On the possibility of blowing a gas jet into a supersonic flow without formation of a three-dimensional boundary-layer separation zone

We consider the flow formed by the interaction of a supersonic flow and a transverse sonic or supersonic jet blown at right angles to the direction of the main flow through a nozzle whose exit section is in a flat wall. When a gas jet is blown through a circular opening [1] the pressure rises in front of the jet because of the stagnation of the oncoming flow. This leads to separation of the boundary layer formed on the wall in front of the blowing nozzle. The resulting three-dimensional separation zone leads to a sharp increase in the pressure and the heat fluxes to the wall in front of the blowing nozzle, which is undesirable in many modern applications. The aim of the present investigation was to find a shape of the exit section of the blowing nozzle for which there is no three-dimensional separation zone of the boundary layer in front of the blowing nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–165, May–June, 1979.     

Interaction of a jet exhausting from a body with an opposing supersonic stream of rarefied gas

The experimental investigation of supersonic flow past a sphere with a jet exhausting from the front point of the sphere into the flow at large [1] and moderate [2] Reynolds numbers Re has revealed an effect of shielding from the oncoming stream, this leading to a decrease in the drag coefficient of the sphere and of the energy flux to it. A numerical simulation of the flow has been made in the case of supersonic flow past a sphere with a sonic jet from a nozzle situated on the symmetry axis in the continuum regime [3]. In the present paper, this problem is investigated for flow of a rarefied gas on the basis of numerical solution of a model kinetic equation for a monatomic gas.     

Formation of a pulsed jet behind a supersonic nozzle when the gas can relax at the entrance to the nozzle

The formation of a pulsed jet behind supersonic nozzles is considered when relaxation processes take place in the gas entering the nozzle. In a general formulation, the problem of the motion of the front of the exhausting matter and the disturbances accompanying it in the process of formation of a pulsed jet is determined by a large number of parameters, which characterize the exhausting gas and the residual gas of the pressure chamber and also the geometry of the flow conditions. A reliable computational model of a pulsed jet does not exist. To construct such a model, experiments are required in a wide range of boundary and initial conditions. An investigation was made into flow of shockheated argon, nitrogen, and carbon dioxide out of nozzles set up at the end of a shock tube. Generalized dependences were obtained for describing the motion of the front of the nonstationary jet and the wave in front of it in a wide range of the initial pressure-difference parameters and variation of the stagnation temperatures. The choice of the generalized parameters when relaxation of the excited internal degrees of freedom of the molecules of the gas can occur at the entrance to the nozzle is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 129–135, November–December, 1980.     

Flow structure at the initial section of a supersonic jet exhausting from a nozzle with chevrons

The spatial structure of the flow in a supersonic underexpanded jet exhausting from a convergent nozzle with vortex generators (chevrons) at the exit is experimentally studied. Exhaustion of a supersonic underexpanded jet from a nozzle with chevrons at the nozzle exit is numerically simulated with the use of the Fluent commercial software package. The experimental and numerical data are demonstrated to be in reasonable agreement. The influence of chevrons on the process of gas mixing is estimated.     

Mechanism of self-oscillations in a supersonic jet impact onto an obstacle 1. Obstacle with a spike

Results of numerical simulations and experimental investigations of self-oscillations arising in the case of impingement of an overexpanded or underexpanded jet onto an obstacle with a spike are reported. The mechanisms of the emergence and maintaining of self-oscillations for overexpanded and underexpanded jets are elucidated. It is demonstrated that self-oscillations are caused by disturbances in a supersonic jet, which induce mass transfer between the supersonic flow and the region between the shock wave and the obstacle. The feedback is ensured by acoustic waves generated by the radial jet on the obstacle. These waves propagate in the gas surrounding the jet, impinge onto the nozzle exit, and initiate disturbances of the supersonic jet parameters. In the overexpanded jet, these disturbances penetrate into the jet core, where they are amplified in oblique shock waves.     

Calculations of axisymmetric jet leaving a nozzle at jet pressure lower than pressure in medium

The problem of discharge of a supersonic axisymmetric jet from a nozzle at a jet pressure less than the pressure in the surrounding medium is considered. A calculation method is presented with account for the subsonic flow downstream of the central shock which forms near the axis of symmetry. Comparison of the results of the computation on a digital computer with the experimental data show the effectiveness of this method for determining the structure of the initial section of such an axisymmetric jet.     

Numerical study of flows of a viscous compressible gas and of an equilibrium gas mixture in a flat nozzle in the presence of strong blowing

The problem of the interaction of a viscous supersonic stream in a flat nozzle with a transverse gas jet of the same composition blown through a slot in one wall of the nozzle is examined. The complete Navier-Stokes equations are used as the initial equations. The statement of the problem in the case of the absence of blowing coincides with [1]. The conditions at the blowing cut are obtained on the assumption that the flow of the blown jet up to the blowing cut is described by one-dimensional equations of ideal gasdynamics. The proposed model of the interaction is generalized to the case of flow of a multicomponent gas mixture in chemical equilibrium. The exact solutions found in [2] are used as the boundary conditions at the entrance to the section of the nozzle under consideration. The results of numerical calculations of the flows of a homogeneous nonreacting gas and of an equilibrium mixture of gases consisting of four components (H₂, H₂O, CO, CO₂) are given for different values of the parameters of the main stream and of the blown jet. In the latter case it is assumed that the effect of thermo- and barodiffusion can be neglected.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 55–63, July–August, 1974.     

Similarity with the outflow of strongly unexpanded jets into a hypersonic wake

The article discusses the outflow of a nonviscous gas from a strongly unexpanded supersonic nozzle into a supersonic wake. Under the assumption that the radius of the outlet cross section of the nozzle is negligibly small in comparison with the characteristic dimensions of the jet, expressions are obtained for the transverse and longitudinal dimensions of the jet, as well as similarity criteria determining the dimensionless gasdynamic functions. The satisfaction of the similarity criteria was verified by comparison with numerical calculations. Similarity with the outflow of strongly unexpanded jets was discussed in [1–3], where, specifically, the characteristic dimension of the flow was determined. In [4] it was demonstrated that the experimentally observed structure of the jet can be best described with the introduction of two characteristic dimensions, longitudinal and transverse. The effective construction of these two characteristic dimensions for the case of nonviscous outflow into a flooded space was carried out in [5], in which it was shown that using the longitudinal and transverse dimensions the geometries of the flow and the gasdynamic parameters are found to depend on the adiabatic index of the outflowing gas and on a parameter formed from the integral characteristics of the nozzle. The present work is a generalization of the results of [5] for the outflow of a jet into a hypersonic wake.     

Investigation of interaction between a plane transverse gas jet and a supersonic stream

The problem of interaction between a two-dimensional transverse gas jet emerging from a slot on a flat plate and a supersonic stream is considered. Several theoretical methods based on various approaches and physical models have been proposed to determine the characteristics of such a flow. The following fundamental directions can be isolated: a quasi-one-dimensional method [1], use of blast theory [2], and methods based on the equivalence of the effect of the jet and some solid on the external flow [3, 4]. However, the listed computational schemes [1–4] do not permit any clarification of the flow configuration in the jet and in the outer stream (the shock configuration, the jet boundaries, the distribution of the gasdynamic parameters in the flow field, etc.). Extensive experimental investigations of this phenomenon have been carried out simultaneously with the development of the theoretical methods, wherein the flow picture was determined, the pressure distribution was measured in the interaction domain, etc. [5, 6]. A computation method is proposed in this paper which will permit a detailed investigation of the flow structure in the jet and in the outer flow outside the separation region. Underlying the method is a hypothesis verified experimentally: The separating streamline in the mixing layer of the separated boundary layer (the “constant mass∝ line) intersects the jet boundary at the point of maximum jet standoff from the nozzle exit towards the incoming stream.     

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.     

Shock structure in separated nozzle flows

In the case of high overexpansion, the exhaust jet of the supersonic nozzle of rocket engines separates from nozzle wall because of the large adverse pressure gradient. Correspondingly, to match the pressure of the separated flow region, an oblique shock is generated which evolves through the supersonic jet starting approximately at the separation point. This shock reflects on the nozzle axis with a Mach reflection. Thus, a peculiar Mach reflection takes place whose features depend on the upstream flow conditions, which are usually not uniform. The expected features of Mach reflection may become much difficult to predict, depending on the nozzle shape and the position of the separation point along the divergent section of the nozzle.      

“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.     

Solution of the direct problem of the mixed flow of a conducting gas in a laval nozzle with a meridional magnetic field

We consider the direct problem in the theory of the axisymmetric Laval nozzle (including sonic transition) for the steady flow of an inviscid and nonheat-conducting gas of finite electrical conductivity. The problem is solved by numerical integration of the equations of unsteady gas flow using an explicit difference scheme that was proposed by Godunov [1,2], and was used to calculate steady and unsteady flows of a nonconducting gas in nozzles by Ivanov and Kraiko [3]. The subsonic and the supersonic flows of a conducting gas in an axisymmetric channel when there is no external electric field, the magnetic field is meridional, and the magnetic Reynolds numbers are small have previously been completely investigated. Thus, Kheins, Ioller and Élers [4] investigated experimentally and theoretically the flow of a conducting gas in a cylindrical pipe when there is interaction between the flow and the magnetic field of a loop current that is coaxial with the pipe. Two different approaches were used in the theoretical analysis in [4]: linearization with respect to the parameter S of the magnetogasdynamic interaction and numerical calculation by the method of characteristics. The first approach was used for weakly perturbed subsonic and supersonic flows and the solutions obtained in analytic form hold only for small S. This is the approach used by Bam-Zelikovich [5] to investigate subsonic and supersonic jet flows through a current loop. The numerical calculations of supersonic flows in a cylindrical pipe in [4] were restricted to comparatively small values of S since, as S increases, shock waves and subsonic waves appear in the flow. Katskova and Chushkin [6] used the method of characteristics to calculate the flow of the type in the supersonic part of an axisymmetric nozzle with a point of inflection. The flow at the entrance to the section of the nozzle under consideration was supersonic and uniform, while the magnetic field was assumed to be constant and parallel to the axis of symmetry. The plane case was also studied in [6]. The solution of the direct problem is the subject of a paper by Brushlinskii, Gerlakh, and Morozov [7], who considered the flow of an electrically conducting gas between two coaxial electrodes of given shape. There was no applied magnetic field, and the induced magnetic field was in the direction perpendicular to the meridional plane. The problem was solved numerically in [7] using a standard process. However, the boundary conditions adopted, which were chosen largely to simplify the calculations, and the accuracy achieved only allowed the authors [7] to make reliable judgments about the qualitative features of the flow. Recently, in addition to [7], several papers have been published [8–10] in which the authors used a similar approach to solve the direct problem in the theory of the Laval nozzle (in the case of a nonconducting gas).Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 5, pp. 14–20, September–October, 1971.In conclusion the author wishes to thank M. Ya. Ivanov, who kindly made available his program for calculating the flow of a conducting gas, and also A. B. Vatazhin and A. N. Kraiko for useful advice.     

Oscillation flow induced by underwater supersonic gas jets

This paper describes an experimental study on the oscillation flow characteristics of submerged supersonic gas jets issued from Laval nozzles. The flow pattern during the jet development and the jet expansion feedback phenomenon are studied using a high-speed camera and a pressure measurement system. The experimental results indicate that along the downstream distance, the jet has three flow regimes: (1) momentum jet; (2) buoyant jet; (3) plume. In the region near the nozzle exit a so-called bulge phenomenon is found. Bulging of the jet occurs many times before the more violent jet expansion feedback occurs. During the feedback process, the jet diameter can become several times that of the original one depending on the jet Mach number. The frequencies of the jet bulging and the jet expansion feedback are measured.     

Detonation combustion of hydrogen in a convergent-divergent nozzle with a central coaxial cylinder

The feasibility of steady detonation combustion of a hydrogen-air mixture entering at a supersonic velocity in an axisymmetric convergent-divergent nozzle with a central coaxial cylinder is considered. The problem of the nozzle starting and the initiation of detonation combustion is numerically solved with account for the interaction of the outflowing gas with the external supersonic flow. The modeling is based on the gasdynamic Euler equations for an axisymmetric flow. The calculations are carried out using the Godunov scheme on a fine fixed grid which allows one to study in detail the interaction of an oblique shock wave formed in the diffuser with the nozzle axis. It is shown that a central coaxial cylinder ensures the starting with the formation of supersonic flow throughout the entire nozzle and stable detonation combustion of a stoichiometric hydrogen-air mixture in the divergent section of the nozzle.     

Interaction of a supersonic flow with a transverse jet injected through a circular aperture in a plate

A flow pattern created by the interaction of a supersonic flow with a transverse sonic or supersonic jet injected normally to the direction of the main flow through a circular aperture in a plate is considered. The pressure rises in front of the jet owing to the retarding action of the incident flow. The boundary layer building up on the wall in front of the injection nozzle is accordingly detached. The flow pattern in the region of interaction between the jet and the external flow is illustrated in Fig. 1. The three-dimensional zone of detachment thus formed deflects the incident flow from the wall, and in front of the jet a complicated system of sharp jumps in contraction develops. A three-dimensional system of jumps also develops in the jet itself.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 5, pp. 193–197, September–October, 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.     

On the mechanism of self-oscillations of a supersonic radial jet exhausting into an ambient space

Results of an experimental study and numerical simulation of self-oscillations of a supersonic radial jet exhausting from a plane radial nozzle into an ambient space are reported. It is demonstrated that flexural oscillations develop in the jet, leading to its destruction. Feedback ensured by acoustic waves in the gas surrounding the supersonic jet is found to play a key role in the emergence of self-oscillations.     

Flow of a mixture of gas and solid particles in supersonic underexpanded jets

The presence of a second phase in a gas jet flowing out of a nozzle leads to considerable changes in the flow pattern [1–3]. Thus, as the particle concentration increases, the central jump in compression [shock wave] moves in the direction of the nozzle cutoff, while the Mach number on the axis of the jet in front of the forward jump diminishes. In this paper we shall consider the numerical solution of the problem of an axisymmetrical, two-phase, underexpanded jet flowing out of a straight nozzle into a submerged space. It is assumed that the distribution of the flow parameters is uniform over the jet cross section and that no thermal or dynamic retardation of the particles occurs.