Investigation of the characteristics of particulate flows through fibrous filters using the lattice Boltzmann method

A fibrous filter is one of the most common systems used to separate suspended particles from air.Two important factors(i.e.,the pressure drop and capture efficiency) are usually used to evaluate the performance of this type of filter.This study considers three two-dimensional arrangements of fibers(parallel,staggered,and random) to geometrically model fibrous media.The lattice Boltzmann method is employed to numerically simulate fluid flow through the filter.The Lagrangian form of the equation of motion of a particle is numerically solved to track the path of each particle in the flow field,where a one-way interaction between the fluid and particles is considered.The effects of pertinent parameters such as the fiber arrangement,solid volume fraction,particle-to-fiber diameter ratio,particle-to-fluid density ratio,Reynolds number,Stokes number,and size of the fibrous medium on the pressure drop and capture efficiency are studied.The obtained results are compared with existing empirical and theoretical findings and discussed.     

Fluid flow simulation in a random elliptical porous medium by using the lattice Boltzmann method

A fluid flow through an isotropic porous medium with randomly arranged elliptical particles is simulated by the lattice Boltzmann method. The dimensionless pressure drop and the dimensionless permeability are evaluated as functions of the Reynolds number. The effect of the aspect ratio of the major to minor semi-axis of the ellipse on the dimensionless permeability is considered for different values of porosity. The pressure drop is thoroughly investigated as a function of fluid viscosity for different values of the aspect ratio and porosity. The influence of various parameters of the problem on the mean tortuosity of the medium is considered.     

Hydrodynamic and thermal fields analysis in gas-solid two-phase flow

The present work aims to investigate numerically the flowfield and heat transfer process in gas-solid suspension in a vertical pneumatic conveying pipe. The Eulerian-Lagrangian model is used to simulate the flow of the two-phases. The gas phase is simulated based on Reynolds Average Navier-Stokes equations (RANS) with low Reynolds number k-ε model, while particle tracking procedure is used for the solid phase. An anisotropic model is used to calculate the Reynolds stresses and the turbulent Prandtl number is calculated as a function of the turbulent viscosity. The model takes into account the lift and drag forces and the effect of particle rotation as well as the particles dispersion by turbulence effect. The effects of inter-particles collisions and turbulence modulation by the solid particles, i.e. four-way coupling, are also included in the model. Comparisons between different models for turbulence modulation with experimental data are carried out to select the best model. The model is validated against published experimental data for velocities of the two phases, turbulence intensity, solids concentration, pressure drop, heat transfer rates and Nusselt number distribution. The comparisons indicate that the present model is able to predict the complex interaction between the two phases in non-isothermal gas-solid flow in the tested range. The results indicate that the particle-particle collision, turbulence dispersion and lift force play a key role in the concentration distribution. In addition, the heat transfer rate increases as the mass loading ratio increases and Nusselt number increases as the pipe diameter increases.     

Experimental study on forced convective heat transfer of flowing gaseous solid suspension at high temperature

The results of an experimental study of the forced convective heat transfer to helium-graphite suspension at high temperatures up to 1173K are presented. Entering gas Reynolds number ranges from 1.0 x 10⁴ to 2.0 x 10⁴ and the particle loading ratio reaches about 4. The ratio of the Nusselt number of the suspension to that of gas alone increases considerably in a range of high loading ratios as the wall temperature increases. Subsequently, two kinds of turbulence promoters (200 and 400 mm pitch twisted tapes) are inserted in the flowing gaseous solid suspensions to make use of the large inertia forces of particles. The current results show that the local heat fluxes with use of the tapes increase significantly with the rise in the wall temperature owing to the radiative effect of the particulate phase.     

Effect of void fraction and friction factor models on the prediction of pressure drop of R134a during downward condensation in a vertical tube

The theoretical flow models of homogeneous and separated flow are applied to in-tube condensation to predict the pressure drop characteristics of R134a. The homogeneous flow model is modified by ten different dynamic viscosity correlations and various alternative correlations of total, frictional and momentum pressure drops to take account of the partial condensation inside the tube. Numerical analyses were performed to determine the average and local homogeneous wall shear stresses and friction factors by means of a CFD program. The equivalent Reynolds number model is modified by six different two-phase friction factors to determine the total condensation pressure drop in the separated flow model. The refrigerant side total pressure drops, frictional pressure drops, friction factors and wall shear stresses are determined within a ±30% error band. The importance of using the alternative total, momentum and frictional pressure drop correlations for the homogeneous flow model is also shown.     

Peristaltic Hemodynamic Flow of Couple-Stress Fluids Through a Porous Medium with Slip Effect

The present investigation deals with a theoretical study of the peristaltic hemodynamic flow of couple-stress fluids through a porous medium under the influence of wall slip condition. This study is motivated towards the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. Reynolds number is small enough and the wavelength to diameter ratio is large enough to negate inertial effects. Analytical solutions for axial velocity, pressure gradient, frictional force, stream function and mechanical efficiency are obtained. Effects of different physical parameters reflecting couple-stress parameter, permeability parameter, slip parameter, as well as amplitude ratio on pumping characteristics and frictional force, streamlines pattern and trapping of peristaltic flow pattern are studied with particular emphasis. The computational results are presented in graphical form. This study puts forward an important observation that pressure reduces by increasing the magnitude of couple-stress parameter, permeability parameter, slip parameter, whereas it enhances by increasing the amplitude ratio.     

Interfacial instabilities in a stratified flow of two superposed fluids

Here we shall present a linear stability analysis of a laminar, stratified flow of two superposed fluids which are a clear liquid and a suspension of solid particles. The investigation is based upon the assumption that the concentration remains constant within the suspension layer. Even for moderate flow-rates the base-state results for a shear induced resuspension flow justify the latter assumption. The numerical solutions display the existence of two different branches that contribute to convective instability: long and short waves which coexist in a certain range of parameters. Also, a range exists where the flow is absolutely unstable. That means a convectively unstable resuspension flow can be only observed for Reynolds numbers larger than a lower, critical Reynolds number but still smaller than a second critical Reynolds number. For flow rates which give rise to a Reynolds number larger than the second critical Reynolds number, the flow is absolutely unstable. In some cases, however, there exists a third bound beyond that the flow is convectively unstable again. Experiments show the same phenomena: for small flow-rates short waves were usually observed but occasionally also the coexistence of short and long waves. These findings are qualitatively in good agreement with the linear stability analysis. Larger flow-rates in the range of the second critical Reynolds number yield strong interfacial waves with wave breaking and detached particles. In this range, the measured flow-parameters, like the resuspension height and the pressure drop are far beyond the theoretical results. Evidently, a further increase of the Reynolds number indicates the transition to a less wavy interface. Finally, the linear stability analysis also predicts interfacial waves in the case of relatively small suspension heights. These results are in accordance with measurements for ripple-type instabilities as they occur under laminar and viscous conditions for a mono-layer of particles.     

A Semi-empirical Correlation for Pressure Drop in Packed Beds of Spherical Particles

The effect of a confining wall on the pressure drop of fluid flow through packed beds of spherical particles with small bed-to-particle diameter ratios was investigated to develop an improved pressure drop correlation. The dependency of pressure loss on both wall friction and increased porosity near the wall was accounted for by using a theoretical approach. A semi-empirical model was created based upon the capillary-orifice model, which included a wall correction factor for the inertial pressure loss. In this model, packed beds were treated as a bundle of capillary tubes whose orifice diameter in the core region was different from that of the wall region. Using this model, a new pressure drop correlation was obtained, based on the Ergun equation and applicable for a wide range of Reynolds numbers (10⁻²–10³). The proposed correlation was compared with previous correlations, as well as with experimental data. This correlation showed close agreement with the experimental data for both low- and high-Reynolds number regimes and for a wide range of bed-to-particle diameter ratios. The ratio of the pressure drop in finite packing to that in homogeneous packing was then calculated. This ratio clearly shows how the wall effect depends on the Reynolds number and the bed-to-particle diameter ratio.     

Modelling the flow of power law fluids in a packed bed using a volume-averaged equation of motion

The development of a theoretical model for the prediction of velocity and pressure drop for the flow of a viscous power law fluid through a bed packed with uniform spherical particles is presented. The model is developed by volume averaging the equation of motion. A porous microstructure model based on a cell model is used. Numerical solution of the resulting equation is effected using a penalty Galerkin finite element method. Experimental pressure drop values for dilute solutions of carboxymethylcellulose flowing in narrow tubes packed with uniformly sized spherical particles are compared to theoretical predictions over a range of operating conditions. Overall agreement between experimental and theoretical values is within 15%. The extra pressure drop due to the presence of the wall is incorporated directly into the model through the application of the no-slip boundary condition at the container wall. The extra pressure drop reaches a maximum of about 10% of the bed pressure drop without wall effect. The wall effect increases as the ratio of tube diameter to particle diameter decreases, as the Reynolds number decreases and as the power law index increases.     

带扰流小槽道内单相流动阻力特性实验

采用水作为工质, 实验研究入口或出口端加入圆柱扰流的不同高宽比多槽道散热器的压降特性; 结果表明: 单位长度压降随雷诺数成线性关系. 提出了雷诺数、水力学直径和槽道高宽比的拟合准则; 拟合公式在实验数据误差范围内很好反应类似系统的流阻特性. 对于线切割小槽道, 其摩阻系数和雷诺数成反比, 且较圆管理论值偏大; 对线切割槽道阻力特性分析发现, 表面粗糙度是其最主要的影响因素, 而扰流对其影响较小; 在槽道前部设置扰流柱可以增强换热.      

Rheology of a suspension of particles in viscoelastic fluids

In this paper we study the bulk stress of a suspension of rigid particles in viscoelastic fluids. We first apply the theoretical framework provided by Batchelor [J. Fluid Mech. 41 (1970) 545] to derive an analytical expression for the bulk stress of a suspension of rigid particles in a second-order fluid under the limit of dilute and creeping flow conditions. The application of the suspension balance model using this analytical expression leads to the prediction of the migration of particles towards the centerline of the channel in pressure-driven flows. This is in agreement with experimental observations. We next examine the effects of inertia (or flow Reynolds number) on the rheology of dilute suspensions in Oldroyd-B fluids by two-dimensional direct numerical simulations. Simulation results are verified by comparing them with the analytical expression in the creeping flow limit. It is seen that the particle contribution to the first normal stress difference is positive and increases with the elasticity of the fluid and the Reynolds number. The ratio of the first normal stress coefficient of the suspension and the suspending fluid decreases as the Reynolds number is increased. The effective viscosity of the suspension shows a shear-thinning behavior (in spite of a non-shear-thinning suspending fluid) which becomes more pronounced as the fluid elasticity increases.     

Pressure drop in two phase slug/bubble flows in mini scale capillaries

A segmented two phase slug/bubble flow occurs where a liquid and a gas are pumped into the same tube over a range of Reynolds numbers. This segmented two phase flow regime is accompanied by an increase in pressure drop relative to the single phase flow where only one fluid is flowing in a capillary. This work experimentally and theoretically examines the pressure drop encountered by the slug/bubble flow with varying slug lengths in mini channels. In the experimental work the dimensionless parameters of Reynolds number and Capillary number span over three orders of magnitude, and dimensionless slug length ranges over two orders of magnitude to represent flows typical of mini- and micro-scale systems. It is found, in agreement with previous work, that these dimensionless groups provide the correct scaling to represent the pressure drop in two phase slug/bubble flow, although the additional pressure drop caused by the interface regions was found to be ∼40% less than previously reported.     

Three-dimensional numerical simulation of drops suspended in simple shear flow at finite Reynolds numbers

A three-dimensional study of suspension of drops in simple shear flow has been performed at finite Reynolds numbers. Results are obtained using a finite difference/front tracking method in a periodic domain. The effects of the Reynolds number and the Capillary number are addressed at two volume fractions: 0.195 and 0.34. It is observed that suspensions of deformable drops exhibit a shear-thinning behavior. Similar to the motion of a single drop, drops migrate away from the walls. The effective viscosity, the first and the second normal stress differences oscillate around a mean value in all cases. The first normal stress difference increases with the Capillary number, the Reynolds number and the volume fraction. Results show that drops deform more and orient more in the flow direction as the Capillary number or the volume fraction is increased. Also, the average size of clusters is smaller than for suspension of rigid particles. The radial dependence of the pair distribution function across the channel has been studied. This dependency shows that the tendency to form clusters is reduced as the Capillary number increases or the volume fraction decreases.     

Numerical simulation of drop migration in channell flow under zero-gravity

The migration of deformable drops in the channel flow neglecting the gravity influence is investigated numerically by solving the incompressible Navier-Stokes equations using the finitedifference method coupled with the front-tracking technique. The objectives of this study are to examine the effectiveness of the present approach for predicting the migration of drops in a shear flow and to investigate the behavior of the drop migration in the channel flow under zero-gravity. To validate the present calculation, some typical results are compared with available computational and theoretical data, which confirms that the present approach is reliable in predicting the drop migration. With respect to the drop migration in the channel flow at finite Reynolds numbers, the drops either move to an equilibrium lateral position or undergo an oscillatory motion under different conditions. The effects of some typical parameters, e.g., the Reynolds number, the Weber number, the viscosity ratio and the density ratio of the drop fluid to the suspending medium, and the drop size, on the migration of drops are discussed and analyzed. The project supported by the National Natural Science Foundation of China (10125210) and the Hundred-Talent Programme of the Chinese Academy of Sciences     

Friction factor improved correlations for laminar and turbulent gas–liquid flow in horizontal pipelines

We develop improved correlations for two-phase flow friction factor that consider the effect of the relative velocity of the phases, based on a database that includes 2560 gas–liquid flow experiments in horizontal pipes. The database includes a wide range of operational conditions and fluid properties for two-phase friction factor correlations. We classify the experiments by liquid holdup ranges to obtain composite analytical expressions for two-phase friction factor vs. the Reynolds number by fitting logistic dose curves to the experimental data with. We compute the liquid holdup values used to classify the experimental data using correlations proposed previously. The Reynolds number is based on the mixture velocity and the liquid kinematic viscosity. The Fanning friction factor for gas–liquid is defined in term of the mixture velocity and density. Additionally, we sort the experimental data by flow regime and obtain the two-phase friction factor improved correlations for dispersed bubble, slug, stratified and annular flow for different holdup ranges. We report error estimates for the predicted vs. measured friction factor together with standard deviation for each correlation. The accuracy of the correlations developed in this study is compared with that of other 21 correlations and models widely available in the specialized literature. Since different authors use different definitions for friction factors and Reynolds numbers, we present comparisons of the predicted pressure drop for each and every data point in the database. In most cases our correlations predict the pressure drop with much greater accuracy than those presented by previous authors.     

Friction characteristics of compressible gas flows in microtubes

The characteristics of a gaseous flow of nitrogen in commercial stainless steel microtubes for gas chromatography having a nominal inner diameter of 762, 508, 254 and 127 μm are experimentally investigated. The friction factor is calculated as a function of the Reynolds number and plotted in a Moody chart. A comparison among three different methods to calculate the friction factor is made in order to evidence limitations and advantages of each method. It was observed that in the laminar regime the Poiseuille law correctly predicts the value of the pressure drop. It has been evidenced that in order to make accurate experiments on the frictional characteristics of commercial microtubes the value of the inner diameter given by the manufacturer has to be always verified. The experimental data presented in this work remark how in microtubes the compressibility effects related to the axial variation of the gas density tend to become important at large Reynolds numbers and small diameters even if the average Mach number is low. The effects due to the gas acceleration on the laminar-to-turbulent transition in microtubes are investigated by evidencing the role of the L/D (length to diameter) ratio on the transition to turbulence. No early transition to turbulence has been evidenced in the tests, instead it takes place at Reynolds numbers ranging between 1800 and 2900.     

Experimental validation of a two equation RANS transitional turbulence model for compressible microflows

Laminar-to-turbulent flow transition in microchannels can be useful to enhance mixing and heat transfer in microsystems. Typically, the small characteristic dimensions of these devices hinder in attaining higher Reynolds numbers to limit the total pressure drop. This is true especially in the presence of a liquid as a working medium. On the contrary, due to lower density, Reynolds number larger than 2000 can be easily reached for gas microflows with an acceptable pressure drop. Since microchannels are used as elementary building blocks of micro heat exchangers and micro heat-sinks, it is essential to predict under which conditions, the laminar-to-turbulent flow transition inside such geometries can be expected. In this paper, experimental validation of a two equations transitional turbulence model, capable of predicting the laminar-to-turbulent flow transition for internal flows as proposed by Abraham etal. (2008), is presented for the first time for microchannels. This is done by employing microchannels in which Nitrogen gas is used as a working fluid. Two different cross-sections namely circular and rectangular are utilized for numerical and experimental investigations. The inlet mass flow rate of the gas is varied to cover all the flow regimes from laminar to fully turbulent flow. Pressure loss experiments are performed for both cross-sectional geometries and friction factor results from experiments and numerical simulations are compared. From the analysis of the friction factor as a function of the Reynolds number, the critical value of the Reynolds number linked to the laminar-to-turbulent transition has been determined. The experimental and numerical critical Reynolds number for all the tested microchannels showed a maximum deviation of less than 12%. These results demonstrate that the transitional turbulence model proposed by Abraham etal. (2008) for internal flows can be extended to microchannels and proficiently employed for the design of micro heat exchangers in presence of gas flows.     

Effect of diameter on two-phase pressure drop in narrow tubes

The effect of tube diameter on two-phase frictional pressure drop was investigated in circular tubes with inner diameters of 0.6, 1.2, 1.7, 2.6 and 3.4 mm using air and water. The gas and liquid superficial velocity ranges were 0.01-50 m/s and 0.01-3 m/s, respectively. The gas and liquid flow rates were measured and the two-phase flow pattern images were recorded using high-speed CMOS camera. Unique flow patterns were observed for smaller tube diameters. Pressure drop was measured and compared with various existing models such as homogeneous model and Lockhart-Martinelli model. It appears that the dominant effect of surface tension shrinking the flow stratification in the annular regime is important. It was found that existing models are inadequate in predicting the pressure drop for all the flow regimes visualized. Based on the analysis of present experimental frictional pressure drop data a correlation is proposed for predicting Chisholm parameter “C” in slug annular flow pattern. For all other flow regimes Chisholm’s original correlation appears to be adequate except the bubbly flow regime where homogeneous model works well. The modification results in overall mean deviation of pressure drop within 25% for all tube diameters considered. This approach of flow regime based modification of liquid gas interaction parameter appears to be the key to pressure drop prediction in narrow tubes.     

Unsteady fluid flow and heat transfer over a bank of flat tubes

Transient numerical simulations of fluid flow and heat transfer over a bank of flat tubes have been carried for both in-line and staggered configurations for the following boundary conditions: (a) isothermal and (b) isoflux. The effect of Reynolds number, Prandtl number, length ratio, and the height ratio, on the Nusselt number, and the dimensionless pressure drop are elucidated. Correlations are proposed for both pressure drop and Nusselt number and optimum configurations have been determined.     

Numerical Study of Heat Transfer in a Rectangular Channel with Porous Covering Obstacles

A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered. The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with the increase of Reynolds number.