Numerical Simulation for Particle Penetration Depth Distribution in Deep Bed Filtration

A two‐dimensional model has been developed to simulate particle penetration through porous media. The particle penetration depends on many parameters including the Reynolds number, particle drag coefficient, the ratio of the diameter of injected to filtered particles, fluid velocity, and pore size, etc. The numerical model for separation efficiency in periodic porous media was studied. Previous work has described the effects of injected particle size, Reynolds number and particle drag coefficient. In this study, the porous media flow is modeled (solution of the Navier‐Stokes equations) by using the finite element method, and the analysis is restricted to the case of two‐dimensional periodic porous media. The effects of these factors and particle depth distribution in porous media are investigated. It is noted that the results for the three Reynolds numbers 1, 16.56, and 100, are qualitatively similar, and about 40 % of particles are trapped in the top part of the filter.     

Viscoelastic flow in packed beds or porous media

An analysis of viscoelastic flow in packed beds or porous media is presented based on a capillary hybrid model of the flow which incorporates a viscous mode and an elongational mode. The development includes modelling of the elongational mode of the flow to obtain the elongational flow contribution to the potential drop for a viscoelastic fluid. A general expression describing viscoelastic flow in porous media is developed which utilizes the viscous response determined by the fluid model equation and an elongational flow response characterized by an elongational viscosity difference for the fluid. The expression applies to all three traditional bed models employing the tortuosity and Kozeny constant. The relationship yielded extensions of Darcy's law applicable to viscoelastic flow in porous media and an expression representing the flow of a viscoelastic fluid in a packed bed or porous core of length L. The relationship of the friction factors and respective Reynolds numbers is also presented.     

Coupled Mass and Heat Transfer between a Cone and a Power‐Law Fluid

Coupled mass and heat transfer between a cone and a non‐Newtonian fluid was studied when the concentration level of the solute in the solvent is finite (finite dilution of solute approximation). Convective heat and mass transfer between a laminar flow and a stationary cone and between a rotating cone and a quiescent fluid is investigated. Solutions of both problems are found in the form of the dependencies of Sherwood number vs. Reynolds and Schmidt numbers. Coupled thermal effects during dissolution and solute concentration level effect on the rate of mass transfer are investigated. It is found that the rate of mass transfer between a cone and a non‐Newtonian fluid increases with the increase of the solute concentration level. The suggested approach is valid for high Peclet and Schmidt numbers. Isothermal and nonisothermal cases of dissolution are considered whereby the latter is described by the coupled equations of mass and heat transfer. It is shown that for positive dimensionless heat of dissolution, K > 0, thermal effects cause the increase of the mass transfer rate in comparison with the isothermal case. On the contrary, for K < 0 thermal effects cause the decrease of the mass transfer rate in comparison with the isothermal case. The latter effect becomes more pronounced with the increase of the concentration level of the solute in a solvent.     

Transitional flow in a Rushton turbine stirred tank

The way in which the single phase flow of Newtonian liquids in the vicinity of the impeller in a Rushton turbine stirred tank goes through a laminar‐turbulent transition has been studied in detail experimentally (with Particle Image Velocimetry) as well as computationally. For Reynolds numbers equal to or higher than 6000, the average velocities and velocity fluctuation levels scale well with the impeller tip speed, that is, show Reynolds independent behavior. Surprising flow structures were measured—and confirmed through independent experimental repetitions—at Reynolds numbers around 1300. Upon reducing the Reynolds number from values in the fully turbulent regime, the trailing vortex system behind the impeller blades weakens with the upper vortex weakening much stronger than the lower vortex. Simulations with a variety of methods (direct numerical simulations, transitional turbulence modeling) and software implementations (ANSYS‐Fluent commercial software, lattice‐Boltzmann in‐house software) have only partial success in representing the experimentally observed laminar‐turbulent transition. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3610–3623, 2017     

Flow pattern variations of viscoelastic fluid flows in three‐dimensional branching channel

Transport phenomena in three‐dimensional branching channel are important because of their relevance in polymer processing. In this article, an experimental study on viscoelastic flow in a three‐dimensional cylindrical branching channel is carried out to investigate variations of flow pattern. Flow visualization in representative symmetric planes is made both for the viscoelastic fluid and Newtonian flow. From the results of the present investigation, the flow field in the three‐dimensional cylindrical branching channel is clarified within the range of laminar flow. It is confirmed that corner vortex, shedding vortex, and secondary vortex flow are all obviously changed with the fluid concentration and the Reynolds number, which are much more three‐dimensional and complex than the Newtonian fluid, and the flow pattern of the viscoelastic fliud flow largely depends on the Reynolds number and fluid concentration. Even for the viscoelastic flow at the low Reynolds number, shedding vortex and secondary vortex and complex three‐dimensional flow occur in the cylinder. The flow field is not symmetric space for the viscoelastic flow and however is fairly symmetric for the Newtonian fluid. The above reasons explain why the flow deflection happens even at the low Reynolds number flow. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Flow of a FENE Fluid in Packed Beds or Porous Media

An analysis describing viscoelastic flow of a FENE fluid in packed beds or porous media is presented based on the capillary hybrid model of the flow. A close similarity is revealed between the functional relationship of the reduced elongational viscosity to and that relating the reduced mean elongational viscosity λ_H ? to the Deborah number which is utilized in the flow expressions. The agreement obtained between the predicted and experimentally determined evaluations of the resistance factor, including the effects of variation of polymer concentration, molecular weight and solvent quality was found to be satisfactory. Onset Reynolds numbers for enhanced flow resistance are also predicted successfully.     

Non-Newtonian purely viscous flow through isotropic granular porous media

An analytical model for predicting non-Newtonian purely viscous power law flow through isotropic granular porous media is proposed. Application of the method of volume averaging leads to macroscopic momentum transport equations describing the physical flow phenomena within the porous medium. The geometrical properties of the granular porous medium are incorporated through the introduction of a rectangular representative unit cell model. The relative positioning of neighbouring cells leads to staggered- and non-staggered arrays of solid constituents. Volume partitioning of the flow domain allows for the tortuosity to be expressed as a ratio of fluid volumes. In order to support the assumption of average geometrical isotropy of the unit cell model, a weighted average is performed over the different arrays. The coefficient obtained from the averaging procedure is based purely on physical principles. Through application of an asymptotic matching technique, the proposed model produces pressure gradient predictions for Reynolds numbers within the entire laminar flow regime. The analytical model is compared to published experimental data to verify the validity of the model.     

Flow,Solidification, and Solute Transport in a Continuous Casting Mold with Electromagnetic Brake

A three‐dimensional mathematical model is developed to study coupled turbulent flow, heat, solute transport, and solidification in a slab continuous caster with electromagnetic brake. Based on the analogy analysis, all the governing equations can be expressed as a general differential equation and be solved by a general numerical method. Numerical results show that a small corner‐vortex appears near the free surface due to the interaction between the moving solidified shell and the upward flow. Influenced by the fluid flow, the temperature and solute distribution can also be divided into the upper and lower recirculation zones but the distribution of carbon concentration is opposite to that of temperature. The three‐dimensional magnetic field can effectively damp the local flow and affect heat and solute transfer in the mold.     

Experimental and numerical analysis of the hydrodynamic behaviors of aerobic granules

Aerobic granular sludge has been recognized to be promising for wastewater treatment. Their hydrodynamic characteristics have a significant impact on the mass transfer process in reactors. In this study, the hydrodynamic characteristics of aerobic granules were studied using an experimental approach, and their fluid dynamic behaviors were analyzed using a numerical approach. Experimental results show that the aerobic granules are fractal‐like aggregates with porosity. Their porosity and permeability were found to increase with increasing granule size. The numerical model simulated the flow field surrounding a granule, which distinguished the flow behaviors of the granules with different permeability at different outflow Reynolds numbers. The velocity vectors colored by velocity magnitude in the granule internal depended significantly on the permeability of the granule and the Reynolds number. The results provided a helpful tool to investigate the hydrodynamic behavior of aerobic granules with a consideration of their porous structure characteristics. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

The effect of particle shape on pipeline friction for newtonian slurries of fine particles

Experiments have been conducted to assess the effect of particle shape on pipeline friction in turbulent flow, using laboratory pipelines of nominal diameter 50 mm and 150 mm. The experiments were intended to examine the extent to which a fluid model is appropriate for slurries of this type, especially at high solids concentrations. The experiments confirm that fluid friction at low and moderate solids concentrations is proportional to slurry density, with particle shape being of minor importance. At high solids concentrations, additional increases in friction are observed and these depend upon the ratio of the solids concentration to the maximum settled concentration. Although this friction increase is qualitatively similar to that which would result from increased slurry viscosity, the evidence suggests that particle‐wall contact is the mechanism. However, the transition from turbulent to laminar flow indicates that an effective viscosity should be used in calculating critical Reynolds numbers.     

Pore scale inertial flow simulations in 3‐D smooth and rough sphere packs using lattice Boltzmann method

Pore‐scale inertial flows in periodic body centered cubic (BCC) arrays of smooth and rough sphere packs were simulated using lattice Boltzmann method. Computed velocity fields were visualized and averaged to calculate macroscopic flow parameters characteristic of porous media such as permeability, tortuosity, and β factor as well as the transition Reynolds number values and compared well with established correlations. Furthermore, hemispherical depositions on the smooth spheres in the regular BCC array were used to calculate roughness induced changes in macroscopic flow parameters. As the next step toward simulating inertia dominated flow in natural porous media, simulations were validated for low Reynolds number flow in a three‐dimensional (3‐D) CT image of irregular pack of uniform diameter spheres. This work aims to define 3‐D canonical studies for roughness induced inertial flows in porous media and to assess the capability of LBM for simultaneous prediction of absolute permeability and β factor. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4858–4870, 2013     

Dynamic Adsorption of CO2 from Methane: Studies on Mass and Heat Transfer

Three‐dimensional computational fluid dynamics studies related to dynamics adsorption of CO₂ from natural gas is found to be limited. 3D analyses for dynamics adsorption are substantially crucial to give a better prediction on the adsorption process by considering the actual fluid flow behavior within the packed‐bed porous media. A kinetic adsorption model has been integrated in a commercial fluid dynamics simulator to simulate the 3D hydrodynamics and adsorption phenomenon in a zeolite‐filled packed column for a CO₂‐methane separation system. The effects of various parameters such as Reynolds number, CO₂ feed concentration, feed temperature, and column dimension on CO₂ adsorption efficiency have been investigated. A correlation for adsorption efficiency based on the CO₂ concentration profiles has been developed and validated.     

Heat and mass transfer in granular potash fertilizer with a surface dissolution reaction

Potash is a widely used granular fertilizer and when exposed to high humidities it readily adsorbs water vapour forming a liquid electrolyte solution on each particle. Heat and mass transfer due to air flow through granular potash beds is studied experimentally and numerically. A one dimensional experimental setup is used to measure the temperature and air humidity response and mass gain of a potash bed subjected to a change in air flow. A porous media mathematical model is developed to predict the transient temperature and moisture content distributions. The processes are modelled as nonequilibrium heat and mass transfers between the porous solid and air flow gaseous phases. The state of the surface electrolyte solution is modelled by the thermodynamics of electrolyte solutions. Experimental and numerical results show non‐equilibrium internal moisture and heat transfer processes exist with significant differences in the pore air and particle temperature and surface relative humidity.     

Mass/heat transfer from a neutrally buoyant sphere in simple shear flow at finite Reynolds and Peclet numbers

Theoretical analyses of mass/heat transfer from a neutrally buoyant particle in simple shear flow indicate that mass/heat must diffuse across a region of closed streamlines of finite thickness at zero Reynolds number, whereas spiraling streamlines allow the formation of a thin mass transfer boundary layer at small but non‐zero Reynolds numbers (Subramanian and Koch, Phys Rev Lett. 2006;96:134503; Subramanian and Koch, Phys Fluids. 2006;18: 073302). This article presents the first numerical results for mass/heat transfer at finite Reynolds and Peclet numbers. The simulations indicate that fluid particles in the flow‐gradient plane spiral away from the particle for Reynolds numbers smaller than about 2.5 while they spiral toward the particle for higher Reynolds numbers. Solutions of the Navier‐Stokes equations coupled with a boundary layer analysis of mass transfer yield predictions for the rate of mass transfer at asymptotically large Peclet numbers and Reynolds numbers up to 10. Simulations of mass transfer for zero Reynolds number and finite Peclet numbers confirm Acrivos' (Acrivos, J Fluid Mech. 1971;46:233–240) prediction that the Nusselt number approaches a finite value with increasing Peclet number. Simulations at finite Reynolds numbers and Peclet numbers up to 10,000 confirm the theoretical predictions for the concentration gradient at the particle surface at angular positions away from the flow‐gradient plane. However, the wake near the flow‐gradient plane remains too large at this Peclet number to yield a quantitative agreement of the overall rate of mass transfer with the theory for asymptotically large Peclet number. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Inertia Effects on the Flow of Bingham Plastics Through Sudden Contractions in a Pipe

The present numerical study concentrates on the effects of moderate and high Reynolds numbers on the laminar flow of a non-Newtonian rigid viscoplastic (Bingham) fluid through a sudden contraction in a pipe. The flow is assumed to be steady, incompressible, and isothermal. Results are presented for a wide range of the governing Reynolds and yield numbers and the significant effects of these two parameters both on the integral and local kinematic properties of the flow field are established. Low yield numbers result in the disappearance of the recirculating flow region at the corner replacing it with a region of very low rates of deformation. The evolution of the centerline velocity in the vicinity of the contraction plane is shown to be independent of the yield number and dependent on the Reynolds number, while the concavities in the streamwise velocity profiles appearing at high Reynolds numbers are independent of the yield number. The pressure losses through the contraction increase with yield number with the effect being more pronounced at lower Reynolds numbers.     

Characterization of unsteady flow in a 3D-printed Schwarz Diamond monolith using magnetic resonance velocimetry

Process engineering applications such as heat transfer, reactions, and separations involve passing fluid through a porous medium. Historically, random-channel porous media have been used for these operations. Such systems do not represent optimal configurations for process performance because of poor flow distribution and high-pressure drop. It is now possible to fabricate porous monoliths with tailored morphology and regular channel structure using 3D-printing. In this work, we use magnetic resonance imaging to study flow through a Schwarz Diamond triply periodic minimal surface (TPMS) monolith for Reynolds numbers up to 350. A transition to unsteady flow was observed experimentally for the first time. The channel structure diverts flow such that free shear layers form in the channel centers that contribute to flow instability. These measurements serve to inform the design of novel transport processes with enhanced performance.     

Laminar flow with injection through a long dead‐end cylindrical porous tube: Application to a hollow fiber membrane

Effects of membrane length and hydraulic resistance on the steady‐state laminar flow of a fluid with injection in a dead‐end cylindrical porous tube have been investigated using the perturbation approach of the Navier‐Stokes and continuity equations. Analytic solutions of the dynamic equations, reduced to non linear differential equations, were obtained and applied to submerged, dead‐end hollow fiber membranes of large resistances and small wall Reynolds numbers. The velocity and pressure profiles were solved using the method of separation of variables as with physical properties of the membrane and fluid and the wall velocity at the dead end. The constant flux approximation was found to be valid only for a short membrane with a large hydraulic resistance. The constant permeability approximation used in this study is universal for a membrane of an arbitrary length, through which the fluid velocities and pressure increase exponentially from the dead end to the open end. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Al_2O_3-水纳米流体在微圆管内的流动特性

测定了不同体积分数下A l2O3-水纳米流体在内径0.193 mm和0.508 mm 2种玻璃微圆管内的流动阻力特性。结果表明:纳米流体流动从层流向湍流转变的临界雷诺数Rec发生在2 100附近;对0.508 mm微圆管,纳米流体由层流向湍流的转变与去离子水基本一致,对0.193 mm微圆管纳米流体流型转变较去离子水略有提前。在雷诺数小于1 500—1 700的层流范围,纳米流体和水的摩擦因子都与经典理论预测值吻合良好,同Hagen-Poiseu ille公式偏差小于7.5%,雷诺数大于此范围后前者的摩擦因子比后者和理论值有所偏高;而在过渡区和湍流范围,纳米流体的摩擦因子比水有较大提高,且随体积分数增加摩擦因子增加的趋势更为明显。     

Numerical Analysis of Isothermal Gaseous Flows in Microchannel

Two‐dimensional compressible momentum equations were solved by a perturbation analysis and the PISO algorithm to investigate the effects of compressibility and rarefaction on the local flow resistance of isothermal gas flow in circular microchannels. The computations were performed for a wide range of Reynolds numbers and inlet Mach numbers. The explicit expression of the normalized local Fanning friction factor along the microchannel was derived in the present paper. The results reveal that the local Fanning friction factor is a function of the inlet Mach number, the Reynolds number and the length‐diameter ratio of the channel. For larger Reynolds and inlet Mach numbers, the friction coefficient in the microchannel is higher than the value in a macrotube, and the gas flow in the microchannel is dominated only by compressibility. For smaller Reynolds and inlet Mach numbers, the Fanning friction factor of gas flow in the microchannel is lower than that in a circular tube of conventional size due to slip flow at the wall and thus, rarefaction has a significant effect on the fluid flow characteristics in a microchannel.     

Laminar and turbulent flow in annuli of unit eccentricity

Experimental results are presented for the flow of water in eccentric annuli having unit eccentricity in the laminar, transition and turbulent flow regimes at Reynolds numbers between 200 and 20,000. In both the laminar and turbulent regimes the interesting result is obtained that, for a given Reynolds number, the friction factor is a minimum at a diameter ratio of about 0.750. The experimental results are compared with previous theoretical analyses in the laminar region, and with previous experimental data at Reynolds numbers exceeding 20,000 in the turbulent region. A further interesting result relates to the transition region where, at intermediate diameter ratios, the transition from laminar to turbulent flow becomes more diffuse. This appears to be a consequence of the gradual change from laminar to turbulent flow brought about by the variation in local Reynolds number from zero to a maximum value within the eccentric annulus. It is believed that sufficent experimental data are now available for the pressure gradient to be predicted for flow in eccentric annuli of unit eccentricity over a relatively wide range of Reynolds number.