Modeling of ascending polydisperse flow with allowance for heterogeneous combustion,particle rotation,and turbulent and pseudoturbulent effects

A closed system of equations that describes motion and physicochemical processes in ascending polydisperse flow with allowance for the rotation of the dispersed phase, the aerodynamic-drag, gravity, and Magnus forces, and the interaction of particles with each other and with the reactor wall is constructed. The equations of motion and heat transfer of the solid phase are closed at the level of equations for the second moments of pulsations of the linear and angular velocities of particles and their temperature. The pulsation characteristics of the carrying medium are computed using the equation for the turbulent gas energy.     

Calculation of a turbulent monodisperse flow in an axisymmetric channel

A stationary isothermal model of the aerodynamics of a two-phase flow in an axisymmetric channel has been constructed with allowance for the turbulent and pseudoturbulent mechanisms underlying the transfer of the solid phase momentum. The equations of dispersed phase motion are closed at the level of the equations for the second moments of the pulsation velocities of particles, whereas the equation of momentum transfer of the carrier is closed on the basis of a one-parameter model of turbulence extended to the case of two-phase turbulent flows. The results of calculations are compared with experimental data. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 5, pp. 844–855, September–October, 2008.     

Use of equations for transfer of particle pulsation characteristics for calculating two-phase flows in the stabilized section of a tube

A stationary isothermal system of equations defining the behavior of a two-phase rising flow in the region of steady motion of a gas suspension in an axially symmetric channel has been developed. The equation of motion of the carrying medium is closed using a one-parameter model of turbulence, and the equation of momentum transfer in the dispersed phase is closed with the use of the equations for the second, third, and fourth moments of the pulsation velocities of the particles. The main mechanisms of two-phase turbulent flows were numerically investigated. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 4, pp. 99–109, July–August, 2007.     

Hydrodynamics and Heat Transfer in Pulsating Turbulent Pipe Flow of a Liquid of Variable Properties

The effect of the variability of properties on the characteristic features of heat transfer and of pulsating turbulent pipe flow of incompressible liquid is investigated. The results are obtained by using the method of finite differences to solve numerically a set of equations of motion, continuity, and energy written in a narrow channel approximation. The set is closed by relaxation equations for turbulent stress and turbulent heat flux. A stable difference scheme is used, which is valid for high relative amplitudes of oscillation. The calculations are performed for a dropping liquid in view of the temperature dependence of viscosity. The results of calculation of heat transfer and friction resistance for two limiting cases of steady-state flow of a liquid of variable properties and of pulsating weakly nonisothermal flow fit well the available experimental data.     

Modeling nonlocal mass transfer of a dispersed impurity in turbulent flows of a gas suspension

The effect of nonlocal phenomena occurring with the motion of inertial particles on the rate of mass transfer of the dispersed phase is studied on the basis of a closed expression constructed for the probability density function determining the transport of these particles in a turbulent nonuniform flow.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 59, No. 3, pp. 454–466, September, 1990.     

Heat Transfer in a Turbulent Flow of Gas in a Tube under Conditions of Resonance Oscillation of the Flow Rate

A prediction study is made into the heat transfer in a turbulent flow of gas (air) in a narrow tube with superimposed resonance oscillation. The model of turbulent transfer includes the effect of nonstationarity on the turbulent stress and heat flux. The finite difference method is used to solve the equations of motion and energy. The distribution of the flow rate and pressure along the tube is found by way of numerical solution of a set of cross section-averaged nonstationary equations of motion, continuity, and energy. The effect of the process parameters (Reynolds number, dimensionless oscillation frequency, thermal boundary conditions on the wall) on the period-average heat transfer and heat flux to the wall is analyzed.     

Influence of particle density and size on turbulence, friction, and heat exchange characteristics

Numerical simulation of turbulent flows of a gas suspension in the vicinity of the critical point and in a channel with permeable walls has been carried out. The influence of the concentration of the dispersed phase and the size of its particles on the distribution of mean and pulsation characteristics of the flow, as well as on the friction and heat transfer coefficients, is discussed.     

Effect of the phase transformations on acoustics of a mixture of gas with vapor,droplets, and solid particles

The propagation of acoustic waves in the two-fraction mixtures of gas with vapor, droplets, and solid particles of different materials and sizes with phase transformations has been studied. Nonstationary and nonequilibrium effects of the interphase exchange of the impulse, mass, and heat have been taken into account. A system of the differential equations of the motion of the mixture has been presented, and the dispersion relation has been deduced. The high- and low-frequency asymptotics of the attenuation coefficient have been obtained and analyzed. The effect of the heat and mass exchange on dispersion and dissipation of acoustic waves in the two-fraction mixtures of gas with vapor, droplet, and solid particles has been studied.     

Approximate method for calculating turbulent two-phase flow in a channel with permeable walls

Based on a model of a double-velocity and two-temperature medium the authors constructed a system of equations that describes plane or axisymmetric turbulent flow of a gas suspension in a channel with permeable walls. The system of equations of motion and heat transfer reduces to a system of ordinary differential equations, whose integration is much less difficult than solution of the initial system. The authors obtained the distribution of the velocity and local characteristics of turbulence in the channel with injection with allowance for the inverse effect of a condensed phase.     

Calculation of a Three-Dimensional Temperature Field with Allowance for the Radiation Heat Exchange in Chambers of Tubular Ovens with Acoustic Burners

A three-dimensional calculation of the heat transfer in the chamber of a technological tubular oven with the combustion of methane in air with acoustical burners of a floor flame has been carried out. The calculation method is based on the joint numerical solution of the difference analogs of the three-dimensional equations of radiation, energy transfer, and turbulent motion of flue gases and the model of methane combustion in air. The entire spectral region is divided into six bands to account for radiation selectivity. The organization scheme of three-dimensional modeling of the burner operation is shown. Some results of numerical studies of heat and mass transfer in a combustion chamber are given.     

Influence of particles on the turbulent heat-transfer intensity

The influence of particles on the intensity of turbulent heat transfer by a gas-suspension is investigated on the basis of a system of equations of the second single-point moments of the carrier phase velocity and temperature fluctuations.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 4, pp. 554–560, April, 1985.     

Wave motion of porous particles in a pulsating gas flow in the presence of heat and mass transfer with deepening of the evaporation zone

Based on numerical solution of the dynamics equations of a monodisperse gas suspension with allowance for the interphase forces of aerodynamic drag, virtual masses, and the forces caused by nonstationary effects around particles, the influence of different forms of low-frequency harmonic and anharmonic oscillations of the gas on the motion of porous particles in the presence of heat and mass transfer accompanied by deepening of the evaporation zone has been investigated. The dependences of the solid-phase motion, kinetics of evaporation-zone deepening, and heat and mass transfer on the parameters of gas oscillations have been established. It is shown that on removal of free moisture, oscillations at certain parameters lead to enhancement of interphase heat and mass transfer. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 5, pp. 11–19, September–October 2006.     

The Hydrodynamics and Heat and Mass Transfer of Particles under Conditions of Turbulent Flow of Gas Suspension in a Pipe and in an Axisymmetric Jet

A mathematical model for the calculation of the hydrodynamic and thermal parameters of dispersed impurity in a round pipe and in a jet is given in Eulerian variables. The model is based on a unified set of equations describing the turbulent characteristics of particles in nonisothermal flow and of boundary conditions representing the interaction of the particles with the rough channel surface and the boundary of submerged jet. The effect of the anisotropy of turbulent fluctuations of the particle velocity and of the correlation between the thermal properties of the particle material and carrier gas on the intensity of momentum, heat, and mass transfer in the dispersed phase is investigated. The calculation results are compared with the experimental data.     

Temperature distribution in cylindrical packed beds

The heat transfer problem in a cylindrical packed bed with continuous flow of gases has been studied by treating the solid phase as a pseudo-homogeneous substance. A set of finite difference equations governing the temperature distributions in the solid and gaseous phases have been obtained using a mixing-cells model, to account for the turbulent mixing phenomenon. Numerical solutions are obtained by solving this set of equations of temperature distributions using relaxation method.     

Effect of Flow Swirling on Heat Transfer in Gas-Droplet Flow Downstream of Abrupt Pipe Expansion

The effect the flow swirl parameter on heat transfer in a gas-droplet flow is numerically modeled by the Euler approach. The gaseous phase is described by a system of 3D RANS equations with consideration of the back effect of particles on transfer processes in the carrier phase. The gaseous phase turbulence is calculated according to the Reynolds stress transport model with consideration of the dispersed phase effect on the turbulent characteristics. A rapid dispersion of droplets over the pipe cross section is observed in a nonswirling gas-droplet flow downstream of an abrupt pipe expansion. A swirling flow is characterized by a growing concentration of fine particles at the pipe axis due to the accumulation of particles in the zone of flow recirculation and to the turbophoresis force. In a swirling flow, the separated-flow region becomes significantly shorter (by almost a factor of two as compared to that in a nonswirling flow). It is shown that addition of droplets results in a significant growth of heat transfer intensity (by more than a factor of 2.5) in comparison with single-phase swirling flow.     

Unsteady-state heat transfer in the region of interaction between a turbulent jet and an obstacle

Unsteady-state heat transfer is considered in the region of interaction between a round turbulent jet and a normally positioned flat obstacle. The Navier-Stokes equations filtered over space are closed by the RNG-model of eddy viscosity which takes into account the curvature of the lines of flow in the region of turning of flow. The calculations are performed for different relative distances from the nozzle exit section to the obstacle and for different values of Reynolds number. The correlation between the distribution of characteristics of heat transfer over the obstacle surface and the eddy structure of the jet is discussed.     

A thermodynamical formulation for chemically active multiphase turbulent flows

A general thermodynamic theory for chemically active multiphase solid–fluid mixtures in turbulent state of motion is formulated. The global equations of balance for each phase are ensemble averaged and the local conservation laws for the mean motions are derived. As a classical treatment, the averaged form of the Clausius–Duhem inequality is used and the thermodynamics of the chemically active mixtures in turbulent state of motion is studied. Particular attention is given to the species concentration of the miscible fluid constituents and chemical reaction effects, in addition to the transport of the phasic fluctuation energies between phases. Based on the averaged entropy inequality, constitutive equations for the stresses, energy, heat and mass fluxes of various species are developed. Explicit governing equations of motion, along with the equation of the dissipation rate of the turbulent kinetic energy are also derived and discussed. A particular emphasis is on the thermodynamically consistent formulation of different solid–fluid interaction terms in these equations.     

Effect of the size of air bubbles on enhancement of heat transfer in an impinging liquid jet

The numerical modeling of heat transfer in a bubbly impinging jet is carried out. The axisymmetric system of RANS equations that take into account the two-phase nature of the flow is resolved based on the Euler approach. The turbulence of the liquid phase is described by the Reynolds stress transport model with taking into account the effect of bubbles on modification of the turbulence. The effect of the gas volumetric flow rate ratio and the bubble size on the flow structure and the heat transfer in a gas–liquid impact stream is studied. It is shown that the addition of the gas phase in a turbulent fluid causes an increase up to 1.5-fold in heat transfer. The comparison of the simulation results with experimental data showed that the developed model enables the simulation of turbulent bubbly impinging jet with heat transfer with the pipe wall in a wide range of gas fraction.     

Large eddy simulation of turbulent open channel flow with heat transfer at high Prandtl numbers

Summary. Large eddy simulation of a fully developed turbulent open channel flow with heat transfer is performed. The three-dimensional filtered Navier-Stokes and energy equations are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. The objective of this study is to analyze the behavior of turbulent flow and heat transfer in turbulent open channel flow, in particular for high Prandtl number, and to examine the reliability of the LES technique for predicting turbulent heat transfer near the free surface. The turbulent open channel flow with constant difference of temperature imposed on the free surface and bottom wall is calculated for the Prandtl number (Pr) from 1 up to 100, the Reynolds number (Re) 180 based on the wall friction velocity and the channel depth. To illustrate the turbulent flow and heat transfer behaviors, some typical quantities, including the mean velocity, temperature and their fluctuations, heat transfer coefficients, turbulent heat fluxes, and flow structures of velocity and temperature fluctuations, are exhibited and analyzed.     

A critical review of models of coupled heat and mass transfer in falling-film absorption

In absorption space-conditioning systems, the performance of the absorber is critical to the overall system performance, size, and first-cost. The objective of this paper is to provide a comprehensive review of the significant efforts that researchers have made to mathematically model the coupled heat and mass transfer phenomena that occur during falling-film absorption. A detailed review of the governing equations, boundary conditions, assumptions, solution methods, results, and validation of these investigations is presented. This review excludes experimental work in this area, the effect of additives, and the effect of non-absorbable gases. It is shown that most work found in the literature has focused on the particularly simplified case of absorption in laminar vertical films of water-lithium bromide. Fewer researchers have considered the important situations of wavy films, turbulent films, and films on horizontal tubes. Investigations of the ammonia-water fluid pair have been generally more empirical in nature and/or restricted to vertical laminar films. This review is used to highlight key areas which need attention such as film and vapor hydrodynamics, especially the non-periodicity, instability, and recirculatory motion of waves in the vertical wall case and droplets and waves in the horizontal tube case. Also the potential interaction of the heat and mass transfer process on the film hydrodynamics, surface wetting, heat transfer in the vapor phase, and common simplifications to the governing equations should all be considered carefully. Finally, emphasis must be placed on experimental validation of the local conditions and transfer processes within the absorber, not just overall transport values.