Numerical study and acceleration of LBM-RANS simulation of turbulent flow

The coupled models of LBM(Lattice Boltzmann Method) and RANS(Reynolds-Averaged Navier–Stokes) are more practical for the transient simulation of mixing processes at large spatial and temporal scales such as crude oil mixing in large-diameter storage tanks. To keep the efficiency of parallel computation of LBM, the RANS model should also be explicitly solved; whereas to keep the numerical stability the implicit method should be better for RANS model. This article explores the numerical stability of explicit methods in 2D cases on one hand, and on the other hand how to accelerate the computation of the coupled model of LBM and an implicitly solved RANS model in 3D cases. To ensure the numerical stability and meanwhile avoid the use of empirical artificial limitations on turbulent quantities in 2D cases, we investigated the impacts of collision models in LBM(LBGK, MRT)and the numerical schemes for convection terms(WENO, TVD) and production terms(FDM, NEQM) in an explicitly solved standard k–ε model. The combination of MRT and TVD or MRT and NEQM can be screened out for the 2D simulation of backward-facing step flow even at Re = 10~7. This scheme combination, however, may still not guarantee the numerical stability in 3D cases and hence much finer grids are required, which is not suitable for the simulation of industrial-scale processes. Then we proposed a new method to accelerate the coupled model of LBM with RANS(implicitly solved). When implemented on multiple GPUs, this new method can achieve 13.5-fold acceleration relative to the original coupled model and 40-fold acceleration compared to the traditional CFD simulation based on Finite Volume(FV) method accelerated by multiple CPUs. This study provides the basis for the transient flow simulation of larger spatial and temporal scales in industrial applications with LBM–RANS methods.     

Aerosol Deposition Measurements as a Function of Reynolds Number for Turbulent Flow in a Ninety-Degree Pipe Bend

An experimental and numerical investigation of the effect of the Reynolds number (Re) on the deposition of aerosol particles in a 90° pipe bend for turbulent flow was performed. Deposition fraction data were measured for a range of Stokes numbers (Stk) at different flow Re (10,250, 20,500, and 30,750) higher than those of most previous studies where Re was ?10,000. The data show good agreement with previous studies for Stk > 0.4, demonstrating that increased Re does not significantly alter the trend of deposition fraction with Stokes number (Stk) in this range. However, a noticeable increase in deposition was detected for 0.1 ? Stk ? 0.4. At Stk = 0.15, an increase in Re from 10,250 to 30,750 caused a factor of 2.6 increase in deposition fraction from 0.14 to 0.36. Numerical simulations were completed, using the Reynolds Averaged Navier-Stokes (RANS) equations with the Shear Stress Transport turbulence model. Modeling with inertial impaction only (i.e., neglecting turbulent dispersion), the results accurately reproduced the general trends seen in the experimental data; however, they failed to detect the Re effect at low Stk seen experimentally. The inclusion of turbulent particle tracking in the RANS simulation via an eddy interaction model did not improve the results. However, an analytical analysis of the particle tracking equation drawing data from the numerical results, showed that the experimentally observed effect of Re at low Stk can be attributed to damped particle response to velocity fluctuations at the eddy frequency scale.     

Applications of computational fluid dynamics in the chemical industry

In order to illustrate the use of CFD in providing an understanding of mixing processes, three examples, mixing in a pipe, homogenization with a static mixer and flow in a mixing vessel with a Rushton turbine, are discussed and compared with experimental results. Special attention is focussed on the resultant concentration distribution, which is closely linked to turbulent properties. A semi-empirical model is presented for a quantitative prediction of the initial turbulent conditions. Using special numerical techniques a mixing vessel with wall-separated baffles, which represents a problem generally regarded as beyond the capabilities of numerical analysis, can be simulated.     

STUDY OF THE TURBULENT FLOW IN AN UNBAFFLED STIRRED TANK BY DETACHED EDDY SIMULATION

Detached eddy simulation (DES) of the liquid-phase turbulent flow in an unbaffled stirred tank agitated by a six-blade, 45°-pitched blade turbine was performed in this study. The tank wall is cylindrical with no baffle and the fluid flow problem was solved in a single reference frame (SRF) rotating with the impeller. For the purpose of comparison, computation based on large eddy simulation (LES) was also carried out. The commercial code Fluent was used for all simulations. Predictions of the phase-averaged turbulent flow quantities and power consumption were conducted. Results obtained by DES were compared with experimental laser Doppler velocimetry (LDV) data from the literature and with the predictions obtained by LES. It was found that numerical results of mean velocity and turbulent kinetic energy profiles as well as the power consumption are in good agreement with the LDV data. When performed on the same computational grid, which is under-resolved in the sense of LES, DES allows better accuracy than LES in that it works better in the boundary layers on the surface of the impeller and the stirred tank walls. It can be concluded that DES has the potential to predict accurately the turbulent flow in stirred tanks and can be used as an effective tool to study the hydrodynamics in stirred tanks.     

A new model of turbulent fibre suspension and its application in the pipe flow

A new model of turbulent fibre suspension in pipe flow is developed by deriving the equations of Reynolds averaged Navier‐Stokes, turbulence kinetic energy and turbulence dissipation rate with the additional term of the fibres, and the equation of probability distribution function for mean fibre orientation. The equations are solved numerically. The numerical mean velocity is in agreement with the experimental data. The effects of Reynolds number, fibre concentration, and fibre aspect‐ratio on the mean velocity, turbulent kinetic energy and turbulent dissipation rate are analysed. The results show that the effect of Reynolds number on the flow behaviour is insignificant. The turbulent kinetic energy and turbulent dissipation rate increase with an increasing fibre concentration and fibre aspect‐ratio. © 2012 Canadian Society for Chemical Engineering     

等温反应湍流流动标量关联量输运的直接模拟

用谱方法对等温反应槽道湍流流动中标量关联量输运进行了三维直接模拟。所得到的无反应情况下的单标量时均值和脉动值与文献中差分法的直接模拟（DNS）数据一致。瞬态模拟结果显示有反应情况下标量脉动量也有条带结构。用直接模拟数据库对标量关联量输运方程各项的贡献进行了先验性统计,发现产生项和耗散项的贡献最大,扩散项和反应项的贡献很小,然而化学反应对各项的大小和分布规律影响很大。对标量关联量方程RANS模拟各项的封闭模型进行了后验性检验。与DNS的统计值相比,除了近壁区之外,在流场的大部分区域,模拟值与精确的统计值基本一致。     

RANS modeling of a particulate turbulent round jet

A complete and accurate model for the symmetric gas–solid turbulent round jet is accomplished using the Reynolds Averaged Navier–Stokes (RANS) equations. The two-fluid model was used to describe the averaged characteristics of the two phases, including the particle mass concentration, the turbulent kinetic energy and its dissipation in the mixture. Particle–turbulence interaction (turbulence modulation) is described by a two-way coupling model. The drag, lift and gravitation forces are incorporated into the system of equations using appropriate closure equations. A finite difference numerical scheme was used for the solution of the set of the governing equations and the results of the model were validated by comparison with data from several experiments. The influence of two types of particles, namely glass and electrocorundum, of different sizes and different loadings on the velocity and turbulence structure of the jet is examined. The computational results show the influence of the particulate phase on the velocity and turbulence structure of the jet.The significance of this study is that for the first time it presents explicitly the full RANS equations for a fluid jet with particles in an unabridged way and specifies the entire set of closure relations that are used for fluid–particle interactions including the equations for the extended k–ε model, the two-way particle–turbulence interactions and turbulence modulation as well as the inclusion of a lateral Saffman force.     

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     

CFD modelling of fast chemical reactions in turbulent liquid flows

In this work an in-house CFD code is used to simulate a single-phase acid–base neutralisation in a tubular reactor. The Reynolds averaged Navier–Stokes (RANS) equations including the k–ε-turbulence model is used to simulate the turbulent flow. Different models are tested to describe the chemical reaction, including the Eddy dissipation concept (EDC) and the presumed probability density function (PDF) models. The EDC-model was developed for gas phase reactions and the objective of this work was to modify the model to make it more suitable for liquid phase reactions. Two different PDF-models are tested, namely the battlement- and the beta-PDF. The simulation results are compared to experimental data and the results has shown that the standard EDC-model is not suitable for liquid phase reactions, a modified version of the model has shown good results. The most promising PDF-model is shown to be the beta-PDF-model.     

Large-eddy simulation and laser diagnostic measurements of mixing in a coaxial jet mixer

Numerical and experimental investigation of the turbulent mixing in a coaxial jet mixer is presented. Laser doppler velocimetry (LDV) and planar laser induced fluorescence (PLIF) were applied for measurements of velocity and scalar fields and their fluctuations. Numerical simulations were performed using large-eddy simulation and RANS with different closure models. These results are used for validation of numerical models and a detailed study of flow physics within the recirculation zone.     

Validation of CFD simulations of a stirred tank using particle image velocimetry data

Methods for validating CFD simulations based on the Reynolds Average Navier-Stokes equation (RANS) against Particle Image Velocimetry (PIV) measurements are investigated and applied to one of the most common problems in the chemical process industry — the prediction of flow field in a stirred vessel. A total of 1024 sequential instantaneous 2D velocity fields along the central axial plane of a stirred vessel with a P-4 axial impeller are obtained through PIV measurement. From the PIV data, the mean velocity, turbulent kinetic energy, Reynolds stresses and dissipation rate fields are extracted. By introducing several tools to quantify the similarities and differences between two-dimensional fields, CFD predictions of the flow field are validated against PIV data. Furthermore, using PIV and LDV data, the effect of boundary conditions on CFD simulation results is examined. The effect of different Reynolds stress closures on the flow prediction is also studied.     

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     

Effects of the variation of mass loading and particle density in gas-solid particle flow in pipes

The method of two dimensional Reynolds Averaged Navier-Stokes (RANS) equations has been employed for the simulation of turbulent particulate flow. This approach was fitted with appropriate closure equations that take into account all the pertinent forces and effects on the solid particles, such as: particle-turbulence interactions; turbulence modulation; particle-particle interactions; particle-wall interactions; gravitation, viscous drag and lift forces. The flow domain in all cases was a cylindrical pipe and the computations were carried for upward pipe flow. The finite volume technique was used for the numerical solution of the governing and closure equations. The results show the effect of loading and particle density on the profiles of the velocity, the turbulence intensity and the solids concentration.     

Turbulence modelling of multiphase flow in high-pressure trickle-bed reactors

Computational fluid dynamics (CFD) has been used as a successful tool for single-phase reactors. However, fixed-bed reactors design depends overly in empirical correlations for the prediction of heat and mass transfer phenomena. Therefore, the aim of this work is to present the application of CFD to the simulation of three-dimensional interstitial flow in a multiphase reactor. A case study comprising a high-pressure trickle-bed reactor (30 bar) was modelled by means of an Euler-Euler CFD model. The numerical simulations were evaluated quantitatively by experimental data from the literature. During grid optimization and validation, the effects of mesh size, time step and convergence criteria were evaluated plotting the hydrodynamic predictions as a function of liquid flow rate. Among the discretization methods for the momentum equation, a monotonic upwind scheme for conservation laws was found to give better computed results for either liquid holdup or two-phase pressure drop since it reduces effectively the numerical dispersion in convective terms of transport equation.After the parametric optimization of numerical solution parameters, four RANS multiphase turbulence models were investigated in the whole range of simulated gas and liquid flow rates. During RANS turbulence modelling, standard k-ε dispersed turbulence model gave the better compromise between computer expense and numerical accuracy in comparison with both realizable, renormalization group and Reynolds stress based models. Finally, several computational runs were performed at different temperatures for the evaluation of either axial averaged velocity and turbulent kinetic energy profiles for gas and liquid phases. Flow disequilibrium and strong heterogeneities detected along the packed bed demonstrated liquid distribution issues with slighter impact at high temperatures.     

Characteristic time scales for predicting the scalar flux at a free surface in turbulent open‐channel flows

The purpose of this study is to predict the turbulent scalar flux at a free surface subject to a fully developed turbulent flow based on a hydrodynamic analysis of turbulence in the region close to the free surface. The effect of the Reynolds number on turbulent scalar transfer mechanisms is extensively examined. A direct numerical simulation technique is applied to achieve the purpose. The surface‐renewal approximation is used to correlate the free‐surface hydrodynamics and scalar transport at the free surface. Two types of characteristic time scales have been examined for predicting turbulent scalar flux. One is the time scale derived from the characteristic length and velocity scale at the free surface. The other is the reciprocal of the root‐mean‐square surface divergence. The results of this study show that scalar transport at the free surface can be predicted successfully using these time scales based on the concept of the surface‐renewal approximation. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Numerical Investigation of Three‐Dimensional Bubble Column Flows: A Detached Eddy Simulation Approach

Numerical simulations were performed employing detached eddy simulation (DES) in a three‐dimensional transient Euler‐Euler framework for bubble columns, and all the computational fluid dynamics results were compared with a k‐? model and available experimental data. The numerical results are in good agreement with the experiments in predicting the time‐averaged axial velocity and turbulent kinetic energy profiles. The flow‐resolving capabilities of the DES model are highlighted, and it is shown that the DES turbulence model can be efficiently used for simulating flow field and turbulent quantities in the case of bubble columns.     

Investigation of Energy Loss Mechanisms in Cyclone Separators

Based on the transient Navier‐Stokes equation of an incompressible Newtonian fluid, a vorticity form of the mean mechanical energy equation is derived which is suitable for strongly swirling flow or vortex flow, and reveals the mechanism of mean mechanical energy losses in cyclone separators. Results show that the mean mechanical energy losses in cyclone separators are mainly caused by mean viscous dissipation, turbulent diffusion, and turbulent energy production in a steady turbulent flow. Order‐of‐magnitude analysis indicates that the rate of local turbulent energy production and mean viscous dissipation is related to the local turbulent Reynolds number at each point in cyclone separators. A large local turbulent Reynolds number designates the turbulent energy production as the primary contributor to mean mechanical energy losses, whereas in the case of a small turbulent Reynolds number the order‐of‐magnitude quotient between the two quantities decreases, indicating the increased significance of the mean viscous dissipation contribution to mean mechanical energy losses. A combination of theoretical analysis and LDV experimental results indicates the mean viscous dissipation is larger in the quasi‐forced vortex region and the boundary layer than in other regions of cyclone separators. The energy losses are mainly caused by turbulent energy production in a majority of the regions (except in the laminar sublayer very close to the wall), especially the largest energy losses in the central quasi‐forced vortex region. Hence, decreasing turbulence is an effective approach for drag reduction in cyclone separators.     

Effects of embedded streamwise vorticity on turbulent mixing

This work concerns the characterization of turbulent flow underlying mixing in the presence of streamwise vorticity. An experimental test section made of a cylindrical tube equipped with seven rows of streamwise vortex generators was designed and constructed for this study. Each row is composed of four vortex generators fixed symmetrically on the tube wall. This new type of mixer, called a high-efficiency vortex (HEV) mixer, generates coherent structures in the form of longitudinal counter-rotating vortices. The resulting flow enhances radial mass transfer and thus facilitates particle dispersion and mixing. The energy cost of this mixer used as an emulsifier has been evaluated as up to a thousand times less than that of other static mixers for a given interface area generation (Lemenand et al. [1] and [2]).The aim of this work is to study experimentally and numerically the turbulence structure and mixing properties of the flow composed of streamwise vortices superimposed on a turbulent flow, in particular the more energetic structures present in the base flow. Experiments were carried out in the test section in a flow loop by measuring instantaneous velocities by laser Doppler anemometry. Numerical simulations of the velocity distribution and turbulence field inside the flow were conducted for various turbulence models using a computational fluid dynamic CFD package. Attention is focused on the evolution and distribution of turbulent kinetic energy dissipation as the underlying mechanism for turbulent mixing. Mean and turbulent quantities are compared with experimental results.Both laboratory experiments and numerical simulations show a vortex zone behind each tab that could explain the efficiency of the HEV mixer. This study provides a basis for understanding the physical mechanisms in the mixing and homogenizing of the flow and therefore the efficiency of the mixer.     

不可压缩湍流反应流动的直接模拟和RANS-SOM燃烧模型的检验

The second-order moment combustion model, proposed by the authors is validated using the direct numerical simulation （DNS） of incompressible turbulent reacting channel flows. The instantaneous DNS results show the near-wall strip structures of concentration and temperature fluctuations. The DNS statistical results give the budget of the terms in the correlation equations, showing that the production and dissipation terms are most important. The DNS statistical data are used to validate the closure model in RANS second-order moment （SOM） combustion model. It is found that the simulated diffusion and production terms are in agreement with the DNS data in most flow regions, except in the near-wall region, where the near-wall modification should be made, and the closure model for the dissipation term needs further improvement. The algebraic second-order moment （ASOM） combustion model is well validated by DNS.