Flow of a two-phase medium in a laval nozzle

The back reaction of particles on a gas flow in Laval nozzles was investigated experimentally. Experimental data were obtained that characterize the change produced by the particles of a solid phase in the shape of the sonic line, the pressure distribution on the nozzle profile, and the configuration of the shock waves in the jet. Flow rate coefficients are given for different nozzle profiles and mass fraction and sizes of the particles in the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–111, January–February, 1981.     

Flow of viscous gas out of a cylindrical channel into vacuum

A study is made of the exhausting of a jet of viscous gas from a cylindrical channel into vacuum in the presence of a flat bounding surface outside the channel in the plane of its exit section. The problem is solved numerically using the complete system of Navier—Stokes equations. The developed flow model makes it possible to take into account the influence of an external medium into which the jet exhausts on the structure of the flow in the exit section of the channel, and also the influence of the subsonic part of the boundary layer in the channel on the flow field of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–128, January–February, 1981.     

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.     

Numerical investigation of unsteady subsonic viscous gas flows in a plane channel with a sudden expansion

The nonlinear processes of development of instability in an unsteady subsonic viscous gas flow in a plane channel with a sudden expansion are investigated numerically with allowance for acoustico-vortex interaction over a broad interval of the characteristic parameters. Effects associated with the acoustic self-excitation of the jet flowing into the wider part of the channel are determined. Approximate relations are obtained for the resonance conditions of self-excitation. The effect of the inlet mean-velocity profiles on the evolution of the flow is estimated. The processes of formation and subsequent interaction of the coherent structures are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 32–41, July–August, 1988.     

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.     

Equations and forms of motion of a jet flowing onto a liquid

A nonlinear theory is constructed for a thin jet of nonviscous, incompressible, weightless fluid flowing from a nozzle onto the surface of an immobile heavy liquid. The theory is asymptotically (over jet thickness) more accurate than that presented in [1]. Forms of the flow are studied as functions of nozzle, jet, and heavy liquid parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 20–28, November–December, 1976.     

Calculation of three-dimensional weakly expanding flow in jets and channels

The results are given of a calculation of laminar flow in a channel of square section and the motion of a turbulent jet from a cruciform nozzle in an ambient flow. To calculate the secondary flows, the field of the transverse velocity is decomposed into irrotational and solenoidal components. The results of the calculation of the flow in the channel are compared with the calculations of other authors and experimental data. To calculate the flow in the turbulent jet, a one-parameter turbulence model is used, and the influence of the inhomogeneity of the distribution of the longitudinal component of the velocity on the components of the Reynolds stress tensor is taken into account. The results of calculation of the flow in the jet behind a cruciform nozzle are compared with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 36–44, July–August, 1984.     

Underexpanded wall jet in a cocurrent flow

The flow of a two-dimensional underexpanded wall jet flowing out of a sonic nozzle along a channel wall has been experimentally investigated. The dependence of the dimension of the first barrel of the jet on the underexpansion is obtained. It is shown that the flow of the jet in the channel is associated with a significant axial pressure gradient on the initial interval of the induced cocurrent flow and that this leads to a substantial change in the geometric dimensions of the jet.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 196–199, January–February, 1993.     

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.     

Some problems of turbulent electrohydrodynamic jets

The problem of an axisymmetric turbulent electrohydrodynamic jet exhausting from a nozzle into an interelectrode gap is formulated. A numerical method of integrating the system of equations describing this flow is developed. This method is used to investigate three-dimensional effects in the jet (expansion of the jet, reverse flows). The influence on the jet characteristics (currents of the charge carried out of the nozzle, jet diameter, etc.) of the geometrical and electrical parameters and also of purely hydrodynamic factors (level of turbulence, relative velocity of parallel flow, etc.) is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 144–149, September–October, 1980.     

Diffusion processes in the mixing zone of a supersonic jet of low density

Results of an investigation into the diffusion processes in a jet of low density behind a strongly underexpanded sonic nozzle, in the zone of mixing with the surrounding gas, are presented. By means of electron-beam methods, the structure of the jet was studied in the case of expanding N₂, into an atmosphere of CO₂ + N₂ in transient regimes of flow varying from solid to rarefied. The results of an analysis of the fields of concentration of the separate components are given in a generalized form.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 121–127, January–February, 1973.     

Flow in the peripheral zone of a freely expanding axisymmetric ideal-gas jet

When an ideal gas flows from a nozzle into a vacuum a substantial part of the jet is occupied by the peripheral zone in which the angle of inclination of the velocity vector W to the axis of symmetry is close to or exceeds /2. The known solutions [1–4] for the far field are unsuitable for describing the jet, since they are valid only at relatively small values of . In this study the author obtains an analytic solution describing in explicit form the shape of the streamlines and the distribution of the parameters in the peripheral zone of a jet flowing into a vacuum from a nozzle with an arbitrary parameter distribution in the exit section. At the nozzle edge the solution describes Prandtl-Mayer flow. As the radial coordinate tends to infinity, the streamlines tend to asymptotes whose angle of inclination depends on the distribution of the parameters in the nozzle exit section, and the local Mach numbers increase without bound.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 145–153, May–June, 1987.     

Calculation of interaction of a turbulent near-wake behind a step with a supersonic jet

Existing computational methods [1–5] do not enable one to calculate complex flows behind steps, accounting for nonuniformity of the incident supersonic flow and the effect of compression and expansion waves arriving in the near-wake region. For example, computational methods based on the methods of [1] or [2] are used mainly in uniform supersonic flow ahead of the base edge and, for the most part, cannot be used to calculate flow in annular nozzles with irregular conditions. An exception is reference [6], which investigated flow in an annular nozzle behind a cylindrical center-body. The present paper suggests a method, based on references [7, 8] for calculating the base pressure behind two-dimensional and three-dimensional steps, washed by a supersonic jet.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 43–51, November– December 1977.     

Semiempirical method of calculating overexpanded turbulent separated flow in a conical laval nozzle

A mathematical model of separated nozzle flow is developed. The model takes into account the effect of the boundary layer and the pressure variation over the entire separation zone inside the nozzle. The effect of the geometric and gas dynamic factors on the separated flow pattern is investigated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 60–66, November–December, 1988.     

Interaction of a supersonic jet exhausting into vacuum with an obstacle

A study is made of the interaction between an axisymmetric supersonic jet exhausting into vacuum and an obstacle of a fairly complicated configuration and positioned relative to the nozzle in such a way that in the interaction region behind the detached shock wave there is a three-dimensional flow possessing a symmetry plane. The flow in the interaction region is described by the system of equations of motion of an inviscid perfect gas with boundary conditions on the shock wave (Rankine-Hugoniot relation) and on the surface of the obstacle (no-flow condition). The other boundaries of the region are the symmetry plane of the flow and an arbitrarily chosen surface in the supersonic part of the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti Gaza, No. 1, pp. 156–161, January–February, 1981.     

Mechanism of energy separation in a gas ejector

A new phenomenon is revealed — the rotation of an ejecting jet, discharging from a nozzle and adhering to the wall of the mixing chamber, in an axisymmetric gas ejector in modes with zero and negative ejection coefficients — and a possible mechanism for its origin is discussed. It is suggested that the rotation of an adhering jet, which induces axisymmetric vortex motion of the gas in the injector, is responsible for the inverse separation of the initially energetically homogeneous stream into heated and cooled sections.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 145–151, November–December, 1977.     

Gas flow from a finite volume through a laval nozzle

Self-similar nonsteady flow in a Laval nozzle is considered; the flow is established when an ideal gas issues from a volume into a space at a sufficiently small pressure. The flow in the nozzle is assumed to be one-dimensional. Qualitative conclusions are formed on the effect of the nonsteady flow conditions on the distribution of M. For the case when the nonsteady properties have little effect, an asymptotic solution is obtained in quadratures and an example of a calculation is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 71–76, March–April, 1978.     

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.     

Calculation of the swirling flow of an ideal gas in a laval nozzle

The numerical solution of the problem of the motion of a swirling flow of an ideal gas in a Laval nozzle in axisymmetric formulation is obtained by the method of stabilization. As a result, a number of effects appear that are essentially not one-dimensional, in particular, the drawing-in of the sonic line into the nozzle, an effect that leads to a decrease in the nozzle's expansion coefficient. The dependence of this coefficient on the intensity of the swirling is obtained. A number of problems connected with the control of the expansion of a gas through a Laval nozzle and with variation of the thrust of a nozzle can be solved successfully in cases where a rotary motion is imparted to the flow of gas exhausted from the nozzle. Investigation of such a swirling flow in [1, 2] and a number of other papers are based on a one-dimensional model of gas flow, which makes it possible in principle to obtain integrated characteristics of the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 72–76, September–October, 1971.     

One-dimensional theory of off-design supersonic gas jets

A method based on the quasi-one-dimensional treatment of off-design supersonic jet flow is presented, together with the results of calculating the parameters of the jet on the interval of adaptation to the external conditions in the immediate vicinity of the nozzle exit section. On the jet formation interval the region of flow with strong discontinuities (shocks) is replaced by a surface of discontinuity. The mixing effect is taken into account by means of a concentrated mass flux in the section of discontinuity. It is shown that taking into account the real properties of the jet flow on the formation interval makes it possible considerably to improve the accuracy of a number of important flow parameters and to obtain a series of quantitative results that coincide with the experimental data.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 48–56, January–February, 1993.The author is grateful to E. A. Kapustin for his interest in the work and useful discussions.