One-dimensional transonic gas flow in a wind tunnel with perforated walls

Near-sonic inviscid gas flow in the working section of a wind tunnel with perforated walls is investigated in the context of the one-dimensional theory with Darcy's boundary condition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 143–148, November–December, 1988.     

The study of the induction of subsonic wind tunnels with an axisymmetric working part

For the case of small perturbations of the velocity on the boundary of the flow and arbitrary degree of perforation of the wall of the wind tunnel which is constant along its length, a solution has been found for the axisymmetric boundary-value problem of subsonic flow around a thin body of revolution in perforated boundaries. The boundary condition connects the tangential component of the perturbed velocity and the component normal to the wall, and has a general form for the whole boundary. From the solution obtained, the optimum degree of perforation of the wall is found for which distortion of the pressure coefficient on the surface of the model is a minimum in comparison with the unbounded flow round the body. The questions of the induction of the walls of the working part of the wind tunnel, the formulation of the boundary condition, and the determination of the corrections to the aerodynamic characteristics of the model are considered in a number of studies [1–5]. Lately a promising method was been worked out for reducing the influence of the walls directly in the process of experiment by regulating the parameters of the gas near the boundary in such a way that they correspond to the parameters in flow round the same body by an unbounded flow [3, 5]. However, the design properties of many working tunnels do not permit this method to be applied. The induction of such tunnels as these can be reduced only by the choice of an optimum degree of perforation of the walls. In the articles [6–8] there is a study of the effect of perforated boundaries on the flow round a profile, the degree of perforation in [7] being assumed to be small.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–154, January–February, 1985.The author is grateful to V. M. Neiland for his constant attention to the study and for discussion of the results.     

Transonic flows around an airfoil in wind tunnels with porous walls

A study is made of two-dimensional transonic flows of gas around an airfoil in the working part of a wind tunnel with porous walls. The values of the flow parameters are determined by the numerical solution of a boundary-value problem for the equation of the velocity potential; this problem simulates the gas flow around the profile in the tunnel with porous walls. The obtained results are then used to construct an asymptotic theory of the influence of the wind-tunnel height and the Mach number M of the flow in it on the characteristics of the flow around the airfoil.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1980.     

Flow blockage in model testing in the perforated working section of a wind tunnel as M∞→1

The third flow blockage regime associated with the finite length of the perforated tunnel walls is investigated. In the case of infinitely long permeable boundaries blockage is impossible, since all the air displaced by the body can flow out through the walls even when their permeability is very low. If, however, the length of the permeable boundary is finite, blockage is in principle possible, given a low degree of permeability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 151–157, May–June, 1991.The authors are grateful to Yu. B. Lifshits for useful comments.     

Heat mass transfer in a turbulent layer above permeable membranes

The temperature and concentration fields in a boundary layer above perforated membranes are presented, and their relationship with the velocity fields given in [1] is established. Measurements of the thermal state of membranes are made with various geometric and thermophysical properties and various coolant drafts. Empirical formulas are also presented for thermal flux and temperature of the permeable walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 22–31, July–August, 1973.     

Self-aeration and turbulence in a stepped channel: Influence of cavity surface roughness

The strong interactions between free-surface flows and atmospheric surroundings may lead to substantial air–water mixing with void fractions ranging from zero in clear-water to 100%. In this study, the air–water flow properties were studied in a large stepped water channel operating at large Reynolds numbers. Interactions between free-surface and cavity recirculation were systematically investigated in the skimming flow regime. Some surface roughness was introduced on the cavity walls and identical experiments were performed with several configurations. Basic results demonstrated some influence of step surface roughness on the flow properties leading to some counter-intuitive finding. The presence of cavity roughness was associated with higher flow velocities and comparatively lower turbulence levels. Distributions of bubble/droplet chords spanned over several orders of magnitude without significant influence of the cavity roughness. The distributions of turbulence levels and bubble count rates showed some correlation and highlighted strong interactions between entrained particles (bubbles, drops) and the flow turbulence.     

Turbulent flow of gas in a curvilinear channel in the presence of suction from a separation region

Integral parameters that characterize reversible and irreversible changes in the flux of the total pressure in channels with perforated walls are introduced. An experimental investigation was made of subsonic gas flow in curvilinear channels of rectangular cross section in the presence of suction of gas from a separation region of the flow formed on an internal (convex) strongly curved wall of the channel. The optimal position of the suction slit was determined and it was shown to be possible to reduce appreciably the loss in the channel and improve its gas-dynamic characteristics. Two-dimensional turbulent flow of an incompressible fluid in curvilinear channels in the presence of suction was simulated numerically. The mathematical model is based on the complete system of Navier-Stokes equations, additional differential equations for the energy of the turbulence and the rate of its dissipation, special correction equations to take into account the curvature of the streamlines, and model boundary conditions for the sections of the walls through which the suction of the fluid takes place.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza, No. 4, pp. 72–80, July–August, 1984.     

Pulsating regime corresponding to an obstacle in a stationary inhomogeneous flow

The pulsating regime produced by the presence of a cylindrical cavity in a stationary inhomogeneous supersonic flow is simulated mathematically. The system of equations for an inviscid thermally nonconducting gas is solved by a numerical method based on a two-step difference scheme of second order of approximation. This method makes it possible to calculate in each time step the complete flow field at once, which makes it possible to follow the development of the nonstationary flow, which in the present case is a pulsating flow. The flow pattern in the pulsating regime is studied in detail. The pressure pulsations in the cavity are due to the alternating passage through it of shock waves and rarefaction waves, and the pulsations are nonlinear. The influence of the basic parameters on the characteristics of the pulsating flow is studied and some estimates are made.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 64–71, September–October, 1979.     

Heat transfer from gas escaping from the cavity of an underground explosion

A study is made of the influence of heat transfer on the dynamical characteristics of gas escaping from the cavity of an underground explosion. Numerical calculations are made for the plane and spherically symmetric cases. The dynamical characteristics (density, temperature, flow velocity) are compared for isothermal, isentropic, and adiabatic flow and flow with heat transfer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 80–86, March–April, 1984.     

Investigation of transonic bounded gas flow past three-dimensional slender bodies

The pressure coefficient distributions induced in the process of a bounded gas flow past a schematized vehicle of the Khotol type are obtained for various transonic regimes in a wind tunnel with a perforated working section as a result of simultaneously solving the boundary-value problems for the near and far flow fields. These distributions are compared with the pressure coefficient distributions in the case of unbounded flow past the body. The additional pressure coefficient induced by the tunnel walls is calculated for subsonic flow past a vehicle in a cylindrical wind tunnel of large radius. The calculation results are consistent with the asymptotic Malmuth theory for subsonic velocities.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 149–158, March–April, 1995.     

On the length of annular jets interacting with an ambient medium

Annular jets of immiscible fluids are the subject of intense study. Particularly topical in applications are jets in the shape of a right circular cylinder. The space within annular jets may be reduced or increased by the influence of transverse forces and also by hydrodynamic instability of the jet flow. Twisting of the jet tends to make it close up. In the present paper, a study is made of ways of obtaining annular jets with nearly cylindrical shape and the greatest cavity length possible, allowance being made for gravity, capillary pressure surface forces, a pressure difference between the two sides of the phase interface, and the interaction with the ambient medium. A study is made of the influence of the velocity of the fluid and the medium in the initial section on the shape of the joint steady axisymmetric flow of immiscible viscous phases, including the shape of the middle surface of the annular jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–11, November–December, 1983.     

Experimental investigation of flow in a trench

An experimental investigation was made of the flow of a viscous incompressible liquid in a trench of square transverse cross section, using a laser Doppler velocimeter. The investigation was made with two values of the Reynolds number Re, corresponding to laminar and turbulent flow conditions in the channel. The experimental data show that a core with a constant vorticity is formed in the trench, that a jet propagates near the walls of the trench, and that there are secondary eddies in the corners of the trench. The motion of a viscous liquid in a trench of rectangular cross section is part of a broad class of breakaway flows. Experimental data on the investigation of flow in trenches are extremely few. A majority of the existing information is limited to visual observations [1–4]. In [2, 5, 6] the question of the unstable character of flow in trenches was discussed. Quantitative measurements of stable eddy flows in trenches were made in [7–9] using a thermoanemometer, and in [7] measurements were made of the pressure at the bottom and walls of trenches; there are data on the distribution of the velocity in the middle sections of trenches. In [8] the mean velocity, the intensity of the turbulence, and the stress of the turbulent flow were obtained in several sections parallel to the side walls of the trench, In [9] a measurement was made of the velocities also in two cross sections of a trench in which one component of the velocity prevails. A brief analysis of the existing experimental results shows that these data are insufficient to form a detailed representation of the character of flow in a trench.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 76–86, March–April, 1976.     

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.     

On the heating effect in gas flow over deep cavities

The results of experiments on hollow models in a stationary gas flow are analyzed. Certain quantitative characteristics of the observed temperature rise above the stagnation temperature in the flow are determined. It is shown that this effect is associated with the formation in the cavity of shock waves, the dissipation of energy in which leads to gradual heating of the gas and the model walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 8–18, May–June, 1971.     

Boundary-layer flow characteristics on perforated plates and a method of approximately computing their temperature under combined cooling

Results of an experimental investigation of the heat elimination from perforated plates to cooling air during its motion along walls and partial drainage through the perforations are elucidated. Boundary-layer characteristics on perforated plates, their thermal state, and their efflux coefficients are presented for a set of orifices. An approximate method to compute the temperature of the permeable wall under combined cooling is given and its domain of application is estimated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 182–187, March–April, 1977.     

Sensitivity of plane Poiseuille flow to vibration of the channel walls

An accurate quantitative investigation of the disturbances induced in a Poiseuille flow by vibration of the walls is made on the basis of the Fourier transformation method.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 12–19, July–August, 1992.     

Dynamics of a flat cavity in a low-viscosity liquid

The problem of the motion of a cavity in a plane-parallel flow of an ideal liquid, taking account of surface tension, was first discussed in [1], in which an exact equation was obtained describing the equilibrium form of the cavity. In [2] an analysis was made of this equation, and, in a particular case, the existence of an analytical solution was demonstrated. Articles [3, 4] give the results of numerical solutions. In the present article, the cavity is defined by an infinite set of generalized coordinates, and Lagrange equations determining the dynamics of the cavity are given in explicit form. The problem discussed in [1–4] is reduced to the problem of seeking a minimum of a function of an infinite number of variables. The explicit form of this function is found. In distinction from [1–4], on the basis of the Lagrauge equations, a study is also made of the unsteady-state motion of the cavity. The dynamic equations are generalized for the case of a cavity moving in a heavy viscous liquid with surface tension at large Reynolds numbers. Under these circumstances, the steady-state motion of the cavity is determined from an infinite system of algebraic equations written in explicit form. An exact solution of the dynamic equations is obtained for an elliptical cavity in the case of an ideal liquid. An approximation of the cavity by an ellipse is used to find the approximate analytical dependence of the Weber number on the deformation, and a comparison is made with numerical calculations [3, 4]. The problem of the motion of an elliptical cavity is considered in a manner analogous to the problem of an ellipsoidal cavity for an axisymmetric flow [5, 6]. In distinction from [6], the equilibrium form of a flat cavity in a heavy viscous liquid becomes unstable if the ratio of the axes of the cavity is greater than 2.06.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 15–23, September–October, 1973.The author thanks G. Yu. Stepanov for his useful observations.     

Unsteady reflection of a shock wave from a body with a cylindrical recess

In a number of cases of supersonic flow past bodies with recesses pulsations in the flow arise [1–3]. Experiments [4, 5] indicate that stabilization of the steady supersonic flow past the body with a recess on which a shock wave is incident takes place after a series of oscillations of the bow wave. Numerical calculation of the interaction of a supersonic jet with a cylindrical cavity [6] reveals that damped pressure pulsations arise inside the cavity if the jet is homogeneous, and undamped pulsations it is inhomogeneous. The authors explain the damping of the pulsations by the influence of artificial viscosity. This paper investigates experimentally and theoretically (by numerical methods) the oscillations of the bow shock wave and the parameters of the flow behind it in the case of unsteady reflection of a shock wave from a body with a cylindrical recess turned towards the flow. The problem is posed as follows. A plane shock wave with constant parameters impinges on a cylinder with a cavity. The unsteady flow originating from this interaction is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 199–202, September–October, 1984.     

Influence of nozzle profile on the characteristics of a gas-dynamic laser

The results are given of numerical profiling and analysis of the influence of nozzle shape and the gas-dynamic parameters on the characteristics of gas-dynamic lasers. Investigation of the two-dimensional nonequilbrium flow in a family of similar nozzles and nozzles with different angles of inclination of the contracting part show that it is expedient to choose a shape of the subsonic part that ensures a straight sonic line. Relationships between the geometrical parameters of the subsonic and transonic part of the nozzle are recommended which ensure separationless flow and a shape of the sonic surface that is nearly flat. A parametric investigation was made of the supersonic section of two classes of planar gas-dynamic laser nozzles constructed on the basis of uniform and symmetric characteristics at the exit. The parametric investigations of the influence of the degree of expansion, the total pressure and the temperature, and also the gas composition show that the smallest losses of useful vibrational energy in the cavity are achieved for nozzles constructed on the basis of uniform characteristics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 163–167, November–December, 1982.     

Shock-initiated implosion of an elliptical cavity and detonation in a liquid layer

Many papers [1–9] have been devoted to the dynamical analysis of bubble implosion in a liquid layer. Experiments have shown that an initially circular cavity is displaced or transformed into an elliptical cavity during the implosion process due to instability, whereupon its further contraction produces cumulative jets. This problem is important in the study of surface wear in cavitation flow [7] and in the analysis of the impact sensitivity of liquid explosives [1–6]. The onset of accumulation is conveniently investigated by starting with an elliptical cavity or by displacing a circular cavity relative to the impact axis, thereby creating an asymmetrical pressure field about the center of the cavity. In the present article certain theoretical notions are advanced with regard to the onset of the cumulative jet in an elliptical or displaced cavity and its influence on the ignition of liquid explosives due to the formation of minute droplets [4] in the adiabatically heated gas inside the cavity. Experimental data on the jet formation time and the frequency of nitroglycerin detonations qualitatively support the theoretical predictions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 78–85, September–October, 1971.