Density distribution in rarefied gas flow behind a perforated plate

The relative density distribution in the rarefied CO₂ flow field behind a perforated plate has been experimentally investigated on the range of Knudsen numbers 10^–3 Kn 10^–1. The results of these experiments serve to demonstrate the validity of using the molecular velocity distribution function for determining the relative density on the Knudsen number interval in question. This distribution function was previously employed for calculating the parameters in molecular beams formed by capillary sieves in the free-molecular flow regime [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 183–184, May–June, 1989.     

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.     

Wavy flow of a liquid film in the presence of a cocurrent turbulent gas flow

Wavy downflow of viscous liquid films in the presence of a cocurrent turbulent gas flow is analyzed theoretically. The parameters of two-dimensional steady-state traveling waves are calculated for wide ranges of liquid Reynolds number and gas flow velocity. The hydrodynamic characteristics of the liquid flow are computed using the full Navier-Stokes equations. The wavy interface is regarded as a small perturbation, and the equations for the gas are linearized in the vicinity of the main turbulent flow. Various optimal film flow regimes are obtained for the calculated nonlinear waves branching from the plane-parallel flow. It is shown that for high velocities of the cocurrent gas flow, the calculated wave characteristics correspond to those of ripple waves observed in experiments.     

Investigation of turbulent boundary layers on perforated surfaces in the presence of blowing

The results are given of an investigation of the averaged and fluctuation velocity and concentration fields of the turbulent boundary layers on perforated surfaces in the presence of blowing. The influence of the boundary conditions on the permeable wall on the parameters of the boundary layer is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 32–38, September–October, 1981.     

Stability of fluid flow in the presence of a compliant surface

This paper is concerned with the dynamic behaviour of a thin elastic plate in the presence of flow. The plate is excited by a time varying force applied on a line which is at right angles to the direction of flow. Causality is invoked to make the solution unique. It is found that the system responds differently for flow speeds above and below a critical value. Above this value, a temporal instability occurs and the amplitude of the motion grows with time at each point on the plate. Below this value there are travelling waves upstream of the driver, whilst downstream the behaviour is dominated by a disturbance which does not grow with time at any one position, but nevertheless grows as it is convected downstream. This type of instability is less severe than the temperal one and is of the type generally referred to as convective.     

Symmetric cavitation flow past a wedge in the presence of a source on the wedge or in the flow

A solution is found to the problem of symmetric cavitation flow over a wedge by an ideal incompressible fluid (in accordance with Efros's scheme [1]) in the presence of a point source in the flow or on the wedge. Expressions are obtained for the forces exerted on the source and the wedge by the fluid, the conditions under which there is a negative resistance (thrust) are indicated, and the profiles of the free streamlines are constructed for different values of the flow parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 6, pp. 137–141, November–December, 1979.We thank L. I. Sedov for his interest in the work.     

Viscous flow in a cylindrical vessel in the presence of a rotating disk

Viscous flows in the cylinder-disk system have been investigated theoretically and experimentally, over a broad range of Reynolds numbers Re, H/R_T, and R_k/R_T in order to explore the characteristics of the flow, which is a function of time, the depth of the liquid, the Reynolds number, the radii of the disk and the cylinder, and their geometry (flat, convex or concave disk). The results of comparing the data of numerical and laboratory simulations are presented. The appearance of secondary eddies in the axial region at large Reynolds numbers has been detected and diagrams of flows of different spatial configuration constructed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 33–40, September–October, 1985.     

Fluid flow in a helical vessel in presence of a stenosis

Large arteries are not straight and rather present curvature and torsion. The present study analyzed fluid flow in a helical vessel without and with a stenosis in comparison with an analogous rectilinear vessel. The analysis is performed by three-dimensional numerical simulation of the Navier–Stokes equations under steady conditions considering stenosis as an axially symmetric reduction of vessel lumen. Results show that the double curvature gives rise to persistent secondary motion which combines with the vorticity separated behind the constriction to develop a complex three-dimensional vorticity structure. The curved streamlines and the three-dimensional vortex wake result in a increase of energetic losses in helical vessels. However, the same symmetry break due to the double curvature improves the capacity of self-cleaning and allows a more rapid wash-out of the flowing blood.     

Vibrations of a cylinder in a uniform flow in the presence of a no-slip side-wall

A circular cylinder placed in a uniform flow, and that spans the entire length between two side walls, may experience either parallel or oblique vortex shedding depending on the end conditions. It was shown by Mittal and Sidharth (2014) that the spatio-temporal periodicity of the oblique vortex shedding results in constant-in-time force experienced by the cylinder. On the contrary, parallel vortex shedding leads to fluid force that fluctuates with time. The free vibrations of a circular cylinder, in the presence of a wall, are investigated. For comparison, computations with end walls, where a slip condition on velocity is specified, are also carried out. The Reynolds number, based on the diameter of the cylinder and free-stream speed of the flow, is Re=100. The initial condition for the free vibrations is the fully developed unsteady flow past a stationary cylinder with oblique shedding. It is found that as the amplitude of vibration of the cylinder builds up, the vortices shed from the cylinder align with its axis leading to parallel shedding. The response of the cylinder is associated with two branches: initial and lower. On the lower branch, the response of the cylinder is virtually identical from two- and three-dimensional computations. The flow as well as the response is different on the initial branch and outside the synchronization regime. Forced vibrations confirm the phenomena.     

Mathematical modeling of viscous gas flow in a doubly connected volume with perforated walls

A numerical method is proposed for computing viscous gas flow in an initial doubly connected domain which is a volume having perforated walls and enclosing a sphere. The types of subdomains (finite volumes) into which the initial domain can be divided are considered. For each type of finite volume, there is a curvilinear coordinate system. Results of flow computation for Re = 100 and 500, and M = 0.6 are given.     

Mathematical modeling of flow in sound-absorbing structures of resonance type in the presence of a grazing flow

Sound-absorbing structures of resonance type are studied on the basis of integration of the unsteady Reynolds-averaged Navier-Stokes equations. The formation of the boundary layer over a sound-absorbing panel is compared with that on a flat plate in the presence of an incident wave. The dependence of the panel reflection coefficient on the presence of a grazing flow and the boundary layer thickness is investigated. The results of the numerical experiment are compared with the available experimental data.     

Stability of plane Couette-Poiseuille flow in the presence of a magnetic field

Within the framework of the linear theory, a study was made of the hydrodynamic stability of the Couette-Poiseuille flow of a viscous conducting fluid in a transverse magnetic field. The total spectrum of small perturbations was studied for characteristic Hartmann numbers. A classification of perturbations was made in accordance with the behavior of their phase velocity with large wave numbers. Dependences of the critical Reynolds number and of the critical wave number on a parameter characterizing the relationship between the parts of the flow, determined by the motion of plates and by the pressure gradient, were obtained. The character of the asymptotic dependences at large Hartmann numbers was clarified. The article gives an example of a neutral curve formed by two branches of the neutral fluctuations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 11–17, November–December, 1970.The author thanks M. A. Gol'dshtik for his interest in the work, V. A. Sapozhnikov for his useful observations, and V. N. Shtern for his help in the work and for his valuable remarks.     

Stability of Poiseuille flow in the presence of a longitudinal magnetic field

The stability of the plane flow of an electrically conducting fluid with respect to small perturbations was studied at large Reynolds numbers in the presence of a longitudinal magnetic field. The dependence of the critical Reynolds number on the electrical conductivity is investigated. At large Reynolds numbers, a new branch of instability and a sudden change in the critical Reynolds numbers is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 45–53, May–June, 2008.     

Magnetohydrodynamic flow past a plate by the presence of radiation

An analysis of the unsteady magnetohydrodynamic flow of a viscous and electrically conducting fluid past to a plate by the presence of radiation is considered. The fluid is a gray, absorbing-emitting but nonscattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. Analytical solutions for the mean temperature, velocity and the magnetic field have been derived and the effect of the radiation on the temperature is discussed. Received on 20 November 1997     

Unsteady flow through a porous medium in the presence of chemical reactions

The underground leaching of uranium ores and nonferrous and precious metals under natural conditions is one of the latest methods of mineral extraction [1]. It consists of pumping into isolated formations through reaction wells an acid solution which upon reacting with the rock yields a readily soluble salt that can be brought to the surface with water through extraction wells. Together with the acid solution, it is also possible to pump in other reactants to participate in the chemical reaction, for example, gases such as oxygen. Moreover, secondary gases may be formed as a result of the chemical reaction. Thus, the chemical reaction proceeds in the presence of a one or two-phase flow in the porous medium. The mathematical modeling of these processes is usually based on the approximation of one-phase flow without allowance for the changes in the porosity and permeability of the medium as a result of the reaction [2]. In this paper we solve the problem of unsteady flow in the presence of a chemical reaction for a two-phase system taking into account the changes in the flow parameters of the porous medium. The condition of stability of the plane reaction front is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 82–87, January–February, 1987.The author is grateful to R. I. Nigmatulin for his useful comments and interest in the work.     

Unsteady stagnation-point flow of a Newtonian fluid in the presence of a magnetic field

The unsteady stagnation-point flow of a viscous fluid impinging on an infinite plate in the presence of a transverse magnetic field is examined and solutions are obtained. It is assumed that the infinite plate at y=0 is making harmonic oscillations in its own plane. A finite difference technique is employed and solutions for small and large frequencies of the oscillations are obtained for various values of the Hartmann's number.     

Problem of heavy fluid flow above a plate in the presence of a vortex

The free-surface flow of a heavy incompressible inviscid ideal fluid along a semi-infinite plate with the formation of a vortex near its edge is investigated. Solitary wave type flows are considered. A unique solution with a free vortex is obtained.     

Change in the parameters of a supersonic flow in the presence of transverse blowing

A study has been made of the flow formed in a supersonic nozzle when gas is blown in a transverse jet into an expanding supersonic flow. Measurements were made of the total and static pressures of the flow at several sections of the nozzle. It was established that, depending on the relative flow rate = m_j/(m_j+ m₀) of the blown gas (m_jand m₀ are the flow rates of the blown gas and the main flow, respectively), there exist two flow regimes with different dependences of the Mach number of the flow. At small , the experimental flow parameters correspond satisfactorily to the parameters calculated in a one-dimensional model with a narrow mixing layer near the blowing section. Agreement was observed at flow rates less than a certain ^*, this critical value being determined in the model as the flow rate at which the flow after mixing becomes sonic. In the experiments at large flow rates of the blown gas, ^* < < 1, the value of M for the flow hardly depends on and corresponds to the calculated value of M for a supersonic flow having the velocity of sound near the blowing section. A scheme is proposed for calculating the flow in a nozzle with transverse blowing in the supersonic part; it describes satisfactorily the experimental results in the complete range of blown-gas-main-flow flow rate ratios (0 1) over the complete length of the nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 188–192, May–June, 1984.     

Couette flow of a nematic liquid crystal in the presence of a magnetic field

Summary We derive the equations governing helical flow of a nematic liquid crystal in the presence of a magnetic field. These equations are used to investigate Couette flow, and a study is made of the large number of possible solutions.