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.     

On turbulent separated flow past a truncated body of revolution

Results of testing a series of truncated bodies of revolution with convergent afterbodies in a hydrodynamic tunnel are presented. It is shown that the base pressure can be substantially raised and hence the total drag reduced by varying the shape and convergence of the afterbodies. This effect is caused by intense reverse jets formed as a result of the collision of flow particles moving toward the axis of symmetry.The turbulent flow past the bodies is calculated using the method of viscous-inviscid interaction. The formulas derived for the base pressure and drag coefficients agree satisfactorily with the experimental data.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 50–55, November–December, 1996.     

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.     

“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.     

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.     

Solution of three-dimensional nonlinear problems of the theory of jets in ideal fluids

A method of successive approximations is proposed for solving three-dimensional nonlinear problems of the theory of jets in ideal fluids (see, for example, [1–3]). Each approximation includes the calculation of the flow over a known surface, i.e., the solution of the exterior Neumann problem for the Laplace equation in the velocity potential and the correction of part of that surface for the purpose of reducing the discrepancy in the constant-pressure condition at the surface of the jets. The correction takes the form of small deformations found from a system of integral equations; the shape of the cavity in plan is also refined. The results of calculating the flow past triaxial ellipsoids, obtained using the generalized Zhukovskii-Roshko method for closing the jets, are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 175–179, March–April, 1989.The authors are grateful to V. P. Karlikov for useful comments.     

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.     

Spatial interaction of jets propagating in an accompanying supersonic flow

A numerical method of calculating a three-dimensional laminar supersonic underexpanded jet escaping into an accompanying supersonic flow is developed. The simplified Navier-Stokes equations for a steady-state three-dimensional flow are employed. Numerical calculations are carried out for several cases relating the outflow of jets from a four-nozzle assembly into an accompanying supersonic flow, and a number of the characteristics of three-dimensional flows of this kind are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 88–93, November–December, 1972.     

Acceleration of a gas compressed under conditions of acuteangled geometry

In obtaining high velocities (10–100 km/sec) by methods employing the mechanical motion of compressible media it is customary to use the flow scheme obtained with shaped charges [1–4]. This paper presents the results of a study of an apparatus that can be used to obtain gas jets in the same velocity range but at higher densities by means of a different type of flow.     

Experimental investigation of the interaction of a supersonic annular jet and an obstacle

There has been much interest in recent years in gas-dynamic problems involving the interaction of gas jets with obstacles, and there have been studies of combinations of individual jets, systems of jets, and also annular jets. Various papers have been published with the results of theoretical and experimental investigations of the interaction of axisymmetric continuous jets with obstacles [1–3]. However, there have been only a few experiments on the fluctuations of an annular system of jets that encounter an obstacle [4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 109–117, May–June, 1983.     

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.     

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.     

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 heat transfer on models in subsonic jets of an induction plasmatron

The results are given of an investigation of the flow parameters in an induction plasmatron and of heat transfer on water-cooled models in subsonic jets of dissociated air in the range of pressures p = 5·10³–1.0·10⁵ N/m². The obtained experimental data confirm the well-known theoretical conclusion that the catalytic activity of the surface influences the heat fluxes at low pressures when the boundary layer flow is nonequilibrium. The problem of the flow of a subsonic jet of a viscous heat-conducting gas past a model of cylindrical shape with flat end has been solved numerically. The experimental and calculated data are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 6, pp. 129–135, November–December, 1983.We are very grateful to Yu, K. Rulev and V. M. Mysova for assistance in the experiment.     

Sonic annular jet in a counterstreaming supersonic flow

When sonic annular jets encounter a supersonic flow, two interaction regimes are possible with open or closed central separation regions. When the flow regimes change, there is an abrupt change in the separation of the shock wave from the nozzle and of the pressure in the central separation region, and hysteresis is also observed. The flow regimes with open central separation region are stationary and can be calculated numerically on the basis of Euler's equations fairly accurately.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–180, September–October, 1979.     

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.     

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.     

Collision of two jets of perfect fluid with different Bernoulli constants

We consider the problem of the collision between two plane jets of perfect fluid with different Bernoulli constants in jets flowing into a mediumfilled space out of channels with parallel walls, converging at an angle. In [1–3] the problem is reduced to a system of nonlinear equations, whose solution is obtained in the form of a formal series in powers of the small quantity , equal to the ratio of the total dynamic heads of the colliding jets. The zeroth and first approximations of the unknown, and also the second approximation for the angle of deflection of the jets, are calculated. Here the nonlinear problem of the collision of two jets is solved in an exact mathematical formulation [4]. The results of the calculations are given for different geometric parameters of the problem in the entire range of variation of the Bernoulli number Be equal to the ratio of the difference between the Bernoulli constants of the jets to the dynamic head of one of them.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 38–42, March–April, 1987.     

Turbulence measurements in a flow generated by the collision of radially flowing wall jets

Early results of an experimental investigation of the abnormally high turbulence level and mixing layer growth rate characteristics found in the upwash regions of aircraft with vertical short takeoff and landing (V/STOL) flows in ground effect are presented. The upwash flow is formed from the collision of two opposing radially flowing wall jets. The wall jets are created in a unique way that allows the upwash to form without any interference due to the source jets. The objective of this work is to systematically characterize the development and structure of the flow. The upwash flow exhibits very large mixing rates compared to turbulent free or wall jet flows. A unique set of two component velocity profiles was taken in the upwash flow field. These measurements include several higher moment terms that appear in the turbulent kinetic energy equations, as well as length scales and intermittency determinations. Measurements were taken' along the axis connecting the two source jets as well as off this axis at six measurement stations above ground. The results provide detailed data on an important class of flows where none existed, and they are expected to significantly improve the computational empirical tools available for predicting V/STOL behavior near the ground.A version of this paper was presented at the 10th Symposium on Turbulence, University of Missouri-Rolla, September 22–24, 1986     

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.