Showing papers in "Fluid Dynamics in 1995"

On “vortex breakdown”

Abstract: The well-known investigations of vortex breakdown are supplemented with an exact analytic representation of this phenomenon on the basis of the complete Navier-Stokes equations for the case of a potential swirl of the input flow about the axis of symmetry.

Model of the physico-chemical kinetics behind the front of a very intense shock wave in air

Abstract: A model of the physico-chemical kinetics of the reactions taking place behind the front of an intense shock wave propagating in air with a speed of 9–14 km/s is proposed. The problem of describing the chemical reactions, namely, molecular dissociation and exchange reactions involving vibrationally excited molecules in the absence of vibrational equilibrium, is solved. The vital role of the vibrational excitation delay in the dissociation of oxygen and nitrogen is established. The rate of the exchange reaction between nitrogen molecules and oxygen atoms in the shock wave depends only slightly on the vibrational excitation level. It is demonstrated that the rate constants for thermally nonequilibrium dissociation reactions can be represented within the framework of the one-temperature approximation at constant vibrational temperatures of the dissociating species satisfying quasi-stationary conditions.

Experimental study of surface waves with Faraday resonance excitation

Abstract: The results of an investigation of standing two-dimensional gravity waves on the free surface of a homogeneous liquid, induced by the vertical oscillations of a rectangular vessel under Faraday resonance conditions, are presented. The frequency ranges of excitation are determined and resonance relationships for the second and third modes are obtained and analyzed. Nonlinearities of the waves generated, such as wave profile asymmetry and node oscillations, are evaluated. Wave breakdown and the onset of unstable oscillation modes are considered. Experimental results are compared with the theoretical data. The experimental studies [1–4], devoted to Faraday resonance, deal mainly with the conditions under which resonance arises and the frequency response.

Effect of an electric field on the nitrogen oxide emission and structure of a laminar propane diffusion flame

Abstract: The effect of an electric field E on the structure and nitrogen oxide NOx emission of an individual laminar propane diffusion flame is experimentally investigated. The current-voltage characteristics of the flame, its deformation, the fuel-air ratio and the NOx emission are determined for positive and negative burner polarities. A reduction in NOx emission (up to 30% with respect to the emission index) is demonstrated in the case of negative burner polarity. A cause-and-effect relationship between the processes in the flame is proposed: the presence in the flame of positively charged ions and soot particles; the motion of the ions in the E field and the onset of an induced electrohydrodynamic flow directed towards the negatively charged burner; the retention and increase in the concentration of soot particles in the lower region of the flame, which leads to an increase in soot particle radiation and hence to a decrease in the temperature of the flame front and a corresponding reduction in NOx emission. The electrohydrodynamic aspects of the problem are subjected to a qualitative analysis.

Optimal shock-wave systems

Abstract: Academician G. I. Petrov was among the first to investigate systems consisting of several plane inclined shocks and a closing normal shock [1]. In his studies the intensities of the inclined shocks in which the static and total pressure restoration coefficients reach maximum values were determined by numerical investigation. These shock systems were called optimal. A theoretical analysis of these systems is presented in [2, 5]. Exact analytic solutions determining the intensities in the optimal system in which there are maxima of not only the pressure restoration coefficients but also the values of the velocity head or density, as well as the angle of flow rotation in the wave, are obtained. Apart from shocks, the system include simple rarefaction and compression waves. The solutions obtained are not only theoretically meaningful but also have practical applications and can be used in the gasdynamic design of supersonic air intakes, jet technology devices, and other technical apparatus.

Stability of rarefied dusty gas and suspension flows in a plane channel

Abstract: The stability of two-dimensional dispersed Poiseuille flow is analyzed within the framework of the linear theory. A numerical solution of the corresponding Orr-Sommerfeld equation is constructed. The effect of the particle mass concentration, dimensions, and relaxation time on the flow stability is considered.

Impingement of surface waves on the edge of compressed ice

Abstract: The impingement of small-amplitude surface waves on the edge of a solid compressed ice sheet in a basin of finite constant depth is considered. The influence of the cylindrical rigidity and the value of the compressing force on the dependence of the amplitude coefficients of reflection and transmission on the incident wave period is analyzed.

Gas dynamics with local energy release in subsonic and supersonic flow

Abstract: The flows developing in the interaction of a supersonic gas stream with a continuously operating axisymmetric energy release source or as a result of the action of pulsed periodic energy injection on a subsonic gas stream are investigated numerically. For a continuously operating energy source two types of flow can be distinguished: with a shock wave detached from the source and with a shock attached to it. Approximate formulas for the gas density in the center of the energy release zone are obtained for the cases of constantly operating and periodic energy sources.

Surface porosity and permeability of porous media with a periodic microstructure

Abstract: Various ways of determining the surface porosity, the relation between the porosity and the surface porosity and the representation of the permeability in terms of the characteristics of the microstructure of the porous medium are analyzed with reference to model porous media with a periodic microstructure. It is shown that it is necessary to distinguish between the geometric (scalar) and physical (tensor) suface porosities and that the geometric surface porosity, the physical surface porosity and the porosity are different characteristics of the porous medium.

Drag reduction in riblet-lined pipes

Abstract: The possibilities of reducing the drag in pipes with a circular cross section by lining them with riblets have been investigated experimentally for developed turbulent air flow. The maximum drag reduction of 6–7% in the riblet-lined as compared with the smooth pipe was obtained for a dimensionless riblet pitch, expressed in law-of-the-wall parameters,s +=14−18.

Calculation of the thrust of a wave-powered marine propelling device

Abstract: A scheme for calculating the thrust of a wave propelling device with limiters is proposed. The scheme can be extended to similar propelling devices with a more complex wing suspension or a more complex wing system.

Groundwater flow in a medium with periodic inclusions

Abstract: A study is made of the problem of two-dimensional confined steady flow through a porous reservoir whose percolation coefficient is a step function, while the homogeneity zones are rectangular inclusions (blocks) and a matrix (fractures). The velocity distributions, streamlines, isochrones of the motion of marked particles, and their time of passage through the elementary cell are found for this doubly periodic structure under conditions of continuity of the fluid head and the normal component of the flow on the phase contact boundary. Conclusions concerning the “convective component” of the longitudinal and transverse dispersion are drawn on the basis of these essentially two-dimensional hydrodynamic characteristics. The exact solutions obtained are compared with the results of numerical calculations carried out by the finite-difference method.

Two-phase multicomponent turbulent jet with phase transitions

Abstract: A mathematical model of a gas-droplet nonisothermal multicomponent polydisperse turbulent jet is proposed. This model takes into account phase velocity and temperature nonequilibrium, gas and liquid phase inhomogeneity, the droplet coagulation and disintegration, and the possibility of the presence of vapor condensation or fluid evaporation, depending on the specific conditions in the jet. Certain results of calculating the parameters of both a nonisothermal two-component polydisperse gas-disperse jet with phase transitions and droplet coagulation and a three-component polydisperse gas-disperse jet without allowance for phase transitions are presented. The results obtained are analyzed.

Optimization of laminar-turbulent transition delay by means of local heating of the surface

Abstract: The stability and position of laminar-turbulent transition in the boundary layer on a body heated near the leading edge are analyzed. The point of transition is found using the linear theory of the stability of plane-parallel flow and theeN-method. It is shown that by heating a tiny area near the leading edge to a temperature exceeding that of the oncoming flow by a factor of two to four, transition may be delayed, even on a thermally insulated surface. For highly radiating surfaces the energy saved by reducing the friction drag may exceed the heating energy by a factor of three. It is shown that by varying the pressure distribution and surface heating it is possible either to increase the airfoil lift for a fixed transition point or delay transition for a fixed lift.

Hydrodynamical modeling of the development of non-homogeneous oil reservoirs

Abstract: Results of mathematical modeling of two-phase flow in non-homogeneous (layered) reservoirs are reported. Characteristic patterns of flow in reservoirs with high layer permeability contrast are investigated. It is shown that in such reservoirs crossflow between layers must be taken into account. Specific features of the use of hydrodynamic methods of improving oil recovery in such reservoirs based upon flow pattern control are studied. The possibility of using rational flow management to improve oil recovery partially blocking the reservoir in the neighborhood of the wells is demonstrated.

Nonequilibrium condensation of metal vapor mixed with an inert gas in nozzle expansion in cluster beam generators

Abstract: A closed mathematical model of flows of a mixture consisting of a homogeneously condensible vapor and an inert gas is described. This model is a further development of the pure metal vapor condensation model [1 – 4] and, as distinct from the latter, makes it possible to take into account the effect of molecules of inert gas not only on the thermodynamics of the mixture but on the detailed kinetics of the processes of the cluster formation and breakdown. The results of numerical calculations of the formation of iron and silver clusters in experimental installations are presented.

Sphere scattering of nonlinearly interacting acoustic waves

Abstract: Sphere scattering of the field of nonlinearly interacting plane acoustic waves when the sphere is located in the region of nonlinear interaction between the primary pumping waves of a parametric antenna is considered. An analytic expression for the secondary field pressure at the difference frequency is obtained. This expression describes the process of nonlinear interaction of the incident and scattered waves. The secondary-field total pressure components, which characterize the interaction between the incident plane waves and scattered spherical waves are analyzed. The numerical results and experimental data are given.

Micro-scale instability in a continuously stratified fluid

Abstract: Experimental observations of small-scale structures caused by flow instabilities at layers of high density gradient in the wake behind a cylinder in a fluid with a continuous salt concentration stratification are reported. In the density wake it is possible to discern a number of structures such as wedge-like structures or cusps; small-scale instabilities (breakers) in the zones of interaction of attached internal waves and the high-gradient wake envelope; small-scale instability of the density boundary layer with a complicated density gradient pattern superimposed on a smooth velocity profile, and small-scale wake structures behind attached vortices in the case of a closed (central) wake envelope.

A model problem of deceleration of a body in a resisting medium with a jet flow around the body

Abstract: A mathematical model is constructed describing the deceleration of a solid body moving in a medium with a jet flow around the body. The regime of translational deceleration is shown to be normally unstable. This has made it possible to develop a relatively simple technique for determining model parameters experimentally. An example of the application of this technique to a cylindrical body is presented.

Influence of a floating elastic plate on the surfaceeffects of internal waves generated by motion of a source in a non-homogeneous liquid

Abstract: Perturbations of the surface of an exponentially stratified liquid of finite depth, free or covered by an elastic plate, are studied on the assumption that the perturbations are caused by internal waves generated by the steady motion of a constant -intensity source. The dependence of the spatial distribution of perturbations on the plate properties, velocity and the submersion depth of the source is considered.

Thermoconcentration convection under uniform lateral heating

Abstract: The fine structure of thermoconvective flow near an inclined- plane heat source within a fluid with a stable density stratification due to salinity gradient is investigated using optical and probe techniques. The time dependence of the parameters of optical refraction coefficient gradient, specific electric conductivity, velocity and temperature fields is determined for different values of the heat source inclination angle. The difference in the spatial scales of variation of the different variables is demonstrated. The Nusselt numbers range from 1.8 to 5.4 for the structures under the plate and from 1.8 to 10.6 for the structures above the plate for Rayleigh numbers on the range from 2·105 to 2·106.

Boussinesq approximation in the Rayleigh-Benard problem

Abstract: Instability of mechanical equilibrium and initiation of plane steady-state convective flows in an infinite horizontal fluid layer heated from below (Rayleigh-Benard problem) are investigated. The convection model for an isothermal incompressible fluid is not assumed to have small thermal expansion (contrary to the Oberbeck-Boussinesq approximation). The influence of a supplementary thermal expansion parameter on the convection process is numerically investigated. The results are compared with the known results for the Oberbeck-Boussinesq approximation. It is shown that subcritical instability is possible if the thermal expansion parameter increases. The linearization and Lyapunov-Schmidt methods are applied.

Effect of gel plugs on water and oil flow in a nonhomogeneous porous reservoir

Abstract: The factors influencing gel plug emplacement, their breakdown time, and the effect of the plugging on the flow distribution in a reservoir and the water-oil ratio in producing wells after plug emplacement are discussed

Natural vibrations of a hummock ridge in an elastic ice sheet floating on the surface of an infinitely deep fluid

Abstract: The properties of the natural vibrations of a hummock ridge in an elastic ice sheet are investigated. Typical shapes of the dispersion curves for symmetric and antisymmetric boundary waves which propagate along the hummock and damp exponentially with distance from the latter are obtained. It is shown that natural vibrations can initiate failure of the ice sheet at a certain distance from the hummock. Under compression this process leads to the formation of a parallel hummock ridge.

Macrokinetic model of the trapping process in two-phase fluid displacement in a porous medium

Abstract: A microinhomogeneity-averaged model of the kinetics of the trapping process is proposed for a porous medium in which two fluids are mutually displaced. The traps are treated as a new hydrodynamic phase, and the trapping process as a phase transition. Kinetic relations for the average trapping process are obtained. The structure and quantitative values of the kinetic coefficients are obtained for a model of a porous medium in the form of a system of doublets. The dependence of the characteristic time of the process on the degree of inhomogeneity of the medium is investigated. A variant of the macroscopic model of the process of two-phase flow, in which the kinetic relations obtained are used as the closing relations, is proposed.

Long-wave instability of a vortex ring

Abstract: The instability of barrel-shaped vibrations of a vortex ring in an ideal fluid is investigated. These vibrations, stable for a vortex ring with a piecewise-uniform vorticity profile, appear to be unstable for a vortex ring with a smooth vorticity profile. The instability growth rate is found on the basis of the energy balance equation determining the energy transport from perturbations with negative energy in the critical layer to perturbations with positive energy in the rest of the flow. The curvature of the vortex ring, by virtue of which the perturbations with energies of different signs appear to be connected, plays a prominent role in the mechanism under consideration.

Calculation the internal gravity wave field associated with arbitrary unsteady motion of a source

Abstract: The problem of calculating the linear internal gravity wave field excited by the arbitrary unsteady motion of a point source in a layer of stratified fluid is considered. The solution of this problem makes it possible to investigate the fields of linear internal waves generated under various conditions of motion of the perturbation source, for example, when the source moves at a velocity close to the maximum internal-wave group propagation velocity, or when the motion occurs at variable depth, etc. In certain cases (uniform motion of the source, model density distributions) these problems can be investigated using various asymptotic methods. However, in the linear formulation the exact solution of the problem of internal wave generation by arbitrary moving sources should be the starting point. In most previous studies of this problem, both the internal waves generated by an arbitrary moving source in an exponentially stratified fluid and the internal wave fields induced by a uniformly moving source in a layer of arbitrarily stratified fluid were investigated. In the present study we assume that both the trajectory of the source and the stratification, i.e., the density distribution over depth, are arbitrary.

Numerical simulation of instabilities and secondary regimes in spherical Couette flow

Abstract: In all previous numerical investigations of spherical Couette flow only axisymmetric regimes were considered. At the same time, in experiments [1–4] it was found that when both spheres rotate and the layer is thin centrifugal instability of the main flow leads to the appearance of nonaxisymmetric secondary flows of the azimuthal traveling wave type. The results of an initial numerical investigation of these flows are presented below. Solving the linear problem of the stability of the main flow and simulating the secondary flows on the basis of the complete nonlinear Navier-Stokes equations has made it possible to supplement and explain many of the results obtained experimentally. The type of bifurcation and the structure of the disturbances whose growth leads to the appearance of three-dimensional nonstationary flows are determined, and the transitions between different secondary regimes in the region of weak supercriticality are described.

Asymptotics of steady axisymmetric flow of incompressible fluid past a bluff body at high Reynolds number

Abstract: Steady axisymmetric separated flow at high Reynolds number is considered It is shown that the body scale flow does not correspond to the Kirchhoff model because near the body there is a fairly strong reversed flow causing the secondary separation which is observed in numerical computations Quantitative theoretical results are compared with the numerical results

Modeling of particle motion in a turbulent flow with allowance for collisions

Abstract: On the basis of the kinetic equation for the colliding-particle velocity probability density distribution in a turbulent flow, a model for calculating the dispersed phase motion is constructed for a broad range of variation of the number density and particle size.