Transverse subsonic flow past a cylinder

At around the critical Reynolds number Re = (1.5–4.0)·10⁵ there is an abrupt change in the pattern of transverse subsonic flow past a circular cylinder, and the drag coefficient C_x decreases sharply [1]. A large body of both experimental and computational investigations has now been made into subsonic flow past a cylinder [1–4]. A significant contribution to a deeper understanding of the phenomenon was made by [4], which gives a physical interpretation of a number of theoretical and experimental results obtained in a wide range of Re. Nevertheless, the complicated nonstationary nature of flow past a cylinder with separation and the occurrence of three-dimensional flows when two-dimensional flow is simulated in wind tunnels do not permit one to regard the problem as fully studied. The aim of the present work was to make additional experimental investigations into transverse subsonic flow past a cylinder and, in particular, to study the possible asymmetric stable flow regimes near the critical Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–157, March–April, 1980.     

Aerodynamic characteristics of permeable disks at subsonic free-stream flow velocities

A large number of investigations have been carried out to study the aerodynamic characteristics of grids and permeable plates completely covering a pipe section [1]. The theoretical bases of the external aerodynamics of permeable bodies are established in [2], where the concept of a uniformly permeable surface is introduced and the problem of flow past a permeable plate at a small angle of attack is solved. Papers [3, 4] are devoted to the solution of problems of a jet flow of ideal incompressible fluid past a permeable wedge and a plate. The flow past a wedge with a high degree of permeability at low subsonic velocities was investigated theoretically and experimentally in [5]. Papers [6, 7] are devoted to the experimental investigation of the aerodynamic characteristics of plates and disks at low subsonic velocities. The results of the experimental investigations of permeable bodies are given in [8]. In the present paper the aerodynamic characteristics of permeable disks positioned perpendicular to the direction of the oncoming flow are investigated experimentally in a wide range of variation of the perforation parameters and the subsonic free-stream flow velocities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 123–128, July–August, 1986.     

Detached flows past a cylinder with a flat end

In the framework of the Navier-Stokes equations, a numerical solution is found to the problem of longitudinal (axisymmetric) flow of a viscous perfect heat conducting gas past a cylinder with a flat front end at subsonic and transonic velocities of the oncoming flow. The flow in the neighborhood of the corner of the cylinder is investigated and a study made of the occurrence and development of detached flow along the side of the cylinder. Tie heat fluxes to the surface of the cylinder are determined, and the influence of the temperature of the wall of the cylinder on the development of the separation is found. The investigations yield the critical Reynolds number Re₀ for the occurrence of a detached flow as a function of the Mach number of the oncoming flow for the investigated bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–10, March–April, 1979.I am grateful to Yu. A. Dem'yanov for discussing the work and for a number of valuable comments.     

Transonic crossflow of condensing wet steam past a cylinder

The shadow and interferometric methods and the laser probe method are used to investigate crossflow past a cylinder on the free-stream Mach number interval M _a =0.5–1.2 for subcritical Reynolds numbers Re _d and various initial steam states. Detailed pressure distributions are obtained and the pressure fluctuations on the cylinder surface are measured. The dependence of the Strouhal number on the velocity and thermodynamic parameters of the flow are determined. In single-phase steam flow past a cylinder the greatest fluctuations occur in the separation zone in regimes corresponding to transonic drag crisis. It is shown that spontaneous condensation in the turbulent wake and local supersonic zones may cause an increase in the periodic pressure fluctuations in the separation zone, the maximum increase in the fluctuations being noted when the critical pressure ratio is reached at the rear of the cylinder. The initial wetness of the steam has the greatest effect on the periodic separation characteristics at subsonic flow velocities, and in the case of supersonic flow leads to a substantial increase in the level of the low-frequency pressure fluctuations at the front of the cylinder.(deceased)Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 118–138, November–December, 1994.     

Plane problem of uniform flow of a two-layer fluid past a circular cylinder

An explicit solution is found for the problem of uniform horizontal flow of a two-layer fluid of infinite depth past a circular cylinder. The cylinder axis is perpendicular to the flow. The problem is solved within a linear formulation. The solution of the problem is expressed in the form of rapidly converging series with coefficients determined from a recurrence relation. The first seven terms of the series yield the values of the hydrodynamic loads with a relative accuracy of 10^–6. The results are in good agreement with the known values for similar problems in a homogeneous fluid. Tables of the lift and wave drag are given for homogeneous and two-layer fluids.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–97, January–February, 1996.     

Flow past a thin profile in a channel with permeable working part

An exact solution is obtained to the problem of flow of an ideal incompressible fluid past a thin profile in a straight channel. The channel walls are continuous except for the working part, where they are permeable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 180–185, July–August, 1982.I thank Yu. B. Lifshitz for constant interest in the work.     

Self-similar problems of propagation of an extended hydrofracture in a permeable medium

The propagation of an extended hydrofracture in a permeable elastic medium under the influence of an injected viscous fluid is considered within the framework of the model proposed in [1, 2]. It is assumed that the motion of the fluid in the fracture is turbulent. The flow of the fluid in the porous medium is described by the filtration equation. In the quasisteady approximation and for locally one-dimensional leakage [3] new self-similarity solutions of the problem of the hydraulic fracture of a permeable reservoir with an exponential self-similar variable are obtained for plane and axial symmetry. The solution of this two-dimensional evolution problem is reduced to the integration of a one-dimensional integral equation. The asymptotic behavior of the solution near the well and the tip of the fracture is analyzed. The difficulties of using the quasisteady approximation for solving problems of the hydraulic fracture of permeable reservoirs are discussed. Other similarity solutions of the problem of the propagation of plane hydrofractures in the locally one-dimensional leakage approximation were considered in [3, 4] and for leakage constant along the surface of the fracture in [5–7].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 91–101, March–April, 1992.     

Estimation of the hate of flow in porous media

In a number of problems of the theory of flow in porous media it is particularly important to find the integral characteristics of the flow for regions that constitute extended stream tubes. (Such a region can be imagined as the result of the continuous deformation of a cylinder whose lateral surfaces are impermeable while the bases are surfaces of constant pressure, the inlet and outlet of the flow. In the plane case the cylinder becomes a rectangle.) Usually, the flow rate Q is to be found from the difference of head H. In some cases it possible to obtain upper and lower bounds for the flow rate by varying the flow region, the flow resistance field or the form of the flow law [1–4]. The aim of the present study is to find the shape of the region of fixed volume (in the plane case area) which for given constraints realizes an extremum of the steady-state flow rate. It is shown that the extremality requirement leads to an additional local condition on the unknown part of the boundary. A class of plane problems for which the resulting boundary-value problem with an unknown boundary is effectively solved is identified. Examples are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 80–87, March–April, 1986.     

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.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

Disturbances, lift and drag forces due to the translation of a horizontal circular cylinder in stratified water

The uniform flow of a fluid with a narrow stratified layer past a horizontal circular cylinder is studied experimentally. This is done through a Galilean transformation of the problem to a situation where the cylinder moves, and the water is at rest. Measurements were made of the interfacial waves formed behind the cylinder towed horizontally at constant speeds. A specially designed stiff force measuring system with a resolution of 0.5 mN measured the drag and lift forces exerted upon the cylinder. When fluid buoyancy forces dominate, it is shown that the increased drag force and other pertinent properties of the problem are efficiently described in terms of a densimetric Froude number, and explicitly independent of the Reynolds number. Lee-waves were detected at all towing speeds less than the speed of long interfacial gravity waves. Maximum wave heights occurred at half of that speed. Vortex shedding was hampered for speeds less than 0.65 of the long interfacial wave speed. Recommended values of increased drag-coefficients are given. The importance of a finite thickness of the stratified layer is documented. The critical densimetric Froude number defining when stratification starts to be important becomes lower with increasing layer thickness. And, with the cylinder located in the stratified layer, the drag-force does not increase although internal waves of appreciable height develop. The situation modelled has its engineering counterpart in the flow past submerged tube bridges.The research presented here is based on parts of my doctoral work carried out during 1988–1990, partially supported by the Norwegian Road Research Laboratory.     

Mixed Convection in Non-Newtonian Fluids Along an Isothermal Vertical Cylinder in a Porous Medium

Mixed convection in power-law type non-Newtonian fluids along an isothermal vertical cylinder in porous media is studied. The problem is solved by means of a finite difference method for the case of uniform wall temperature. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5–1.5.     

Three-dimensional thin viscous shock layer in the absence of planes of symmetry in the flow

The basic laws of viscous homogeneous gas flow at high supersonic speeds past smooth blunt bodies with a permeable surface are investigated within the framework of the thin viscous shock layer model. An efficient numerical method of solving these equations, which makes it possible to consider cases of flow past bodies at angles of attack and slip, when there are no planes of symmetry in the flow, is proposed. Some results of calculating the flow past a triaxial ellipsoid with an axial ratio of 103n73 at angles of attack =0–45° and slip angles =0–45° over a broad interval of Reynolds numbers are presented as an example. The effect of the principal determining parameters of the problem on the flow structure in the shock layer and the surface friction and heat transfer coefficients is analyzed. An expression for calculating the heat fluxes to the impermeable surface of smooth blunt bodies in a supersonic homogeneous viscous gas flow over a broad interval of Reynolds numbers is proposed on the basis of the solutions obtained and the results of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 150–158, March–April, 1989.     

Rotating cylinder in a flowing viscous incompressible fluid

New results are obtained in the problem of flow of a viscous fluid past a rotating cylinder by numerical solution of the Navier—Stokes equations for Reynolds numbers 10 Re 100. The drag and lift have been calculated. The oscillatory flow regime in the wake behind a fixed cylinder is investigated for Re = 80. The Strouhal number for auto-oscillations is 0.16.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–21, January–February, 1982.I am grateful to G. I. Petrov and V. Ya. Shkadov for constant interest in the work and helpful discussions.     

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.     

Solution of a problem of flow in a porous medium with limiting gradient

For the law of flow in a porous medium with limiting gradient studied previously in [1], an exact solution is found for the problem formulated in [2] of the plane steady motion of an incompressible fluid in a channel with a rectangular step. Particular cases of the solution obtained are given; these represent the solutions of the problem of flow past a broken wall and of motion from a point source in a strip.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–78, January–February, 1985.     

Laminar flow between porous disks for intense homogeneous asymmetric inflow and outflow

In [1–3], a class of self-similar solutions was considered for the flow of incompressible fluid in a plane channel with porous walls, through which there is homogeneous symmetric inflow or outflow. An analogous class of self-similar solutions for flow between porous disks with natural homogeneous conditions at the periphery was considered in [4], where the asymptotic behavior of these solutions at a small Reynolds number of the outflow R was investigated, and the limiting form of the solution for symmetric outflow with R= was noted. In the present paper, the boundary-function method is applied to the singular problem corresponding to the flow between porous disks for asymmetric inflow and outflow characterized by large R.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 13–19, November–December, 1976.     

Slow motion of a permeable sphere in a viscous fluid

Flow of a viscous fluid past a permeable sphere is investigated in the Stokes approximation. An example of such a flow is flow past a perforated or meshed spherical surface. The elements of the sphere contain rigid impermeable sections and openings through which the fluid can flow. The interaction of the sphere with the flow is described by two drag coefficients, which established the connection between the flow velocity of the fluid at the sphere and the stress tensor on it. The dependence of the flow pattern and also the drag and flow rate of the fluid on these coefficients is investigated. In special cases, the obtained solution describes flow past solid and liquid spheres.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 165–167, September–October, 1982.     

Oblique shock/bow shock interference in rarefied flow past a cylinder

Direct statistical simulation is employed to study the flow of a rarefied diatomic gas past a cylinder in the presence of an incident oblique shock. The distinctive features of the formation of a high-pressure compressed-gas jet in the case of interference between the oblique shock and the bow shock are studied for different Reynolds numbers. The variation of the pressure and the heat transfer to the surface with the shock position relative to the center of the cylinder, the Reynolds number, and the surface temperature is analyzed. The results obtained are compared with the experimental data and the results of the numerical solutions of the Euler and boundary layer equations. Free-molecular-to-continuum flow transition is demonstrated with reference to the example of interference-free flow past a cylinder.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 171–180. Original Russian Text Copyright © 2004 by Gusev and Erofeev.     

Natural convection in a porous bed with a permeable boundary

Natural convection in a vertical porous bed heated from the side was investigated numerically for the case where mass transfer occurs between the bed and the surroundings. On the permeable part of the boundary we assign conditions of the first or second kind for the pressure, which corresponds to a free surface or a thin permeable skin. We obtained information about the structure and regimes of steady convection in the bed and the dependences of the mean and local heat-transfer characteristics on the Rayleigh number. The results are compared with the results of [1–3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 145–148, July–August, 1978.The author thanks V. I. Polezhaev for supervision of the work.