Numerical Simulation of Laminar Flow Field in a Stirred Tank

Stirred tanks are used extensively in process industry and one of the most commonly used impellers in stirred tanks is the R.ushton disk turbine. Surprisingly few data are available regarding flow and mixing in stirred-tank reactors with Rushton turbine in the laminar regime, in particular the laminar flow in baffled tanks.In this paper, the laminar flow field in a baffled tank stirred by a standard R.ushton turbine is simulated with the improved inner-outer iterative method. The non-inertial coordinate system is used for the impeller region, which is in turn used as the boundary conditions for iteration. It is found that the simulation results are in good agreement with previous experiments. In addition, the flow number and impeller power number calculated from the simulated flow field are in satisfactory agreement with experimental data. This numerical method allows prediction of flow structure requiring no experimental data as the boundary conditions and has the potential of being used to scale-up and design of related process equipment.

NUMERICAL SIMULATION OF 3-D DENSE SOLID-LIQUID TWO-PHASE TURBULENT FLOW IN A NON-CLOGGING MUD PUMP

A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to TECPLOT as the post-processor, the simulation results isvisualized. The results show the main flow characteristics: There exists backflow and aberrantvelocities at inlet area and a relative velocity slip between two phases; A jet-wake flow pattern isdiscerned around the shroud-suction side area; The relative velocity vector of solid phase iscloser to the pressure surface than that of liquid phase and the trend is more obvious with theincrease of diameter; The kinetic energy of turbulence k and the dissipation rate e reach theirpeaks at the corner of pressure and suction surface. The simulation results show a good agreementwith the experimental flow features in the impeller channel, which prove the turbulent model used isvalid and provide a theoretical design basis to non-clogging pumps.

Numerical Simulation of Gas Holdup Distribution in a Standard Rushton Stirred Tank Using Discrete Particle Method

The discrete particle method was used to simulate the distribution of gas holdup in a gas-liquid standard Rushton stirred tank. The gas phase was treated as a large number of bubbles and their trajectories were tracked with the results of motion equations. The two-way approach was performed to couple the interphase momentum exchange. The turbulent dispersion of bubbles with a size distribution was modeled using a stochastic tracking model, and the added mass force was involved to account for the effect of bubble acceleration on the surrounding fluid. The predicted gas holdup distribution showed that this method could give reasonable prediction comparable to the reported experimental data when the effect of turbulence was took into account in modification for drag coefficient.

NUMERICAL SIMULATION FOR INCOMPRESSIBLE TURBULENT FLOW IN THE IMPELLER OF SEWAGE PUMP

The 3-D turbulent flow in the impeller of sewage pump is simulated. Thetime-averaged N-S equations and the kappa-epsilon turbulent model is modified. The calculation iscarried out in body-fitted coordinated grid by applying SIMPLE-C algorithm. The calculated velocity,pressure distributions of the turbulent flow in the sewage pump are obtained for the first time,which will be helpful for the optimal design and performance prediction of sewage pumps on the basisof flow field simulation.

Numerical simulation on turbulent flow field in convergentdiveroent nozzle

Because of the complication of turbulence＇s mechanism and law as well as the jet pressure in nozzle is difficult to test by experiment, five turbulent models were applied to numerically simulate the turbulent flow field in convergent-divergent nozzle. Theory analysis and experiment results of mass flow rates conclude that the RNG k-ε model is the most suitable model. The pressure distribution in the convergent-divergent nozzle was revealed by computational fluid dynamic （CFD） simulating on the turbulent flow field under different pressure conditions. The growing conditions of cavitation bubbles were shown; meanwhile, the phenomena in the experiment could be explained. The differential pres- sure between the upstream and downstream in nozzle throat section can improve the cavitating effect of cavitation water jet.

Numerical Simulation of the Effect of Air Distribution on Turbulent Flow and Combustion in a Tubular Heating Furnace

A three-dimension full-size numerical simulation of the effect of air distribution on turbulent flow and combustion in a tubular heating furnace was carried out. A standard k –ε turbulent model, a simplified PDF combustion model and a discrete ordinate transfer radiation model were used. The hybrid grid combining a structured and a non-structured grid was generated without any simplification of the complicated geometric configuration around the burner. It was found that the multistage combustion could reduce and control the peak value of temperature. At the same time, it was concluded that the amount of primary air had little effect on the global distribution of velocity and temperature in the furnace, but a great effect on that around the burner. It is recommended that 45% - 65% of the total amount of air be taken in in primary air inlets in the furnace. All the results are important to optimize the combustion progress.

THE NUMERICAL SIMULATION OF TURBULENT FLOWS OF NEWTONIAN AND A SORT OF NON-NEWTONIAN FLUID IN 180-DEGREE SQUARE SECTIONED BEND

Using k- model of turbulence and measured wall functions, turbulent flows of Newtonian (pure water) andasort of non-Newtonian fluid (dilute, drag-reduction solution of polymer) in a 180-degree curved bend were simulated numerically. The calculated results agreed well with the measured velocity profiles. On the basis of calculation and measurement, appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.

Numerical simulation of micro-mixing in gas–liquid and solid–liquid stirred tanks with the coupled CFD-E-model

The coupled CFD-E-model for multiphase micro-mixing was developed,and used to predict the micro-mixing effects on the parallel competing chemical reactions in semi-batch gas–liquid and solid–liquid stirred tanks.Based on the multiphase macro-flow field,the key parameters of the micro-mixing E-model were obtained with solving the Reynolds-averaged transport equations of mixture fraction and its variance at low computational costs.Compared with experimental data,the multiphase numerical method shows the satisfactory predicting ability.For the gas–liquid system,the segregated reaction zone is mainly near the feed point,and shrinks to the exit of feed-pipe when the feed position is closer to the impeller.Besides,surface feed requires more time to completely exhaust the added H+solution than that of impeller region feed at the same operating condition.For the solid–liquid system,when the solid suspension cloud is formed at high solid holdups,the flow velocity in the clear liquid layer above the cloud is notably reduced and the reactions proceed slowly in this almost stagnant zone.Therefore,the segregation index in this case is larger than that in the dilute solid–liquid system.

NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS OVER DREDGED TRENCHES

A 3- D free surface flow in open channels based on the Reynolds equations with the k-ε turbulence closure model is presented in this paper. Insted of the 'rigid lid' approximation, the solution of the free surface equation is implemented in the velocity-pressure iterative procedure on the basis of the conventional SIMPLE method. This model was used to compute the flow in rectangular channels with trenches dredged across the bottom. The velocity, eddy viscosity coefficient, turbulent shear stress, turbulent kinetic energy and elevation of the free surface can be obtained. The computed results are in good agreement with previous experimental data.

Numerical Simulation of Macroscopic Mixing in a Rushton Impeller Stirred Tank

The macroscopic mixing in a stirred tank with different tracer injection locations, impeller speeds and impeller positions is simulated numerically by solving the transport equation of the tracer based on the whole flow field in the baffled tank with a Rushton disk turbine numerically resolved using the improved inner-outer iterative procedure. Predicted mixing time is compared well with the literature correlations. The predicted residence time distribution of the stirred tank is very close to the present experimental results. The effect of the installation of a draft tube on the mixing time and residence time distributions is addressed.

Numerical Simulation on Gas-Solid Two-Phase Turbulent Flow in FCC Riser Reactors(Ⅱ) Numerical Simulation on the Gas-Solid Two-Phase Turbulent Flow

Numerical simulation on the flow,heat transfer and cracking reactions in commercial fluid catalyticcracking(FCC)riser reactors were carried out employing the developed turbulent gas-solid two-phase flow-reac-tion model for FCC riser reactors given in Part Ⅰ of the present paper.Detailed information about the turbulentflow fields in the riser reactor obtained revealed the basic characteristics of the gas-solid two-phase turbulentflows when heat transfer and catalytic cracking reactions were co-existing in the riser.Results showed that thedistributions of the flow,the turbulence kinetic energy and the catalyst particle concentration are not uniform inthe axial,radial and tangential directions.The most complicated part of the riser reactor is the feed injectingzone.The complicated configuration of the turbulent gas-solid two-phase flows would exert a great influence onthe results of interphase heat transfer and cracking reactions.

Numerical Study of Solid-Liquid Two-Phase Flow in Stirred Tanks with Rushton Impeller (Ⅰ) Formulation and Simulation of Flow Field

The critical impeller speed, N_(JS), for complete suspension of solidparticles in the agitated solid-liquid two-phase system in baffled stirred tanks with a standardRushton impeller is predicted using the computational procedure proposed in Part Ⅰ. Three differentnumerical criteria are tested for determining the critical solid suspension. The predicted N_(JS)is compared with those obtained from several empirical correlations. It is suggested the mostreasonable criterion for determining the complete suspension of solid particles is the positive signof simulated axial velocity of solid phase at the location where the solid particles are mostdifficult to be suspended.

Large Eddy Simulation of Liquid Flow in a Stirred Tank with Improved Inner-Outer Iterative Algorithm

In this study, the large eddy simulation technique was applied on the flow in a baffled stirred tank driven by a Rushton turbine at Re=29000. The interaction between the rotating impeller and the static baffles was accounted for by means of the improved inner-outer iterative algorithm. The sub-grid scale model was a conventional Smagorinsky model. The numerical solution of the governing equations was conducted in a cylindrical staggered grid. The momentum and the continuity equations were discretized using the finite difference method, with a third-order QUICK scheme used for convective terms. The phase-resolved predictions were compared with the experimental data of Wu and Patterson and good agreement was observed for both the mean and the turbulence quantities. They were much better than the Reynolds-averaged Navier-Stokes model including the Reynolds Stress Model for simulating the turbulence. The study also suggests the feasibility of LES in combination with the improved inner-outer iterative algorithm for the simulation of turbulent flow in stirred tanks.

Large Eddy Simulations of Flow Instabilities in a Stirred Tank Gen-erated by a Rushton Turbine

The aim of this work is to investigate the flow instabilities in a baffled, stirred tank generated by a single Rushton turbine by means of large eddy simulation （LES）. The sliding mesh method was used for the coupling between the rotating and the stationary frame of references. The calculations were carried out on the ＂Shengcao-21C＂ supercomputer using a computational fluid dynamics （CFD） code CFX5. The flow fields predicted by the LES simulation and the simulation using standard κ-ε model were compared to the results from particle image velocimetry （PIV） measurements. It is shown that the CFD simulations using the LES approach and the standard κ-ε model agree well with the PIV measurements. Fluctuations of the radial and axial velocity are predicted at different frequencies by the LES simulation. Velocity fluctuations of high frequencies are seen in the impeller region, while low frequencies velocity fluctuations are observed in the bulk flow. A low frequency velocity fluctuation with a nondimensional frequency of 0.027Hz is predicted by the LES simulation, which agrees with experimental investigations in the literature. Flow circulation patterns predicted by the LES simulation are asymmetric, stochastic and complex, spanning a large portion of the tanks and varying with time, while circulation patterns calculated by the simulation using the standard κ-ε model are symmetric. The results of the present work give better understanding to the flow instabilities in the mechanically agitated tank. However, further analysis of the LES calculated velocity series by means of fast Fourier transform （FFT） and/or spectra analysis are recommended in future work in order to gain more knowledge of the complicated flow phenomena.

Numerical simulation of flow field and optimization of structure parameters of seed precipitation tank for production of alumina

In order to overcome the defects of air-agitated seed precipitation, such as scaring, liquid short-(circuiting,) the three-dimension flow fields with different structure are numerically simulated by computational fluid dynamics software. Euler/Euler approach was used to study the effects of structure on the flow field in the tank. Multi-fluid model, body-fitted coordinates and multi-block gird were adopted in the simulation. The simulating results are well consonant with the practical situations. The flow field is improved obviously when the flow velocity increases from (0.089m/s) to 0.1920.300m/s at the bottom of the optimized tank and therefore the scaring is reduced greatly in the industrial production. With a gathering sill, the problem of short-circuiting, which always appeares in the upper of the tank, can be solved very well.

Computer Simulation of Turbulent Flow through a Hydraulic Turbine Draft Tube

Based on the Naviev-Stokes equations and the standard κ-ε turbulence model, this paper presents the derivation of the governing equations for the turbulent flow field in a draft tube. The mathematical model for the turbulent flow through a draft tube is set up when the boundary conditions, including the inlet boundary conditions, the outlet boundary conditions and the wall boundary conditions, have been implemented. The governing equations are formulated in a discrete form on a staggered grid system by the finite volume method. The second-order central difference approximation and hybrid scheme are used for discretization. The computation and analysis on internal flow through a draft tube have been carried out by using the simplee algorithm and cfx-tasc flow software so as to obtain the simulated flow fields. The calculation results at the design operating condition for the draft tube are presented in this paper. Thereby, an effective method for simulating the internal flow field in a draft tube has been explored.

Effect of pitched short blades on the flow characteristics in a stirred tank with long-short blades impeller

This work focuses on the design improvement of the long-short blades(LSB)impeller by using pitched short blades(SBs)to regulate the flow field in the stirred vessel.After mesh size evaluation and velocity field validation by the particle image velocimetry,large eddy simulation method coupled with sliding mesh approach was used to study the effect of the pitched SBs on the flow characteristics.We changed the inclined angles of the SBs from 30°to 60°and compared the flow characteristics when the impeller was operated in the down-pumping and up-pumping modes.In the case of down-pumping mode,the power number is relatively smaller and vortexes below the SBs are suppressed,leading to turbulence intensification in the bottom of the vessel.Whereas in the case of up-pumping mode,the axial flow rate in the center increased significantly with bigger power number,resulting in more efficient mass exchange between the axial and radial flows in the whole vessel.The LSB with 45°inclined angle of the SBs in the up-pumping mode has the most uniform distributions of flow field and turbulent kinetic energy compared with other impeller configurations.

Numerical simulation of three-dimensional combustion flows

A finite-rate method is used to simulate the three-dimensional combustion process in a plasma generator with CH4 as the fuel. The simulation was run with RNG k-ε model to simulate turbulence, with eddy-dissipation-concept (EDC) model to simulate the combustion and with discrete ordinates model to simulate radiation. The numerical results show that the flow field characteristics and the parameter distributions are under the condition of rich fuels, and these results provide valuable information when optimizing the plasma generator design and organizing its flow fields.