EFFECT OF FREE STREAM TURBULENCE ON HEAT AND MASS TRANSFER FROM A SPHERE

A model has been proposed for the momentum eddy diffusivity induced by free stream turbulence intensity. The eddy diffusivity model is applied to a sphere situated in a uniform crossflow in the presence of free stream turbulence. Numerical solution of the governing momentum and energy equations with the proposed eddy diffusivity model yielded results for the heat/mass transfer rates. The numerical predictions of the present work are compared with experimental data and the agreement between the two is seen to be very good.     

TWO DIMENSIONAL MODEL ANALYSIS OF TURBULENT FLOW IN AN AGITATED VESSEL WITH PADDLE IMPELLER*

A two-dimensional model for the turbulent flow in an agitated vessel is developed by modifying a two-dimensional laminar flow model. The proposed model is based on the assumption that the tangential velocity adjacent to the vessel wall satisfies the slip condition. Specifically, it is assumed that the tangential velocity is inversely proportional to the radius. The eddy diffusivity of momentum is assumed to be constant. The eddy diffusivity calculated from the model is in good agreement with the available experimental data, while the calculated tangential velocity depends on the Reynolds number in a manner similar to that observed experimentally.     

鼓泡塔中的有效涡扩散系数及湍流特性

依据湍流模式理论提出新的有效涡扩散系数关系式,讨论其与既有关系式的异同并与湍流实测数据比较,结果表明,本文关系式给出与实测值更为一致的结果,而既有的一些关系式的计算值偏高．由此讨论了涡扩散系数与鼓泡塔流动模型的关系,指出了数据偏差产生的原因．     

An engineering model of solids diffusivity in hydraulic conveying

An engineering model of solids diffusivity in a turbulent pipeline slurry flow is developed. While the model assumes that the liquid eddy diffusivity is uniform across a pipe the non-uniform distribution of solids diffusivity is obtained by analyzing the dependence of the turbulence kinetic energy transferred from liquid to particles on solids concentration. The turbulence kinetic energy transferred to particles is determined as the turbulence kinetic energy calculated for slurry minus the energy spent on the liquid-solids viscous friction due to turbulence induced liquid-solids velocity difference. The two empirical coefficients of the equation of the solids diffusivity have been identified from the measured solids concentration profiles. The numerical study has shown that the model accurately predicts the slurry concentration distribution in the wide range of flow parameters. The predictive capability of the developed model is much better that that of the conventional model of the solids diffusivity.     

Radial distribution of diffusivity in the core of turbulent pipe flow

Tests are described which yield the radial distribution of the turbulent diffusivity for enthalpy (eddy diffusivity) for fully-developed flow of water in a smooth straight pipe, with Reynolds number 10⁵. It is found that this closely resembles the distribution of the turbulent diffusivity for momentum (eddy viscosity), with an average value of turbulent Prandtl number of 0·977. This is somewhat greater than the value predicted by the Jenkins model.     

Measurement of eddy diffusivity in bubble column and validation based on the intermittency models

This paper discusses methods for the estimation of eddy diffusivity using the instantaneous velocity-time data measured in a bubble column reactor. In the first method, the analysis uses the eddy isolation methodology with a correction for the bubble-beam path interruption in the data. The correction is estimated from the observation of the time-varying data acquisition rate in the time series. The method is oblivious to the type of anemometer used for the data acquisition and is useful for all kinds of multiphase measurements. For validation of the results, we have proposed a strategy based on the synergistic combination of energy spectrum and the intermittency models for revealing different stages in the turbulent cascades. The method uses the actual scales in the cascade for the estimation of eddy diffusivity and hence such a combination has resulted in a robust validation tool. The comparison of the estimations based on the standard k-? model and integral length scales is also discussed.     

Settling velocity of droplets in turbulent flows

Two parameters of particle or droplet dynamics which are of importance in describing their behaviour in turbulent pipe flows are their settling velocity and eddy diffusivity. It is usually assumed that the settling velocity in turbulent flow is equal to that in still fluid and on the basis of this assumption the eddy diffusivity is usually determined experimentally from the distribution of droplets or particles in horizontal turbulent flow. Since the settling velocity has a strong influence on the resultant value of the eddy diffusivity, the influence of turbulence on settling velocity is investigated in this work. A simple stochastic model of settling in turbulent flow is developed and it is shown that a considerable retardation of still fluid settling velocity is possible for a wide range of conditions.     

TURBULENT VARIABLE PROPERTY GAS FLOWS

The surface renewal model of wall turbulence is coupled with the classical eddy diffusivity/mixing length approach for the turbulent core to analyze turbulent variable property gas flows with moderate heating and cooling. The analysis indicates that the mean frequency of wall turbulence is decreased by heating and increased by cooling, with the heating effect being significantly greater than the cooling effect. The analysis also gives rise to mean velocity and temperature distributions, friction factors and Stanton numbers that are consistent with most of the experimental data for both heating and cooling.     

MASS TRANSFER INTO A FREE LIQUID SURFACE EFFECTED BY SUBMERGED JETS

A theoretical and experimental analysis of mass transfer into a turbulent free liquid surface effected by submerged jets has been presented. Theoretical considerations concentrated on hydrodynamic characteristics of the system which enabled us to derive the radial velocity distribution in the surface jet flow. Some conclusions have been drawn from the two-parameter models of turbulence. The results of experimental measurements of the average mass transfer coefficients have been interpreted in terms of our own model of mass transfer accounting for eddy diffusivity. The model parameters were correlated with the basic hydrodynamic parameters of the system. Radial distributions of the local values of the mass transfer coefficients were estimated. The applicability of other models of mass transfer has also been verified. It has been shown that the model presented here is the most general and applicable for interpretation of the experimental data obtained when studying the system under consideration     

CFD SIMULATION ON INFLUENCE OF SUPERFICIAL GAS VELOCITY,COLUMN SIZE,SPARGER ARRANGEMENT,AND TAPER ANGLE ON HYDRODYNAMICS OF THE COLUMN FLOTATION CELL

The use of flotation columns in the mineral processing industry has experienced a remarkable growth over the years. The detailed hydrodynamics study of a column flotation cell demands the solution of mass, momentum, phase-transfer, and turbulence quantities. Simulations have been carried out to examine the influence of superficial air velocity, column size, column taper angle, and sparger arrangement on hydrodynamics of the column flotation cell. A commercial CFD software package (ANSYS CFX 10.0) has been used to predict the complex unsteady air-water flow. The k-ε turbulence model for shear-induced turbulence, Sato's eddy viscosity model for bubble-induced turbulence, and the effect of interfacial momentum transfer terms (lift force, wall force) were considered. Present findings suggest use of low height-to-diameter ratio, low airflow rate, small column taper angle, and uniformly distributed sparger to achieve good separation in a column flotation cell.     

Validation of an anisotropic model of turbulent flows containing dispersed solid particles applied to gas–solid jets

A mathematical model of turbulent flows containing dispersed solid particles is described together with its application to gas–solid jets. Flow fields are predicted by solution of the density-weighted transport equations expressing conservation of mass and momentum, with closure achieved through the k–? turbulence model and a second-moment closure. The particle phase is calculated using a Lagrangian particle tracking technique which involves solving the particle momentum equation in a form that accounts for the spatial, temporal and directional correlations of the Reynolds stresses experienced by a particle. The two phases are coupled via modification of the fluid-phase momentum equations. Predictions of the complete model are validated against available experimental data on a number of single-phase and two-phase, gas–solid jet flows with various particle loadings, and both mono- and poly-dispersed particle size distributions. Overall, predictions of the models compare favourably with the data examined, with results obtained from the anisotropic second-moment turbulence closure being superior to eddy viscosity-based predictions.     

Numerical Simulation of a Two-Phase Gas-Particle Jet in a Crossflow

A computational model using Lagrangian approach has been proposed to analyze momentum and heat transfers of a gas-particle jet in a crossflow. The effect of the free stream velocity gradient on the two-phase crossjet trajectories and the heat transfer mechanism was investigated in this study. Estimate of average temperature of a particle-laden gas jet was obtained by accounting for thermal energy losses of the gas jet flow due to forced convection and to entrainment of free stream fluid into the jet and for thermal energy transferred from the particles to the gas jet. According to the computational results of the heated two-phase temperature of a gas-particle jet in a crossflow. crossjet, the mean temperature of the carrier gas phase near the jet exit is dependent upon the forced convection and entrainment of the free stream, while far downstream, it is mainly affected by the quantity of thermal energy transferred from the solid particles to the carrier gas phase. When the ratio of the gas jet momentum flux to the momentum flux of the cross free-stream at the jet exit and the free stream conditions are constant, the trajectories of the particle-laden gas and particle phases and the normalized mean temperature difference between both phases are not significantly affected by the change of injection gas     

鼓泡塔中Reynolds剪切力及涡扩散系数的局部分布

根据鼓泡塔内的两相湍流特性,提出估算塔内局部Ｒｅｙｎｏｌｄｓ剪切力的方法,由尼导出新的局部涡扩散系数关系式,讨论其与关系式的异同并与湍流实测数据比较。结果表明,新关系式给出与实测值更为一致的结果,而既有的一些关系式的计算值偏高,较之单相管流关系式,新关系式具有物理意义。     

加齿被动控制自由湍射流多尺度涡结构的实验研究

1 INTRODUCTION Noncircular jets were identified as an efficient tech- nique of passive control that allows significant im- provements of performance on various practical sys- tems at a relatively low cost because noncircular jets rely solely on the change in the geometry of the noz- zle. In both aerospace industry and chemical industry noncircular jets are widely applied to promote frag- mentation of the large eddy structures in the flow, enhance mixing of various fluid components, speed u…     

Experimental studies of interphase mass transfer with chemical reaction — Saponification of esters

This study concerns the transfer of ethyl acetate from a supernatant still liquid into a lower layer of caustic solution in which a saponification reaction occurs. Apparatus and techniques for measuring the concentration profiles which develop in the turbulent reaction layer in the aqueous phase at the liquid-liquid interface are described. In particular, the effects of turbulence on the reaction layer propagation, the reaction zone in the turbulent layer, and the concentration distribution of various components of the system were observed and measured. From these data, mass transfer rates and enhancement factors were deduced. The effects of turbulence in the aqueous phase were presented in terms of an eddy diffusivity model.     

The important role of local dispersed phase hold-ups for the calculation of three-phase bubble columns

A computational fluid dynamics model is used to calculate a three-phase (air-water-solid particles) flow in a bubble column. The calculation of multi-phase flows is significantly influenced by the formulation of the inter-phase drag and the modelling of the turbulence. Both are influenced by the dispersed phases. The k-ε turbulence model extended with terms accounting for the bubble-induced turbulence is used to calculate the eddy viscosity of the liquid phase. Bubble-bubble and particle-particle interactions are considered as well as a direct momentum transfer between the two dispersed phases bubbles and solid particles. The local volume fractions of the dispersed phases are considered for the calculation of the drag coefficients between the dispersed phases and the continuous phase. Measured local gas and solid hold-ups as well as measured liquid velocities are compared with the corresponding calculated results. The measured and the calculated results show good agreement.     

A multi‐scale theoretical model for gas–Liquid interface mass transfer based on the wide spectrum eddy contact concept

On the basis of the wide spectrum eddy contact concept and the isotropic turbulence theory, a multi‐scale theoretical model for the prediction of liquid‐side mass transfer coefficient in gas–liquid system was developed. The model was derived from an unsteady‐state convection and diffusion equation and considered the contributions of eddies with different sizes to the overall mass transfer coefficient. The proper contact time distribution at the surface is need to be determined to obtain satisfactory results with this model. Moreover, a simplified model was also proposed based on the assumption of steady‐state mass transfer mechanism for single eddy. The results predicted by this model showed a very good agreement with the available experimental data in a comparatively wide range of turbulence intensities. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

大涡模拟搅拌槽中的液相流动

采采用大涡模拟湍流模型对有档板的Rushton 桨搅拌槽进行了数值模拟研究。控制方程采用控制容积法进行离散,对流项用三阶QUICK格式,扩散项是二阶中心差分。压力 速度耦合方程在交错网格上采用SIMPLE算法进行求解。小尺度流动的模化采用动力学（dynamic）亚格子模型。搅拌桨与档板之间的相互作用采用改进的内外迭代法进行处理。计算结果和文献值吻合得很好。     

颗粒尾涡增强湍流的大涡模拟以及气固两相流中湍流变动的数值模拟

The turbulence enhancement by particle wake effect is studied by large eddy simulation （LES） of turbulent gas flows passing a single particle. The predicted time-averaged and root-mean-square fluctuation velocities behind the particle are in agreement with the Reynolds-averaged Navier-Stokes modeling results and experimental results. A semi-empirical turbulence enhancement model is proposed by the present-authors based on the LES resuits. This model is incorporated into the second-order moment two-phase turbulence model for simulating vertical gas-particle pipe flows and horizontal gas-particle channel flows. The simulation results show that compared with the model not accounting for the particle wake effect, the present model gives simulation results for the gas turbulence modulation in much better agreement with the experimental results.     

Two-way coupled bubble laden mixing layer

A discrete vortex model is used to approximate adequately large eddy features in turbulent free shear flows and the effects of two-way mass and momentum coupling on Lagrangian bubble trajectories and dispersion in such eddy structures are investigated. The number of bubbles introduced into the flow is sufficiently large enough for cumulative effects of bubbles to influence the flow but is still small enough so that bubble-bubble interactions can be neglected. It is demonstrated that for two-way coupling case, a reduction in the magnitude of the vorticity and pressure gradients around the large-scale vortex centre is observed. In addition to modification of the vortex structures, it is found that the tendency of the accumulation of bubbles becomes weaker in comparison to the one-way coupling case. In seeking quantification of the bubble dispersion, the Eulerian approach based on the bubble number fluxes at different downstream cross-sections of the mixing layer in terms of ensemble trajectory statistics and Lagrangian approach based on the bubble mean square displacement are adopted. It is observed that the ensemble average flux profiles of bubbles for two-way coupling case are farther skewed towards the high-speed stream of the shear layer in contrast to its one-way coupling case.