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     

Stereo‐PIV experiments and large eddy simulations of flow fields in stirred tanks with Rushton and curved‐Blade turbines

The flow characteristics in pilot‐scale stirred tanks with Rushton and curved‐blade turbines were investigated by using stereoscopic particle image velocimetry (SPIV) experiments and large eddy simulation (LES) methods. The velocity and turbulent kinetic energy (TKE) in the impeller discharge regions were carefully resolved with a high resolution SPIV system, and the detailed phase‐resolved velocity and TKE profiles were used to validate the LES results. The effects of Reynolds number and blade shape on the flow characteristics were discussed. The LES results of velocity, TKE, and the evolution of trailing vortices were compared with the SPIV experimental data, and good agreement was obtained at various phase angles. The effects of subgrid scale model and hybrid grid with different mesh resolutions on the LES results were investigated. LES is a computationally affordable method for the accurate predictions of the complex flow fields in pilot‐scale stirred tanks is presented. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3986–4003, 2013     

Large eddy simulation of microbubble dispersion and flow field modulation in vertical channel flows

Turbulent liquid–gas vertical channel flows laden with microbubbles are investigated using large eddy simulation (LES) two-way coupled to a Lagrangian bubble tracking technique. Upward and downward flows at shear Reynolds numbers of Re _τ = 150 and 590 are analyzed for three different microbubble diameters of 110, 220, and 330 μm. Predicted results are compared with published direct numerical simulation results although, with respect to comparable studies available in the literature, the range of bubble diameters and shear Reynolds numbers considered herein is extended to larger values. Microbubble concentration profiles are analyzed, with the microbubbles segregating at the wall in upflow conditions and moving toward the channel centre in downflow. The various forces acting on the bubbles, and the effect of the flow turbulence on the bubble concentration, are considered and quantified. Overall, the results suggest that the level of detail achievable with LES is sufficient to predict the fluid structures impacting bubble behavior. Therefore, LES coupled with Lagrangian bubble tracking shows promise for enabling the reliable prediction of bubble-laden flows that are of industrial relevance. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1325–1339, 2019     

Detached eddy simulation on the turbulent flow in a stirred tank

A detached eddy simulation (DES), a large‐eddy simulation (LES), and a k‐ε‐based Reynolds averaged Navier‐Stokes (RANS) calculation on the single phase turbulent flow in a fully baffled stirred tank, agitated by a Rushton turbine is presented. The DES used here is based on the Spalart‐Allmaras turbulence model solved on a grid containing about a million control volumes. The standard k‐ε and LES were considered here for comparison purposes. Predictions of the impeller‐angle‐resolved and time‐averaged turbulent flow have been evaluated and compared with data from laser doppler anemometry measurements. The effects of the turbulence model on the predictions of the mean velocity components and the turbulent kinetic energy are most pronounced in the (highly anisotropic) trailing vortex core region, with specifically DES performing well. The LES—that was performed on the same grid as the DES—appears to lack resolution in the boundary layers on the surface of the impeller. The findings suggest that DES provides a more accurate prediction of the features of the turbulent flows in a stirred tank compared with RANS‐based models and at the same time alleviates resolution requirements of LES close to walls. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3224–3241, 2012     

Numerical study on steady and transient mass/heat transfer involving a liquid sphere in simple shear creeping flow

A numerical method is utilized to examine the steady and transient mass/heat transfer processes that involve a neutrally buoyant liquid sphere suspended in simple shear flow at low Reynolds numbers is described. By making use of the known Stokes velocity field, the convection‐diffusion equations are solved in the three‐dimensional spherical coordinates system. For the mass transfer either outside or inside a liquid sphere, Sherwood number Sh approaches an asymptotic value for a given viscosity ratio at sufficiently high Peclet number Pe. In terms of the numerical results obtained in this work, two new correlations are derived to predict Sh at finite Pe for various viscosity ratios. © 2013 American Institute of Chemical Engineers AIChE J, 60: 343–352, 2014     

Direct numerical simulation of the turbulent flow in a baffled tank driven by a Rushton turbine

We present a direct numerical simulation (DNS) of the turbulent flow in a baffled tank driven by by a Rushton turbine. The DNS is compared to a Large Eddy Simulation (LES), a Reynolds Averaged Navier‐Stokes (RANS) simulation, Laser Doppler Velocimetry data, and Particle Image Velocimetry data from the literature. By Reynolds averaging the DNS‐data, we validate the turbulent viscosity hypothesis by demonstrating strong alignment between the Reynolds stress and the mean strain rate. Although the turbulent viscosity ν_T in the DNS is larger than in the RANS simulation, the turbulent viscosity parameter C_μ = ν_T?/k², is an order of magnitude smaller than the standard 0.09 value of the k‐? model. By filtering the DNS‐data, we show that the Smagorinsky constant C_S is uniformly distributed over the tank with C_S ≈ 0.1. Consequently, the dynamic Smagorisnky model does not improve the accuracy of the LES. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Application of different CFD multiphase models to investigate effects of baffles and nanoparticles on heat transfer enhancement

In this work, the effect of baffles in a pipe on heat transfer enhancement was studied using computational fluid dynamics (CFD) in the presence of Al₂O₃ nanoparticles which are dispersed into water. Fluid flow through the horizontal tube with uniform heat flux was simulated numerically and three dimensional governing partial differential equations were solved. To find an accurate model for CFD simulations, the results obtained by the single phase were compared with those obtained by three different multiphase models including Eulerian, mixture and volume of fluid (VOF) at Reynolds numbers in range of 600 to 3000, and two different nanoparticle concentrations (1% and 1.6%). It was found that multiphase models could better predict the heat transfer in nanofluids. The effect of baffles on heat transfer of nanofluid flow was also investigated through a baffled geometry. The numerical results show that at Reynolds numbers in the range of 600 to 2100, the heat transfer of nanofluid flowing in the geometry without baffle is greater than that of water flowing through a tube with baffle, whereas the difference between these effects (nanofluid and baffle) decreases with increasing the Reynolds number. At higher Reynolds numbers (2100–3000) the baffle has a greater effect on heat transfer enhancement than the nanofluid.     

Heat transfer performance of NETmix—A novel micro‐meso structured mixer and reactor

NETmix is a novel static mixing technology consisting on a network of unit cells, comprising chambers interconnected by channels. To assess the heat transfer capacity of NETmix, the NUB model was implemented to perform hydrodynamics and heat transfer simulations. Due to the periodic nature of the NETmix structure, two central chambers and six half‐chambers were found to be sufficient to be representative of the whole network. The Nusselt numbers were determined based on the CFD simulations, and when compared with theoretical results for laminar flow between parallel plates, 3–5 times higher Nusselt number values were obtained with NETmix. This observed heat transfer rate enhancement, makes it suitable for fast reactions where heat transfer is crucial. Finally, results obtained from this study show that NETmix presents a heat transfer capacity one order of magnitude greater than microreactors, and 2–5 orders of magnitude greater than the most commonly used devices in industry. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2496–2508, 2017     

LES–Lagrangian‐particles‐simulation of turbulent reactive flows at high Sc number using approximate deconvolution model

Large eddy simulation (LES) with the approximate deconvolution model is combined with Lagrangian particles simulation (LPS) for simulating turbulent reactive flows at high Schmidt numbers Sc. The LES is used to simulate velocity and nonreactive scalar while reactive scalars are simulated by the LPS using the mixing volume model for molecular diffusion. The LES–LPS is applied to turbulent scalar mixing layers with a second‐order isothermal irreversible reaction at Sc = 600. The mixing volume model is implemented with the IEM, Curl's, and modified Curl's mixing schemes. The mixing volume model provides a correct decay rate of nonreactive scalar variance at high Sc independently of the number of particles. The statistics in the LES–LPS with the IEM or modified Curl's mixing scheme agree well with the experiments for both moderately‐fast and rapid reactions. However, the LPS with the Curl's mixing scheme overpredicts the effects of the rapid reaction. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2912–2922, 2016     

CFD study of turbulent jet impingement on curved surface

The heat transfer and flow characteristics of air jet impingement on a curved surface are investigated with computational fluid dynamics(CFD)approach.The first applied model is a one-equation SGS model for large eddy simulation(LES)and the second one is the SST-SAS hybrid RANS-LES.These models are utilized to study the flow physics in impinging process on a curved surface for different jet-to-surface(h/B)distances at two Reynolds numbers namely,2960 and 4740 based on the jet exit velocity(U_e)and the hydraulic diameter(2B).The predictions are compared with the experimental data in the literature and also the results from RANS k-εmodel.Comparisons show that both models can produce relatively good results.However,one-equation model(OEM)produced more accurate results especially at impingement region at lower jet-to-surface distances.In terms of heat transfer,the OEM also predicted better at different jet-to-surface spacings.It is also observed that both models show similar performance at higher h/B ratios.     

Dynamic delayed detached eddy simulation of a multi‐inlet vortex reactor

The multi‐inlet vortex reactor (MIVR) is used for flash nanoprecipitation to manufacture functional nanoparticles. A validated computational fluid dynamics model is needed for the design, scale‐up, and optimization of the MIVR. Unfortunately, available Reynolds‐averaged Navier‐Stokes methods are unable to accurately model the highly swirling flow in the MIVR. Large‐eddy simulations (LES) are also problematic, as excessively fine grids are required to accurately model this flow. These dilemmas led to the application of the dynamic delayed detached eddy simulation (DDES) method to the MIVR. In the dynamic DDES model, the eddy viscosity has a form similar to the Smagorinsky sub‐grid viscosity in LES, which allows the implementation of a dynamic procedure to determine its model coefficient. Simulation results using the dynamic DDES model are found to match well with experimental data in terms of mean velocity and turbulence intensity, suggesting that the dynamic DDES model is a good option for modeling the turbulent swirling flow in the MIVR. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2570–2578, 2016     

LDA measurements and CFD simulations of an in‐line high shear mixer with ultrafine teeth

Hydrodynamics of a pilot‐scale in‐line high shear mixer (HSM) with double rows of ultrafine rotor and stator teeth, including the velocity profiles and power consumptions, were measured using laser Doppler anemometry and a torque transducer, respectively. Computational fluid dynamics simulations were conducted using the standard k‐ε turbulence model with first‐ and second‐order accuracy and large eddy simulation (LES) with the standard Smagorinsky–Lilly subgrid scale model. Predictive capabilities of the different turbulence models and discretization schemes were assessed based on the experimental data. It is found that the current LES can predict accurately the flow patterns for the strongly rotating and locally anisotropic turbulent flows in the complex in‐line HSM. The results obtained are fundamental to explore potential applications of the in‐line teethed HSMs to intensify chemical reaction processes. © 2013 American Institute of Chemical Engineers AIChE J, 60: 1143–1155, 2014     

螺旋隔板套管换热器壳程传热与压降的数值模拟

以水-润滑油换热为对象,对螺旋隔板套管换热器的壳程传热与压降性能进行了实验研究与数值模拟。通过威尔逊图解法获得了管程的传热系数,并计算出了壳程的努塞尔特准数。采用Fluent软件模拟了润滑油在螺旋隔板套管换热器壳程层流流动时的流场、温度场以及传热与压降性能。结果表明,流体在螺旋隔板换热器的壳程流动均匀,在隔板附近没有返混和流动死区,但温度梯度最大。在相同雷诺常数下,壳程的努塞尔特准数和压降模拟值分别比实验值高1.3%～8%和4%～38.1%,模拟值与实验值吻合较好。     

Heat/mass transfer from a neutrally buoyant sphere by mixed natural and forced convection in a simple shear flow

Building on the work of Yang et al. in 2011, the finite difference method and the Boussinesq approximation were applied to solve the time‐dependent Navier‐Stokes, convection diffusion and continuity equations in spherical coordinates. An idealized condition, the mass transfer from a neutrally buoyant sphere in a horizontal simple shear flow with natural convection was numerically simulated for the first time in this work. In the hybrid transfer case, the outwardly spiraling streamlines enhanced the transfer process, but the counter‐gravity spiraling streamlines near the sphere hindered the natural convection and the spatial dilution action weakened the natural convection transfer process. These competing effects led to nonmonotonic behavior of the Nusselt number with Reynolds number. Results from these previously undocumented cases were summarized into correlations for predicting Nusselt numbers at finite Reynolds numbers for various Grashof and Prandtl numbers. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2816–2827, 2018     

A numerical comparison of precipitating turbulent flows between large‐eddy simulation and one‐dimensional turbulence

This study presents the results of computational fluid dynamics simulations of a multiphase, reacting, turbulent mixing layer in an idealized geometry. The purpose is to compare large‐eddy simulation (LES) to one‐dimensional turbulence (ODT) and examine the trends of the flow under differing mixing conditions. Aqueous streams are mixed together to precipitate polymorphs of calcium carbonate. The polymorphs of calcium carbonate are tracked numerically using population balance equations (PBE). Each PBE contains all of the relevant physical models to track the particle evolution including nucleation, growth, and aggregation. A simple subgrid mixing model that is convenient for use with PBEs was implemented in the LES code. The higher spatial resolution achievable with ODT allowed an investigation on the effect of resolution on the mixing‐model error. The Reynolds number of the flow is varied and is shown to cause a decrease in average particle sizes with higher mixing rates. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3185–3197, 2015     

Numerical simulation of turbulent flow in a baffled stirred tank with an explicit algebraic stress model

An explicit algebraic stress model (EASM) was used to simulate anisotropic turbulent flows in baffled stirred tanks equipped with a standard Rushton turbine. The quantitative predictions of velocity components, turbulence kinetic energy, Reynolds stresses and turbulence energy dissipation rate in the context of anisotropic turbulence were conducted to assess the comprehensive performance of the EASM. A lot of efforts have been made to ensure numerical stability during the calculations such as using a good initial flow field, manipulating source terms and adjusting under-relaxation factors. The predicted results were also compared with experimental data and other simulation results obtained using the standard k–ε model, algebraic stress model (ASM), Reynolds stress model (RSM) and large eddy simulation (LES). All the simulations were run with in-house codes. The simulation results show that agreement between the EASM predictions and experimental values is satisfactory. The EASM is consistently superior to the standard k–ε model when predicting both peak values and trend of variation in velocities and turbulence quantities. In comparison to the RSM, the EASM has almost the same predictive accuracy. The EASM is inferior to the LES on the prediction of turbulence kinetic energy. Nevertheless, the computational cost of the EASM is significantly lower than that of the LES, which is an obvious advantage in practical applications.     

Numerical prediction of a nusselt number equation for stirred tanks with helical coils

A methodology to obtain a Nusselt correlation for stirred tank reactors is presented. The novelty of the approach is the use of a validated computational model to obtain the heat‐transfer coefficients. The advantages of this new approach are many, including the possibility of testing different heat‐transfer configurations to obtain their Nusselt correlation without performing experimental runs. Physical phenomena involved was represented both qualitatively and quantitatively. The classical experimental work of (Oldshue and Gretton, Chem Eng Prog. 1954;50(12):615–621) illustrates the procedure. A sufficient number of virtual points in the whole range of the Reynolds number should be obtained. Results strongly depend on mesh refinement in the boundary layer, so a procedure is suggested to guarantee heat‐transfer coefficients are accurately estimated. The final Nusselt correlation was compared against all the 107 experimental points of the work by (Oldshue and Gretton, Chem Eng Prog. 1954;50(12):615–621), and an average deviation on the results of 10.7%. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3912–3924, 2017     

Laminar Forced Convection of a Water‐TiO2 Nanofluid in Annuli Considering Mass Conservation for Particles

Hydrothermal characteristics of a water‐TiO₂ nanofluid were evaluated numerically within annuli considering the effects of particle migration. The convective heat transfer coefficients increased at both inner and outer walls of the annulus by raising the concentration. Along the annulus, the friction coefficient decreased more rapidly at lower Reynolds numbers. Taking the particle migration into account, a nonuniform concentration distribution was observed at the annulus cross section, higher heat transfer coefficients were obtained at both walls, and the velocity profile became flatter. In addition, the influence of thermophoresis on the convective heat transfer proved to be more significant than that of Brownian diffusion.     

Effects of Viscous Dissipation on Heat Transfer between an Array of Long Circular Cylinders and Power Law Fluids

The free surface model has been combined with the equations of motion and of thermal energy to investigate the role of viscous dissipation on heat transfer between banks of long cylinders and power law (shear‐thinning and shear‐thickening) fluids. The equations of motion cast in the stream function/vorticity formulation have been solved numerically using a second‐order accurate finite difference method to obtain extensive information on the behaviour of local and surface‐averaged Nusselt numbers over a range of Reynolds numbers 1 – 500, for a wide range of power law indices (0.4 ≤ n ≤ 2.0), Brinkman numbers (0 ≤ Br ≤ 5) and Prandtl numbers (Pr = 1, 1000) at two representative solid volume fractions corresponding to the porosities of e = 0.4 and 0.9. Two different thermal boundary conditions are considered at the cylinder surface: constant temperature (CT) and constant heat flux (CHF). The results presented herein provide a fundamental knowledge about the influence of viscous dissipation on the heat transfer characteristics. The results reported herein further show that the effect of Brinkman number on heat transfer is strongly conditioned by the thermal boundary condition, Prandtl number and the power law index.     

Measurements and computation of low mass transfer coefficients for FCC particles with ozone decomposition reaction

The mass transfer coefficients and Sherwood numbers for catalyzed fluid cracking catalyst particles were measured and computed in a two‐dimensional (2‐D) bubbling fluidized bed, with ozone decomposition reaction. The measured and computed Sherwood numbers, using 3‐ and 2‐D kinetic theory based computational fluid dynamics simulations, were of the order of 10^?6–10^?2. The low Sherwood numbers were in reasonable agreement with the literature data for small particles, at low Reynolds numbers. The computational fluid dynamics simulations showed that it is possible to compute conversions in fluidized bed reactors without using the conventional model with empirical mass transfer coefficients. © 2011 American Institute of Chemical Engineers AIChE J, 2012