Showing papers in "Fluid Dynamics in 1986"

Development of a steady relief at the interface of fluids in a vibrational field

Abstract: The vibrations of a vessel strongly influence the behavior of the interface of the fluids in it. Thus, vertical vibrations can lead both to the parametric excitation of waves (Faraday ripples) and to the suppression of the Rayleigh-Taylor instability [1–2]. At the present time, the influence of vertical vibrations on the behavior of a fluid surface have been studied in sufficient detail (see, for example, review [3]). The behavior of an interface of fluids in the case of horizontal vibrations has been studied less. An interesting phenomenon has been revealed in the experimental papers [4, 5]: in the case of fairly strong horizontal vibrations of a vessel containing a fluid with a free surface, the fluid collects near one of the vertical vessel walls, the free surface being practically plane and stationary with respect to the vessel, while its angle of inclination to the horizon depends on the vibration rate. But if there is a system of immiscible fluids with comparable but different densities in the vessel, horizontal vibrations lead to the formation of a steady wave relief at the interface. An explanation of the behavior of a fluid with a free boundary was given in [6] on the basis of averaged equations of fluid motion in a vibrational field. The present paper is devoted to an analysis of the behavior of the interface of fluids with comparable densities in a high-frequency vibrational field.

Three-parameter model of turbulence: Heat transfer calculations

Abstract: One of the directions being followed in constructing methods of calculating turbulent flows is the development of models of turbulence that include the transfer equations for the turbulence characteristics. The literature on this subject now consists of hundreds of studies, many of which are reviewed in [I, 2]. Most authors use oneparameter [3, 4] and two-parameter [5, 6] models which together with the transfer equations contain algebraic relations. In [7-12] models of turbulence that do not include algebraic relations between the turbulence characteristics entering into the model were developed. These models have certain features in common but also important differences, which were examined in [13]. Three-parameter models, which include viscosity terms [12], have been used for calculating a broad class of incompressible flows in the boundarylayer approximation [12-14].

Numerical investigation of supersonic flow past blunt bodies with protruding spikes

Abstract: A procedure for the calculation of a supersonic flow of ideal gas near axisymmetric blunt bodies with protruding spikes is developed. The flow past a frustum of a cone with a protruding spherically blunt cylindrical spike as a dependence on the ratio K of the spike length1 to the diameter D of the flat end of the body and the Mach number M of the oncoming flow is studied. Several steady flow regimes are obtained, including the formation of circulation zones and internal shock waves in the shock layer. It is shown that mounting a spike in front of the frustum of a cone can lead to a 40–50% reduction in its drag. A full investigation of the variation of the drag coefficient as a dependence on K is carried out for M = 3.

Turbulent thermal in a stratified atmosphere

Abstract: An approximate analytical model of a turbulent thermal in a stratified atmosphere is proposed. This model makes it possible to predict the dynamics of the ascent, suspension and oscillation processes of a buoyant cloud both within the troposphere and on entering the stratossphere. The values of the heat energy needed for the thermal to penetrate the tropopause in northern and southern latitudes are estimated. Estimates are obtained for the amount of material dumped into the stratosphere. A method of determining the thermal energy of volcanic eruptions of the explosive type is proposed.

Existence and nonuniqueness of local separation zones in viscous jets

Abstract: The plane steady problem of the flow of a viscous wall jet past a smoothed break in the contour of a body is considered. For convenience, the flow in the neighborhood of the junction between two flat plates inclined at an angle to each other is chosen for study. As a result of the small extent of the region investigated the flow field is divided into two layers: the main part of the jet, which undergoes inviscid rotation, and a thin sublayer at the wall, which ensures the satisfaction of the no-slip condition. Particular interest attaches to the flow regime in which the solution in the sublayer satisfies the Prandtl boundary layer equations with a given pressure gradient. A similar problem was studied in [1–4]. The present case is distinguished by the structure of the free interaction region in a small neighborhood of the point of zero surface friction stress. By means of the method of matched asymptotic expansions, applied to the analysis of the Navier-Stokes equations, it is established that the interaction mechanism is that described in [5–7]. As a result, an integrodifferential equation describing the behavior of the surface friction stress function is obtained. A numerical solution of this equation is presented. The range of plate angles on which solutions of the equation obtained exist and, therefore, flows of this general type are realized is determined. The essential nonuniqueness of the possible solutions is established, and in particular attention is drawn to the possible existence of six permissible friction distributions.

Thermocapillary convection in two-layer systems in the presence of a surface active agent at the interface

Abstract: Convective instability in a layered system due to the thermocapillary effect was investigated in [1–5]. In these studies it was shown that the perturbations responsible for equilibrium crisis may build up either monotonically or in an oscillatory fashion. In [6] the stabilizing effect of a surface active agent (SAA) on thermocapillary instability was established for a layer with a free surface. For layers of infinite thickness the effect of SAA on thermocapillary convection was studied in [7–9]. The present investigation is concerned with thermocapillary convection in a system of two layers of finite thickness in the presence of an SAA. Convection due to the lift force is not considered. It is established that the principal result of the action of the SAA is not the stabilizing effect on the monotonic mode but the appearance of a new type of oscillatory instability.

Motion of two vortex rings

Abstract: It is well-known [1] that two coaxial rings which are moving in the same direction pass through each other alternately. In the case of thin vortex rings this phenomenon was first considered qualitatively in [2]. The assumption that the vortex rings are thin means that when their interaction is considered they can be assumed to be annular vortex filaments. In the present paper, on the basis of the approach suggested in [2], certain new properties are determined for a system of two coaxial vortex rings of the same intensity.

Effect of viscosity on the propagation of nonlinear Alfvén waves along a tangential magnetohydrodynamic discontinuity in an incompressible fluid

Abstract: It is proposed to consider the propagation of surface waves along a tangential magnetohydrodynamic discontinuity in the particular case where the fluid velocities on both sides of the interface are equal to zero. In [1] it was shown that waves called surface Alfven waves may be propagated along the surface separating a semi-infinite region without a field from a region with a uniform magnetic field. The linear theory of surface Alfven waves in a compressible medium was considered in [2]. In [3] the damping of surface Alfven waves as a result of viscosity and heat conduction was investigated. The propagation of low-amplitude nonlinear surface Alfven waves in an incompressible fluid in the absence of dissipative processes is described by the integrodifferential equation obtained in [4]. By means of a numerical solution of this equation it was shown that a perturbation initially in the form of a sinusoidal wave will break. The breaking time was determined. In this paper the equation derived in [4] is extended to the case of a viscous fluid. It is shown that the equation obtained does not have steady-state solutions. The propagation of periodic disturbances is investigated numerically.

On the theory of solitons in systems with dissipation

Abstract: In the weakly nonlinear approximation wave processes in flowing films, the propagation of concentration waves in chemical reactions, the hydrodynamic instability of a laminar flame, and thermocapillary convection in a thin layer are described by equations of the type ht + 4hhx + hxx + hxxxx=0. A special role in wave processes is played by nonlinear localized signals-solitary waves or solitons. In this paper the methods of the theory of dynamical systems are used to carry out a full investigation of solutions of the stationary soliton type for the above-mentioned equation.

Unsteady natural convection in a triangular enclosure

Abstract: This paper investigates the finite-difference solution of the unsteady problem of natural convection in a triangular enclosure based on the use of physical variables: velocity components, pressure, and temperature.

The flow structure near the windward side of V-shaped wings with an attached shock wave on the leading edges

Abstract: The results of a numerical calculation of a symmetric flow of supersonic gas with the Mach number M=3 past the windward side of V-shaped wings with an opening angle γ=40° and apex angles β=30, 45, and 90° are given. The possibility of the ascent of one or two Ferri points from the break point of the transverse contour of the wing is discovered and explained. It is shown that conical flow near wings of finite length need not exist in flow regimes corresponding to angles of attack α at which a Ferri point ascends, while at angles of attack smaller and larger than a certain interval, conical flow will exist. The investigation is conducted by means of a numerical method of stabilization with an artificial viscosity. The longitudinal coordinate, relative to which the steady system of equations is hyperbolic, played the part of the time variable, usual for methods of stabilization. The numerical method constructed using the scheme of [1] is described in [2] and was successfully applied to the calculation of different regimes of supersonic flow past conical wings with supersonic leading edges [2–6]. In. the present investigation the calculation algorithm of [2] is modified and makes it possible to realize motion with respect to the parameter a, this being particularly important for the stabilization of the solution in the calculation of flow regimes for which regions with a total velocity Mach number close to unity arise in the flow.

Distribution of radiant heat fluxes over the surface of three-dimensional and axisymmetric bodies in a supersonic ideal-gas flow

Abstract: Numerous studies have been devoted to the calculation of supersonic radiating flow past bodies (see the bibliography in [1, 2]). In almost all these studies the gas flows investigated are plane or axisymmetric. Three-dimensional flows, however, have received little attention. The flow of air past three-dimensional bodies was considered in [3], where the chief object was to investigate the accuracy with which a real radiating volume can be simulated by the widely used plane-layer approximation. In [4] the flow of a hydrogen-helium mixture past three-dimensional bodies was investigated in the hypersonic approximation in the neighborhood of the stagnation point and in two planes of symmetry with allowance for the screening of the radiation of vaporized material.

Connective instability of a two-layer system with thermally insulated boundaries

Abstract: The investigation of the convective stability of mechanical equilibrium of two horizontal layers of immiscible fluids has revealed the characteristics of such systems [1–3]. In particular, it has been found that, as distinct from a homogeneous horizontal layer, under certain conditions two-layer systems experience convective instability when uniformly heated from above and, moreover, oscillatory instability when heated from below. In [1–3] the problem was solved for a system with isothermal outer boundaries. In this paper the stability of equilibrium of two-layer systems is investigated for thermally insulated outer boundaries. Special attention is given to the study of the long wave instability mode.

Dynamics of sprinkler jets

Abstract: The problem of the motion of droplet-air sprinkler jets is examined. On the basis of the equations of a turbulent two-phase boundary layer the trajectories and range of these jets are calculated. A comparison of the calculation results with experiment indicates satisfactory agreement. It is shown that the expression for the range of a body projected at an angle to the horizontal gives exaggerated values for the range, while calculating the range for a single droplet with allowance for the air resistance gives values that are much too low. It has been established that in calculating the motion of sprinkler jets it is necessary to take into account the air resistance to the water droplets reduced as a result of the acceleration of the air in the immediate vicinity of the preceding droplets.

Linear stability of viscous incompressible flow in a circular viscoelastic tube

Abstract: Flow stability in rigid tubes has been the subject of much research [1] The overwhelming majority of authors of both theoretical and experimental studies now conclude that Poiseuille flow in a circular rigid tube is linearly stable However, real tubes all possess elastic properties, the influence of which has not been investigated in such detail For certain selected values of the parameters characterizing an elastic tube it has been shown that with respect to infinitesimal axisymmetric perturbations Poiseuille flow in the tube can be unstable [2] In this case boundary conditions that did not take into account the fairly large velocity gradient of the undisturbed flow near the tube wall were used The present paper reports the results of a numerical investigation of the linear stability of Poiseuille flow in a circular elastic tube with respect to three-dimensional perturbations in the form of traveling waves propagated along the system (azimuthal perturbation modes with numbers 0, 1, 2, 3, 4, and 5 are considered) It is shown that the elastic properties of the tube can have an important influence on the linear stability spectrum In the case of axisymmetric perturbations it is possible to detect an instability which, at Reynolds numbers of more than 200, exists only for tubes whose modulus of elasticity is substantially less than that of materials in common use The instability to perturbations of the second azimuthal mode is different in character, inasmuch as at Reynolds numbers greater than unity it occurs in stiffer tubes Moreover, as the Reynolds number increases it can also occur in tubes of greater stiffness

Averaging of stochastic evolution equations of transport in porous media

Abstract: A study is made of the problem of averaging the simplest one-dimensional evolution equations of stochastic transport in a porous medium. A number of exact functional equations corresponding to distributions of the random parameters of a special form is obtained. In some cases, the functional equations can be localized and reduced to differential equations of fairly high order. The first part of the paper (Secs. 1–6) considers the process of transport of a neutral admixture in porous media. The functional approach and technique for decoupling the correlations explained by Klyatskin [4] is used. The second part of the paper studies the process of transport in porous media of two immiscible incompressible fluids in the framework of the Buckley—Leverett model. A linear equation is obtained for the joint probability density of the solution of the stochastic quasilinear transport equation and its derivative. An infinite chain of equations for the moments of the solution is obtained. A scheme of approximate closure is proposed, and the solution of the approximate equations for the mean concentration is compared with the exactly averaged concentration.

Occurrence of rotational motion resulting from hydrodynamic instability

Abstract: It is shown that the stable secondary regime of a parallel flow simulating the entrance length of a jet includes a steady differential rotation. The mechanism of occurrence of nonzero angular momentum is discussed and a comparison is made with the available experimental data.

Effect of suspended particles on the stability of plane poiseuille flow

Abstract: The behavior of the neutral stability curves is investigated for various values of the particle relaxation time and mass concentration 0 ⩽ τ ⩽ 100 and 0 ⩽ f ⩽ 0.1. It is shown that as τ increases from zero the flow is at first destabilized and then at τ>6 becomes stable, while at τ>40 the stabilizing effect of the dispersed phase grows weaker. It is found that there is a certain interval 10<τ <40 on which the flow is most stable.

Vertical entry of solids into water

Abstract: The vertical inertial entry of spheres and disks of various masses into water has been investigated experimentally. The values of the virtual mass and the drag coefficients are estimated with the aid of high-speed photography of the penetration process. An expression is obtained for the nonstationary cavity near the body.

Propagation of perturbations in the boundary layer on the walls of a flat channel

Abstract: The interaction of the boundary layer and the Inviscid part of the flow is considered for the laminar, steady-state motion of a perfect gas in a symmetrical plane channel at large characteristic Reynolds numbers. The interaction zone lies at a large distance from the channel entrance and has a longitudinal dimension that exceeds the channel width in order of magnitude. It is shown that at supersonic flow velocities in the main part of the channel the perturbations introduced into the boundary layer are damped exponentially upstream from the perturbation source. In the case of a subsonic flow, as in an incompressible fluid, there is no propagation of the perturbations upstream. The propagation of perturbations in the boundary layer upstream from the perturbation source is encountered in many problems of fluid dynamics at large Reynolds numbers. A rational mathematical description of this effect has been obtained within the framework of the asymptotic theory of interaction between the boundary layer and the inviscid part of the flow (see reviews [1, 2]). Here we shall consider one of the possible interaction regimes for steady motion of a perfect gas in a symmetric plane channel (the various types of interaction for internal incompressible flows are reviewed in [2]). Attention is concentrated on the particular features of the supersonic and subsonic flow regimes in fairly long channels.

Asymptotic form of the solution to the problem of multicomponent mixture flow through a porous medium with a boundary layer

Abstract: In problems of two-phase mixture flow through a porous medium in a subterranean stratum a boundary layer phenomenon arises caused by the fact that relative phase motion exists in the system, and so having no analogy with the single-phase case. The physical nature of boundary layer phenomena is explained, and an asymptotic solution is constructed for the self-similar problem with an arbitrary number of components in the system, by using the method of matched asymptotic forms. The conditions are established for the motions of a multicomponent and a binary mixture to be equivalent, and a study is made of the role of convective factors in the formation of averaged working indices for the stratum.

Investigation of a hypersonic viscous shock layer on rotating axisymmetric bodies in the presence of blowing

Abstract: The hypersonic flow of a laminar stream of viscous compressible gas past blunt axisyrametric bodies rotating about the longitudinal axis is considered. It is assumed that gas blows from the surface of the body. The solution of the problem is obtained by a finite-difference method in a wide range of Reynolds numbers and blowing and rotation parameters. Some results of the calculations characterizing the effect of the rotation on the velocity and temperature profiles across the shock layer, on the friction and heat transfer coefficients, and the shock wave separation are given for the neighborhood of the stagnation point. For large Reynolds numbers and strong blowing an analytic solution of the problem is found in an approximation of two inviscid layers separated by a contact surface. The calculations are made for the flow past a sphere and a paraboloid and it is shown that in the presence of rotation the maximum of the heat flux is shifted from the stagnation point onto the side surface of the body. The dependence of the pressure distribution, the heat flux, and the friction coefficient is investigated for cases of constant and variable blowing over the contour of the body.

Flow in the neighborhood of the stagnation point of an axisymmetric wake

Abstract: The solutions of the equations of parabolic type describing the development of the flow in an axisymmetric wake under the Influence of viscosity and an adverse pressure gradient are considered. It is then shown that in the general case in the neighborhood of the stagnation point on the axis of the wake the solution is a singular one, the possibility of its continuation beyond the stagnation point being excluded. The following solutions are also obtained: a regular solution in the neighborhood of the stagnation point and a singular solution continuable downstream. This singular solution is the limit for the class of regular solutions having a miniumum in the velocity distribution on the axis as the minimum velocity tends to zero.