Experimental investigation of the flow in the mixing layer in the initial section of an underexpanded jet in a parallel stream

The results are given of an experimental investigation of the flow in the initial section of a turbulent underexpanded jet exhausting from a profiled nozzle with Mach number M _a = 2.56 at the exit into a parallel stream with Mach number M = 3.1. Analysis of the results of measurement of the fields of the total head p₀ and the stagnation temperature T₀ in conjunction with results of calculation of a jet of an ideal gas make it possible to construct the velocity profile in the mixing layer of the underexpanded jet in the parallel supersonic flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 161–163, January–February, 1981.     

Experimental investigation of a three-dimensional viscous underexpanded jet

The three-dimensional interaction of jet issuing from two- and four-nozzle systems into ambient space or an outer flow has been investigated experimentally. The range of the important parameters include the following: pressure imbalance n=P_a=/P=10–1.5·10², Mach number at the nozzle exit M_a=3.15, Mach number of the outer flow M=0, 3.1, and 6, the flow is turbulent in the mixing layer (P_a and P are the static pressures at the nozzle exit and in the outer flow). It is shown that the interaction of the jets broadens a multinozzle jet considerably in the plane of interaction, which is a plane of symmetry and which passes through the axis of the system between neighboring nozzles. The cross-sectional shape of a four-nozzle jet is cross-like over the entire length of the initial segment of the jet. The width of the mixing layer in the plane of interaction is considerably larger than in the central plane, which passes through the axis of opposed nozzles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 21–26, September–October, 1974.     

Separated inviscid gas flow past a disk and a body with maximum critical Mach numbers

The problem of the separated axisymmetric subsonic flow of an inviscid perfect gas with the specific heat ratio 1.4 past a disk in accordance with the Riabouchinsky scheme is solved using the method developed in [1]. Formulas relating the main parameters with the base pressure coefficient and the Mach number at the free boundary are presented. Formulas which make it possible to determine the shape of the body of revolution giving the maximum critical Mach numbers are also derived.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–172, May–June, 1996.     

Effect of the wake on flow in an annular jet

The flow of an annular jet in a channel is studied. The effect of the Mach number of the wake on the structure of the jet is determined. It is shown that with a near-sonic velocity a reorganization occurs in the mode of flow from an open to a closed base region accompanied by a reduction in the level of pressure pulsations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 74–79, November–December, 1974.     

Low-density jets beyond a sonic nozzle at large pressure drops

The gas-dynamical structure of jets of a low-density diatomic gas beyond a sonic nozzle at large pressure drops under conditions of a transition from continuous medium processes to rarefied gas processes is examined on the basis of experimental data obtained in low-density gas-dynamical tubes using electron-beam diagnostics and the Pitot tube method. Isomorphism is shown in the density distribution and total pressure in all cross sections of the jet with respect to pressures at a constant value of the complex R_L=R_*/N^1/2(R_* is the Reynolds number in the critical cross section of the nozzle, and N is the ratio of the Pitot pressure and the pressure in the discharge chamber). It is shown on the basis of a comparison of local Reynolds numbers for all zones of the jet that this is an analog complex. The experimental data on the variation in the jet structure are presented as a function of the number R_L in the range of 5–600. For R_L> 100 the flow in the jet can be considered as continuous; for R_L< 5–10 the flow corresponds to a scattering process; the range of 5–10< R_L< 100 corresponds to a transitional state. Ranges of isomorphism of the jet with respect to R_* and N are indicated. Based on the results of the measurements, it is shown that the flow behind a Mach disk for R_L> 200 remains subsonic on the axis to a distance of several lengths of the primary cycle. A transition to supersonic velocity on the jet axis can occur with a decrease in the numbers R_L owing to ejection acceleration by the supersonic ring-shaped compressed layer.This word is apparently interchangeable with self-similarity-Translator.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 64–73, March–April, 1973.     

Effect of the flow regime in an underexpanded jet issuing into a subsonic counterstream on the pressure distribution on a body

The pressure distribution on a cone with a half-angle =75°, from which a single central underexpanded jet issues into a subsonic counterstream, has been experimentally investigated. The effect of the flow regime in the jet on the pressure distribution is demonstrated. Generalized relations for the pressure on the body are obtained for various jet-flow momentum ratios J and flow Mach numbers M = 0.35–0.9; the Mach number M_a at the exit of the conical nozzle with half-angle _a=10° was equal to 2.9. The working medium of the jet and the flow was air with stagnation temperatures T_0a = T₀ 260–265°K. The ratio of the nozzle outlet radius to the radius of the maximum cross section of the cone _a/R_M=0.1.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 182–185, January-February, 1988.     

Self-oscillations in an underexpanded jet flowing into a barrier

The distribution of the phases and amplitudes of the static pressure fluctuations with self-oscillations of an underexpanded jet flowing into a barrier is obtained experimentally in the present paper. The distribution of the Mach number in the compressed layer and in the subsonic flow in front of the barrier is shown. The results of the measurements of the characteristics of the self-oscillation process are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 38–43, November–December, 1977.     

Calculation of hysteresis and flow-rate oscillations of base pressure in supersonic annular nozzles

The interaction of the turbulent axisymmetric near wake behind the face of the central body of an annular nozzle with the supersonic annular jet discharging from this nozzle is analyzed. The flow in the monoparametric near wake is calculated by the integral method [1] while the flow in the nonviscous jet is calculated by the method of through calculation using a monotonic explicit difference system of the first order of accuracy [2]. The interaction between the nonviscous and turbulent streams is determined by the displacement thickness of the wake. The initial conditions of the wake are determined from the integral conditions of attachment with the mixing flow in the isobaric base region. The interaction flow is described by the particular solution of the equations which passes through the singular saddle point — the throat of the wake. The near wake and base pressure in different modes of discharge from an annular nozzle at the exit cross section of which the ratio of outer and inner radii is y₂/y₁ = 1.3 and the Mach number is M = 2.54 are calculated as an example. The region of hysteresis of the base pressure, connected with the ambiguity of the interaction flow owing to the formation of the throat of the wake within the first or second barrel of the jet, and the parameters of the low-frequency flow-rate oscillations of base pressure in this region are determined. The results of the calculations are in satisfactory agreement with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 125–130, January–February, 1977.     

Outflow of an unexpanded jet into counter supersonic and subsonic flows

The article gives the results of an experimental investigation of the geometric structure of an opposing unexpanded jet. It discusses flow conditions with interaction between the jet and sub- and supersonic flows. It is shown that, with the outflow of an unexpanded jet counter to a supersonic flow, there are unstable flow conditions. For stable flow conditions with one roll, dependences are proposed determining the form of a jet in a supersonic opposing flow. A generalized dependence is obtained for the distribution of the pressure at the surface of a body with a jet, flowing out counter to a subsonic flow. The range of change in the determining parameters are the following: Mach numbers at outlet cross section of nozzle, M _a = 1 and 3; Mach numbers of opposing flow, M = 0.6–0.9 and 2.9; degree of effectiveness of jet, n = p _a /p = 0.5–800 (p _a and p are the static pressures at the outlet cross section of the nozzle and in the opposing flow); the ratios of the specific heat capacities, _a = = 1.4; the drag temperatures of the jet and the flow, T_o = T_oa = 290°K.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 89–96, January–February, 1977.     

Types of wave structure in the interaction of a convergent jet with an infinite two-dimensional obstruction

Possible types of wave structure formed in the first roll of a convergent supersonic jet as it interacts with an infinite two-dimensional object are indicated in this work based on a generalization of results from theoretical and experimental studies. The influence of the Mach number, over pressure parameter n, isentropic exponent k, and the location h of the obstacle on the wave structure is considered.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 45–50, January–February, 1976.     

Experimental investigation of the separation of flow around a sphere

The results of an experimental investigation of the flow around a sphere over a broad range of Mach numbers M=0.3–3 and Reynolds numbers Re=3·10⁴–3·10⁷ are presented. The experiments were carried out on a ballistic test stand and in a wind tunnel. Flow patterns and pressure distributions were obtained. In particular, the effect of the Mach and Reynolds numbers on the position of the separation point and the edge shock was studied; the pressure distribution on the sphere was measured; and a nonmonotonic displacement of the flow separation point upon passage through the speed of sound was established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–156, January–February, 1991.     

Effect of external flow on the flow rate of a gas discharged through an orifice

The dependence of the flow coefficient of a gas jet ejected from an orifice/nozzle into a subsonic/transonic cross-flow on the flow and the jet Mach numbers, the off-design ratio, the nozzle inclination angle, β, and other determining parameters is considered. The physical nozzle flow pattern is constructed on the basis of experimental data obtained for 0.3< M_∞<1.75 and β=60°, 90°, and 120°. The results of measuring the pressure upstream and downstream of the orifice and on the windward and leeward orifice generators are presented. It is shown that the flow rate coefficient of a jet ejected into a cross-flow may exceed that of a similar jet outflowing into a flooded space. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 65–70, May–June, 1998.     

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.     

Supersonic flow past obstacles on the edges of dihedrals

Supersonic flow with M=3 and P₀=1.2 MPa past cylindrical obstacles located in the plane of symmetry at the edges of exterior and interior dihedrals at a distance ₀=140 mm from the leading edge of a model consisting of two intersecting flat sharp-edged plates is investigated in the presence of a turbulent boundary layer on the faces of the dihedral. The linear angle of the model dihedral was varied discretely from 45 to 310°. Interchangeable cylinders with diameters d=16 and 10 mm and variable height h=0–64 mm were used. The models were tapped along the axis of symmetry and rays starting from the center of the cylinder base and inclined to the edge of the model at angles = 30, 60, and 90°. The pressure was measured with IKD transducers. The results of the measurements were processed on a IVK-1 computer system. The flow past the model was photographed with a Töpler schlieren instrument. Before the experiment the surface of the model was coated with a carbon-oil solution. After the experiment the distribution of the visualizing composition was photographed and the dimensions of the region of separated flow near the obstacle were measured.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–184, September–October, 1989.     

Cone in a supersonic flow near a surface with a turbulent boundary layer

The published information about the interaction of incident shocks and a turbulent boundary layer relate to cases of a thin boundary layer ( 1–3 mm) on a flat surface. The present study relates to supersonic flow with Mach number M = 3 and stagnation pressure p₀=1.2 MPa past cones near a surface with a thick boundary layer formed on a plate abutting the lower edge of a plane nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 177–180, July–August, 1991.     

Transonic crossflow of condensing wet steam past a cylinder

The shadow and interferometric methods and the laser probe method are used to investigate crossflow past a cylinder on the free-stream Mach number interval M _a =0.5–1.2 for subcritical Reynolds numbers Re _d and various initial steam states. Detailed pressure distributions are obtained and the pressure fluctuations on the cylinder surface are measured. The dependence of the Strouhal number on the velocity and thermodynamic parameters of the flow are determined. In single-phase steam flow past a cylinder the greatest fluctuations occur in the separation zone in regimes corresponding to transonic drag crisis. It is shown that spontaneous condensation in the turbulent wake and local supersonic zones may cause an increase in the periodic pressure fluctuations in the separation zone, the maximum increase in the fluctuations being noted when the critical pressure ratio is reached at the rear of the cylinder. The initial wetness of the steam has the greatest effect on the periodic separation characteristics at subsonic flow velocities, and in the case of supersonic flow leads to a substantial increase in the level of the low-frequency pressure fluctuations at the front of the cylinder.(deceased)Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 118–138, November–December, 1994.     

Effect of proximity of barrier on lifting force produced by vertical solid jets

The effect of proximity to the ground on the lifting force generated by a vertical solid jet is studied in connection with development of vertical takeoff and landing devices and of air cushion devices. Such a study was made in [1 ] for planar flow by an incompressible ideal fluid. There a generalization of the results obtained on a compressible fluid was made by the approximation method. In the present work the planar problem of streamline flow past a dihedral barrier of a gas jet emerging from a channel with parallel walls was solved by the Chaplygin-Fal'kovich method [2, 3], The results of [1, 4–9] follow as a particular case from the solution obtained. Calculations were carried out clarifying the effect of the proximity of a barrier and the lifting effect of a fluid on flow characteristics at subsonic speeds.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 123–131, September–October, 1971.     

Flow and acoustic features of a supersonic tapered nozzle

The acoustic and flow characteristics of a supersonic tapered jet were measured for free and shrouded flow configurations. Measurements were performed for a full range of pressure ratios including over- and underexpanded and design conditions. The supersonic tapered jet is issued from a converging-diverging nozzle with a 31 rectangular slotted throat and a conical diverging section leading to a circular exit. The jet was compared to circular and rectangular supersonic jets operating at identical conditions. The distinct feature of the jet is the absence of screech tones in the entire range of operation. Its near-field pressure fluctuations have a wide band spectrum in the entire range of measurements, for Mach numbers of 1 to 2.5, for over- and underexpanded conditions. The free jet's spreading rate is nearly constant and similar to the rectangular jet, and in a shroud, the pressure drop it is inducing is linearly proportional to the primary jet Mach number. This behavior persisted in high adverse pressure gradients at overexpanded conditions, and with nozzle divergence angles of up to 35°, no inside flow separation was observed.     

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.     

Investigation of supersonic isobaric submerged turbulent jets

Turbulent supersonic submerged air jets have been investigated on the Mach number interval M_a = 1.5–3.4 and on the interval of ratios of the total enthalpies in the external medium and the jet i₀ = 0.01 – 1. Oxyhydrogen jets with oxidizer ratios = 0.3–5 flowing from a nozzle at Mach numbers M_a = 1 and 2.4 have also been investigated. When < 1 the excess hydrogen in the jet burns up on mixing with the air. Special attention has been paid to obtaining experimental data free of the influence on the level of turbulence in the jet of the initial turbulence in the nozzle forechamber, shock waves occurring in the nozzle or in the jet at the nozzle exit, and the external acoustic field. The jet can be divided into two parts: an initial part and a main part. The initial part extends from the nozzle exit from the section x, in which the dimensionless velocity on the jet axis u_m = u_x/u_d = 0.75. Here, u_x is the velocity on the jet axis at distance x from the nozzle exit, and u_a is the nozzle exit velocity. The main part of the jet extends downstream from the section x. For the dimensionless length of the initial part x_m = x/d_a, where d_a is the diameter of the nozzle outlet section, empirical dependences on M_a and i₀ are obtained. It is shown, that in the main part of the jet the parameters on the flow axis — the dimensionless velocity and temperature — vary in inverse proportion to the distance, measured in units of length x, and do not depend on the flow characteristics which determine the length of the initial part of the jet. The angles of expansion of the viscous turbulent mixing layer in the submerged heated or burning jet increase with decrease in i₀ and M_a and are practically independent of the afterburning process.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza. No. 4, pp. 56–62, July–August, 1988.