P·[αβS + (1 ? α)βS}{}^2\text{+ α(1 ? α)]}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ corresponds to Mach number is gasdynamics where u_G is the gas velocity, α: the void fraction, ρ_L: the liquid density, P: the pressure, S: the velocity ratio of the gas and liquid flows and β: the proportional constant for the virtual mass. From a theoretical analysis of the small disturbance field, it is clarified that the parameter m also plays an essential and important role as Mach number, although the propagation performance of the disturbance is very complicated compared with that in gasdynamics. It is also shown that the pressure waves are divided into four groups depending on the velocity ratio S. Two of them are rather realistic, but the other two are required of a further investigation in future.     

Delta wing in a subsonic flow

On the basis of experimental wind tunnel research, a topological classification of possible delta wing flow regimes is given and a diagram in angle of attack-sweep angle coordinates is constructed. A regime with two pairs of symmetrically disposed whirlwind like vortices formed on the surface of the wing is detected. The effect of the V-shape of the wing is considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 161–164, March–April, 1994.     

Outflow of an unexpanded jet into counter supersonic and subsonic flows

The article gives the results of an experimental investigation of the geometric structure of an opposing unexpanded jet. It discusses flow conditions with interaction between the jet and sub- and supersonic flows. It is shown that, with the outflow of an unexpanded jet counter to a supersonic flow, there are unstable flow conditions. For stable flow conditions with one roll, dependences are proposed determining the form of a jet in a supersonic opposing flow. A generalized dependence is obtained for the distribution of the pressure at the surface of a body with a jet, flowing out counter to a subsonic flow. The range of change in the determining parameters are the following: Mach numbers at outlet cross section of nozzle, M _a = 1 and 3; Mach numbers of opposing flow, M = 0.6–0.9 and 2.9; degree of effectiveness of jet, n = p _a /p = 0.5–800 (p _a and p are the static pressures at the outlet cross section of the nozzle and in the opposing flow); the ratios of the specific heat capacities, _a = = 1.4; the drag temperatures of the jet and the flow, T_o = T_oa = 290°K.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 89–96, January–February, 1977.     

Distinctive features of the flow past high-speed flight vehicles with air-breathing engines on subsonic,transonic, and low supersonic velocity ranges

The aerodynamic characteristics and distinctive features of the flow past hypersonic integral-layout flight vehicles with air-breathing engines intended for cruise flight in the atmosphere are experimentally investigated. The experiments were conducted on a simplified model designed with regard for the general principles of integration of vehicles of the class considered. The tests were performed in a wind tunnel over the Mach and Reynolds number ranges 0.6 ≤ M ≤ 4 and 6.3 × 10⁶ ≤ Re ≤ 16 × 10⁶, respectively. Balance testing was carried out, the pressure distributions over the vehicle surface were measured, and the flowfields on the model surface were photographed. The effects of mounting a nacelle and contouring the internal duct are considered. The effect of the corrections on the duct flow in the absence of jet modeling is estimated. The results obtained can be used as a basis for developing the aerodynamic configurations of integral-layout flight vehicles, for forming their thrust and aerodynamic parameters under full-scale flight conditions, and for testing computation methods.