Nonlinear problem of a thin jet impinging on the surface of a heavy fluid

In a previous note by the author [1] the problem of symmetric forms of contact with oblique incidence of a free jet on a liquid was posed as a problem of the eigenfunctions of a nonlinear integral equation.Here we consider a more general flow scheme-a model of the jet curtain of an air cushion vehicle above the water surface (Fig. 1); the jet of inviscid, incompressible, weightless fluid of density ₁ impinges from a nozzle on the surface of a stationary liquid of density ₂, where, generally speaking, the pressures p₀ and p₁ are different. The problem is two-dimensional. We derive nonlinear integral equations, one of which is analogous to the Nekrasov equation for exact wave theory [2], In the limiting case of a thin jet we obtain a simple differential equation and exact solutions of the problem are constructed.Some data from the numerical calculations for the nonlinear problem of a thin jet curtain are presented in [3]; the problem has been solved in linearized form in [4],The author wishes to thank M. I. Gurevich and G. Yu. Stepanov, to whom he is indebted for his interest in the problem on jet impingement on a liquid and whose advice has been of assistance in improving the present note.     

Self-oscillations in an underexpanded jet flowing into a barrier

The distribution of the phases and amplitudes of the static pressure fluctuations with self-oscillations of an underexpanded jet flowing into a barrier is obtained experimentally in the present paper. The distribution of the Mach number in the compressed layer and in the subsonic flow in front of the barrier is shown. The results of the measurements of the characteristics of the self-oscillation process are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 38–43, November–December, 1977.     

Propagation of acoustic perturbations along a supersonic jet flowing out into the atmosphere

The propagation of acoustic perturbations (specified in the outlet cross section of a particular channel) along a supersonic jet flowing out of the channel is considered; also considered is acoustic emission from the surface of the jet into the atmosphere. The solution of these problems is obtained by a numerical method on the linear approximation. The laws governing the propagation of the perturbations as a function of the perturbation frequency and other determining parameters are investigated; these parameters include the velocity and temperature of the jet, the velocity of the subsonic accompanying flow in the external medium, and the character of the perturbation in the initial cross section of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 92–99, March–April, 1977.     

Investigation of the stability of a heavy fluid film in a hot heat-conducting gas jet on an inclined phase-transition surface

The stability of the flow of a heavy viscous fluid film flowing along the inclined phase-transition surface is examined. In contrast to [1] wherein it was assumed that a constant temperature is maintained on the free surface, it is assumed here that the fluid film is on the boundary with a gas jet which has finite specific heat and heat conduction. In this connection, the stability criteria differ substantially from [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 10–18, July–August, 1974.     

Nonlinear capillary waves on a viscous fluid jet surface

Capillary instability of a fluid jet is one of the classical problems of hydrodynamics [1]. Studying it is of practical interest, particularly for the optimization of the ignition of a liquid propellant and the development of granulating apparatus in the chemical industry [2]. Until recently, the main attention has been paid to analyzing linear problems. Dispersion equations have been obtained for small perturbations of a jet surface with the viscosity of the external medium taken into account [3]. The construction of a theory of finite-amplitude waves on an ideal fluid jet surface was started in [4, 5]. Up to now this theory has achieved substantial results, as can be assessed by the successful numerical modeling of the dissociation of an inviscid fluid jet into drops [6] (see [7, 8] also). This paper is devoted to a discussion of the nonlinear development stage of viscous fluid jet instability under conditions allowing the influence of the surrounding medium and the gravity field to be neglected.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 179–182, March–April, 1977.The author is grateful to B. M. Konyukhov and G. D. Kuvatov for suggesting this problem and performing the experiment and to M. I. Rabinovich for useful discussions.     

Symmetric shapes of contact of a jet with the surface of a heavy liquid

The plane linearized problem of oblique impingement of a weightless jet of an ideal incompressible fluid on the surface of a heavy fluid is considered. Flows are sought with symmetric forms of the contact region. Mathematically we arrive at the problem of the eigenvalues and eigenfunctions of an integral equation; solving this problem we obtain various contact forms. The fundamental result for the infinitesimally thin jet of finite intensity is derived by passing to the limit, yielding a result analagous with the forms of free vibrations of a string. Some results are presented for the problem under consideration in the nonlinear formulation.The two-dimensional problem on (vertical) impingement of a jet on a liquid was solved by Olmstead and Raynor [1]. Some results for oblique impingement of a sufficiently thin, slightly curved jet are presented by Frolov [2], Information on other studies, primarily experimental, is presented in [3].This problem is related to the model of a jet curtain of an air-cushion vehicle; in this regard we note the study of Stepanov [4] in which, in particular, a result is obtained for an infinitesimally thin jet curtain.     

Density field of a jet of viscous gas flowing from a conical nozzle into a vacuum

An approximate dependence for calculating the density field in a jet of viscous gas flowing from a conical nozzle into a vacuum is proposed on the basis of an experimental investigation and an analysis of the results of a numerical solution of the complete system of Navier-Stokes equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–30, May–June, 1986.     

Interaction of a heavy fluid flow in a channel with a transverse jet barrier

An experimental and numerical analysis of the interaction between a plane horizontal water flow in a rectangular channel (free water current) and a plane thin water jet (water jet curtain) is presented; the jet flows out vertically from either a slot nozzle in the bottom of the channel or the crest of a rigid spillway at a velocity appreciably (several times) greater than the water velocity in the channel. Numerical calculations were carried out using the STAR-CD software package preliminarily tested against the experimental data obtained. The dependence of the water level in the channel at a certain distance ahead of the jet barrier on the main jet parameters and the water flow rate in the horizontal channel is studied. It is found that in the region of the interface between the flows both steady and unsteady (self-oscillatory) flow patterns can be realized. Steady stream/jet interaction patterns of the “ejection” and “ejection-spillway” types are distinguished and a criterion separating these regimes is obtained. The notion of a rigid spillway equivalent to a jet curtain is introduced and an approximate dependence of its height on the relevant parameters of the problem is derived. The possibility of effectively controlling the water level ahead of a rigid spillway with a sharp edge by means of a plane water jet flowing from its crest is investigated. The boundary of transition to self-oscillation interaction patterns in the region of the flow interface is determined. The structure of these flows and a possible mechanism of their generation are described. Within the framework of the inviscid incompressible fluid model in the approximate formulation for a “thin” jet, an analytical dependence of the greatest possible depth of a reservoir filled with a heavy fluid at rest and screened by a vertical jet barrier on the jet parameters is obtained.     

Nonstationary motion of a shell on the surface of a heavy fluid

A three-dimensional nonstationary problem of vibrations of a flexible shell moving on the surface of an ideal heavy fluid. The forces due to surface tension are ignored. The problem is formulated in the space of the acceleration potential. The potential of the pulsating source is found by solving the Euler equation and the continuity equation taking into account the free-surface conditions (linear theory of small waves) and the conditions at infinity. The density distribution function of the dipole layer is determined from the boundary conditions on the surface of the shell. Formulas for determining the shape of gravity waves on the fluid surface and the natural frequencies of vibrations of the shell are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 66–75, July–August, 2009.     

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.     

Effects of inertia and surface tension on a power-law fluid flowing down a wavy incline

We consider a thin film of a power-law liquid flowing down an inclined wall with sinusoidal topography. Based on the von Kármán–Pohlhausen method an integral boundary-layer model for the film thickness and the flow rate is derived. This allows us to study the influence of the non-Newtonian properties on the steady free surface deformation. For weakly undulated walls we solve the governing equation analytically by a perturbation approach and find a resonant interaction of the free surface with the wavy bottom. Furthermore, the analytical approximation is validated by numerical simulations. Increasing the steepness of the wall reveals that nonlinear effects like the resonance of higher harmonics grow in importance. We find that shear-thickening flows lead to a decrease while shear thinning flows lead to an amplification of the steady free surface. A linear stability analysis of the steady state shows that the bottom undulation has in most cases a stabilizing influence on the free surface. Shear thickening fluids enhance this effect. The open questions which occurred in the linear analysis are then clarified by a nonlinear stability analysis. Finally, we show the important role of capillarity and discuss its influence on the steady solution and on the stability.     

Apparatus for investigating the liquid-nitrogen distribution in the spray cone of a jet flowing out of a nozzle into an air flow

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 93–97, September–October, 1991.     

ROUNDED FLOWING STATES OF OBSTRUCTED BUOYANT JET

The mutual relationships of three effective factors, the diameter D/d (d is the diameter of exit) of obstructed plate, exit densimetric Froude number and the distance H/d of the plate from jet orifice for obstructed buoyant jet in static ambient, are analyzed to explain normal and abnormal rounded flowing (reverberated and bifurcated flowing). The critical Froude numbers for obstructed buoyant jets with H/d=2, 4, 6, 8 which distinguished normal and abnormal flowing pattern are obtained. Normal rounded flowing is found only for a plate under a special value of H/d. A fitted formula of critical Froude numbers with H/d and D/d is presented to distinguish rounded flowing types. The occurring of reverberated or bifurcated flowing in abnormal rounded flow is analyzed. Based on the results of obstructed buoyant jets with D/d=1, normal rounded flowing occurred only for all conditions and axial dilution behind the plate under different H/D is obtained.     

Equations and forms of motion of a jet flowing onto a liquid

A nonlinear theory is constructed for a thin jet of nonviscous, incompressible, weightless fluid flowing from a nozzle onto the surface of an immobile heavy liquid. The theory is asymptotically (over jet thickness) more accurate than that presented in [1]. Forms of the flow are studied as functions of nozzle, jet, and heavy liquid parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 20–28, November–December, 1976.     

Effects of fluid recirculation on mass transfer from the arterial surface to flowing blood

The effect of disturbed flow on the mass transfer from arterial surface to flowing blood was studied numerically,and the results were compared with that of our previous work.The arterial wall was assumed to be viscoelastic and the blood was assumed to be incompressible and non-Newtonian fluid,which is more close to human arterial system.Numerical results indicated that the mass transfer from the arterial surface to flowing blood in regions of disturbed flow is positively related with the wall shear rates and it is significantly enhanced in regions of disturbed flow with a local minimum around the reattachment point which is higher than the average value of the downstream.Therefore,it may be implied that the accumulation of cholesterol or lipids within atheromatous plaques is not caused by the reduced efflux of cholesterol or lipids,but by the infiltration of the LDL(low-density lipoprotein) from the flowing blood to the arterial wall.