Sliding Mesh Model

The sliding mesh model is the most rigorous and informative solution method for stirred tank simulations. Transient simulations using this model can capture low-frequency (well below the blade passing frequency) oscillations in the flow field (Bakker et ak, 2000 Roussinova et al., 2000) in addition to those that result from the periodic impeller-baffle interaction. 

An alternative way to bypass calculation of the startup period is to solve for a steady-state solution first using the MRF model. The MRF model (Section 5-5.2) provides a solution for the moving impeller at a fixed orientation relative to the baffles. Tools are available in commercial codes to use the solution data from the MRF simulation and apply it to the sliding mesh simulation as an initial condition. A moderately coarse time step can be nsed initially (say, corresponding to a 10° rotation, as in the example above) and rednced at a qnicker rate than would otherwise be advisable. This approach can also be nsed if inflow and outflow boundaries are present or if a multiphase calculation is to be performed. In the case of multiphase flows, however, care must be taken to wait until the periodic steady-state condition has been reached before introducing the secondary phase. 

2 Validation ofthe Sliding Mesh Model. One validation of the sliding 

3 Unstable Flows. In recent years, much attention has been paid to instabilities that are observed in stirred tanks. These instabilities typically have frequencies that are low compared to the impeller frequency and involve the slow asymmetric wobble of material or momentum fi om one side of the vessel to the other. Instabilities of this type can be predicted using the sliding mesh technique on a 360° model of a stirred tank, particularly if the LES turbulence model is 

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To model the geometry of the impeller exactly, a 3D simulation must be performed. A number of solution approaches are available to incorporate the motion of the impeller, and the computational grid used must be able to adapt to the solver method employed. The models in popular use today are reviewed in the following sections. Particular attention is paid to the sliding mesh model, the most rigorous of them all. The solver methods described are aU designed to capture the motion of a rotating impeller in a stationary tank, but they vary in accuracy. Three of the models are steady-state and one is time-dependent. 

Figure 5-14 Flow number based on experimental measurements and computed by the sliding mesh model.

When the VOF model is solved in conjunction with the sliding mesh model, the smallest required time step for the two models must be used. Since a smaller time step is often required for the VOF calculation than for the sliding mesh... 

S.3 Turbulence. As discussed in Section 5-2, there are several steady-state turbulence models in widespread use today. These so-called RANS models address a time-averaged state of the fluid such that all turbulent fluctuations are represented by averaged values. The RANS models are often used with both the MRF and sliding mesh models, as well as with many other transient models used in CFD analysis. This practice is justified in part because the time scales of turbulence fluctuations are assumed small compared to those of the other processes being modeled, such as the blade passing time in a stirred tank. It has also been justified because until recently, other more rigorous treatments have not been available in commercial software or solvable in a realistic time on the computers of the day. 

Isosurfaces of vorticity trailing from a rotating impeller in a sliding mesh model... 

There are two exceptions to the use of the method described above, in which the flow field calculation can be disabled during the species calculation. First, if the sliding mesh model is used, the flow field data are required for each time step, so it is not possible to disable the flow field calculation to perform the species transport calculation. Second, if the tracer is to be added through an inlet or dip tube for a finite period of time, after which the inlet flow is disabled, calculation of the flow field should resume at that time, especially if the inlet delivers a jet of significant momentum to the vessel. 

To simulate turbulent flows, Reynolds-averaged Navier-Stokes (RANS) equations form the basis for most codes. Several turbulence models are usually provided. A new turbulence model may also usually be incorporated via user-defined routines. Recently, many of the commercial CFD codes have announced the inclusion of large eddy simulation (LES) capabilities. Considering the importance of rotating equipment used in reactor engineering applications, the ability to handle multiple reference frames or sliding meshes is important. Most leading commercial CFD codes provide... 

FIGURE 10.3 Approaches to modeling flow in stirred reactors, (a) Black box approach, (b) sliding mesh approach, (c) multiple reference frame or inner-outer approach, (d) snapshot approach. 

Ranade, V.V, Tayaliya, Y. and Choudhury, D. (1997), Modeling of flow in stirred vessels comparison of snapshot, multiple reference frame and sliding mesh approaches. Presented at 16th NAME Meeting, Williamsberg, June 22-21. 

Basara et al [3] simulated single- and two-phase turbulent flows in stirred vessels equipped with six- and four blade Rushton-t3q)e turbines using the sliding mesh impeller method. To describe turbulence in the liquid phase a standard k-e model was used for single phase calculations and an extended k-e model was employed for the two-phase simulations. These simulations were performed in transient mode with 1 (ms) time steps. The whole calculation contains 3900 time steps, which means approximately 4s of real time and 17 complete rotations of the impeller. One such simulation took 13 days of CPU time using an Intel single processor with 2.6 GHz). The flow patter predictions were compared with experimental data and fair agreement was obtained. It was stated that the standard k-e model over-predicted the... 

The third standard for modeling rotating impellers is the sliding mesh approach (Rai 1985). Here, a grid is attached to the impeller that does not extend much beyond the outer radius of the impeller. This is the most computationally intensive of the three standard techniques, but also the most accurate. In principle, it fully captures the effect of the agitator on the flow. 

For the hybrid model (ANSYS FLUENT POLYFLOW), the moving parts were taken into consideration using a sliding and dynamic mesh model in FLUENT. As shown in Fig. 4, smoothing and dynamic layering methods were adopted to adjust the mesh of a zone with moving and/or deforming boundaries. The total cell count for the hybrid model is 126,000. 

In this section, two methods of modeling the impeller have been discussed general mathematical models and use of experimental data, The newer sliding mesh techniques were reviewed earlier in this chapter. A final alternative which has been suggested is to model the impeller as a source of momentum. It is not clear, however, how this method should be applied, and successful simulations have never, to the knowledge of the author, been published. 

It has been demonstrated that accurate representation of the impeller is central to obtaining accurate CFD simulations. Four alternatives are available for impeller modeling. The sliding mesh technique requires no measurements or assumptions but consumes large amounts of CPU time. Impeller modeling based on generalized mathematical models assumes that there is no interaction between the impeller and... 

Where new models are being developed, a qualitatively reasonable result is the first requirement, and convergence criteria are typically looser. Luo et al., who reported an early sliding mesh simulation in a short note, used the flow pattern became cyclically repeatable as their convergence criterion [13]. Gosman et al., who report early multiphase simulations, simply required that residuals in the equations solved become smaller than a prescribed tolerance. [9]... 

Preprosessing and grid generation was done with the commercial Fluent Gambit 1.3. The CFD code Fluent 5.5 was used in the simulation. Standard k-e turbulence model and standard wall functions were used. Multiple reference frame method was used in all simulations instead of the computationally slower sliding mesh method. Simulations were done in one phase (t). 

Figure 5-19 shows an example of the dispersion of a chemical tracer in a stirred tank. A standard pitched blade turbine is used to mix two waterlike materials. The neutrally buoyant tracer is injected at time zero as a blob above the impeller, as shown on the top left in the figure. The flow field is calculated using the sliding mesh and LES models, and the dispersion of the tracer is derived from the flow field. The blob is stretched and the chemical is mixed with the rest of the fluid over time. It is interesting to see that despite the fact that there are four impeller blades and four baffles, the concentration field is not symmetric because of the off-axis injection. The consequence is that the full tank needs to be modeled instead of a 90° section. Bakker and Fasano (1993b) presented a successful comparison between blend time predicted by CFD and calculated from experimental correlations. 

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