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9.5.3 Turbulence Modeling in Swirling Flows

If you are modeling turbulent flow with a significant amount of swirl (e.g., cyclone flows, swirling jets), you should consider using one of FLUENT's advanced turbulence models: the RNG $k$- $\epsilon$ model, realizable $k$- $\epsilon$ model, or Reynolds stress model. The appropriate choice depends on the strength of the swirl, which can be gauged by the swirl number. The swirl number is defined as the ratio of the axial flux of angular momentum to the axial flux of axial momentum:

 S = \frac{{\displaystyle \int} rw {\vec v} \cdot d {\vec A}}{\bar{R} {\displaystyle \int} u {\vec v} \cdot d {\vec A}} (9.5-3)

where $\bar{R}$ is the hydraulic radius.

For flows with weak to moderate swirl ( $S < 0.5$), both the RNG $k$- $\epsilon$ model and the realizable $k$- $\epsilon$ model yield appreciable improvements over the standard $k$- $\epsilon$ model. See Sections  12.4.2, 12.4.3, and 12.19.6 for details about these models.

For highly swirling flows ( $S > 0.5$), the Reynolds stress model (RSM) is strongly recommended. The effects of strong turbulence anisotropy can be modeled rigorously only by the second-moment closure adopted in the RSM. See Sections  12.7 and 12.12 for details about this model.

For swirling flows encountered in devices such as cyclone separators and swirl combustors, near-wall turbulence modeling is quite often a secondary issue at most. The fidelity of the predictions in these cases is mainly determined by the accuracy of the turbulence model in the core region. However, in cases where walls actively participate in the generation of swirl (i.e., where the secondary flows and vortical flows are generated by pressure gradients), non-equilibrium wall functions can often improve the predictions since they use a law of the wall for mean velocity sensitized to pressure gradients. See Section  12.10 for additional details about near-wall treatments for turbulence.

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