The filtered drag force is well accepted as the most important constitutive term in practical coarse-grid simulations of gas-solid flows. Currently, four critical issues including considering the effect of macroscale condition, reducing complexity of the model, improving the scale independence and enhancing the adaptability for different flow regimes, have been addressed in recent studies[1-4] on modeling the filtered drag correlation. To improve the performance of the filtered drag model in these aspects, a novel modeling approach has been developed. In this modeling approach, the modeling database is generated through fully resolved two-fluid model (TFM) simulations coupled with kinetic theory of granular flows in periodic sedimentation systems. To consider the effect of macroscale condition, a new marker, the filtered solid volume fraction at a larger scale whose side length is three times of the filter size, is introduced. The raw data are filtered and binned in terms of the available markers including dimensionless filter size, filtered solid volume fraction, filtered solid volume fraction at the second scale, dimensionless filtered slip velocity and dimensionless filtered gas pressure gradient. A good linear correlation between filtered gas pressure gradient and the bin-averaged filtered drag force has been obtained. And this correlation is independent of the filter size owing to introduction of the filtered solid volume fraction at large scale. Moreover, the effect of the filtered slip velocity on this correlation is only moderate at the dilute region. Based on these features, the ratio between the filtered drag force and filtered gas pressure gradient is treated as the dependent variable and the effect of the filtered slip velocity is neglected to make the modeling process concisely. With these simplifications, the models only correlated to the filtered solid volume fraction at the filter scale and that at the larger scale are developed. Subsequently, the new developed models are evaluated in terms of a priori test and a posteriori test for three typical fluidized regimes including bubbling, turbulent and fast fluidized bed. Compared with the gas pressure gradient-dependent model proposed in our previous study[5],the new developed models exhibit an obvious improvement. Additionally, the predictions of the new developed models have good agreements with experiments and the fine-grid results for different flow regimes.
Reference
[1] Y. Jiang, J. Kolehmainen, Y. Gu, Y.G. Kevrekidis, A. Ozel, S. Sundaresan, Neural-network-based filtered drag model for gas-particle flows, Powder Technol. 346 (2018) 403-413.
[2] J.H. Cloete, S. Cloete, S. Radl, S. Amini, On the choice of closure complexity in anisotropic drag closures for filtered Two Fluid Models, Chem. Eng. Sci. 207 (2019) 379-396.
[3] J. Mouallem, N. Chavez-Cussy, S.R. Niaki, C.C. Milioli, F.E. Milioli, On the effects of the flow macro-scale over meso-scale filtered parameters in gas-solid riser flows, Chem. Eng. Sci. 182(2018) 200-211.
[4] S.R. Niaki, J. Mouallem, N. Chavez-Cussy, C.C. Milioli, F.E. Milioli, Improving the accuracy of two-fluid sub-grid modeling of dense gas-solid fluidized flows, Chem. Eng. Sci. 229 (2021) 116021.
[5] M. Jiang, X. Chen, Q. Zhou, A gas pressure gradient-dependent subgrid drift velocity model for drag prediction in fluidized gas-particle flows, AIChE J. 66 (4) (2020) e16884.
