On the shapes of swirling annular jets of a liquid

Annular jets of an incompressible liquid moving in a gas at rest are of interest for applications. A critical analysis of the investigations into jets from centrifugal nozzles is contained in [1]. These investigations elucidated the experimentally observed tulip and bubble jet shapes, and also predict the existence of annular jets of periodic shape. However, simplifications of the flow details are made to obtain the results. For example, in the equations describing the equilibrium of the forces acting on the film, no allowance is made for forces that arise on account of the curving of its shape in the meridional sections nor for the variability of the tangential velocity component in the field of the centrifugal forces. In the present paper, the method of [2] is used to derive equations that describe the flow of swirling annular jets of liquid with uniform profile of the longitudinal velocities in an undisturbed ideal medium with allowance for surface tension and gravity forces and also the pressure difference outside and within the jet. The results of calculations are given that illustrate the dependence of the jet shapes on the relative contributions of the capillary and inertial forces and also the pressure difference, the intensity of the initial swirling, the angle at which the liquid leaves the nozzle, and the gravity force.Translated from Izyestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 144–148, September–October, 1979.I am grateful to V. Ya. Shkadov for interest in the work.     

Asymptotic method for solving problems with radial laminar jets of immiscible liquids

Two problems involving radial laminar jets of immiscible liquids are considered: a free radial slit jet and a jet on a rotating disk. An asymptotic method of solution is proposed that makes it possible to determine the flow parameters far from the source. The difference between these flows and those of homogeneous liquids is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 192–28, May–June, 1980.     

Mathematical simulation of unsteady flow past a wing with jets

The various approximate approaches to the investigation of the unsteady aerodynamic characteristics of an airfoil with jet flap [1–3] are applicable only for an airfoil, low jet intensity, and low oscillation frequencies. In the present paper, the method of discrete vortices [4] is generalized to the case of unsteady flow past a wing with jets and arbitrary shape in plan. The problem is solved in the linear formulation; the conditions used are standard: no flow through the wing and jet, finite velocities at the trailing edges where there is no jet, and also a dynamical condition on the jet. The wing and jet are assumed to be thin and the medium inviscid and incompressible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 139–144, May–June, 1982.     

Ultrasonic jet in an external acoustic field

The interaction of supersonic jets with external acoustic waves is investigated in connection with the emission of sound of discrete frequency by the jets. A plausible physical scheme explaining the appearance and maintenance of the oscillations of supersonic jets with discrete frequency was proposed in [1]. A model problem of the effect of pressure perturbations of a given frequency, traveling along the surface of a two-dimensional jet is also investigated there. The results of the solution of this problem (in particular, the presence of critical frequencies at which the perturbations in the jet grow indefinitely in the direction of motion of the flow) substantiate the hypothesis that by virtue of its periodic (cellular) structure a supersonic jet has the properties of a resonator. In [1] the more general problem of interaction of a supersonic jet with an external acoustic field is also formulated, which is in complete correspondence with the physical scheme of the phenomena developed in that article. In the present work this problem is solved in its complete form for plane and cylindrical jets for symmetric and antisymmetric perturbations in an external acoustic field, and also in the presence of subsonic accompanying flow in the outer medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 105–113, March–April 1974.     

“Lateral” interaction of a supersonic underexpanded ideal-gas jet with surfaces of different shape

A numerical investigation is made of the interaction of an underexpanded jet of an inviscid and nonheat-conducting gas issuing from an axisymmetric conical nozzle with plane, cylindrical, and spherical surfaces. It is assumed that the flow turning angle for flow about a barrier is smaller than the critical angle, and subsonic regions are absent in the flow field studied. The effect of the characteristic parameters (Mach number at the nozzle exit, jet underexpansion) on the flow pattern and jet forces is analyzed. The results of numerical calculations are compared to the results of approximate theories and experimental data. A theoretical solution of the problem of the effect of a supersonic jet on a surface of given shape, even in the approximation of an inviscid, nonheat-conducting gas, is quite difficult. A reason for this is that the flow region contains shock waves interacting with each other, contact discontinuities, and zones of mixed sub-and supersonic flow. As far as is known to the authors, the results obtained for three-dimensional problems for the interaction of supersonic jets with each other or with barriers are primarily experimental (for example, [1–6]). A numerical analysis of the interaction of axisymmetric ideal-gas jets was carried out in [7–10]. In [7] a three-dimensional form of the method of characteristics was used to calculate the initial interaction region for two supersonic cylindrical jets (with Mach number M=10) intersecting at an angle of 60. The interaction of several jets has been considered in [8, 9], where the solution was obtained according to the Lax—Wendroff method without elimination of the discontinuity lines of flow parameters. In [10] the lateral interaction of axisymmetric supersonic jets with each other and with a plate is investigated by means of a straight-through calculationTranslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–8, November–December, 1974.The authors thank A. N. Kraiko for useful discussions of the results, and A. L. Isakov and É. N. Gasparyan for kindly providing the experimental data.     

The mathematical simulation of various condensation regimes in turbulent isobaric jets

Mathematical models are considered and calculations made for flows in turbulent isobaric steam—air jets in the presence of condensation of the water vapor they contain. The models consist of gasdynamic equations for a turbulent jet, equations for a differential two-parameter model of turbulence, thermodynamic relations, and kinetic equations. A study is made of steam—air jets in a regime of condensation in equilibrium, when the flow region is broken down into zones of frozen flow and flow in equilibrium, described by the equations for a turbulent jet with the use of the traditional thermodynamic relations and of the thermodynamic relations for condensation in equilibrium. An analysis is made of the influence of pulsating motion on the kinetic parameters: rate of nucleation, the critical size of the nuclei, and rate of growth of the drops. It is shown that the rate of nucleation, determined from a quasilaminar averaging model, is several orders of magnitude less than the mean value obtained by averaging using the density distribution of the passive admixture concentration probability. A numerical study is made of the heterogeneous condensation in turbulent jets on extraneous particles entering from the nozzle. Kinetic equations are written down for the case when the rate of growth of the drops does not depend on their radius. A study is made of the dynamics of the transition of heterogeneous condensation from disequilibrium to equilibriumTranslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–67, January–February, 1985.     

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.     

Coaxial turbulent jets with strong central blowing

The results of solving the problem of the initial section of isothermal coaxial jets with strong central blowing, when the transverse pressure gradient has only a slight effect and there is no circulation zone in the central jet are given. The problem is solved by the integral relation method with allowance for jet interference and the presence of a cocurrent flow. The results of an experimental investigation of these jets over a wide range of the geometric and regime parameters are also given. The results of the calculations made using the formulas obtained are compared with the experimental data.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 52–59, May–June, 1996.     

Propagation of a jet of viscous liquid in a medium containing a density jump

The results of an experimental investigation into the laws governing the propagation of a jet of viscous liquid in a medium incorporating a density jump are studied for a Reynolds number range of 25 R 20·10³. In addition to jets normal to the jump surface (vertical jets), horizontal jets travelling along the interface between the heavy and light liquids (jump surface) are examined. Photographs are presented, together with dynamic pressure measurements, illustrating properties of the jets studied which are unusual for a uniform medium: the extinction of turbulence, the existence of a limiting jet length, anisotropy of the jet, etc. An approximate explanation (within the framework of boundary-layer theory) is given for the effects in question.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 115–122, May–June, 1972.     

Flow of viscous gas out of a cylindrical channel into vacuum

A study is made of the exhausting of a jet of viscous gas from a cylindrical channel into vacuum in the presence of a flat bounding surface outside the channel in the plane of its exit section. The problem is solved numerically using the complete system of Navier—Stokes equations. The developed flow model makes it possible to take into account the influence of an external medium into which the jet exhausts on the structure of the flow in the exit section of the channel, and also the influence of the subsonic part of the boundary layer in the channel on the flow field of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–128, January–February, 1981.     

Experimental investigation of the structure of coaxial nonisobaric reacting jets

This study, a continuation of an experimental program of research on isobaric coaxial jets [2], was primarily directed towards obtaining a more detailed picture of the flow structure, in particular by measuring the static pressure in the flow field of the jet with simultaneous visualization. It is shown that the nature of the axial static pressure distribution and the ignition lag are determined by the characteristics of the outer jet and are almost independent of the pressure ratio number (degree of underexpansion) of the inner nozzle and the rate of flow of fuel through it. The fuel forming the central jet self-ignites in a zone where not only the composition but also the temperature reach values corresponding to the ignition limits.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 184–186, January–February, 1987.     

Space–time correlation measurements of high-speed axisymmetric jets using optical deflectometry

An optical deflectometry system is used to provide unique space–time correlation measurements at two positions separated by varying axial distances within a high-speed jet shear layer. The measurements were made for both pure air and for helium/air mixture jets at Mach numbers M=0.9 and M=1.5. The jets issue from round nozzles and the sensing volumes at the two measurement positions consist of small light filaments along spanwise lines that are tangential to the annular jet shear layer. Applying this technique to obtain measurements detailing the level of correlation, spectral content, and convection velocity for jet flows in these flow regimes near the end of the potential core is particularly important in the understanding and prediction of jet noise. Measurements near the end of the potential core along the jet lip line exhibit distinct cross-correlation curves for the pure air jet cases. However, helium/air mixture jets display much lower levels of correlation and little evidence of large-scale structure in the measured spectra. It is believed that the thick visual density gradients dominated by smaller scales throughout the shear layer of the helium/air mixture jets effectively mask the large-scale structure, thus, reflecting a limitation of this optical deflectometer. Finally, a decrease in normalized convection velocity with helium addition is observed.     

Numerical Simulation of a Supersonic Flow with Transverse Injection of Jets

A plane supersonic flow with symmetric perpendicular injection of jets through slots in the walls is numerically simulated with the use of Navier–Stokes equations. The effect of the jet pressure ratio and Mach number on the flow structure is considered. The angle of inclination of the shock wave and the separationregion length are found as functions of the jet pressure ratio. The influence of the jet pressure ratio on the increase in the lift force arising owing to interaction of the flow with the injected jet is found.     

Investigation of turbulent vapor-air jets in the presence of condensation and the injection of foreign particles

A study is made of flow in turbulent jets when there is condensation of the water vapor contained in them. A necessary condition for condensation in vapor-air jets is formulated. Relations are obtained for the regime of equilibrium condensation. An experimental investigation was made of the local characteristics of an isobaric turbulent vapor jet exhausting into air at rest when condensation develops in the jet and foreign condensation nuclei (smoke particles) and charged particles (ions produced in a corona discharge) are introduced into the flow. Measurements were made of the local characteristics of the condensed disperse phase — the Sauter diameter d₃₂ of the drops and their volume concentration c_s — using the optical method of an integrating diaphragm. It is shown that d₃₂ and₃₂ c_s increase downstream in the main section of the jet. Specific features of temperature measurements using an end-type microthermocouple were established. Quantitative data were obtained about the influence on the condensation of the thermal conditions and the presence of the foreign particles. The conditions under which there is an intensification of the condensation in vapor-air jets in the presence of ions were determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 53–61, May–June, 1984.     

Investigation of gas blowing into a base cavity

The results of an experimental investigation of various methods of influencing the flow in the near wake by injecting a system of jets and varying the rear-end configuration for a Mach number M=3 are presented. The structure of the base flow and the pressure fluctuations behind an axisymmetric body with a base cavity when circular and annular gas jets are injected is investigated. The results are compared with the data for bodies with a flat base.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 170–172, July–August, 1989.     

FORCE FIELDS ON INVISCID,SLENDER, ANNULAR LIQUID JETS

Regular perturbation expansions are used to analyse the fluid dynamics of unsteady, inviscid, slender, thin, incompressible (constant density), axisymmetric, upward and downward, annular liquid jets subjected to non-homogeneous, conservative body forces when both the annular jets are very thin and the gases enclosed by and surrounding the jet are dynamically passive. Both inertia- and capillarity-dominated annular jets are considered. It is shown that, for inertia-dominated jets, closure of the leading-order equations is achieved at second order in the perturbation parameter, which is the slenderness ratio, whereas closure is achieved at first order for capillarity-dominated jets. The steady leading-order equations are solved numerically by means of both an adaptive finite difference method which maps the curvilinear geometry of the jet onto a unit square and a fourth-order-accurate Runge–Kutta technique. It is shown that the fluid dynamics of steady, annular liquid jets is very sensitive to the Froude and Weber numbers and nozzle exit angle in the presence of non-homogeneous, conservative body forces. For upward jets with inwardly or axially directed velocities at the nozzle exit the effect of the non-homogeneous, conservative body forces is to increase the leading-order axial velocity component, decrease the jet's mean radius and move the stagnation point downstream. For downward jets with radially outward velocity at the nozzle exit the axial velocity component decreases monotonically as the magnitude of the non-homogeneous, conservative body forces is increased.     

Supersonic flow past a body with transverse jets

The results of an experimental study of the flow past a body with transverse jets are presented. The gas jets flowed out simultaneously from several nozzles arranged on the body's lateral surface. Various flow regimes were considered to such parameters as the relative jet momentum, the angle of incidence, etc. The experimental results were generalized on the basis of an approximate similarity law.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 75–80, July–August, 1995.     

Calculation of the interaction of planar jets of ideal gas with different Bernoulli constants

A numerical method is proposed for calculating stationary planar jet flows with unequal total heads in different jets in the case when the medium is ideal and compressible and the flow is subsonic, adiabatic, and irrotational in each individual jet. Features of the method are considered in the example of the calculation of the interaction of two free jets flowing along the sides of a wedge. The line separating the jets is the line of a shear discontinuity. The results of the calculations are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 140–143, May–June, 1981.I thank V. P. Karlikov for helpful discussions of the results.     

Propagation of an ion jet near a dielectric surface

Difficulties in determining experimentally the local electrical parameters of unipolar-charged jets are arousing interest in the theoretical investigation of electrogasdynamic (EGD) flows. Free EGD jets were examined, for example, in [1–3]. In order to control the charge on the dielectric parts of aircraft surfaces, which results from their static electrification and may have certain negative consequences [4], and, moreover, to influence the flow in the boundary layer use is being made of unipolar-charged jets propagating near the dielectric [5, 6]. In [6] the case of an ion jet near a dielectric surface possessing surface conductivity was investigated. In these circumstances it is possible to neglect charge diffusion, which considerably simplifies the problem. Space charge diffusion was taken into account in [7], but subject to certain very important simplifications. The author has calculated the electrical parameters of a unipolar-charged jet propagating in a viscous incompressible gas near an ideal dielectric plate, with allowance for surface and polarization charges and, moreover, the diffusion processes near the surface. An asymptotic solution is obtained for the equations of the ionic diffusion layer as the ratio of the thickness of the diffusion layer to the thickness of the hydrodynamic boundary layer tends to zero.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–180, September–October, 1984.The author is grateful to V. V. Mikhailov and A. V. Kazakov for valuable advice and comments.     

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.