(41b) Spatially-Averaged Models for Large-Scale Gas-Solid Flows
However, due to computational limitations a fully resolved simulation of industrial scale reactors is still unfeasible. In our previous study (Schneiderbauer 2017), we have presented a spatially-averaged two-fluid model (SA-TFM), which enables the coarse grid simulation of dense large-scale gas-solid flows. However, these averaged TFM equations require constitutive models for the residual correlations appearing due to averaging. On the one hand, the unresolved part of the gas-solid drag force has been derived by employing a series expansion to the microscopic drag coefficient and on the other hand the Reynolds-stress like contributions are closed similar to Boussinesq-approximation in single phase flows. The subsequent averaging of this linearized drag force reveals that the unresolved part of the interphase momentum exchange is a function of the turbulent kinetic energies (TKE) of both, the gas and solid phase, and the variance of the solids volume fraction. Closure models for these quantities have been derived from first principles.
In contrast to TFM, parcel based approaches, such as MP-PIC (OâRourke & Snider 2010) and DDPM (Cloete & Amini 2016), have become quite popular recently to access the numerical simulation of large scale gas-solid flows. However, similar to TFM computational limitations restrict such simulations of large scale gas-solid flows to coarse grids (for the continuous phase) as well (Li et al. 2012; Benyahia & Sundaresan 2012). In this paper, we show that the constitutive relation derived for the SA-TFM apply also to the parcel based approaches since the parcel approach represents a Lagrangian discretization of the solids transport and momentum equations. We refer this coarse grained parcel approach as SA-DDPM.
Finally, the SA-TFM and SA-DDPM models are validated for three different fluidization regimes: First, we apply these coarse grid models to the NETL challenging problem (Panday et al. 2014), where the flow of Geldart A and B particles in a riser section of a circulating fluidized bed has been studied. Second, the predictions of SA-TFM in the turbulent fluidization regime is examined (Zhu et al. 2008). Finally, a bubbling fluidized bed is studied (Zhu et al. 2008). The numerical results obtained on coarse grids demonstrates that the SA-TFM and SA-DDPM reveal nearly identical results and further fairly good agreement of pressure drop, solids volume fraction as well as velocity profiles. Thus, the results proof the SA-TFM and SA-DDPM are applicable to a wide range of particle diameters and different fluidization regimes.
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