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.     

Calculation of the principal parameters of free supersonic jets of an ideal compressible fluid

An approximate method of determining the principal parameters of axially symmetrical under-expanded jets is set out. The results are presented in the form of computing formulas for the geometrical characteristics of the configuration of the shock waves and the boundaries of the jet. On the basis of experience with these calculations, some simple approximating relationships are recommended.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 51–57, May–June, 1971.     

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.     

Buckling of thin fluid jets and threads

The quasione-dimensional equations of the dynamics of thin jets are used as the basis for a theoretical study of flexural loss of stability (buckling) in thin jets and threads of high-viscosity fluids flowing slowly and normally onto a plate. The characteristic equation is obtained within linear analysis. Its solution showed that instability arises only in the presence of a longitudinal compressive force in a jet, and when the distance from the exit of the nozzle creating the jet to the plate exceeds a certain value which is critical for the jet in question. This critical value is calculated. It is shown that the instability is aperiodic in nature if gravity is neglected (horizontal jets).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 37–45, July–August, 1987.     

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.     

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.     

“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.     

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.     

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.     

Parameters of jets out of rectangular nozzles when they are free or near a screen

The results are given of an experimental determination of the parameters of jets out of rectangular nozzles. The distributions of the mean velocity and an impurity concentration were measured. The rearrangement of the jet flow associated with the three-dimensional structure of the jet and interaction of the jet and a screen was investigated. A model that describes the occurrence of a pressure difference and curvature of the jet trajectory when it interacts with a screen is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 39–48, July–August, 1979.     

Elastic stresses in capillary jets of dilute polymer solutions

The elastic longitudinal stresses associated with the flow of jets of dilute polymer solutions from a short nozzle and their effect on the stability of the free jet are investigated theoretically and experimentally. The results obtained make it possible to take a fresh look at the ways in which a polymer additive affects the stability of high-velocity capillary jets.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–9, Marc–April, 1985.     

On the length of annular jets interacting with an ambient medium

Annular jets of immiscible fluids are the subject of intense study. Particularly topical in applications are jets in the shape of a right circular cylinder. The space within annular jets may be reduced or increased by the influence of transverse forces and also by hydrodynamic instability of the jet flow. Twisting of the jet tends to make it close up. In the present paper, a study is made of ways of obtaining annular jets with nearly cylindrical shape and the greatest cavity length possible, allowance being made for gravity, capillary pressure surface forces, a pressure difference between the two sides of the phase interface, and the interaction with the ambient medium. A study is made of the influence of the velocity of the fluid and the medium in the initial section on the shape of the joint steady axisymmetric flow of immiscible viscous phases, including the shape of the middle surface of the annular jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–11, November–December, 1983.     

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.     

Discharge of a supersonic jet from a nozzle with an inclined rim

The main results of a numerical study of the effect of the angle of the rim of a nozzle on the shape of the jet boundary and of the free shock and on the distribution of parameters in a three-dimensional underexpanded jet are presented. A noncentered second-order difference scheme is used to solve the gasdynamic equations for an inviscid perfect gas. Conditions are established for which the three-dimensional jet is observed to coincide partially in the radial planes and the corresponding planes of axisymmetric jets.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 105–110, July–August, 1977.In conclusion, the authors thank G. I. Petrov and his colleagues for detailed discussion of the results of the investigation reported here.     

Elongation coefficient of cumulative jets

To calculate the elongation of cumulative jets, the inertial approximation is generally used [1]. It is assumed that each element of the jet moves with constant velocity. Such an approach is valid for very thin jets for which the internal pressure is nearly atmospheric and therefore the pressure gradient along the jet is approximately equal to zero. In the present paper, in which the model of an ideal incompressible fluid is used, a more accurate approximation taking into account the interaction of neighboring elements of the jet is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 167–169, November–December, 1983.     

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.     

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.     

Flexural perturbations of free jets of maxwell and Doi-Edwards liquids

Flexural perturbations of high-velocity free jets of drop liquids moving in air are reinforced by the fact that the air pressure on the concave sections of the jet surface is greater than on the convex sections. The linear and nonlinear stages of development of flexural perturbations were studied in [1–5] for viscous Newtonian fluids. The effect of elastic stresses in the fluid on the growth of flexural perturbations of jets was first examined in [6], where it was assumed in an analysis of the growth of small disturbances that surface tension was constant along the jet, i.e., the investigators actually studied a tensed string. The studies [7, 8] examined the linear stage of growth of flexural perturbations of jets of Maxwell liquids. Our goal here is to analyze the dynamics of long-wave flexural perturbations of jets of viscoelastic fluids in both the linear and nonlinear stages of development. The rheological behavior of the fluid is described by two models — the phenomenological (Maxwell) model and the physical-molecular (Doi-Edwards) model. It is shown that the disturbances are oscillatory in character in the nonlinear stage of development. Meanwhile, the results of calculations performed with the Maxwell (M) and Doi-Edwards (DE) rheological models in the given problem agree with each other quantitatively as well as qualitatively.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 43–53, November–December, 1986.     

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.     

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.