Nonequilibrium gas-condensate flow in a laval nozzle

A scheme is proposed which simplifies the algorithm and reduces the labor involved in solving the system of quasi-linear hyperbolic equations describing supersonic nonequilibrium two-phase flow in an axisymmetric nozzle.     

Oscillation modes of laval nozzle flow

Experimental investigations of Laval nozzle flow show for relatively low supply to exit pressure ratios, which correspond to shock wave positions close to the nozzle throat, three different, oscillatory instabilities.

1. Shock pattern oscillations where the root of a λ-like shock front remains nearly in constant position, but where the proportion between the normal part and the oblique part of the shock changes periodically.
2. Shock wave and separation bubble oscillations where the motion of the shock wave is accompanied by displacements of the separation bubble.
3. Flow rate oscillations where the shock waves leave periodically through the nozzle throat in upstream direction.

     

Analytical study of supersonic isentropic flow in a channel of constant cross section and an adjacent laval nozzle. Comparison with numerical and experimental results

An analytic study of plane supersonic flow based on the use of Prandtl-Meyer invariants is presented. Flow in both a channel of constant cross section and an adjacent Laval nozzle with a corner point is considered. The analytical results are compared with numerical and experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 158–169, July–August, 1994.     

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.     

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.     

Calculation of gas flow in a laval nozzle in the presence of nonequilibrium physicochemical processes

An explicit divergence difference scheme of third order of approximation with respect to the spatial variables is used to calculate two-dimensional steady flows of an inviscid gas that does not conduct heat in contracting-expanding nozzles in the presence of nonequilibrium physicochemical processes. The flow structure is demonstrated for a three-component vibrationally nonequilibrium gas mixture in planar Laval nozzles with different radii of curvature of the nozzle profile in the neighborhood of the critical section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 173–177, July–August, 1982.We thank A. N. Kraiko and Yu. V. Kurochkin for helpful advice and interest in the work.     

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.     

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.     

Thrust of a contracting nozzle

A study is made of the influence of the nonuniformity of the parameters due to the two-dimensional nature of the flow on the specific thrust of a contracting nozzle. It is shown that for continuous flow of an ideal (inviscid and nonheat-conducting) gas the specific thrust in the supercritical regimes exceeds the value determined using the one-dimensional theory for the same stagnation parameters of the gas; in the subcritical regimes the specific thrust of the contracting nozzle is equal to the value found from the one—dimensional approximation.     

Allowance for nonuniformity of the flow at the minimal section in optimal profiling of the expanding part of a nozzle

A study is made of the problem of allowing for the real nonuniform distributions of the flow parameters at the minimal section of a Laval nozzle in the problem of constructing its supersonic part in such a way as to maximize the thrust for fixed counterpressure and fixed maximally allowed dimensions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 184–186, January–February, 1981.We thank L. E. Sternin, who initiated the present investigation, and also V. A. Bugrov and N. N. Slavyanov for assistance in calculating the subsonic and transonic flows.     

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.     

Numerical and experimental investigation of a laval nozzle with a cylindrical throat

The results are reported of experimental and numerical investigation of mixed flow and of the parameters of heat transfer in the transonic region of an axisymmetric Laval nozzle whose throat is formed by a cylindrical surface, i.e., the nozzle contour near the minimum cross section contains two bends.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 189–192, September–October, 1984.