Showing papers in "Fluid Dynamics in 2008"

Interaction between hydraulic and natural fractures

Abstract: The results of a numerical simulation of the interaction between a hydraulic fracture propagating under plane-strain conditions in an infinite impermeable elastic medium and an already existing natural fault are presented. The fracture is created by an incompressible Newtonian fluid injected at a constant flow rate from a source located at its center; the behavior of the fault is described by a dry friction model of the Mohr-Coulomb type. The results obtained are in agreement with the available studies in this field of research.

Shock wave structure in a diatomic gas based on a kinetic model

Abstract: The structure of a normal (direct) shock in a gas for the parameters corresponding to nitrogen is investigated with allowance for the rotational degrees of freedom on the basis of a model kinetic equation. For various Mach numbers the structure is compared with both the known experimental results and the solutions of the Navier-Stokes approximation within the framework of two-temperature hydrodynamics. The possibility of assuming the constancy of the fraction of excited rotational degrees of freedom is studied.

Mechanism of sound radiation by turbulence near a rigid body

Abstract: The problem of aerodynamic sound generation by a transverse turbulent flow past a rigid cylinder is considered. An anomalous displacement of the equivalent dipole source to a region far downstream of the cylinder is found using the method of azimuthal decomposition of the sound field. The effect is explained on the basis of an analysis of the two-dimensional problem of multipole sources near a circle in the incompressible approximation. It is shown that the dipole displacement is a result of the interference of the original quadrupole source and its dipole reflection. It is concluded that in the weakly compressible case the mechanism of dipole noise generation consists in the uncompensated reflection of weak quadrupoles from a curvilinear surface.

Numerical simulation of injection of a solvent into a production well under electromagnetic action

Abstract: The results of a theoretical investigation of the possibility of using powerful radio-frequency (RF) electromagnetic (EM) radiation combined with solvent injection in high-viscosity oil fields for the purpose of intensifying oil recovery are given. A mathematical model of the three-stage stimulation of a high-viscosity oil pool is proposed. The model takes into account the cross-flow heat and mass transfer effects initiated by the movement of a multicomponent system through a porous medium under the action of an EM field. A comparative analysis of the results of calculations of the proposed combined method and its components (EM treatment of the reservoir bottomhole zone without solvent injection and “cold” displacement of oil by a solvent) is carried out.

Vibration effect on convection onset in a system consisting of a horizontal pure liquid layer and a layer of liquid-saturated porous medium

Abstract: The onset of convection in a system of two horizontal layers (a pure liquid and a porous medium saturated with the same liquid) heated from below under the action of vertical vibration is investigated. For describing the free thermal convection, in the liquid layer the Boussinesq approximation and in the porous layer the Darcy-Boussinesq approximation are used. In the limiting case of a thin liquid layer, effective boundary conditions on the upper boundary of the porous layer with account for convection in the liquid layer are obtained and it is shown that vibration has a stabilizing effect, whereas the presence of a liquid layer leads to destabilization. For an arbitrary liquid to porous layer thickness ratio the onset of convection is investigated numerically. In the case of a thin liquid layer there are two (short-and long-wave) unstable modes. In the case of thick layers the neutral curves are unimodal. Vibration has a stabilizing effect on perturbations with any wave number but affects short-wave perturbations much more strongly than long-wave ones.

On the existence of a threshold value of the plate bluntness in the interference of an oblique shock with boundary and entropy layers

Abstract: The heat transfer to sharp and slightly blunted flat plates in the zone of oblique shock incidence has been experimentally investigated. The experiments were performed at the Mach numbers M = 6, 8, and 10 and Reynolds numbers ranging from 0.2 × 106 to 1.3 × 106 corresponding to transitional (laminar-turbulent) flow in the shock-induced separation zone. Emphasis is placed on small values of the bluntness radius r. It is established that there exists a threshold value r th of the radius that bounds the range of its influence on the heat transfer, namely, an increase in r to r th leads to a sharp reduction in the maximum heat transfer coefficient in the interference zone, whereas a further increase (beyond r th) has only a slight effect on the maximum heat transfer coefficient. The dependence of r th on the main hypersonic flow parameters is analyzed. an explanation of the observable phenomena is given.

Stability of a disperse-mixture flow in a boundary layer

Abstract: The hydrodynamic stability of a dilute disperse mixture flow in a quasi-equilibrium region of a boundary layer with a significantly nonuniform particle concentration profile is investigated. The mixture is described by a two-fluid model with an incompressible viscous carrier phase. In addition to the Stokes drag, the Saffman lifting force is taken into account in the interphase momentum exchange. On the basis of a numerical solution of the boundary-value problem for a modified Orr-Sommerfeld equation, neutral stability curves are analyzed and the dependence of the critical Reynolds number on the governing parameters is studied. It is shown that taking into account the particle concentration nonuniformity in the main flow and the Saffman lifting force significantly changes the stability limits of the two-phase laminar boundary layer flow. The effect of these factors on the boundary layer stability is considered for the first time.

Investigation of the Stability of a Plane-Channel Suspension Flow with Account for Finite Particle Volume Fraction

Abstract: Within the framework of the two-fluid approach, a variant of a heterogeneous-medium model which takes into account a finite volume fraction of the inclusions and a small but finite phase velocity slip is proposed. The interphase momentum exchange is described by the Stokes force with the Brinkman correction for the finite particle volume fraction. The suspension viscosity depends on the particle volume fraction in accordance with the Einstein formula. Within the framework of the model constructed, a formulation of the problem of linear stability of plane-parallel two-phase flows is proposed. As an example, the stability of a channel suspension flow is considered. The system of equations for small disturbances with the boundary conditions is reduced to an eigenvalue problem for a fourth-order ordinary differential equation. Using the orthogonalization method, the dependence of the critical Reynolds number on the governing nondimensional parameters of the problem is studied numerically. It is shown that taking a finite volume fraction of the inclusions into account significantly affects the laminar-turbulent transition limit.

Problem of the Free Oscillations of a Capillary Bridge

Abstract: The free oscillations of a capillary bridge whose equilibrium shape is determined by the surface tension forces and the static gravity field are investigated. The values of 25 “lower” levels of the spectrum of natural oscillations of the capillary bridge are found for various control parameters in accordance with the experimental conditions.

Control of separation phenomena in a high-speed flow by means of the surface electric discharge

Abstract: The results of an experimental and theoretical investigation of the interaction between a surface electric discharge and a supersonic air flow in a constant cross-section channel are given. The features of the generation of the surface discharge in the flow are described. A model of the interaction is proposed. The regime of gasdynamic screening of a mechanical obstacle on the channel wall is investigated. Data on the change in the main flow parameters as a result of the generation of a surface discharge are given. The experimental results are compared with the results of calculations based on a simplified model of the interaction.

Reflection of long waves from a “nonreflecting” bottom profile

Abstract: The transformation of long surface waves in a zone of variable depth is investigated within the framework of shallow-water theory. In the particular case of a bottom profile containing a so-called “nonreflecting” relief segment adjacent to an even bottom, expressions for the reflected and transmitted pulse waves are obtained in explicit form. It is shown that waves are reflected from such a profile. The role of distributed and concentrated reflection of a wave propagating above an uneven bottom is discussed.

Numerical simulation of an electric discharge in supersonic flow

Abstract: The two-dimensional problem of supersonic air flow past a spherical electrode is considered on the basis of a joint solution of the Navier-Stokes equations for a neutral gas and the charged-particle transport equations in the diffusion-drift approximation. The self-sustained discharge is considered in the cathode regime of operation of the test electrode in a formulation analogous to that of the experimental study [1]. The thermal and non-thermal (action of the electrostatic force in the cathode layer of the space charge) mechanisms of action of the discharge on the flow field are investigated. Within the framework of the numerical model considered the effect of the electrostatic force turns out to be negligibly small and the main effect of the action on the flow is the heat release driven by the electric currents. The influence of the discharge on the flow field was manifested itself in a reduction of the aerodynamic drag by up to 25%.

Turbulent flows in channels with injection. results of large eddy simulation and the two-equation turbulence model

Abstract: Turbulent flows in channels with intense distributed injection are modeled using the large eddy method and the two-equation k-ɛ turbulence model. The calculations are carried out for different velocities of injection from the channel walls. For a channel with one-sided injection the results of large eddy simulation are in good agreement with the measured data, whereas the calculations in accordance with the k-ɛ model give a less convex cross-sectional velocity profile and an appreciable error in determining the surface friction coefficient on the impermeable wall and also have certain other shortcomings. In the case of two-sided injection, the results of the calculations by the large eddy method and the k-ɛ model are in good agreement with one another and the data of physical experiments.

Vortex structure of separated flows on model wings at low freestream velocities

Abstract: Flow past model wings is experimentally investigated in a subsonic wind tunnel at large angles of attack at which the laminar boundary layer separates near the leading edge of the wing (flow stall). The object of the study was the flow structure within the separation zone. The carbon-oil visualization of surface streamlines used in the experiments showed that in the separation zone there exist one or more pairs of large-scale vortices rotating in the wing plane. Certain general properties of the vortex structures in the separation zone are found to exist, whereas the flow patterns may differ depending on the model aspect ratio, the yaw angle, and other factors.

Three-dimensional convection regimes in a cubical cavity

Abstract: Nonlinear three-dimensional convection regimes in a cubical cavity heated from below are studied numerically for small and moderate supercriticalities and different values of the Prandtl number Pr. The cases of adiabatic and perfectly heat-conducting lateral cavity boundaries are considered. The structure of different supercritical motions and their stability are investigated. The existence of different kinds of convective structures is detected over a wide range of governing parameters.

Application of a droplet cluster to visualize microscale gas and liquid flows

Abstract: The possibility of using microdroplets, which form a dissipative droplet-cluster structure, as tracers localized in the boundary layer of a gas adjoining a liquid-gas interface is experimentally demonstrated. Examples of the visualization of boundary layer flow fields generated by both processes in the gaseous phase and liquid convection are considered.

Controlling the Disturbances in a Hypersonic Flat-Plate Shock Layer by Unsteady Action from the Surface

Abstract: The results of a wind-tunnel experiment on the joint action of periodic acoustic fast-mode disturbances of the outer flow and disturbances generated at the leading edge of a plate on the hypersonic (M∞ = 21) viscous shock layer on the plate are presented. The possibility of positively controlling the intensity of density fluctuations in the plate shock layer by means of disturbances introduced from the leading edge is shown. Direct numerical simulation of the suppression (enhancement) of disturbances under the simultaneous action on the shock layer of the two-dimensional fast-mode acoustic waves in the outer flow and the source of two-dimensional suction/injection disturbances near the leading edge of the plate is performed under the experimental conditions. The experimental and calculated results are shown to be in good agreement.

Homogeneous deformation of a two-fluid plasma with allowance for electron inertia

Abstract: A method of finding the homogeneous deformations of a two-fluid plasma with allowance for the electron inertia is proposed. By homogeneous deformation is meant an axisymmetric plasma flow with a linear dependence of the radial velocity on the radius. Three families of homogeneous deformations are found using this method. One of these families, consisting of deformations with an arbitrary law of variation of the total current, is of particular interest with reference to plasma column dynamics. The method proposed is based on the reduction of the equations of two-fluid plasma dynamics to single-fluid equations of the hydrodynamic type (the equations of electromagnetic hydrodynamics (EMHD)) with a non-diagonal internal stress tensor, three-parameter thermodynamics, and a nonlocal form of the generalized Ohm’s law. Possible applications of the exact solutions found to the analysis of the data obtained using certain experimental apparatus are discussed.

Numerical Simulation of the Process of Autoregulation of the Arterial Blood Flow

Abstract: For describing the autoregulation of the blood flow in an artery under constant transmural pressure a mathematical model that takes into account the multilayer structure of the arterial wall, the diffusion and kinetic processes in the wall, and the nonlinear viscoelastic properties of the wall material is proposed. The limiting case of a thin-walled artery is studied analytically. The arterial-wall viscosity range on which the equilibrium state of the system is stable is estimated. Accurate stationary distributions of the nitric oxide, calcium and myosin concentrations in the arterial wall are found. Numerical simulation of the autoregulation process demonstrated the possibility of arterial adaptation to radius perturbations, the existence of slow oscillations, and system transition to a new equilibrium state with change in blood flow level. The results are in good agreement with the experimental data.

Temperature of a thermally-insulated permeable wall in a compressible flow

Abstract: A numerical solution of the equations of motion and energy supplemented with a differential turbulence model is obtained for the boundary layer on a wall in a compressible flow. Two approaches to determining the temperature of a thermally-insulated permeable wall are considered. The dependence of the temperature recovery coefficient on the permeability parameter approximating the calculated results is derived and compared with experimental data.

Temperature factor effect on the structure of the separated flow within a supersonic gas stream

Abstract: The effect of the temperature factor, that is, the ratio of the body temperature to the freestream stagnation temperature, on the structure of the separated flow formed in the presence of a concave corner in a supersonic stream is studied. The strong influence of the temperature factor on the separation zone length and the flow-generated aerodynamic characteristics is established. It is shown that for fairly large deflection angles this flow cannot be described by free interaction, or triple deck, theory.

Vibrational hydrodynamic interaction between a sphere and the boundaries of a cavity

Abstract: A new type of vibrational lift force [1] acting on a spherical body oscillating in a viscous fluid near a rigid boundary is experimentally investigated. The interaction between the body and the cavity boundary creates a repulsion force which is capable of holding a heavy body in the gravity field at a certain distance from the floor and a light body at a certain distance from the ceiling. The repulsion force appears at a distance comparable with the Stokesian boundary layer thickness and increases as the surface is approached. Outside the viscous interaction range, the repulsion force is replaced by an attraction force which decays with distance. Dimensionless parameters governing the vibrational interaction are found and threshold curves, corresponding to the transition of bodies of different densities to the “suspended” state, are plotted as functions of a dimensionless frequency. The dependence of the repulsion and attraction forces on the distance between the body and the wall is studied.

Onset of self-oscillations upon the loss of stability of spatially periodic two-dimensional viscous fluid flows relative to long-wave perturbations

Abstract: The long-wave asymptotics of the secondary flow that arises after a steady, spatially periodic flow loses stability are studied when one of the periods tends to infinity and the rate of base flow along the longer period is equal to zero. It is shown that if certain non-degeneracy conditions are satisfied, then from the base solution a self-oscillatory regime branches off and both hard and soft stability loss is possible. For the leading terms of the asymptotics explicit formulas are obtained. Examples of self- oscillations calculated for specific flows are presented and the behavior of the fluid particle trajectories in the self-oscillatory regime branching off from the base flow is investigated.

Slow gas motions and the negative drag of a strongly heated spherical particle

Abstract: In the slow flows of a strongly and nonuniformly heated gas, in the continuum regime (Kn → 0) thermal stresses may be present. The theory of slow nonisothermal continuum gas flows with account for thermal stresses was developed in 1969–1974. The action of the thermal stresses on the gas results in certain paradoxical effects, including the reversal of the direction of the force exerted on a spherical particle in Stokes flow. The propulsion force effect is manifested at large but finite temperature differences between the particle and the gas. This study is devoted to the thermal-stress effect on the drag of a strongly heated spherical particle traveling slowly in a gas for small Knudsen numbers (M ∼ Kn → 0), small but finite Reynolds numbers (Re ≤ 1), a linear temperature dependence of the transport coefficients µ ∝ T, and large but finite temperature differences ((Tw − T∞)/TM8 ∼ 1). Two different systems of equations are solved numerically: the simplified Navier-Stokes equations and the modified Navier-Stokes equations with account for the thermal stresses.

Selection of convective rolls in a thin evaporating-fluid layer in an air flow

Abstract: The process of selection of longitudinal convective rolls in a thin layer of evaporating fluid immersed in an air turbulent boundary layer flow is studied numerically. The dependence of the two-dimensional flow patterns on the Rayleigh number and boundary conditions is analyzed. Calculations with account for the thermocapillary effect are carried out. The numerical results are compared with experimental data.

Experimental investigation of secondary steady flows in Faraday surface waves

Abstract: It is shown that in the two-dimensional Faraday surface waves excited in a vertically oscillating rectangular water-filled vessel there is a system of secondary circulatory flows that occupies the entire fluid volume between the vessel bottom and the free surface. In parallel with the oscillations at the wave frequency, the fluid particles are slowly displaced in accordance with these circulatory flows. The secondary flow velocity field is measured and the trajectories of individual fluid particles in the standing wave are determined. The experimental data are compared with the Longuet-Higgins model. It is shown that the initial stage of formation of regular structures on the surface of a sediment layer on the vessel bottom may be related with the presence of secondary circulatory flows.

Effect of the incomplete accommodation of the heterogeneous recombination energy on heat fluxes to a quartz surface

Abstract: Taking both the heterogeneous catalytic processes, including the surface formation of particles with excited internal degrees of freedom, and the processes of multicomponent diffusion and heat transfer in the MESOX apparatus fully into account makes it possible to obtain a recombination coefficient and an accommodation coefficient of the oxygen-atoms-on-quartz recombination energy which are in good agreement with the experimental data. The heterogeneous catalysis model constructed can be used effectively for predicting the heat fluxes to the surface of reentry vehicles on their entry into the Earth’s atmosphere.

High-speed videocamera investigation of the wave structure development on an unstable cavity boundary

Abstract: The formation of wave structures on an unstable (in the Rayleigh-Taylor criterion) boundary of a plane cavity is studied using high-speed video filming. It is shown that at the head of the cavity a quasiperiodic wave regime develops, with a mean wavelength similar to that obtained from a linear stability analysis for the cavity boundary. Observations of the initial-regime breakdown show that its scenarios are similar to the development of subharmonic instability in the one-mode regime. The waves are classified with respect to the wave development rate. It is shown that the large-wave amplitude growth law is on average closely approximated by a quadratic parabola, with the total gas entrainment from the cavity being proportional to the square of the cavity length. The existence of a scaling effect is detected, which in the case considered reduces mainly to a dependence of the gas entrainment coefficient on the Weber number. It is shown that with decrease in the Weber number the gas entrainment coefficient may significantly increase.

Problem of propagation of a gas fracture in a porous medium

Abstract: The problem of gas fracture formation in a porous medium is investigated. An inertialess viscous polytropic gas flow along the fracture is considered. The assumption of small fracture width with respect to the height and length makes it possible to adopt the vertical plane cross-section hypothesis on the basis of which the dependence of the gas pressure inside the fracture on its width can be reduced to a linear law. Initially, the soil surrounding the fracture is soaked with oil-bearing fluid. During fracturing the reservoir gas penetrates into the soil mass and displaces the fluid. A closed system of equations, which describes the evolution of the fracture opening, the depth of gas penetration into the reservoir, and the gas velocities inside the fracture, is constructed. The limiting regimes of gas seepage into the surrounding reservoir are considered and a one-parameter family of self-similar solutions of the system is given for each. The asymptotics of the solution in the neighborhood of the fracture nose is investigated and analytic expressions for the fracture length are obtained. The solution of the problem of gas fracture is compared with the hydraulic fracturing problem in an analogous formulation within the framework of the plane cross-section hypothesis.

Effects of Strong Compressibility in Natural Convective Flows through Porous Media with a Near-Critical Fluid

Abstract: The dynamics and heat transfer in a porous medium occupied by a liquid with parameters in the neighborhood of the critical point of “liquid-gas” transition are simulated numerically within the framework of the equations of dynamics of a porous medium with a compressible liquid phase and the Van-der-Waals equation of state. Adiabatic heating of the liquid phase in a porous layer initiated by a jump in temperature on one of the boundaries is investigated under microgravity conditions. Thermo-gravitational convection in the unsteady and steady-state regimes is simulated in rectangular domains and the effect of adiabatic heating on convection is studied. Calibration relations between the Rayleigh-Darcy and Prandtl numbers in the basic system of equations and their real analogs are obtained. A comparison is made with convection in a porous media occupied by a perfect gas.