On the dynamical equations for liquid jets

Quasi-one-dimensional equations for the three-dimensional motion of thin liquid jets have been derived by Entov and the present author [1, 2] from the balance integral equations for the mass, momentum, and angular momentum written down for a jet section. Simplified equations of this kind make it possible, in particular, to investigate with comparative ease the motion of bending jets and also the loss of stability of jets moving in air associated with the development of kinks, etc. It is of interest to obtain quasi-one-dimensional equations of jet motion by direct integration over the section of a thin jet of the three-dimensional differential equations of hydrodynamics. In the present note, this approach is illustrated by the example of bending of a jet in a plane.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 161–163, January–February, 1983.     

Solution to the problem of a swirling jet from an annular orifice

The problem of the propagation of a laminar immersed fan jet with swirling was considered in [1–3]. In [1], the jet source scheme was used to find a self-similar solution for a weakly swirling jet. An attempt to solve by an integral method the analogous problem for a jet emanating from a slit of finite size was made in [2]. In [3], the equations of motion for a jet with arbitrary swirling were reduced under a number of assumptions to the equations that describe the flow of a flat immersed jet. This paper gives the numerical solution to the problem of the propagation of a radial jet emanating with arbitrary swirling from a slit of finite size and an analytic solution for the main section of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 49–54, March–April, 1991.     

Effect of acoustic oscillations on the stability of a plane jet

The problem of the effect of acoustic oscillations on the stability of a compressible ideal-fluid jet flow is examined in the case of a plane jet with standing acoustic waves superimposed across it. The method of dividing the motion into fast and slow with allowance for nonlinear acoustic effects is employed. The acoustic oscillations are found to affect the growth rate of unstable hydrodynamic disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 54–60, July–August, 1991.     

Initiation of cavitation by injection of hot steam into a cold liquid jet

The problem of the dynamics of a hot steam bubble in the nonuniform flowfield of a plane cold liquid jet is considered. The motion of the bubble along the symmetry axis is analyzed with allowance for nonequilibrium condensation and heat conduction by the steam and the liquid. The domain of jet and steam parameters corresponding to the dynamic cavitation bubble initiation mode, is evaluated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–100, September–October, 1995.     

Mechanism of energy separation in a gas ejector

A new phenomenon is revealed — the rotation of an ejecting jet, discharging from a nozzle and adhering to the wall of the mixing chamber, in an axisymmetric gas ejector in modes with zero and negative ejection coefficients — and a possible mechanism for its origin is discussed. It is suggested that the rotation of an adhering jet, which induces axisymmetric vortex motion of the gas in the injector, is responsible for the inverse separation of the initially energetically homogeneous stream into heated and cooled sections.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 145–151, November–December, 1977.     

Unsteady-state periodic jet structure created by the pulsed motion of a piston jet generator

The results of an experimental and theoretical investigation of the process of formation of an unsteady-state water jet by the pulsed motion of the piston of a piston jet generator are given. An approximate mathematical model of the generator dynamics which can explain the mechanism of formation of the experimentally obtained periodic transverse thickening structure is considered.Nikolaev. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 172–178, July–August, 1996.     

Investigation of unsteady flow structure during discharge of a shock-heated gas

This paper examines the structure of the near-gasdynamic section of a jet discharging into a rarefied volume. The experimental part of the article deals with unsteady discharge of a high-temperature gas. Discharge from a slot and from a circular aperture is investigated for air, nitrogen, CO₂, and argon with nonuniformities from 20–200. Approximate relations are obtained to describe the motion of the front of a discharging substance in dimensionless coordinates and the associated perturbation along the flow axis. It is established that the time for a steady geometric structure to form in the gasdynamic section of the jet is greater than the values obtained from data available in the literature.Translated from Zhurnal Prikladnoi Mekhaniki i Teoreticheskoi Fiziki, No. 5, pp. 34–40, September–October, 1973.     

Horizontal submerged jet in a stratified fluid

The problem of jet flow excited in a viscous density-stratified fluid by a point source of momentum acting horizontally is considered. Simplified asymptotic equations are obtained in the boundary layer approximation. It is shown that the vertical velocity component is small and the motion in the jet has a layered structure. The longitudinal velocity distributions in the jet are measured experimentally. It is shown that these distributions are affine and can be satisfactorily approximated by Schlichting's well-known boundary layer solution for a round submerged jet in a fluid uniform with respect to density.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 10–16, November–December, 1993.We are grateful to I. A. Filippov for assisting with the experiments.     

Investigation of electrogasdynamic jet behind a source of charged particles

We have investigated theoretically and experimentally a submerged jet emerging from a source of charged particles (corona-producing system). Simplest scaling laws are established for the distribution of the electric parameters in a unipolarly charged gas jet in the case of grounded and insulated sources. It is shown that the current from a grounded source and the floating potential to which an insulated system is charged depend strongly on the ambient conditions. Methods of decreasing the floating potential were investiated experimentally. The distributions of the local electric parameters in the jet were measured using a probe method. The propagation of viscous unipolarly-charged jets and the phenomenon of electric wind formation were investigated in [1, 2] and [2–5], respectively. The distinguishing features of the flows considered in the article consisted of their organization (blowing of a jet of uncharged gas over the corona-producing system), absence of walls to limit the flow, and the weak influence of electrostatic forces on the gas motion. The developed setup has made it possible to simulate the processes of accumulation of electric charge on a body as a result of the escape of a jet stream.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–13, September–October, 1971.In conclusion, the authors thank G. M. Bam-Zelikovich for useful discussions.     

Calculation of three-dimensional weakly expanding flow in jets and channels

The results are given of a calculation of laminar flow in a channel of square section and the motion of a turbulent jet from a cruciform nozzle in an ambient flow. To calculate the secondary flows, the field of the transverse velocity is decomposed into irrotational and solenoidal components. The results of the calculation of the flow in the channel are compared with the calculations of other authors and experimental data. To calculate the flow in the turbulent jet, a one-parameter turbulence model is used, and the influence of the inhomogeneity of the distribution of the longitudinal component of the velocity on the components of the Reynolds stress tensor is taken into account. The results of calculation of the flow in the jet behind a cruciform nozzle are compared with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 36–44, July–August, 1984.     

Effect of the atmosphere with the fall of bodies into water

The mechanism of the effect of the atmosphere on the picture of the entrance of a body into water is discussed. The self-similar character of the motion of a spurting jet is demonstrated, and an evaluation is made of the aerodynamic forces acting on spurting jets, which explain the qualitative difference in the character of the motion of the liquid as a function of the density of the atmosphere. These results were set forth briefly in a paper by L. I. Sedov given at the XIII International Congress of Mechanical Engineers in Moscow in August, 1972.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–6, September–October, 1973.     

Formation of a pulsed jet behind a supersonic nozzle when the gas can relax at the entrance to the nozzle

The formation of a pulsed jet behind supersonic nozzles is considered when relaxation processes take place in the gas entering the nozzle. In a general formulation, the problem of the motion of the front of the exhausting matter and the disturbances accompanying it in the process of formation of a pulsed jet is determined by a large number of parameters, which characterize the exhausting gas and the residual gas of the pressure chamber and also the geometry of the flow conditions. A reliable computational model of a pulsed jet does not exist. To construct such a model, experiments are required in a wide range of boundary and initial conditions. An investigation was made into flow of shockheated argon, nitrogen, and carbon dioxide out of nozzles set up at the end of a shock tube. Generalized dependences were obtained for describing the motion of the front of the nonstationary jet and the wave in front of it in a wide range of the initial pressure-difference parameters and variation of the stagnation temperatures. The choice of the generalized parameters when relaxation of the excited internal degrees of freedom of the molecules of the gas can occur at the entrance to the nozzle is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 129–135, November–December, 1980.     

Dynamical equations for a liquid jet

Equations are described for the three-dimensional motion of a thin jet of viscous liquid. The jet is a liquid body whose transverse dimensions are small compared with the other characteristic dimensions of the problem. The aim in the present paper is to establish a closed system of asymptotic equations for the dynamics of such a thin jet. A more detailed derivation of quasi-one-dimensional asymptotic equations for the dynamics of thin liquid jets and an analysis on the basis of them of the curved decay shape of the jet in the linear and nonlinear stages is contained in [1, 2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 11–18, September–October, 1980.     

Nonstationary processes in starting strongly underexpanded jets

Results of the investigation of nonstationary efflux of argon by the electron-beam-sounding method are presented in [1]. Comparing the regularities obtained in that paper for the front motion of material during efflux from a nozzle with computations [2] for nonstationary expansion from a spherical source and the experimental results in [3] permitted clarification of the singularities of the influence of counter pressure and the temperature factor in jet expansion. The density distribution in nonstationary nitrogen and argon jets is obtained in this paper and study of the regularities of the front motion of the escaping gas is continued.Translated from Zhurnal Prikladnoi Mekhiniki i Tekhnicheskoi Fiziki, No. 1, pp. 34–40, January–February, 1978.     

Influence of tangential injection on heat transfer to a cone in the transition reynolds number domain

A gas mist produced by supplying a cooling gas through a separate slot or a system of slots along the surface is a widespread method of obtaining a mass-transfer heat shield. Application of the gas mist for heat-shield purposes can hence be combined with its use to control gasdynamic processes. One possible scheme is gas injection through a slot tangentially to the cooled surface so that the directions of motion of the injected jet and the main flow coincide.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 25–29, September–October, 1977.     

Turbulent mixing of accompanying and opposing flows

The solution of the problem of the edge of a turbulent jet, obtained in [1] starting from a model of the vortical motion of an ideal liquid, is generalized for the case of the turbulent mixing of two plane semibounded (accompanying or opposing) flows of an incompressible liquid. It is shown that the results of calculation are in qualitative agreement with experimental data and that they are close to them quantitatively. Some of the special characteristics of the method are discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 92–101, November–December, 1973.     

Pressure wave breakdown of a gas film in a liquid-filled slit

In [1–4] the results of investigating the breakdown of gas bubbles by medium-intensity pressure waves are presented and various bubble breakdown mechanisms are proposed. It is shown that breakdown may occur as a result of the formation of a cumulative jet on the boundary of the bubble or as a result of instability due to the relative motion of the bubble in the wave. In [5] experimental data on the pressure wave breakdown of a gas film in a liquid on a solid wall are reported. It is shown that at wave amplitudes p/p₀1 a liquid jet is formed at the edge of the gas film. The jet, traveling along the wall, strips off the film and carries it into the surrounding liquid. Below we investigate the pressure wave behavior of a gas film in a liquid-filled slit.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 175–178, September–October, 1992.     

Development of a two-dimensional turbulent jet in an infinite space

The second and third terms in the asymptotic expansion of the stream function in the nonsimilar problem of the development of a two-dimensional turbulent jet in an unbounded space are found in final form. Results of experimental investigations of free turbulent jets are cited, and the effect of the initial velocity profile on the aerodynamic characteristics of the jet is considered. The problem of the development of a two-dimensional turbulent jet in an unbounded space has been considered in [1–3]. The existing solution is similar, and is valid only at a sufficiently large distance from the slit. Allowance for the finite dimensions of the slit leads to a nonsimilar problem. The papers [4–6] are devoted to the experimental investigation of the free two-dimensional turbulent jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–142, July–August, 1971.     

Investigation of the propagation of a two-dimensional wall jet over a step

The propagation of an underexpanded sonic jet over a flat end face has been experimentally investigated. As distinct from previous studies, the object of investigation is not a free jet, but a jet flowing from a nozzle along a horizontal surface. The total separation of the jet from the surface and its attachment to the end wall are related to the propagation characteristics of underexpanded wall jets. The effect of the total pressure in the jet and the height of the step on the separation of the jet and its attachment to the wall and, moreover, on the principal characteristics of the flow — the pressure in the base region, the extent of the circulation zone, the jet trajectory — is examined. The associated hysteresis effects are studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 61–66, July–August, 1991.     

Calculation of the momentum and heat transfer in turbulent gas-particle jet flows

The equations for the second moments of the dispersed-phase velocity and temperature fluctuations are used for calculating gas-suspension jet flows within the framework of the Euler approach. The advantages of introducing the equations for the second moments of the particle velocity fluctuations has previously been quite convincingly demonstrated with reference to the calculation of two-phase channel boundary flows [9–11]. The flows considered below have a low solid particle volume concentration, so that interparticle collisions can be neglected and, consequently, the stochastic motion of the particles is determined exclusively by their involvement in the fluctuating motion of the carrier flow. In addition to the equations for the turbulent energy of the gas and its dissipation, the calculation scheme includes the equations for the turbulent energy and turbulent heat transfer of the solid phase; however, the model constructed does not contain additional empirical constants associated with the presence of the particles in the flow.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 69–80, May–June, 1992.