Numerical study of the wall effect on particle sedimentation

ABSTRACT

In this article, we investigate the abnormal settling of two-disk systems and elliptical shaped particles in infinite two-dimensional channels filled with an incompressible viscous fluid. We apply a distributed Lagrange multiplier/fictitious domain method (DLM/FDM) for the direct numerical simulation of these particulate flows. Due to the wall effect, the two-disk systems can form chains which settle stably instead of having the particles moving apart. Also, sedimentation with the long axis moving to vertical positions in the middle of the infinite channel has been observed for the elliptic shaped particles. The critical Reynolds number for having such an abnormal settling behaviour decreases as the width of the channel increases.     

基于CFD-DEM的高炉风口回旋区形状和传热特性数值模拟研究

采用计算流体力学-离散单元法(CFD-DEM)耦合方法,对高炉风口回旋区进行了数值模拟研究。首先通过与实验结果对比,验证了CFD-DEM模型的正确性;然后考察了不同气速对风口回旋区形状和传热特性及颗粒接触的影响。数值模拟结果表明:风口回旋区的大小和形状均受气速影响较大,在较大进气速度下,颗粒受到的曳力大于颗粒间的摩擦阻力并破坏颗粒间的桥力,形成较大尺寸的回旋区;且颗粒之间接触力较小,形成较大的空隙结构,更有利于热气体向周围扩散以强化传热。目前考察的三种气速结果表明:当气速为11m/s时,热量向下方传递速度最快;当气速为13m/s时,热量向上方传递速度最快;而当气速为15m/s时,热量向右方传递速度最快;此外,气速越大流态化越明显,颗粒间接触越少,接触力也越小。     

Heat and mass transfer study in fluidized bed granulation-Prediction of entry length

Fluidized bed granulation is a process by which granules or coated particles are produced in a single piece of equipment by spraying a binder as solution, suspension, or melt on the fluidized powder bed. Heat and mass transfer correlation useful for designing a granulator has been derived based on the equivalence of evaporation rate of the liquid to the heat transferred from hot gas to particles: (m/A)Dp2λ/(Lmf(1- εmf)(Tg-Tl)Kg)=hDp/Kg . This equation is applied to data on granulation experiments by different workers to calculate Reynolds number and Nusselt number to obtain a relation between heat and mass transfer from gas to particles during granulation on a logarithmic scale from which the following empirical relation is obtained: Nu = 0.0205Re1.3876 which is comparable to Kothari's correlation Nu = 0.03Re1.3. By using the heat and mass transfer correlation obtained, the entry length, that is the length of granulator up to which effective heat transfer from gas to bed particles takes place, is estimated, which is also validated with experimental study. The correct estimation of entry length is useful in optimal design of a granulator.     

Numerical study of heat and mass transfer of ammonia-water in falling film evaporator

To investigate the performance of the heat and mass transfer of ammonia water during the process of falling film evaporation in vertical tube evaporator, a mathematical model of evaporation process was developed and solved based on stream function. Then an experimental study of falling film evaporation was carried out in order to validate the mathematical model. A series of parameters, such as velocity, film thickness and concentration, etc., were obtained from the mathematical model. The calculated results show that the average velocity and the film thickness change sharp at the entrance region when x?x?>?100 mm. The film thickness depends largely on the flow rate of solution. It is observed that the heating power and mass flow of solution significantly affect the concentration difference between the inlet and outlet of evaporation tube. The calculated results reveal that the tube length has a significant impact on the amounts of ammonia vapor evaporated. It is suggested that the roll-worked enhanced tube should be used in order to decrease the concentration gradient in the film thickness direction and enhance the heat and mass transfer rate. Furthermore, the experimental and calculated results indicate that the inlet solution concentration has a great influence on the heat exchange capacity, the amounts of ammonia vapor evaporated and the evaporation pressure.     

Numerical simulation and experimental study of heat and mass transfer in fuel droplet evaporation

Heat and mass transfer in fuel droplet evaporation are investigated through numerical simulation and experimental study. The effect of liquid-phase heat transfer is studied using the temperature difference between the gas- and liquid-phase droplets, different turbulent intensity and oscillatory flow frequency. For the two-droplet array, some differences in heat and mass transfer mechanisms are found. For different spacing of the two-droplet array, the downstream droplet evaporation is affected by the lead droplet.     

Numerical study of unsteady evaporation and heat transfer from a spherical surface

An unsteady radial problem of evaporation and heat transfer from a spherical surface is considered for a model kinetic equation. The problem is solved numerically using a second-order implicit conservative method.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 181–192. Original Russian Text Copyright © 2005 by Titarev and Shakhov.     

Motion and heat and mass transfer in a disperse admixture in turbulent nonisothermal jets of a gas and a low-temperature plasma

The motion and heat and mass transfer of particles of a disperse admixture in nonisothermal jets of a gas and a low-temperature plasma are simulated with allowance for the migration mechanism of particle motion actuated by the turbophoresis force and the influence of turbulent fluctuations of the jet flow velocity on heat and mass transfer of the particle. The temperature distribution inside the particle at each time step is found by solving the equation of unsteady heat conduction. The laws of scattering of the admixture and the laws of melting and evaporation of an individual particle are studied, depending on the injection velocity and on the method of particle insertion into the jet flow. The calculated results are compared with data obtained with ignored influence of turbulent fluctuations on the motion and heat and mass transfer of the disperse phase. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 95–108, May–June, 2008.     

Mixed convection effects on heat and mass transfer in a non Newtonian fluid with chemical reaction over a vertical plate

This paper studies mixed convection, double dispersion and chemical reaction effects on heat and mass transfer in a non-Darcy non-Newtonian fluid over a vertical surface in a porous medium under the constant temperature and concentration. The governing boundary layer equations, namely, momentum, energy and concentration, are converted to ordinary differential equations by introducing similarity variables and then are solved numerically by means of fourth-order Runge-Kutta method coupled with double-shooting technique. The velocity, temperature concentration, heat and mass transfer profiles are presented graphically for various values of the parameters, and the influence of viscosity index n, thermal and solute dispersion, chemical reaction parameter χ are observed.     

Lie group analysis for the effect of temperature-dependent fluid viscosity and thermophoresis particle deposition on free convective heat and mass transfer under variable stream conditions

This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equa- tions. The system remains invariant due to some relations among the transformation parameters. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases but the temperature increases with the decreasing viscosity. The impact of the thermophoresis particle deposition plays an important role in the concentration boundary layer. The obtained results are presented graphically and discussed.     

Finite element solution of heat and mass transfer flow with Hall current, heat source, and viscous dissipation

The aim of the paper is to investigate the effect of heat and mass transfer on the unsteady magnetohydrodynamic free convective flow with Hall current, heat source, and viscous dissipation. The problem is governed by the system of coupled non-linear partial differential equations whose exact solution is difficult to obtain. Therefore, the problem is solved by using the Galerkin finite element method. The effects of the various parameters like Hall current, Eckert number, heat source parameter, Prandtl number, and Schmidt number on the velocity components, the temperature, and the concentration are also examined through graphs.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

Solvabilitity of a model problem of heat and mass transfer in thawing snow

A model problem of the motion of water and air in thawing snow is examined using the Masket-Leverett equations of two-phase filtration. The theorem of existence of a self-similar solution is proved. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 13–23, July–August, 2008.     

Thermo-mechanical modeling of turbulent heat transfer in gas–solid flows including particle collisions

A thermo-mechanical turbulence model is developed and used for predicting heat transfer in a gas–solid flow through a vertical pipe with constant wall heat flux. The new four-way interaction model makes use of the thermal k_θ–τ_θ equations, in addition to the hydrodynamic k–τ transport, and accounts for the particle–particle and particle–wall collisions through a Eulerian/Lagrangian formulation. The simulation results indicate that the level of thermal turbulence intensity and the heat transfer are strongly affected by the particle collisions. Inter-particle collisions attenuate the thermal turbulence intensity near the wall but somewhat amplify the temperature fluctuations in the pipe core region. The hydrodynamic-to-thermal times-scale ratio and the turbulent Prandtl number in the region near the wall increase due to the inter-particle collisions. The results also show that the use of a constant or the single-phase gas turbulent Prandtl number produces error in the thermal eddy diffusivity and thermal turbulent intensity fields. Simulation results also indicate that the inter-particle contact heat conduction during collision has no significant effect in the range of Reynolds number and particle diameter studied.     

Numerical solutions of pulsating flow and heat transfer characteristics in a pipe

Numerical studies are made of flow and heat transfer characteristics of a pulsating flow in a pipe. Complete time-dependent laminar boundary-layer equations are solved numerically over broad ranges of the parameter spaces, i.e., the frequency parameter β and the amplitude of oscillation A. Recently developed numerical solution procedures for unsteady boundary-layer equations are utilized. The capabilities of the present numerical model are satisfactorily tested by comparing the instantaenous axial velocities with the existing data in various parameters. The time-mean axial velocity profiles are substantially unaffected by the changes in β and A. For high frequencies, the prominent effect of pulsations is felt principally in a thin layer near the solid wall. Skin friction is generally greateer than that of a steady flow. The influence of oscillation on skin friction is appreciable both in terms of magnitude and phase relation. Numerical results for temperature are analyzed to reveal significant heat transfer characteristics. In the downstream fully established region, the Nusselt number either increases or decreases over the steady-flow value, depending on the frequency parameter, although the deviations from the steady values are rather small in magnitude for the parameter ranges computed. The Nusselt number trend is amplified as A increases and when the Prandtl number is low below unity. These heat transfer characteristics are qualitatively consistent with previous theoretical predictions.     

Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect

The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimen- sionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are preSented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ the order of.the chemical reaction parameter m, the Soret number St, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.     

Numerical study of heat and mass transfer in adsorption porous medium heated by solar energy: Boubnov-Galerkin method

This paper presents the modelization of heat and mass transfer in cubical reactor of solar adsorption cooling machine. The reactor is heated by solar energy and contains a porous medium constituted of activated carbon reacting by adsorption with ammonia. From real solar data, the model computes the performances of the machine and shows the existence of the optimal dimensioning of the reactor. For the resolution of the equations describing the coupling between heat and mass transfer, we have adapted a Boubnov-Galerkin method combined to an iterative process, this method provides a continuous distribution of the temperature and adsorbed mass. The convergence of the method is discussed and the numerical results are compared with the results provided by finite-difference method. Considering the rapidity of convergence and the order of Algebraic system (That is generally inferior to 10), the proposed method appeared to be very effective in solving such problem.     

Modeling of heat and mass transfer in a hydrocarbon fluid under inductive heating

Results of numerical simulations of the thermal action on a high-viscosity hydrocarbon fluid with temperature-dependent viscosity and thermal conductivity are presented. A system of equations of thermal convection in the Boussinesq approximation is used as the constitutive equations to describe the convection of the hydrocarbon fluid. The dynamics of the temperature field and convective structures in the fluid is studied. The spatial motion of the fluid is found to be locally nonuniform; the motion is accompanied by vortex flows; as a result, two regions with significantly different temperatures are formed in the medium. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 95–100, January–February, 2009.     

Numerical modelling of heat and mass transfer in adsorption solar reactor of ammonia on active carbon

 In this paper, we present a modelling of the performance of a reactor of a solar cooling machine based carbon–ammonia activated bed. Hence, for a solar radiation, measured in the Energetic Laboratory of the Faculty of Sciences in Tetouan (northern Morocco), the proposed model computes the temperature distribution, the pressure and the ammonia concentration within the activated carbon bed. The Dubinin–Radushkevich formula is used to compute the ammonia concentration distribution and the daily cycled mass necessary to produce a cooling effect for an ideal machine. The reactor is heated at a maximum temperature during the day and cool at the night. A numerical simulation is carried out employing the recorded solar radiation data measured locally and the daily ambient temperature for the typical clear days. Initially the reactor is at ambient temperature, evaporating pressure; P _ev =P _st (T _ev =0 ^∘C) and maintained at uniform concentration. It is heated successively until the threshold temperature corresponding to the condensing pressure; P _cond =P _st (T _am ) (saturation pressure at ambient temperature; in the condenser) and until a maximum temperature at a constant pressure; P _cond . The cooling of the reactor is characterised by a fall of temperature to the minimal values at night corresponding to the end of a daily cycle. We use the mass balance equations as well as energy equation to describe heat and mass transfer inside the medium of three phases. A numerical solution of the obtained non linear equations system based on the implicit finite difference method allows to know all parameters characteristic of the thermodynamic cycle and consider principally the daily evolution of temperature, ammonia concentration for divers positions inside the reactor. The tube diameter of the reactor shows the dependence of the optimum value on meteorological parameters for 1 m² of collector surface. Received on 10 January 2001