Investigation of nonequilibrium two-phase flows in axisymmetric laval nozzles

The singularities of two-phase flows in Laval nozzles were investigated within the framework of the model of a two-fluid continuous medium [1, 2] mainly in a quasi-one-dimensional approximation ([3] and the bibliography therein). Two-dimensional computations of such flows were performed only recently by using the method of buildup [4–7]. However, systematic computations to clarify the influence of the second phase on such fundamental nozzle characteristics as the magnitude of the specific impulse, its losses, and discharge coefficient were performed only in the quasi-one-dimensional approximation [8, 9] and only for the supersonic parts of the nozzle in the two-dimensional approximation under the assumption of uniform flow in the throat [10, 3]. Such an investigation is performed in this paper in the two-dimensional case for the nozzle as a whole, including the sub-, trans-, and supersonic flow domains, and a comparative analysis is given of the magnitudes of the loss of a unit pulse obtained in the quasi-one-dimensional approximation [8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 86–91, November–December, 1977.     

Theory of vortical helical ideal gas flows in laval nozzles

An asymptotic solution is found for the direct problem of the motion of an arbitrarily vortical helical ideal gas flow in a nozzle. The solution is constructed in the form of double series in powers of parameters characterizing the curvature of the nozzle wall at the critical section and the intensity of stream vorticity. The solution obtained is compared with available theoretical results of other authors. In particular, it is shown that it permits extension of the known Hall result for the untwisted flow in the transonic domain [1]. The behavior of the sonic line as a function of the vorticity distribution and the radius of curvature of the nozzle wall is analyzed. Spiral flows in nozzles have been investigated by analytic methods in [2–5] in a one-dimensional formulation and under the assumption of weak vorticity. Such flows have been studied by numerical methods in a quasi-one-dimensional approximation in [6, 7]. An analogous problem has recently been solved in an exact formulation by the relaxation method [8, 9]. A number of important nonuniform effects for practice have consequently been clarified and the boundedness of the analytical approach used in [2–7] is shown.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 126–137, March–April, 1978.The authors are grateful to A. N. Kraiko for discussing the research and for valuable remarks.     

Parameters of jets out of rectangular nozzles when they are free or near a screen

The results are given of an experimental determination of the parameters of jets out of rectangular nozzles. The distributions of the mean velocity and an impurity concentration were measured. The rearrangement of the jet flow associated with the three-dimensional structure of the jet and interaction of the jet and a screen was investigated. A model that describes the occurrence of a pressure difference and curvature of the jet trajectory when it interacts with a screen is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 39–48, July–August, 1979.     

Subsonic and transonic flow field in two-dimensional de laval nozzles

This paper presents solutions of subsonic and transonic flow fields in two-dimensional De Laval nozzles with preassinged contraction ration ₁, expansion ration ₂, and throat wall radiusR _*. The effects of the contraction and the expansion angle on nozzle flow, the transformation of flow pattern of a De Laval nozzle in the throat region, and the conditions of occurrence and the governing parameters of the supersonic bubbles are discussed.     

Heat and mass transport in nonisothermal turbulent flow when there is a screen formed by a gas of a different nature

We obtain a limiting relative law for heat and mass transport when there is a gas screen in a turbulent boundary layer, which makes it possible to take into account the effect of nonisothermal flow on the turbulent heat and mass transport beyond the region where the foreign gas is injected. The theoretical results are compared with experimental data on the intensity of burn-up of a graphite surface in an air flow when helium is injected through a tangential slit. The experimental data were obtained from the diffusion region of the burn-up.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 152–156, September–October, 1971.     

Numerical investigation of two-phase flow with coagulation and fragmentation of particles in axisymmetric laval nozzles

The method and results of a calculation of the parameters of a polydis-perse two-phase flow with coagulation and fragmentation of particles in collisions are described. The problem is considered in a two-dimensional formulation. The secondary particles (fragments) formed by fragmentation are assumed to have arbitrary mass and velocity distributions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 145–153, May–June, 1982.We thank F. G. Gaponich for assistance in the computer calculations.     

Calculation of heat transfer in nozzles

The author proposes a simplified method for calculating the heat transfer in subsonic and supersonic nozzles. The method is based on a solution of the energy equation using relative heat transfer laws.     

Experimental and numerical analysis of the structure of pseudo-shock systems in laval nozzles with parallel side walls

Detailed numerical and experimental investigations of pseudo-shock systems in a Laval nozzle with parallel side walls are carried out. The location of the pseudo-shock system is defined in this system of two choked Laval nozzles by the ratio of the critical cross sections A₂^*/A₁^*{{A}_{2}^*/{A}_{1}^*} , the stagnation pressure loss across the shock system and viscous losses. The wall pressure distributions and high-speed schlieren videos recorded in the experiments are compared to the results of a steady and an unsteady numerical simulation. For the steady case, good agreement is found between the calculated and measured shock structure and pressure distribution along the primary nozzle wall, except for a remaining slight deviation in the shock position. For the unsteady case, in which asymmetric shock configurations are observed, deviations of the results with respect to the stochastic wall attachment of the shock system are given which indicate the necessity of further investigations on that topic.     

Heat transfer of spray cooling using alumina/water nanofluids with full cone nozzles

The transient temperatures of a metal testing plate during spray cooling using alumina/water nanofluids were measured. The heat transfer coefficient (HTC) was calculated by an inverse heat-conduction technique using the measured temperatures. The results show a decrease of approximately 20?% of the HTC of spray cooling with the nanoparticle suspension changing from 0 to 16.45?%. The nature and the reason of the HTC deduction were investigated and the HTC correlations with the mass fluxes and nanoparticle fraction were specifically reported.     

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.     

Flow and heat transfer of a viscous fluid when there is a phase transition

A study is made of the problem of the flow and heat transfer of a fluid formed by the phase transition (melting or sublimation) when the end of a rod touches a heated surface. Problems of this kind arise, in particular, when a heated surface is cooled by means of the heats of the phase transitions of materials with an energy content. A solution is obtained to a simplified system of heat and mass transfer equations obtained by estimating the order of magnitude of the various terms in the Navier-Stokes equations in a manner similar to that in [1–3]. The parameters that govern the process are identified, and an approximate analytic solution is found for the quasi-stationary case. The analytic solution is compared with a numerical solution obtained iteratively.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–131, May–June, 1931.     

Numerical investigation of two-phase flows in axisymmetric laval nozzles with allowance for processes of coagulation and division of condensed particles

In the framework of a model in which a polydisperse two-phase medium is represented as a multivelocity continuum [1, 2] a numerical investigation is made into the features of two-phase flows in axisymmetric Laval nozzles with allowance for processes of coagulation and division of particles. Calculations were made for a step distribution of the condensed particles with respect to their diameters (Lagrange's method [3, 4]). The flow pattern as a whole was determined, and also the most important integrated characteristics of the nozzles, including the unit impulse loss. Some qualitative results of calculations of such two-dimensional flows were obtained earlier in [6], but systematic investigations have been made only in the quasione-dimensional approximation (see [3, 4] and the bibliography there).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 82–90, January–February, 1980.I thank A. A. Glazunov for great assistance in the calculations and am indebted to I. M. Vasenin for his interest in the work and also for a number of comments of a critical nature.     

Heat transfer in a tapered passage

Heat transfer to laminar flow in tapered passages is studied for two types of thermal boundary conditions: prescribed heat flux on both walls, and on one wall with the other wall adiabatic. In the analysis, the flow is assumed to be purely radial. Temperature distributions and Nusselt number are obtained for the heat flux q ∞ r^δ. The Nusselt number depends on Reynolds number and taper angle. The fully developed Nusselt number decreases with increase in δ for converging flow and increases for diverging flow. Constant heat flux boundary conditions, δ = 0, for converging flow yield a reduction in Nusselt number when compared with the case of parallel channel flow.     

Heat transfer in a corner flow

The paper describes a method of evaluating heat transfer in corner flow of an incompressible fluid with suction

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Wärmeübertragung in einer Eckenströmung

Zusammenfassung Der Aufsatz beschreibt eine Methode zur Berechnung des Wärmeübergangs bei Strömung eines inkompressiblen Fluids in eine Ecke mit Absaugung.

     

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.