The critical jet flow regime

The critical jet flow regime is investigated on the basis of the equations for the Reynolds stresses, the boundary layer equations and the elements of the theory of thermal explosion. The results of calculating the transition Reynolds numbers for plane and axisymmetric jets and for wake flows are compared with the theoretical values obtained by other methods and with the data of experimental research.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 11–15, May–June, 1990.     

Some problems in the theory of plane jets of conducting fluid

Using the boundary-layer equations as a basis, the author considers the propagation of plane jets of conducting fluid in a transverse magnetic field (noninductive approximation).The propagation of plane jets of conducting fluid is considered in several studies [1–12]. In the first few studies jet flow in a nonuniform magnetic field is considered; here the field strength distribution along the jet axis was chosen in order to obtain self-similar solutions. The solution to such a problem given a constant conductivity of the medium is given in [1–3] for a free jet and in [4] for a semibounded jet; reference [5] contains a solution to the problem of a free jet allowing for the dependence of conductivity on temperature. References [6–8] attempt an exact solution to the problem of jet propagation in any magnetic field. An approximate solution to problems of this type can be obtained by using the integral method. References [9–10] contain the solution obtained by this method for a free jet propagating in a uniform magnetic field.The last study [10] also gives a comparison of the exact solution obtained in [3] with the solution obtained by the integral method using as an example the propagation of a jet in a nonuniform magnetic field. It is shown that for scale values of the jet velocity and thickness the integral method yields almost-exact values. In this study [10], the propagation of a free jet is considered allowing for conduction anisotropy. The solution to the problem of a free jet within the asymptotic boundary layer is obtained in [1] by applying the expansion method to the small magnetic-interaction parameter. With this method, the problem of a turbulent jet is considered in terms of the Prandtl scheme. The Boussinesq formula for the turbulent-viscosity coefficient is used in [12].This study considers the dynamic and thermal problems involved with a laminar free and semibounded jet within the asymptotic boundary layer, propagating in a magnetic field with any distribution. A system of ordinary differential equations and the integral condition are obtained from the initial partial differential equations. The solution of the derived equations is illustrated by the example of jet propagation in a uniform magnetic field. A similar solution is obtained for a turbulent free jet with the turbulent-exchange coefficient defined by the Prandtl scheme.     

Methods of calculation and numerical analysis of conducting-gas flow in high-current electric arcs

The mechanism of conducting-gas acceleration in an electric arc by intrinsic magnetic field was first investigated in [1]. Further theoretical study of this question was associated with the numerical calculation of arcs [2–7]. A more general approach to the solution of the problem was realized in [4], where the finite-difference method was used. Integral calculational models were developed in [5–7]. The present work proposes a modified version of the difference method [4] and a series of integral methods for the calculation of the conducting-gas flow in a high-current electric arc. The development of integral methods is of interest in that they are usually associated with adequate accuracy in determining integral values and values averaged over the cross section by a relatively simple calculation, and also allow the solution of the problem to be obtained in a number of situations when the realization of a difference method is complicated. The results of different calculation methods are compared. The effect of conditions in the initial cross section of the calculation region of the arc on its characteristics is investigated and a numerical analysis of the heating and acceleration of conducting gas is carried out.Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 103–110, September–October, 1978.     

Plasma density and electeic field strength distributions at a boundary with an electrode

Close to the cathode in an arc discharge, or to the surface of a probe operating on the ionic branch of its characteristic, conditions are obtained under which the Langmuir layer freely passes ions coming from the plasma, while the reverse ion flow is virtually zero. The plasma density, ion distribution, and electric fieid-strength close to the electrode are found in the present paper. The extrapolated length is evaluated for the plasma density. The absolute value of the electric field strength increases logarithmically at the boundary with the electrode.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No, 2, pp. 4–6, March–April, 1970.     

Effect of sound on a supersonic jet

It is known that under the influence of sound from an external source or the sound emitted by the supersonic jet itself at discrete frequencies in nonoptimal flow regimes the supersonic jet expands more rapidly and its range is reduced [1, 2], However, the mechanism of action of the sound on the supersonic jet has not been adequately investigated and, in particular, no one has determined the intensity of the external source capable of producing a marked change in the gas dynamic parameters of the jet, its characteristics or how the interaction process develops. These questions are examined below. By means of shadow photography with a pulsed light source it is shown that a significant change in the gas dynamic characteristics of the supersonic jet can be achieved by directing at its base along the normal to the jet boundary sound with an intensity corresponding to 0.1–0.2% of the total pressure in the jet. The appearance of large-scale disturbances on the irradiated side of jet and the directional emission of sound by the jet at the frequency of the external source are noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–174, November–December, 1989.The author is grateful to A. A. Kochetkov for assisting with the work.     

Development of the temperature fields in an electric arc struck on a point electrode in a homogeneous gas stream

A study is made of the problem of a point electric source in a homogeneous gas stream and operating in the arc discharge regime. The development of an electric arc struck on a point cathode in a medium which moves without deformation is studied. The stationary problem of a two-dimensional electric arc that develops in a medium with piecewise constant electrical conductivity is solved. Expressions are obtained for the temperature fields, the thickness of the arc, the current-voltage characteristics, and the power in the arc. The stability of this stationary state with respect to short-wavelength perturbations is investigated. The critical electrical current at which instability commences is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 91–99, March–April, 1981.I thank O. N. Sinkevich and I. M. Rutkevich for discussing the work, and also V. I. Grabovskii and V. A. Mareev for making some calculations.     

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.     

A case of jet flow of a gravity fluid

The problem of plane steady ideal heavy fluid flow bounded by an impermeable polygonal section, a curvilinear arc section, and a finite section of free surface is investigated in an exact nonlinear formulation. Hydrodynamic singularities may exist in the stream. A large class of captation problems of jet theory reduces to studying this kind of flow. The unique solvability of the problem under investigation is proved for sufficiently large Froude numbers and small arc curvature. A method of solution is given and an example is computed. Such problems have been solved earlier by numerical methods [1–3]. Some problems about jet flows of a gravity fluid with polygonal solid boundaries have been investigated by an analogous method in [4, 5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 140–143, May–June, 1975.     

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.     

Ion distribution function at the boundary with an electrode

The ion distribution function is found in the case in which the Langmuir layer freely passes the ions incident from the plasma while the reverse ion flux is zero. These conditions are realized near the cathode in an arc discharge and at the surface of a probe operating on the ion branch of the characteristic. The electric field outside the Langmuir layer is assumed small. We obtain the connection between ion current and plasma density at the boundary with the electrode, the expressions for the ion mean kinetic energy and for the mean energy removed from the plasma by the ion, which differ markedly from the corresponding expressions in the Maxwellian distribution case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 47–54, May–June, 1969.     

Thermal multipoles for a jet in ambient spathermal multipoles for a jet in ambient space

A general solution of the thermal problem for a non-self-similar axisymmetric jet is determined on the basis of the multiple approach developed for problems of non-self-similar jets in ambient space [1, 2], and several problems of convective heat-transfer in simply- or doubly-connected domains are solved. The advantage of expanding the solution of the convective heat conduction equation in eigenfunctions of the problem is demonstrated. As an illustration, the solutions for a thermal dipole and quadrupole and for a jet flow in a heated tube are presented. The corresponding solutions are also obtained for a turbulent jet in ambient space. The most favorable heat-exchange regime for a jet in a heated tube is predicted on the basis of the particular behavior of the eigenfunctions of the thermal problem.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 40–46, January–February, 1996.     

Effect of external turbulence on the development of a turbulent jet

The effect of external turbulent agitation on jet development has been investigated in [1–3]. The difference of the method employed in the present work lies in the assumption that the turbulence scale of the external flow is substantially larger than the turbulence scales in either the jet or the mixing layer. Utilizing this assumption, it becomes possible to solve separately the energy equations for the turbulence of the external flow and of the jet. Solutions obtained on the basis of this assumption are found to be in qualitative agreement with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 24–29, January–February, 1977.     

Parameters of flow near the axis in the shock layer in the interaction of a supersonic jet with a barrier

The axisymmetric interaction between a supersonic jet with a finite expansion ratio and a barrier is accompanied by the formation of complex sub- and supersonic flow in a shock layer whose thickness depends on the parameters of the jet and the position of the barrier. The main relationships of the interaction process have been established experimentally ([1–3] and others) and individual results of numerical calculations of such flows are known [4]. An analytical investigation of the parameters in the shock layer formed ahead of a plane barrier when an underexpanded jet impinges on it is presented below. The results of [5], where the region near the axis of a shock layer of arbitrary thickness is analyzed within the framework of a model of flow with a constant density, is placed at the basis of the analysis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 63–70, September–October, 1978.The author thanks Yu. M. Tsirkunov for useful discussions.     

Speed of Motion of a Short‐Circuit Arc in an Insulated Conductor

The paper deals with different scenarios of electric arc discharge propagation in the ITER tokamak toroidal magnet conductor. Estimates are obtained for the rate of discharge propagation along an insulated conductor and the conditions under which the conductor is cut by a direct current arc with typical values of 10–80 kA. The modes of a vacuum arc and normal and highpressure arcs are considered. The analysis was based on steadystate heat and masstransfer equations in a combination with the model of evaporation of the Knudsen–Langmuir surface.     

Calculations for a cylindrical electric arc with allowance for energy transfer by radiation with the hydrogen at a pressure of 100 atm

An approximate method is described for the consideration of energy transfer by radiation during the utilization of real properties of a gas (in particular, the frequency-dependent absorption coefficient under conditions of local thermal equilibrium). With increasing pressure, it becomes necessary to take self-absorption into account over almost the entire frequency spectrum.Calculations are carried out for a wall-stabilized cylindrical electric arc in hydrogen as an example for a pressure of 100 atm and channel radii of 0.3, 1, and 3 cm at values of current strength up to the order of 10 A. The strong effect of radiation on the current-voltage characteristic of the arc, the gas temperature, and the nature of its distribution over the arc radius is demonstrated.The process of energy transfer by radiation plays a significant and sometimes predominant role in the thermal balance of electric arcs with high current strengths [1–9]. Calculations have been performed for cylindrical arcs in atmospheres of argon and hydrogen [5, 7] with allowance for energy transfer by radiation and for atmospheric pressure in which case the gas is essentially transparent to radiation. Approximate estimates were obtained for the self-absorbed portion of the radiation.The role played by radiation increases with increasing current strength, arc radius, and pressure, while self-absorption in this process extends over an increasingly large region of the spectrum. Hence, calculations must be carried out for the arc if conditions are such that the gas in the arc does not transmit radiation.In [10–13], an approximate method was developed for taking into account energy transfer by radiation in the presence of intense selfabsorption as applied to heat transfer problems under conditions of local thermal equilibrium with allowance for the variation of the absorption coefficient as a function of the frequency. The conditions for local thermal equilibrium in an arc passing through an argon or hydrogen atmosphere are fulfilled for pressures greater than atmospheric pressure and for current strengths greater than 10 A [14–16], The results of [10–12] were used as the foundation for calculations based on an electric arc in argon at atmospheric pressure, under which conditions, self-absorption affects only the transitions to the ground state. The part played by radiation in the heat transfer process is smaller than the part played in the energy transfer by conduction. Calculations confirmed the results of [5, 7].The role of energy transfer by radiation in the energy balance of the arc increases with increasing pressure, while in turn, the role of the continuous spectrum increases for the radiation. The results of calculations performed for a wall-stabilized arc burning in an atmosphere of hydrogen at a pressure of 100 atm are given in the present paper. In this case, almost the entire energy supply is lost by radiation. The approximate method of accounting for energy transfer by radiation is demonstrated by an example.Notation and T gas density and temperature, respectively - u velocity - c_p heat capacity of the gas at constant pressure - coefficient of thermal conductivity - coefficient of electrical conductivity - x and r cylindrical coordinates - r₀ channel radius - I current strength - E electric field strength - u ° equilibrium value of radiation energy density - u value of radiation energy density - radiation frequency - divergence of energy flux density transported by radiation - k absorption coefficient - c speed of light - _i emissivity of the i-th region of the spectrum     

Influence of jet turbulence on flow in the boundary layer near the wall

Results are presented of an experimental investigation of the interaction of a subsonic axisymmetric jet, within the initial section, and a flat plate mounted parallel to the jet axis. Relations are obtained for the mean and fluctuating velocities in the wall boundary layer, and the friction stress on the plate is also given.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 77–82, November–December, 1972.     

Gas flow in a bent channel

The results are given of experimental investigations of flow of gas (air) in a curvilinear cylindrical channel. Patterns of the streamlines near the wall and the separation region were obtained by blowing cold air through a transparent model. In an investigation of the flow of hightemperature gas, in which an electric arc heater was used to supply the thermal energy, the profiles of the total pressure and the stagnation temperature were measured at different sections of the channel. It was found that the deformation of the profiles after the bend ends earlier for the hot gas than for the cold. The heat flux increases sharply after the bend.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 154–157, September–October, 1981.I thank A. B. Vatazhin for helpful discussions.     

Instability of a compound liquid jet

In the linear Rayleigh theory [1] the degree of stability of a jet is determined by the viscosity and inertia characteristics of the fluids and the interphase surface tension. The stability of a jet in an infinite medium increases with increase in the viscosity of both the jet and the medium [2, 3]. The presence of two interfaces is responsible for various features of the development of instability in a liquid layer on the surface of a cylinder, and in particular a layer on the inner surface of a cylinder is more unstable than one on the outer surface [4]. In [5, 6] the breakup of a hollow jet in an external medium was investigated. In this paper we examine, in the linear approximation, the stability of a compound jet of nonmiscible liquids with respect to small axisynmetric perturbations of the interfaces. The instability characteristics are given for jets with inviscid and very viscous outer shells. The conditions governing the suppression of rapidly growing instabilities of the inner part (core) of the jet by a viscous shell are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–8, July–August, 1985.     

The degeneration of nucleate boiling conditions under conditions of free convection

An experimental investigation was made of the effect of the degeneration of nucleate boiling conditions under conditions of natural convection for alkali metals (potassium, cesium) in working sections with diameters of 14 and 11 mm in a pressure range of 0.04–1.7 bar, and for nonmetallic liquids (ethanol, benzene, and carbon tetrachloride) in working sections with diameters from 0.1 to 10 mm in a pressure range of 0.05–2.5 bar. The regions were determined for thermal flows, with which the appearance of a vapor phase after single-phase natural convection leads to the formation of a stable vapor film. The results of high-speed movingpicture photography of this phenomenon are also given.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 69–73, January–February, 1972.     

Investigation of vapor condensation in a vapor-air jet

A vapor-air axisymmetric submerged jet was calculated for various environmental conditions and a number of values of vapor concentration and temperature of the vapor-air mixture in the initial section of the jet. The process of condensation in a vapor-air jet was investigated experimentally with the use of the laser-optical method of measuring the degree of dispersion and concentration of condensate droplets.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 142–144, May–June, 1976.