Z. Jaworski

CFD Study of Homogenization with Dual Rushton Turbines—Comparison with Experimental Results: Part I: Initial Studies☆

The transient responses of six conductivity probes distributed throughout a stirred tank of diameter T (= 0.72m) and an aspect ratio of 2, equipped with dual-Rushton turbines ( D = T/2 ), were measured. Three impeller speeds (75, 100 and 150 rpm) were used and the terminal mixing times, u 95, were also determined. These experiments were also modelled using the structured Fluent CFD code based on the finite volume method with a sliding mesh option. The k − ɛ and RNG k − ɛ models both predicted similar local axial and radial mean velocities. However, both also predicted large areas of tangential circulation in a direction opposite to the impeller rotation and all the local turbulence quantities and the tangential component of mean velocity were considerably different. Stability problems with the RNG k − ɛ model in the version of the Fluent™ CFD code available for this work meant that transient conductivity responses could not be computed using this method. On the other hand, the k − ɛ model gave stable solution and many features of the experimental transient responses and those from the model were similar. However, the computed θ 95 were about two to three times longer than the measured values. It is suggested this difference arises because the mass exchange between the four distinct axial-radial circulation loops was highly underpredicted by CFD.

CFD Study of Homogenization with Dual Rushton Turbines—Comparison with Experimental Results: Part II: The Multiple Reference Frame☆

Experimental transient responses of six conductivity probes distributed throughout a stirred tank have been used to determine the terminal mixing times, θ95, in the turbulent flow regime. These transients were simulated using a fully predictive mode of the structured Fluent CFD code based on a sliding mesh method1. Here, a new procedure based on a multiple reference frame (MRF) method with grid refinement is employed. Both k-E and the standard RNG k-ɛ models with the MRF substantially eliminated the wrongly predicted large areas of tangential circulation in a direction opposite to the impeller rotation reported elsewhere. The simulated distribution of the tracer in time using the new approach is also more realistic and the transient responses are shorter, though the computed mixing times were still about two times longer than the measured values. These computations by k-ɛ E and RNG k-ɛ E models with MRF and mesh refinements for momentum transfer and calculating concentration fields in a single, stationary frame of reference represent an improvement in comparison with those predictions obtained without it.

THE EFFECT OF SIZE, LOCATION AND PUMPING DIRECTION OF PITCHED BLADE TURBINE IMPELLERS ON FLOW PATTERNS: LDA MEASUREMENTS AND CFD PREDICTIONS

A combined LDA-CFD (MRF method) study has been undertaken of the turbulent flow associated with two sizes of 6-bladed 45° pitch blade turbine at three clearances, either pumping up or down. Good quantitative agreement for mean velocity vectors has been obtained but that for RMS values was poor. The mean discharge angle is more vertical: (a) for the smaller impeller at all clearances; (b) for both sizes when an impeller approaches a surface towards which it is pumping.

The Influence of the Addition Position of a Tracer on CFD Simulated Mixing Times in a Vessel Agitated by a Rushton Turbine

Previous papers on simulated mixing times in stirred vessels using CFD have sometimes given predictions in good agreement with empirical equations based on experiments and some have not. In this study, mixing times have been measured for a vessel agitated by a Rushton turbine and compared with those predicted by CFD. The flow field was developed using the sliding mesh approach and computational parameters and the point of addition of the tracer have been varied. The simulations were very insensitive to the former whilst the radial distance from the wall of the latter had a very profound effect on both the mixing time and the development of the concentration field. When the addition point was close to the sliding mesh surface, the simulation was in good agreement with experimental values and empirical predictions whilst that for a point close to the wall was much too long. This finding may explain the contradictions in the literature.

Modelling of the Turbulent Wall Jet Generated by a Pitched Blade Turbine Impeller: The Effect of Turbulence Model

CFD modelling results are presented for a fiat-bottomed tank with a pitched blade turbine impeller and four baffles. Six turbulence models, i.e. the standard k–ɛ , the RNG k–ɛ , the realizable k–ɛ , the Chen-Kim k–ɛ , the optimized Chen–Kim k–ɛ and the Reynolds stress model were used in the modelling. The simulated values of the tangential and axial mean velocity components along with the kinetic energy of turbulence were compared for the wall jet region with the corresponding experimental data from LDA. The best results were obtained for the standard k–ɛ model with a good accuracy for the mean velocity and a significant underprediction of the turbulent kinetic energy.

Predicting the tangential velocity field in stirred tanks using the Multiple Reference Frames (MRF) model with validation by LDA measurements

Publisher Summary This chapter illustrates the use of multiple reference frames (MRF) to model the three-dimensional flow field in a stirred tank agitated with Rushton turbines and pitched-blade turbines. The tangential velocity distribution above the impeller is correctly predicted in regions where the magnitude of the flow is low relative to the impeller tip speed. The occurrence of counter-intuitive reverse swirl in the simulation results is identified as being caused by poor convergence, coarse grid density, the turbulence model of choice and the location of the MRF interface boundary. To eliminate reverse swirl and obtain accurate calculations of integral quantities, such as, power number, the grid must be sufficiently refined in the near impeller region, and adjacent to the walls experiencing direct impingement of the impeller discharge jet. Convergence of the solution, i.e., minimization of errors in variable equations, must be sufficiently deep. The κ-ɛ based models were more likely to produce the reverse swirl than the RSM model. It can be concluded that steady-state modeling with the MRF is a valuable predictive tool in stirred tank analysis and design when single phase, turbulent flow occurs, provided that—a refined grid near the impeller, and wall and baffles in the discharge stream is used; and a vertical interface boundary close to the mid-point between the tip of the impeller and the inner edge of the baffle and two horizontal ones which depend on the impeller type and should correspond to those used in this work.

CFD modelling of turbulent macromixing in stirred tanks. Effect of the probe size and number on mixing indices

A numerical, CFD based approach to model the batch macromixing process in stirred tanks is presented. Simulation method of the effects of the probe size and number on various mixing indices is described in details. The method is successfully validated with the help of published experimental data. The investigated probe effects are estimated and discussed for both the exhaustive and random sampling of the liquid mixture. Important conclusions referring to the experimental and numerical studies of the process are also specified.

Towards multiscale modelling in product engineering

A concept of multiscale modelling of product manufacturing based on integration of three modelling methods currently applied at different scales of length and time: process system modelling, computational fluid dynamics and computational chemistry was presented. Major features of the three key types of modelling in the chemical and process industries were briefly described. The first applications and mutual benefits of joint use of two of the three approaches were presented along with the perspectives for the full integration of all three methods. The crucial role of a universal interface, such as the CAPE-OPEN standard, was emphasized.

Two-Phase Laminar Flow Simulations in a Kenics Static Mixer: Standard Eulerian and Lagrangian Approaches

Modelling of two-phase liquid–liquid flows through a Kenics static mixer by means of computational fluid dynamics (CFD) has been presented. The two modelled phases were assumed viscous and Newtonian with the physical properties mimicking an aqueous solution in the continuous and an oil in the dispersed (secondary) phase. Three levels of superficial flow velocity were chosen to result in Reynolds numbers ( Re ) equal to 100, 200 and 400, respectively. The numerical simulations were performed with the help of the commercial software Fluent™, version 5.4.8. The modelling involved both block-structured grids and fully non-structured grids for a static mixer with 10 Kenics inserts. Each of the two grid types had three density levels. The algebraic slip mixture (ASM) model was used in the Eulerian frame of reference and enabled the prediction of the pressure drop across the inserts, the local velocities and volume fraction of the two phases. The Lagrangian approach was used to track the trajectory of dispersed fluid elements (drops) in the simulated static mixer. The particle history was analysed in terms of the residence time in the mixer.

Quantification of the Radiative and Convective Heat Transfer Processes and their Effect on mSOFC by CFD Modelling

Abstract The CFD modelling of heat transfer in a microtubular Solid Oxide Fuel Cell (mSOFC) stack has been presented. Stack performance predictions were based on a 16 anode-supported microtubular SOFCs sub-stack, which is a component of the overall stack containing 64 fuel cells. Both radiative and convective heat transfer were taken into account in the modelling. The heat flux value corresponded to the cell voltage of 0.7 [V]. Two different cases of the inlet air velocity of 2.0 and 8.5 [ms–1] were considered. It was found that radiation accounted for about 20–30 [%] of the total heat flux from the active tube surface, which means that the convective heat transfer predominated over the radiative one.