Entropy correlation of condensation shocks in hypersonic nozzles

Using an approximate solution [1] a two-parameter correlation is obtained between the maximal supercooling(the Wilson point) and the distribution of gasdynamic parameters in the zone of spontaneous condensation for a hypersonic flow. One parameter is the gas entropy in the injection cup, and the other is the product of the power-law stagnation temperature and the ratio of the characteristic dimension of critical section to the tangent of the nozzle half-angle.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 53–57, March–April, 1976.     

Homogeneous condensation in turbulent submerged isobaric jets

Turbulent isobaric vapor-air jet flows with homogeneous condensation are examined. A general system of equations, including the gas dynamic and kinetic equations, the thermodynamic relations and the equations for the turbulence model, is formulated. The moment kinetic equations valid for the free-molecular regime of drop growth in the surrounding medium are extended to other drop mass transfer regimes. The structure of the condensation shock, which includes the nucleation zone and the zone of drop growth on pre-existing nuclei, is investigated on the basis of a general asymptotic approach. Additional conditions at the nucleation and condensation shocks, the need for which follows from the requirement that the shocks be evolutionary, are obtained. Certain problems of averaging of the source terms in the moment equations are discussed, and with reference to the simple example of averaging of the frozen nucleation rate it is shown that the latter is nonzero for a mean supersaturation less than unity and that the condensation zone is displaced upstream. Condensation in a turbulent jet into which condensation-intensifying charged particles (corona discharge ions) are introduced is studied. A numerical method of analyzing homogeneous condensation in turbulent jets, which makes it possible to obtain the gas dynamic and disperse flow characteristics for various temperature conditions with allowance for the averaging of the source terms, is developed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 43–52, March–April, 1988.The authors wish to thank V. R. Kuznetsov for discussing various aspects of their work.     

The pressure and temperature behind bodies with flat bases in a supersonic flow when inert and active gases are introduced into the base region

The effect of introducing active and inert gases into the base region behind two-dimensional and axisymmetric bodies on the pressure and temperature in that region is studied in the absence of heat transfer between the body and the base region. The flow in the mixing zone is assumed to be turbulent. To investigate the effect of introducing active gases on the parameters in the base region, a model of diffusion combustion is used. The base pressure is calculated by Korst's method [1]. For the velocity profile in the mixing zone an expression is used which results from integrating the equation of motion in von Mises variables. The temperature and concentrations of the components in the base region are determined from integral equations for the conservation of enthalpy and concentration, which make it possible to calculate the parameters in the base region for arbitrary flow rates of the active gas, including arbitrarily small rates. The results are given of calculating the base pressure when hydrogen and argon are blown into the base region. In the latter case computational and experimental results are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 48–57, March–April, 1971.     

Modeling fluid and heat transport in the reactive, porous bed of downdraft (biomass) gasifier

A fluid flow and heat transfer model has been developed for the reactive, porous bed of the biomass gasifier to simulate pressure drop, temperature profile in the bed and flow rates. The conservation equations, momentum equation and energy equation are used to describe fluid and heat transport in porous gasifier bed. The model accounted for drag at wall, and the effect of radial as well as axial variation in bed porosity to predict pressure drop in bed. Heat transfer has been modeled using effective thermal conductivity approach. Model predictions are validated against the experiments, while effective thermal conductivity values are tested qualitatively using models available in literature. Parametric analysis has been carried out to investigate the effect of various parameters on bed temperature profile and pressure drop through the gasifier. The temperature profile is found to be very sensitive to gas flow rate, and heat generation in oxidation zone, while high bed temperature, gas flow rate and the reduction in feedstock particle size are found to cause a marked increase in pressure drop through the gasifier. The temperatures of the down stream zones are more sensitive to any change in heat generation in the bed as compared to upstream zone. Author recommends that the size of preheating zone may be extended up to pyrolysis zone in order to enhance preheating of input air, while thermal insulation should not be less than 15 cm.     

Effect of rotational degrees of freedom of molecules on energy flux in attenuated gas

On the basis of model kinetic equations a solution is obtained by a numerical method for the flow of attenuated gas around a sphere. The effect of rotational degrees of freedom on the energy flux to the body is investigated. Values of the ratio between the energy flux Q and its free-molecular value Q* for monatomic and diatomic gases are compared; for the comparison, the dimensionless temperature of the body, the gas velocity at infinity, and the law of viscosity must be the same in the two cases. For sufficiently cold bodies (when the body temperature is below the equilibrium temperature for a diatomic gas) the difference between Q/Q* for monatomic and diatomic gases is insignificant. For a diatomic gas when the body temperature is close to equilibrium, the ratio Q/Q* is found to have a nonmonotonic dependence on the Knudsen force.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 119–124, September–October, 1977.     

The mathematical simulation of various condensation regimes in turbulent isobaric jets

Mathematical models are considered and calculations made for flows in turbulent isobaric steam—air jets in the presence of condensation of the water vapor they contain. The models consist of gasdynamic equations for a turbulent jet, equations for a differential two-parameter model of turbulence, thermodynamic relations, and kinetic equations. A study is made of steam—air jets in a regime of condensation in equilibrium, when the flow region is broken down into zones of frozen flow and flow in equilibrium, described by the equations for a turbulent jet with the use of the traditional thermodynamic relations and of the thermodynamic relations for condensation in equilibrium. An analysis is made of the influence of pulsating motion on the kinetic parameters: rate of nucleation, the critical size of the nuclei, and rate of growth of the drops. It is shown that the rate of nucleation, determined from a quasilaminar averaging model, is several orders of magnitude less than the mean value obtained by averaging using the density distribution of the passive admixture concentration probability. A numerical study is made of the heterogeneous condensation in turbulent jets on extraneous particles entering from the nozzle. Kinetic equations are written down for the case when the rate of growth of the drops does not depend on their radius. A study is made of the dynamics of the transition of heterogeneous condensation from disequilibrium to equilibriumTranslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–67, January–February, 1985.     

Effect of homogeneous condensation on the dynamics of a hot vapor bubble in a cold liquid jet

The problem of initiating cavitation bubbles in a cold liquid jet by injecting hot steam into high-pressure zone specially organized at the nozzle outlet is considered. Previously, in [1], a plane flowfield in which vapor bubbles were formed at the cusp of the cavity (high-pressure zone) and propagated together with the liquid along the axis of symmetry was considered. In certain cases, in the bubble expansion process the vapor temperature drops below the saturation temperature. In the present paper, vapor condensation in the bubble volume (homogeneous condensation) is also taken into account.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 56–61, November–December, 1996.     

Nonequilibrium homogeneous condensation in rarefaction waves

Results of numerical calculations of condensing vapor expanding into a vacuum and in a supersonic conical nozzle are presented. Nonequilibrium homogeneous condensation is compared with the theory of determining parameters. It is proved that equality of the determining parameters ensures the unity of the course of such processes in different devices. The influence of unsteady nucleation on the maximum supercooling was also investigated. All the calculations were made for water and nitrogen vapors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 152–156, March–April, 1986.     

Boundary layer on a vaporizing surface

The article discusses the laminar boundary layer on the vaporizing surface of liquid hydrogen over which there is a flow of molecular hydrogen. The pressure p in the boundary layer corresponds to the saturation temperature of the oxygen T₀, which is lower than the temperature of the oncoming flow T, but higher than the temperature of the surface of the liquid hydrogen. Under such conditions, within the boundary layer there is condensation of oxygen in the volume, which leads to the formation of drops of liquid oxygen of different sizes. It is proposed in the article that, with the condensation of gas in the volume, drops of one size are formed. Drops of a chosen mean size are regarded as molecules of a heavy gas. The gas drop is a third component present in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 48–53, September–October, 1973.The author thanks G. I. Petrov for his interest in and direction of the work.     

Analysis of the nonequilibrium two-phase flow with coagulation and crushing of condensate particles for arbitrary mass and velocity distributions of the secondary drops

The problem of the nonequilibrium flow of a two-phase gas-polydisperse condensate drop mixture is considered in a one-dimensional approximation taking account of coagulation and crushing of particles of different size during collisions. A closed system of equations in the flow characteristics is obtained in application to the general case of arbitrary size, velocity, and temperature distributions of the secondary drops formed during crushing. Regularities in the interaction of freely moving drops during collisions are investigated experimentally.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 77–79, March–April, 1975.The authors are grateful to L. E. Sternin for attention to the research and to N. S. Kovalgina for assistance in carrying it out.     

Experimental investigation of flow and heat transfer for the ethanol-water solution and FC-72 in rectangular microchannels

Rapid development of super scale integration circuit (IC) provides unprecedented challenge to thermal control for aviation electronic equipments. To solve the problem of cooling electronic chips and devices for aircraft avionics, this paper experimentally investigated the characteristics of single-phase forced convection heat transfer and flow resistance in rectangular microchannels with two liquid coolants. One was 30% of ethanol–water solution, the most commonly used coolant in aviation. The other was FC-72, the latest coolant for electronic equipments. Based on the experimental data collected and those available in the open literature, comparisons and analyses were carried out to evaluate the influences of liquid velocity, supercooling temperature, microchannel structures and wall temperature etc. on the heat transfer behaviors. And the correlations of flow resistance and heat transfer characteristics were provided for the ethanol–water solution and FC-72 respectively. The results indicate transition from laminar to turbulent flow occurs at the Reynolds number of 750–1,250 for FC-72, and the behaviors of flow and heat transfer in rectangular microchannels strongly depend on the kind of coolant and geometric configuration of microchannels.     

Transonic crossflow of condensing wet steam past a cylinder

The shadow and interferometric methods and the laser probe method are used to investigate crossflow past a cylinder on the free-stream Mach number interval M _a =0.5–1.2 for subcritical Reynolds numbers Re _d and various initial steam states. Detailed pressure distributions are obtained and the pressure fluctuations on the cylinder surface are measured. The dependence of the Strouhal number on the velocity and thermodynamic parameters of the flow are determined. In single-phase steam flow past a cylinder the greatest fluctuations occur in the separation zone in regimes corresponding to transonic drag crisis. It is shown that spontaneous condensation in the turbulent wake and local supersonic zones may cause an increase in the periodic pressure fluctuations in the separation zone, the maximum increase in the fluctuations being noted when the critical pressure ratio is reached at the rear of the cylinder. The initial wetness of the steam has the greatest effect on the periodic separation characteristics at subsonic flow velocities, and in the case of supersonic flow leads to a substantial increase in the level of the low-frequency pressure fluctuations at the front of the cylinder.(deceased)Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 118–138, November–December, 1994.     

Contact zone during the noninstantaneous opening of a diaphragm in a shock tube

The structure and nature of motion of the contact zone during the noninstantaneous opening of a diaphragm in a shock tube are analyzed for the case of Re and equal adiabatic indices of the propelling and propelled gases. It is shown that the temperature profiles in the contact zone are self-similar, and an expression is obtained for the trajectory of the interface of the gases in the contact zone.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 159–161, November–December, 1976.     

Propagation of a turbulent jet impinging on a plane surface in an external stream

The results of an investigation of the three-dimensional vortex zone which forms near a plane surface when a turbulent jet impinges on it in an external stream are presented. Problems of this kind occur, for example, in a study of the effects of the entry of exhaust gases into the air intakes of engines when aircraft with thrust reversers turned on fly through an airport and when vertical-take-off-and-landing aircraft move near the earth [1–3]. The structure of the vortex zone and the temperature distribution in it are established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 56–62, September–October, 1978.In conclusion, the author thanks A. N. Sekundov and S. Yu. Krasheninnikov for attention to the work and a discussion of its results.     

Numerical investigation of the effect of inlet condition on self‐excited oscillation of wet steam flow in a supersonic turbine cascade

Self‐excited oscillation can be induced due to the interaction between condensation process and local transonic condition in condensing flow, which is an important problem in wet steam turbine. With an Eulerian/Eulerian numerical model, the self‐excited oscillation of wet steam flow is investigated in a supersonic turbine cascade. Owing to supercritical heat addition to the subsonic flow in the convergent part of the cascade, the oscillation frequency decreases with increased inlet supercooling. Mass flow rate increases in the oscillating flow due to the greater supersaturation in condensation process, while the increase will be suppressed with the flow oscillation. Higher inlet supercooling leads to the fact that the condensation process moves upstream and the loss increases. Moreover, some predictions of oscillation effects on outflow angle and aerodynamic force are also presented. Finally, heterogeneous condensations with inlet wetness and periodic inlet conditions, as a result of the interference between stator and rotor, are discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Effect of the coefficient of condensation on the flow of vapor and the condensation at sub- and supersonic speeds

A method is presented for calculating the process of one-dimensional steady condensation at an arbitrary value of the coefficient of condensation. The method is based on the use of the solutions of [1], which were obtained for the case of total absorption of incident molecules on an interphase surface, and on application of the rule of scaling proposed in [4]. An analysis is made of an experiment [3] on supersonic flow of a stream of air onto a surface cooled by liquid helium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 189–192, March–April, 1988.     

Influence of film thickness and cross-sectional geometry on hydrophilic microchannel condensation

Condensation in hydrophilic microchannel is strongly influenced by the channel cross-sectional geometry and the condensing surfaces hydrophobicity, which govern the evolution of the liquid film. This work makes progress on studying the relationship between channel geometry and condensation through flow regime visualizations, film-thickness measurements with optical interferometery, and temperature profile measurements with heat flux distribution construction. The hydrophilic microchannels have aspect ratios ranging from 1 to 5 and hydraulic diameters from 100 μm through 300 μm. The experimental measurement qualitatively matches the prediction of previous theoretical models accounting for the surface tension effect, which highlights the importance of surface tension force and channel geometry in the microchannel condensation. Pressure drop and mean heat flux measurements show that a larger channel is favorable for minimizing the pressure drop, while a smaller channel size and higher aspect ratio are desirable for maximizing the mean heat flux. The optimization of the channel geometry for a given application lies in the trade-off between these two factors.     

Analysis of temperature jump and partial pressure coefficients of a binary evaporating gas mixture

The Maxwell-Loyalka method is used to derive expressions for the boundary temperature and partial pressure jumps of a binary mixture of gases evaporated (condensed) on a wall. The evaporation (condensation) is assumed to be weak. The expressions for the jumps are written in terms of the components normal to the wall of the reduced heat flux of the gas mixture and the average velocities of its components, which makes possible direct generalization to a multicomponent mixture, invariance of the coefficients of the expressions for the jumps with respect to the number of evaporating components, and symmetry of the cross effects. These coefficients are analyzed in the same way as in [1], and it is shown that they can be considerably simplified with an accuracy acceptable for practical purposes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 150–159, November–December, 1991.     

Investigation of turbulent vapor-air jets in the presence of condensation and the injection of foreign particles

A study is made of flow in turbulent jets when there is condensation of the water vapor contained in them. A necessary condition for condensation in vapor-air jets is formulated. Relations are obtained for the regime of equilibrium condensation. An experimental investigation was made of the local characteristics of an isobaric turbulent vapor jet exhausting into air at rest when condensation develops in the jet and foreign condensation nuclei (smoke particles) and charged particles (ions produced in a corona discharge) are introduced into the flow. Measurements were made of the local characteristics of the condensed disperse phase — the Sauter diameter d₃₂ of the drops and their volume concentration c_s — using the optical method of an integrating diaphragm. It is shown that d₃₂ and₃₂ c_s increase downstream in the main section of the jet. Specific features of temperature measurements using an end-type microthermocouple were established. Quantitative data were obtained about the influence on the condensation of the thermal conditions and the presence of the foreign particles. The conditions under which there is an intensification of the condensation in vapor-air jets in the presence of ions were determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 53–61, May–June, 1984.