Propagation of acoustic perturbations along a supersonic jet flowing out into the atmosphere

The propagation of acoustic perturbations (specified in the outlet cross section of a particular channel) along a supersonic jet flowing out of the channel is considered; also considered is acoustic emission from the surface of the jet into the atmosphere. The solution of these problems is obtained by a numerical method on the linear approximation. The laws governing the propagation of the perturbations as a function of the perturbation frequency and other determining parameters are investigated; these parameters include the velocity and temperature of the jet, the velocity of the subsonic accompanying flow in the external medium, and the character of the perturbation in the initial cross section of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 92–99, March–April, 1977.     

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.     

The supercritical regime of nonlinear interaction of subsonic and supersonic inviscid jets in a two-dimensional channel

The nonlinear problem of the supercritical regime of interaction between sub- and supersonic inviscid jets flowing in a two-dimensional channel is investigated. The propagation of small pressure perturbations is considered. A numerical calculation is made of the shape of the streamline which separates the two jets, whose nonlinear perturbations have an oscillatory nature. The dependence is obtained of the amplitude of the oscillations on the similarity parameter representing the integrated characteristic of the profile of the unperturbed flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 156–160, September–October, 1985.     

Discrete component of the aerodynamic noise spectrum for two parallel supersonic jets

In many practical problems it is essential to know the characteristics of aerodynamic noise generated by a system of parallel supersonic jets. We have conducted an experimental study of aerodynamic noise in the very near acoustic field of two parallel supersonic jets. Our principal objective here was to investigate the discrete component of the pressure fluctuation spectra.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 172–174, September–October, 1976.     

“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.     

Pressure pulsations on an obstacle in a jet

At the present time, much attention is devoted to auto-oscillations that arise from the interaction between a supersonic underexpanded jet and an obstacle that it encounters at right angles [1, 2]. There are far fewer data on the pressure pulsations on an obstacle in the absence of auto-oscillations [3–6]. However, in many cases the highest total levels of the pressure pulsations are observed when the barrier is situated at fairly large distances from the nozzle opening and the pressure pulsations have a random nature. We have investigated the pressure pulsations on a plate normal to a supersonic strongly underexpanded jet. The pulsation characteristics were measured for an arrangement of the obstacle when auto-oscillations are absent. We have established dependences that generalize the results of measurement of the pulsation characteristics at both subsonic and supersonic velocities on the jet axis directly in front of the obstacle. We have also investigated the correlation between the pressure pulsations on the plate and external acoustic noise. We have obtained the dependence of the level of the acoustic noise on the value of the maximal pressure pulsations on the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–167, January–February, 1980.     

Influence of acoustics and the flow regime in the boundary layer on nozzle walls on the mixing layer of an immersed jet

Experimental determinations were made of the width of the mixing layer and the level of turbulent pulsations in the initial section of a subsonic circular immersed jet for different parameters of the boundary layer on the nozzle walls and in the presence of acoustic excitation. It was established that the rate of expansion of the turbulent mixing layer depends on the flow regime in the boundary layer. For laminar initial boundary layer, external acoustic excitation can lead to a decrease in the expansion velocity of the mixing layer and of the intensity of the velocity pulsations on the jet axis within the initial section. If the frequency and amplitude of acoustic excitation at which a decrease in the rate of expansion of the mixing layer and of the pulsation intensity was observed remained unchanged, the influence of the acoustics disappeared when the boundary layer became turbulent. The acoustic vibrations influenced the subsonic jets by generating vortex perturbations when they interact with the edge of the nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 36–42, November–December, 1982.We are grateful to K. I. Artamonov, now deceased, for support and discussing the results, and O. I. Navoznov and S. F. Agafonov for help in organizing and performing the experiments.     

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.     

Influence of acoustic reflectors on the discrete component in the noise spectrum of a supersonic off-design jet

An experimental investigation of the discrete component in the noise spectrum of an axisymmetrie off-design jet emerging from a sonic or supersonic nozzle into a submerged space is conducted. The influence of the diameter of the reflector, placed at the nozzle edge, on the level, frequency, and phase diagram of the discrete component is examined. The discrete component in the jet noise spectrum has been studied in [1–7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 157–160, November–December, 1977.     

Numerical investigation of the steady-state conditions of interaction of a supersonic underexpanded jet with a plane obstacle located perpendicular to its axis

The results are presented of the numerical investigation of the interaction of a supersonic axisymmetrical jet of a nonviscous and nonthermally conductive gas, flowing from a conical nozzle into a space with reduced pressure, with a plane obstacle. The presence of a triple point of intersection of the shock wave issuing from the obstacle with the trailing and reflected oblique compression shock is characteristic for the conditions considered in the paper. The solution of the problem is obtained by numerical integration of the gasdynamic equations by means of monotonic difference schemes of a straight-through calculation with first-order accuracy. The interaction of supersonic gas jets with surfaces is a vast problem and is one of the trends being developed intensively in the theory of jet streams. Of the whole multiplicity of problems of practical interest, the two-dimensional case of the normal collision between a supersonic axisymmetrical jet and a plane obstacle has been studied in most detail. As a result of the investigations carried out, many characteristic mechanisms of these flows have been revealed. Together with the numerous experimental papers, several reports have been published (for example, [1–4]) in which various numerical methods are employed to solve this problem. In addition to the method of integral relations used in [1], an implicit difference scheme [2] and explicit schemes of straight-through calculation [3, 4] have been used to calculate the subsonic zone of increased pressure in front of the obstacle. However, an extensive investigation of the special features of the action of a supersonic underexpanded jet on a plane obstacle, at a very small distance from the nozzle exit, still has not been carried out up to the present. In this paper, a solution of this problem is undertaken by the numerical method described in [4] using difference schemes [5, 8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 49–56, September–October, 1976.The authors express sincere thanks to A. N. Kraiko, é. A. Ashratov, and U. G. Pirumov for constant interest and support in carrying out this project.     

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.     

Instability and breakup of capillary liquid jets in a parallel airstream

The problem of the development and interaction of nonlinear two-dimensional perturbations in a rotating capillary jet is solved. The main attention is devoted to the study of the nonuniform breakup of the jet with allowance for the influence of the parallel airstream and the rotation. The solution is found by Galerkin's method [1–3]. The nonlinear development and interaction of a large number of perturbations is considered. A significant influence of long-wavelength modulation on the nature of drop formation is established. It is shown that an increase in the velocity of the parallel stream leads to a decrease in the relative size of the satellite (for the characteristic wavelengths). It is also shown that the rotation extends the region of unstable wave numbers in the complete range of flow velocities and air densities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–128, May–June, 1981.I am sincerely grateful to G. I. Petrov, V. Ya. Shkadov, and S. Ya. Gertsenshtein for constant interest in the work.     

Numerical investigation of “lateral” interaction with an obstacle of an axisymmetric jet exhausting into vacuum

The problem of the interaction of a strongly underexpanded axisymmetric jet with an obstacle for which the normal to the surface makes an angle near /2 with the jet axis is rather laborious for numerical solution due to the high disequilibrium of the gas-dynamic parameters in the peripheral part of the jet and the three-dimensional nature of the flow in the interaction region. Therefore, the results at present available have mainly been obtained experimentally [1, 2]. Among the theoretical studies made in this direction, it is necessary to mention Ivanov and Nazarov's [3], which gives the results of numerical investigation of lateral interaction of a jet with obstacles of various shapes in the case of weakly underexpanded jets when the flow in the interaction region is everywhere supersonic. In the present paper, a study is made of the case when a jet exhausts into vacuum and in front of the obstacle there is a detached shock wave, behind which there is mixed subsonic and supersonic three-dimensional flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 49–54, November–December, 1982.We thank V. I. Uskov for assistance in the present work.     

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.     

Electrical fluctuations in turbulent electrogasdynamic flows

Processes in turbulent flows containing charged particles are examined. It is shown that fluctuations of the electrical charge, which can be recorded by special apparatus, occur in the jets of aircraft engines in the presence of charged particles of unburned fuel in them and in turbulent jets created under laboratory conditions by blowing corona sources with air. The problem of determining the characteristics of turbulence in jets from measurements of electrical fluctuations sensed by an electrostatic probe is formulated. The electrical fluctuations generated by a submerged electrogasdynamic jet were measured under laboratory conditions and the results were compared with the data of acoustic measurements. A good correlation of the relative electrical and acoustic characteristics was found. The spectra of electrical fluctuations of a jet during its neutralization were studied by means of a special compensator and the mixing zone of opposite electrical charges was determined. The electrical fluctuations generated by the jets of aircraft were measured under airfield conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 148–159, March–April, 1977.The authors thank A. N. Sekundov for a valuable discussion and help in the work and also A. P. Strekalov and V. F. Kudryashov for participating in the experimental investigations.     

Electroconvective jets in liquid dielectrics

The principal feature of electroconvective jets in liquid dielectrics developing under the influence of a high-voltage external field is the large value of the EHD interaction parameter. This leads to the coupling of the hydrodynamic and electric problems. As formulated in [1, 2] the situation is reversed: the EHD interaction parameter is small. In these problems the interest is usually confined to finding the electric characteristics of the jet for a given velocity field. In [3] flows from sharp electrodes in liquid dielectrics were analyzed under two principal assumptions: nonlinear ohmic conductivity and point EHD interaction. This paper deals with the calculation of submerged electroconvective jets with ionic conductivity on the basis of the boundary-value problem formulated in [4]. In this case point EHD interaction is not assumed. It should be noted that in this formulation the problem is of practical as well as theoretical interest, for example, in connection with the problem of designing throttle EHD converters [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 13–19, November–December, 1984.     

Interaction between a supersonic boundary layer and acoustic disturbances

The development of disturbances in a boundary layer that have been induced by an external acoustic field are investigated. The problem is considered in the linear formulation. It is shown that the oscillations inside the supersonic boundary layer can have several times the intensity of the external disturbances. The susceptibility of the boundary layer to the acoustic disturbances increases with increasing Mach number. Cooling of the surface leads to a small decrease in the intensity of the longitudinal velocity oscillations in the layer. The effect of the parameters of the acoustic wave is considered, i.e., the effect of the frequency and phase velocity on the development of the disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 51–56, November–December, 1977.     

Interaction between an external compression shock and a blunt body in a hypersonic stream

A complex shock configuration with two triple points can occur during the interaction between an external oblique compression shock and the detached shock ahead of a blunt body (for instance, ahead of a wing or stabilizer edge). This results in the formation of a high-pressure, low-entropy supersonic gas jet [1–6]. Here two flow modes are possible [1], which differ substantially in the intensity of the thermal and dynamic effects of the stream on the blunt body: mode I corresponds to the impact of a supersonic jet [2–6], while the supersonic jet in mode II does not reach the body surface in the domain of shock interaction because of curvature under the effect of a pressure drop. Conditions for the realization of the above-mentioned flow modes are investigated experimentally and theoretically, and an approximate method is proposed to determine the magnitude of the compression shock standoff in the interaction domain. Blunt bodies with plane and cylindrical leading edges are examined. The results of a computation agree satisfactorily with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 97–103, January–February, 1976.The author is grateful to V. V. Lunev for discussing the research and for useful remarks.     

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.