Explosive discharge of a gas-saturated liquid from channels and tanks

A mathematical model for the discharge of a gas-saturated liquid from cylindrical channels is developed. Two limiting cases of linear and quadratic, relations between the flow friction force and the flow velocity are considered. It is established that the process of evacuation, from a semi-infinite channel consists of two stages. In the initial stage, the flow drag can be ignored, and the process of discharge is described by a Riemann wave solution. For the next stage, in which inertia is insignificant, nonlinear equations are obtained and self-similar solutions are constructed for them. The problem of flow through a slot in a tank of finite volume is solved. It is shown that the discharge proceeds either in a gas-dynamic choking regime or in a subsonic regime, depending on the conditions inside the tank and at the outlet. Examples of numerical calculations are given. Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000 Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 64–73, January–February, 1999.     

Interaction of a gas-droplet turbulent jet with a cocurrent high-velocity high-temperature gas flow

A mathematical model and a method for calculating a gas-droplet turbulent jet with allowance for velocity nonequilibrium and virtual mass of the condensed phase during turbulent fluctuations and also heat and mass transfer within the three-temperature scheme are developed. Methodical calculations are performed. The results of these calculations are in reasonable agreement with available experimental data. The structure of the gas-droplet jet in a cocurrent high-velocity high-temperature gas flow is studied by numerical methods. The ratio of intensities of heat and mass transfer between the phases and turbulent diffusion transfers of substances is found to be different at the initial, transitional, and basic segments of the jet. This difference is responsible for the nonmonotonic axial distribution of vapor density and the lines of the halved mass flow of the condensed phase. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 85–94, May–June, 2008.     

Calculation of a transport current from a nozzle with two-phase flow in the presence of a corona discharge

The operation of a source of charged aerosol particles which consists of a supersonic nozzle, a corona-forming needle-shaped electrode, and a device for injecting liquid droplets into a gas flow is considered. A theoretical model for two-dimensional, two-phase flow in the nozzle is considered. An algorithm of numerical calculation of such a flow is developed, and results of calculations of the electric transport current from the nozzle are given. Institute of Mechanics, Moscow State University, Moscow 117192. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 102–109, November–December, 1998.     

“Ion wind”, a gas-dynamic flow in the corona discharge,and its interaction with the external flow

The “ion wind”, a gas-dynamic flow in the corona discharge that arises owing to transfer of the ion component momentum to the neutral particles of an initially stationary gas, and its interaction with the external flow perpendicular to it are studied. A physico-mathematical model of the flows considered is proposed and the corresponding equations are analyzed numerically. The boundary conditions used for the electric quantities approximately model the conditions in the negative corona discharge between a thin corona-forming electrode and a plane grid electrode transparent to the gas.     

Convective mass transfer across fluid interfaces in straight angular pores

Steady convective mass transfer to or from fluid interfaces in pores of angular cross-section is theoretically investigated. This situation is relevant to a variety of mass transport process in porous media, including the fate of residual non-aqueous phase liquid ganglia and gas bubbles. The model incorporates the essential physics of capillarity and solute mass transfer by convection and diffusion in corner fluid filaments. The geometry of the corner filaments, characterized by the fluid–fluid contact angle, the corner half-angle and the interface meniscus curvature, is accounted for. Boundary conditions of zero surface shear (‘perfect-slip’) and infinite surface shear (‘no-slip’) at the fluid–fluid interface are considered. The governing equations for laminar flow within the corner filament and convective diffusion to or from the fluid–fluid interface are solved using finite-element methods. Flow computations are verified by comparing the dimensionless resistance factor and hydraulic conductance of corner filaments against recent numerical solutions by Patzek and Kristensen (J. Colloid Interface Sci 236, 305–317 2001). Novel results are obtained for the average effluent concentration as a function of flow geometry and pore-scale Peclet number. These results are correlated to a characteristic corner length and local pore-scale Peclet number using empirical equations appropriate for implementation in pore network models. Finally, a previously published “2D-slit” approximation to the problem at hand is checked and found to be in considerable error.     

Effects of Chemical Reaction and Double Dispersion on Non-Darcy Free Convection Heat and Mass Transfer

In this article, the effects of chemical reaction and double dispersion on non-Darcy free convection heat and mass transfer from semi-infinite, impermeable vertical wall in a fluid saturated porous medium are investigated. The Forchheimer extension (non-Darcy term) is considered in the flow equations, while the chemical reaction power–law term is considered in the concentration equation. The first order chemical reaction (n = 1) was used as an example of calculations. The Darcy and non-Darcy flow, temperature and concentration fields in this study are observed to be governed by complex interactions among dispersion and natural convection mechanisms. The governing set of partial differential equations were non-dimensionalized and reduced to a set of ordinary differential equations for which Runge–Kutta-based numerical technique were implemented. Numerical results for the detail of the velocity, temperature, and concentration profiles as well as heat transfer rates (Nusselt number) and mass transfer rates (Sherwood number) are presented in graphs.     

Study on the equivalent convection coefficient of the hot surface of blast furnace stave

The calculation models of the equivalent convection coefficient between blast furnace gas flow and the hot surface of stave body, gas flow and in-laid brick were established by the combination of experiments and numerical calculation when the gas temperature is in the range of 505–1,248°C. The reason why the heat transfer coefficient between gas flow and in-laid brick is much more than that between gas and stave body was analyzed when the gas temperature is high. The opinion just to considering a kind of integration heat transfer coefficient while the numerical calculation of heat transfer model of stave will be changed. The division of above two heat transfer coefficients will increase the degree of heat transfer numerical calculation.     

Mixed Convection in a Vertical Porous Channel

A numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces is studied by taking into account the effect of viscous and Darcy dissipations. The flow is modeled using the Brinkman–Forchheimer-extended Darcy equations. The two boundaries are considered as isothermal–isothermal, isoflux–isothermal and isothermal–isoflux for the left and right walls of the channel and kept either at equal or at different temperatures. The governing equations are solved numerically by finite difference method with Southwell–Over–Relaxation technique for extended Darcy model and analytically using perturbation series method for Darcian model. The velocity and temperature fields are obtained for various porous parameter, inertia effect, product of Brinkman number and Grashof number and the ratio of Grashof number and Reynolds number for equal and different wall temperatures. Nusselt number at the walls is also determined for three types of thermal boundary conditions. The viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. The Darcy and inertial drag terms suppress the flow. It is found that analytical and numerical solutions agree very well for the Darcian model. An erratum to this article is available at .     

Numerical calculations of supersonic underexpanded jets in a cocurrent flow with the use of parabolized Navier-Stokes equations

Results of a numerical study of three-dimensional supersonic jets propagating in a cocurrent flow are described. Averaged parabolized Navier-Stokes equations are solved numerically on the basis of a developed scheme, which allows calculations in supersonic and subsonic flow regions to be performed in a single manner. A jet flow with a cocurrent flow Mach number 0.05 ⩽ M_∞ ⩽ 7.00 is studied, and its effect on the structure of the mixing layer is demonstrated. The calculated results are compared with available experimental and numerical data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 54–63, May–June, 2008.     

Experimental study and mathematical simulation of the characteristics of a turbulent flow in a straight circular pipe rotating about its longitudinal axis

The vorticity formed in the cross section of a turbulent flow in a straight circular pipe rotating about its longitudinal axis decreases the values of the turbulent stresses, turbulence energy, and dissipation rate along the pipe. The results of laboratory experiments and calculations by the second-order closure model of turbulent transfer are presented. On the whole, the model using a system of transport equations yields better agreement with experimental data than the models with algebraic relations for second-order moments. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 103–116, March–April, 1998.     

Explicit Rate–Time Solutions for Modeling Matrix–Fracture Flow of Single Phase Gas in Dual-Porosity Media

One of the widely used methods for modeling matrix–fracture fluid exchange in naturally fractured reservoirs is dual porosity approach. In this type of modeling, matrix blocks are regarded as sources/sinks in the fracture network medium. The rate of fluid transfer from matrix blocks into fracture medium may be modeled using shape factor concept (Warren and Root, SPEJ 3:245–255, 1963); or the rate–time solution is directly derived for the specific matrix geometry (de Swaan, SPEJ 16:117–122, 1976). Numerous works have been conducted to study matrix–fracture fluid exchange for slightly compressible fluids (e.g. oil). However, little attention has been taken to systems containing gas (compressible fluid). The objective of this work is to develop explicit rate–time solutions for matrix–fracture fluid transfer in systems containing single phase gas. For this purpose, the governing equation describing flow of gas from matrix block into fracture system is linearized using pseudopressure and pseudotime functions. Then, the governing equation is solved under specific boundary conditions to obtain an implicit relation between rate and time. Since rate calculations using such an implicit relation need iterations, which may be computationally inconvenient, an explicit rate–time relation is developed with the aid of material balance equation and several specific assumptions. Also, expressions are derived for average pseudopressure in matrix block. Furthermore, simplified solutions (originated from the complex general solutions) are introduced applicable in infinite and finite acting flow periods in matrix. Based on the derived solutions, expressions are developed for shape factor. An important observation is that the shape factor for gas systems is the same as that of oil bearing matrix blocks. Subsequently, a multiplier is introduced which relates rate to matrix pressure instead of matrix pseudopressure. Finally, the introduced equations are verified using a numerical simulator.     

Direct numerical simulation of a liquid sheet in a compressible gas stream in axisymmetric and planar configurations

A thin liquid sheet present in the shear layer of a compressible gas jet is investigated using an Eulerian approach with mixed-fluid treatment for the governing equations describing the gas–liquid two-phase flow system, where the gas is treated as fully compressible and the liquid as incompressible. The effects of different topological configurations, surface tension, gas pressure and liquid sheet thickness on the flow development of the gas–liquid two-phase flow system have been examined by direct solution of the compressible Navier–Stokes equations using highly accurate numerical schemes. The interface dynamics are captured using volume of fluid and continuum surface force models. The simulations show that the dispersion of the liquid sheet is dominated by vortical structures formed at the jet shear layer due to the Kelvin–Helmholtz instability. The axisymmetric case is less vortical than its planar counterpart that exhibits formation of larger vortical structures and larger liquid dispersion. It has been identified that the vorticity development and the liquid dispersion in a planar configuration are increased at the absence of surface tension, which when present, tends to oppose the development of the Kelvin–Helmholtz instability. An opposite trend was observed for an axisymmetric configuration where surface tension tends to promote the development of vorticity. An increase in vorticity development and liquid dispersion was observed for increased liquid sheet thickness, while a decreasing trend was observed for higher gas pressure. Therefore surface tension, liquid sheet thickness and gas pressure factors all affect the flow vorticity which consequently affects the dispersion of the liquid.      

A numerical study on the absorption of water vapor into a film of aqueous LiBr falling along a vertical plate

Absorber is an important component in absorption machines and its characteristics have significant effects on the overall efficiency of absorption machines. This article reports a model of simultaneous heat and mass transfer process in absorption of refrigerant vapor into a lithium bromide solution of water––cooled vertical plate absorber in the Reynolds number range of 5 < Re < 150. The boundary layer assumptions were used for the transport of mass, momentum and energy equations and the fully implicit finite difference method was employed to solve the governing equations in the film flow. Dependence of lithium bromide aqueous properties to the temperature and concentration and film thickness to vapor absorption was employed. This model can predict temperature, concentration and properties of aqueous profiles as well as the absorption heat and mass fluxes, heat and mass transfer coefficients, Nusslet and Sherwood number of absorber. An analysis for linear distribution of wall temperature condition carries out to investigation the reliability of the present numerical method through comparing with previous investigation.     

Gas-dynamic flow structure of a system of plane supersonic intersecting jets in a hypersonic flow

Turbulent motion is described by a system of parabolized Novier-Stokes equations which is closed by the (k-ε) model of turbulence. In the numerical calculations performed by the method of decomposing the flow vectors, the complex pattern of the interaction between perturbation waves is shown. In addition, it is shown that the system of shock waves on a gas-dynamic site causes the production of the pulsation-motion energy and the appearance of dissipative cellular structures in the field of kinetic turbulence energy. Al-Farabi Kazakh National State University, Almaty 480121. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 108–114, January–February, 1999.     

Subsonic rarefied gas flow over a rack of flat transverse plates

Parameters of a rarefied gas flow through a rack of flat plates aligned across the flow are studied by means of the joint numerical solution of the Boltzmann and Navier-Stokes equations. A subsonic flow regime is considered. The changes in flow characteristics are calculated as functions of the free-stream velocity and plate temperature. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 59–67, January–February, 2008.     

Supersonic flow deceleration in plane and axisymmetric channels

Supersonic perfect gas flow in plane and axisymmetric channels with the same duct contour is studied on the basis of a numerical solution of the two-dimensional Navier-Stokes and Euler equations. The calculations were carried out at an inlet Mach number M_∞=4 for various Reynolds numbers and “bell-mouth“ half-angles. The effect of these parameters, as well as that of the flow three-dimensionality, on the flow pattern is demonstrated. In particular, the existence of viscous flow regimes providing the most effective supersonic flow deceleration and a higher degree of total pressure recovery as compared with the inviscid flow is established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 143–152, March–April, 1998. The study was carried out with the support of the Russian Foundation for Fundamental Research (project No. 95-01-01129a).     

Numerical simulation of gas-dynamic processes in a pipe open at one end

The problem of sudden opening of one end of a circular pipe containing a pressurized gas is considered. A new form of the boundary condition at the open end of the pipe is proposed that takes into account the local hydrodynamic drag due to the nonlinearity of the real physical problem. The system of gas-dynamic equations is integrated by the Godunov numerical method of discontinuity decay. The procedure of numerical realization of the nonlinear boundary condition at the open end of the pipe is described in detail. Comparison of the graphs obtained in the calculations with experimental data indicates that the proposed technique is appropriate. Deceased. State Scientific Engineering Center of Systems of Control and Emergency Response, State Atomic Energy Committee of Ukraine, Kiev 252011. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 74–79, January–February, 1999.     

Calculation of the effect of a constant electric field on the gas dynamics and nitrogen oxide emission in a laminar diffusion flame

A laminar methane diffusion flame in a constant electric field whose direction is opposite to that of the velocity of the gas flow from the burner nozzle is considered. The mathematical model used includes the complete system of Navier-Stokes equations for the velocity and passive admixture concentration fields, the charge transport equation, together with the Poisson equation for the self-consistent electric field, and the chemical kinetic equations for a thin combustion zone. The calculations show that the flame shortens and its thickness increases in the root zone when an electric field is imposed. This effect is accompanied by a reduction in the nitrogen oxide emission, while is consistent with the experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 48–53, January–February, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 96-01-014-50).     

CFD modeling and experimental validation of heat and mass transfer in wood poles subjected to high temperatures: a conjugate approach

In this article, a coupling method is presented in the case of high thermal treatment of a wood pole and a three-dimensional numerical simulation is proposed. The conservation equations for the wood sample are obtained using diffusion equation with variables diffusion coefficients and the incompressible Reynolds averaged Navier–Stokes equations have been solved for the flow field. The connection between the two problems is achieved by expressing the continuity of the state variables and their respective fluxes through the interface. Turbulence closure is obtained by the use of the standard k–ɛ model with the usual wall function treatment. The model equations are solved numerically by the commercial package ANSYS-CFX10. The wood pole was subjected to high temperature treatment under different operating conditions. The model validation is carried out via a comparison between the predicted values with those obtained experimentally. The comparison of the numerical and experimental results shows good agreement, implying that the proposed numerical algorithm can be used as a useful tool in designing high-temperature wood treatment processes. A parametric study was also carried out to determine the effects of several parameters such as initial moisture content, wood aspect ratio and final gas temperature on temperature and moisture content distributions within the samples during heat treatment.     

Natural convection due to heat and mass transfer in a composite system

A numerical study is performed to analyse heat and mass transfer phenomena due to natural convection in a composite cavity containing a fluid layer overlying a porous layer saturated with the same fluid. The flow in the porous region is modelled using Brinkman–Forchheimer-extended Darcy model that includes both the effect of macroscopic shear (Brinkman effect) and flow inertia (Forchheimer effect). The vertical walls of the two-dimensional enclosure are isothermal whilst the horizontal walls are adiabatic. The two regions are coupled by equating the velocity and stress components at the interface. The resulting coupled equations in non-dimensional form are solved by an alternating direction implicit method by transforming them into parabolic form by the addition of false transient terms. The numerical results show that the amount of fluid penetration into the porous layer depends strongly upon the Darcy, thermal and solutal Rayleigh numbers. Average Nusselt number decreases while average Sherwood number increases with an increase of the Lewis number. The transfer of heat and mass on the heated wall near the interface depends strongly on the Darcy number. Received on 11 May 1998