Dynamics of a fluid sheet on a curved rigid wall with allowance for phase transformation on the free surface

The flow of a three-dimensional sheet on a curved wall is considered. Gravity and surface tension forces act on the sheet while a droplet stream falls on its free surface. The systems of equations of viscous incompressible fluid dynamics on a curved rigid surface and the boundary conditions with allowance for the falling droplet stream are formulated. The problems of steady axisymmetric motion of the sheet on cylindrical and conical surfaces are considered. The effect of the curvature of the rigid wall on the solution is examined. Kharkov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 42–50, July–August, 1994.     

Force interaction of a sphere and a viscous liquid in the presence of a wall

The problem of the force interaction of a vibrating sphere and a viscous liquid bounded from outside by a rigid wall at rest is studied under the assumption that the largest displacement of the sphere is small compared to its radius and the radius of the sphere is small compared to the distance between the sphere and the wall surface. The liquid flow and the force exerted by the liquid on the sphere are determined. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol 41, No. 1, pp. 57–62, January–February, 2000.     

Stability and nonlinear wavy regimes in downward film flows on a corrugated surface

The linear and nonlinear stability of downward viscous film flows on a corrugated surface to freesurface perturbations is analyzed theoretically. The study is performed with the use of an integral approach in ranges of parameters where the calculated results and the corresponding solutions of Navier-Stokes equations (downward wavy flow on a smooth wall and waveless flow along a corrugated surface) are in good agreement. It is demonstrated that, for moderate Reynolds numbers, there is a range of corrugation parameters (amplitude and period) where all linear perturbations of the free surface decay. For high Reynolds numbers, the waveless downward flow is unstable. Various nonlinear wavy regimes induced by varying the corrugation amplitude are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 110–120, January–February, 2007.     

Mathematical simulation of mixed convection in a vertical cylindrical vessel

Mixed laminar convection in a vertical cylindrical vessel is investigated. A flow model is developed and the temperature distribution in the core is obtained for a given specific heat flux on the lateral surface. The results of the analytic simulation are compared with numerical solutions of the problem for a specific heat flux which is constant on the lateral wall or varies linearly with height. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 9–17, November–December, 1998.     

Bifurcation of self-similar solutions describing a thermocapillary flow of a fluid in a thin layer

Thermocapillary flows of a fluid in a lamina with a rigid lower wall and a free upper surface, along which the temperature gradient is given in the radial direction, are investigated for large Marangoni numbers. Self-similar solutions which describe the axisymmetric flow regimes of a fluid without the circumferential velocity component are constructed numerically and asymptotically for a system of Prandtl equations. It is shown that a pair of new self-similar flow regimes of a fluid with rotation branches off from the regimes obtained. The new regimes ere calculated numerically and asymptotically. Rostov State University, Rostov-on-Don 344090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 137–142, May–June, 1999.     

Turbulent flow past a transverse cavity with inclined side walls. 1. Flow structure

The process of vortex formation in a cavity with inclined walls, which has a moderate aspect ratio, is experimentally studied, and the distribution of pressure coefficients is measured. The angle of inclination of the side walls ϕ is varied from 30 to 90°. It is found that the flow in the cavity becomes unstable in the range of inclination angles ϕ = 60–70°. Flow reconstruction occurs, which substantially alters the surface-temperature and static-pressure distributions. Large changes in these characteristics and their nonuniform distributions for these angles are observed across the cavity on its frontal wall and on the bottom. For small angles (ϕ = 30 and 45°), the pressure on the rear wall drastically increases, which leads to a small increase in pressure averaged over the entire cavity surface. __________ Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 68–76, September–October, 2006.     

Wave flows in a thin layer of a viscous liquid. Influence of a constant electric field

The influence of a constant transverse electric field on the dynamics of longwave, weakly nonlinear flow of a viscous dielectric liquid film down a vertical wall is studied. An amplitude integrodifferential equation in partial derivatives of the Kuramoto-Sivashinskii equation type, which describes the behavior of the free surface of the layer, is derived using the method of multiscale stretching. In the case considered, the potential energy of the electric field is a source of longwave perturbations, but, on the whole, secondary regimes are apparently nonlinearly steady. Probably, the electric polarization effects studied can be used as a factor that governs the dynamics of film flow. Computer Center, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 90–97, January–February, 1998.     

Force Action of a Body with a Permeable Boundary on a Wall in a Fluid

The ideal fluid flow due to fluid penetration through the boundary of an infinitely long solid cylinder in contact with a solid wall is determined. A formula is derived according to which the force exerted by a finite-length part of the cylinder on the wall is directed into the wall and can thus have an arbitrarily large absolute value. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 82–84, January–February, 2006.     

Mixed Convection in a Vertical Porous Channel

A numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces is studied by taking into account the effect of viscous and Darcy dissipations. The flow is modeled using the Brinkman–Forchheimer-extended Darcy equations. The two boundaries are considered as isothermal–isothermal, isoflux–isothermal and isothermal–isoflux for the left and right walls of the channel and kept either at equal or at different temperatures. The governing equations are solved numerically by finite difference method with Southwell–Over–Relaxation technique for extended Darcy model and analytically using perturbation series method for Darcian model. The velocity and temperature fields are obtained for various porous parameter, inertia effect, product of Brinkman number and Grashof number and the ratio of Grashof number and Reynolds number for equal and different wall temperatures. Nusselt number at the walls is also determined for three types of thermal boundary conditions. The viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. The Darcy and inertial drag terms suppress the flow. It is found that analytical and numerical solutions agree very well for the Darcian model. An erratum to this article is available at .     

Mass transfer effects on the non-Newtonian fluids past a vertical plate embedded in a porous medium with non-uniform surface heat flux

 The present study is devoted to investigate the influences of mass transfer on buoyancy induced flow over vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald–de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solution for the transformed governing equations is obtained with prescribed variable surface heat flux. Numerical results for the details of the velocity, temperature and concentration profiles are shown on graphs. Excess surface temperature as well as concentration gradient at the wall associated with heat flux distributions, which are entered in tables, have been presented for different values of the power-law index n, buoyancy ration B and the exponent λ as well as Lewis number Le. Received on 26 April 2000     

Direct numerical simulation of a liquid sheet in a compressible gas stream in axisymmetric and planar configurations

A thin liquid sheet present in the shear layer of a compressible gas jet is investigated using an Eulerian approach with mixed-fluid treatment for the governing equations describing the gas–liquid two-phase flow system, where the gas is treated as fully compressible and the liquid as incompressible. The effects of different topological configurations, surface tension, gas pressure and liquid sheet thickness on the flow development of the gas–liquid two-phase flow system have been examined by direct solution of the compressible Navier–Stokes equations using highly accurate numerical schemes. The interface dynamics are captured using volume of fluid and continuum surface force models. The simulations show that the dispersion of the liquid sheet is dominated by vortical structures formed at the jet shear layer due to the Kelvin–Helmholtz instability. The axisymmetric case is less vortical than its planar counterpart that exhibits formation of larger vortical structures and larger liquid dispersion. It has been identified that the vorticity development and the liquid dispersion in a planar configuration are increased at the absence of surface tension, which when present, tends to oppose the development of the Kelvin–Helmholtz instability. An opposite trend was observed for an axisymmetric configuration where surface tension tends to promote the development of vorticity. An increase in vorticity development and liquid dispersion was observed for increased liquid sheet thickness, while a decreasing trend was observed for higher gas pressure. Therefore surface tension, liquid sheet thickness and gas pressure factors all affect the flow vorticity which consequently affects the dispersion of the liquid.      

Numerical Simulation of Riblet Controlled Spatial Transition in a Zero-Pressure-Gradient Boundary Layer

To analyze the fundamental physical mechanism which determines the damping effect of a riblet surface on three-dimensional transition several numerical simulations of spatial transition in a flat plate zero-pressure-gradient boundary layer above a riblet wall are performed in this study. Two types of forced transition scenarios are investigated. The first type of transition is defined by K-type transition induced by a dominant two-dimensional Tollmien–Schlichting (TS) wave and a weak spanwise disturbance. The second type of transition is purely excited by two oblique waves. By a qualitative analysis of the occurring maximum wall-normal and spanwise velocity components and the Fourier modes of the disturbances the two-dimensional TS waves are found to be amplified by riblets, whereas three-dimensional structures, i.e., Λ-, hairpin, and streamwisely aligned vortices, are damped. At oblique transition the breakdown to turbulence is delayed by the riblets compared to transition on a clean surface. The investigation of the near wall flow structure reveals secondary flows induced by the riblets and reduced wall normal ejections as well as a reduced downwash.     

The effect of roughness on separating flow over two-dimensional hills

Two new experimental data sets for turbulent flow over a steep, rough hill are presented. These include detailed laser Doppler anemometry measurements obtained at the separation and reattachment points and, in particular, within the reverse flow region on the lee side of the hill. These results allow the development of a new parametrization for rough wall boundary layers and validate the use of Stratford’s solution for a separating rough flow. The experiments were conducted in a water channel for two different Reynolds numbers. In the first set of rough wall experiments, the flow conditions and the hill shape are similar to those presented in Loureiro et al. (Exp. Fluids, 42:441–457, 2007a) for a smooth surface, leading to a much reduced separation region. In the second set of experiments, the Reynolds number is raised ten times. The region of separated flow is then observed to increase, but still to a length shorter than that recorded by Loureiro et al. (Exp. Fluids, 42:441–457, 2007a). Detailed data on mean velocity and turbulent quantities are presented. To quantify the wall shear stress, global optimization algorithms are used. The merit function is defined in terms of a local solution that is shown to reduce to the classical law of the wall far away from a separation point and to the expression of Stratford at a separation point. The flow structure at the separation point is also discussed.     

Effect of distributed gas injection on aerodynamic characteristics of a body of revolution in a supersonic flow

Results of experimental and numerical investigations of the effect of gas injection through a permeable porous surface on the drag coefficient of a cone-cylinder body of revolution in a supersonic flow with the Mach number range M _h = 3–6 are presented. It is demonstrated that gas injection through a porous nose cone with gas flow rates being 6–8% of the free-stream flow rate in the mid-section leads to a decrease in the drag coefficient approximately by 5–7%. The contributions of the decrease in the drag force acting on the model forebody and of the increase in the base pressure to the total drag reduction are approximately identical. Gas injection through a porous base surface with the flow rate approximately equal to 1% leads to a threefold increase in the base pressure and to a decrease in the drag coefficient. Gas injection through a porous base surface with the flow rate approximately equal to 5% gives rise to a supersonic flow zone in the base region.     

Turbulent flow past a transverse cavity with inclined side walls. 2. Heat transfer

Convective heat transfer in a transverse cavity with a small aspect ratio, angle of wall inclination ϕ = 30–90°, and heated bottom, frontal, and rear walls of the cavity is studied experimentally. Temperature distributions are measured in longitudinal and transverse sections on three walls; temperature fields are measured over the entire heated surface. Local and mean heat-transfer coefficients are calculated. The highest intensification of heat transfer is found to occur on the rear wall for low values of ϕ Reconstruction of the one-cell structure to the two-cell structure of the primary vortex in the cavity leads to a drastic decrease in heat transfer over the cavity span from the end faces toward the center in the case with ϕ = 60 and 70°. A certain increase in the mean heat-transfer coefficient averaged over the entire heated surface is noted for ϕ = 60°. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 23–29, July–August, 2007.     

A film-based wall shear stress sensor for wall-bounded turbulent flows

In wall-bounded turbulent flows, determination of wall shear stress is an important task. The main objective of the present work is to develop a sensor which is capable of measuring surface shear stress over an extended region applicable to wall-bounded turbulent flows. This sensor, as a direct method for measuring wall shear stress, consists of mounting a thin flexible film on the solid surface. The sensor is made of a homogeneous, isotropic, and incompressible material. The geometry and mechanical properties of the film are measured, and particles with the nominal size of 11 μm in diameter are embedded on the film’s surface to act as markers. An optical technique is used to measure the film deformation caused by the flow. The film has typically deflection of less than 2% of the material thickness under maximum loading. The sensor sensitivity can be adjusted by changing the thickness of the layer or the shear modulus of the film’s material. The paper reports the sensor fabrication, static and dynamic calibration procedure, and its application to a fully developed turbulent channel flow at Reynolds numbers in the range of 90,000–130,000 based on the bulk velocity and channel full height. The results are compared to alternative wall shear stress measurement methods.     

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.     

One method of producing a high-temperature dense plasma

This paper considers the interaction between an absolutely rigid wall or a steel plate and the rarefaction wave arising in solid deuterium when a 30–150 GPa shock wave arrives at the free surface. It is shown that, in the entropy trace near the wall or interface with the plate, a high-temperature plasma arises, in which a thermonuclear fusion is possible, at least, for shock-wave pressures above 70 GPa. The dimension of the plasma region and the time of its establishment are proportional to the distance between the free surface and the wall. Estimates of the proportionality coefficients are given. It is noted that, in this case, unlike in other methods of high-temperature plasma generation, the time of existence of the plasma may not depend on the sound velocity in it. It is shown that, by using a conical solid-state target wit an exit hole, the shock-wave pressure in solid deuterium can be increased from 10 to 100 GPa. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 15–24, May–June, 2009.     

Influence of injection on stabilization of flow over an axisymmetric body with a recess facing into a supersonic oncoming stream

Numerical modeling of supersonic flow over a body with an annular step formed by two coaxial cylinders is performed by the Godunov method within the framework of the model of an ideal gas. Regimes of nonsteady streamline flow and peculiarities of the flow associated with the presence of a cylindrical recess in the nose part of the body are analyzed. The influence of the intensity of injection of an annular wall jet from the bottom of the recess on flow stabilization and the body drag is investigated. The domain of the existence of steady streamline flow is established. Khar'kov Aviation Institute, Khar'kov 310070. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 84–90, July–August, 1998.     

On swirl development in a square cross-sectioned, S-shaped duct

The flow in a uniform square cross-sectioned, S-shaped duct was investigated experimentally, at Reynolds number (Re) = 4.73 × 10⁴ and 1.47 × 10⁵, using three S-ducts of different curvature and turning angle. The hydraulic diameter (D) for each S-duct is 150 mm. Besides studying the square cross-sectioned S-duct flow at moderately higher Re than current literature, the S-ducts’ geometry used in this study also have larger curvatures and higher turning angles than those reported in the literature. With surface pressure measurement and smoke wire flow visualization, flow separation at the inside wall of the first bend was detected. Using surface oil flow visualization on the bottom wall of the S-duct and cross-wires measurement at the duct exit, it is shown here that the swirl developed in the first bend was partly attenuated in the second bend due to the formation of swirl of opposite direction. The swirl of an opposite sign results in the formation of a clear dividing or separation line on the bottom wall (and top wall) of the duct. Additional flow features include the formation of streamwise vortices on the outer-wall of the second bend. These streamwise vortices can either be a pair of counter-rotating vortices or a single vortex. The formation mechanism of these streamwise vortices is explained using the Squire and Winter [J Aeronaut Sci 18(4):271–277, 1951] formula and it is shown that the said mechanism is applicable to both Re in the present study.