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The effect of clusters on the heat transfer in gas-particle flows

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If you have a question about this talk, please contact Rajesh Kumar Bhagat.

Moderately dense gas-particle flows represent a large number of processes, not only in chemical engineering. Reliable simulation predictions are crucial in conception and optimization of reactors. Due to the large difference in scales, from tens of meters in reactor dimensions to a few micro-meters in particle diameters, and the large number of particles involved, Particle-Resolved Direct Numerical Simulations (PR-DNS) are unfeasible even on current supercomputers. An approach, which is suitable for a large number of particles in the moderately dense regime is the Two-Fluid Model (TFM). Thereby, both phases are treated as continua and the collisions between the particles are represented by a granular temperature, which yields a stress-tensor in the Navier-Stokes equations [1]. The interphase forces are modelled by correlations, which are determined empirically or based on PR-DNS data. The TFM with these exchange forces was shown to yield good predictions for the flow variables on sufficiently fine grids, with grid-spacings of a few particle diameters [2]. Coarser numerical grids, however, do not resolve meso-scale heterogeneous structures, such as particle clusters, which form due to an instability if a mean body force is acting on the gas-particle flow. Thus, using the (homogeneous) interphase exchange correlations leads to significantly wrong predictions of the macro-scale flow properties, such as fluidized bed expansion [3], volume fraction and temperature distribution [4,5], and, consequentially, reaction rates. In order to model the influence of the heterogeneous meso-scale structures, we apply spatial averages to the TFM balance equations and described each variable by their mean and fluctuating component. Thereby, we found that the filtered drag force can be approximated by the resolved drag force corrected by a drift velocity [4]. The drift velocity is the gas-phase velocity as seen by the particles, a measure for the sub-filter heterogeneity of the flow. It can be expressed as a covariance between the solid volume fraction and the gas-phase velocity. We choose to model this covariance by the variances of the variables scaled by a (linear) correlation coefficient. Based on the scale-similarity theory, we propose to estimate the values of the correlation coefficients locally and dynamically through the application of test-filters [6]. In addition, transport equations are derived for the variance of the solid volume fraction and the phase velocities, where the unresolved terms were closed using models known from single-phase Large-Eddy-Simulation approaches. Thereby, an additional sub-filter fluctuating kinetic energy production term involving the drift velocity arises naturally. This is referred to as cluster-induced turbulence [7]. In the later part of this talk, the main focus is laid upon the filtered thermal energy balance equation. Thereby, we found that the resolved interphase heat transfer can also be corrected by a construct similar to the drift velocity, which we call the drift temperature [4]. Finally, we give some outlook on how this approach can be extended to include mass transfer.


[1] C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy. Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech., 140:223–256, 1984.

[2] W. D. Fullmer and C. M. Hrenya. Quantitative assessment of fine-grid kinetic-theory- based predictions of mean-slip in unbounded fluidization. AIChE J., 62(1):11–17, 2016.

[3] S. Schneiderbauer and S. Pirker. Filtered and heterogeneity based subgrid modifications for gas-solid drag and solids stresses in bubbling fluidized beds. AIChE J., 60(3):839–854, 2014.

[4] S. Rauchenzauner and S. Schneiderbauer. A dynamic anisotropic Spatially-Averaged Two-Fluid Model for moderately dense gas-particle flows. Int. J. Multiph. Flow, 126: 103237, 2020a.

[5] S. Rauchenzauner and S. Schneiderbauer. A Dynamic Spatially-Averaged Two-Fluid Model for Heat Transport in Moderately Dense Gas-Particle Flows. Phys. Fluids, 32:063307, 2020b.

[6] D. K. Lilly. A proposed modification of the Germano subgrid-scale closure method. Phys.Fluids A, 4(3):633–635, 1992.

[7] J. Capecelatro, O. Desjardins, and R. O. Fox. On fluid–particle dynamics in fully developed cluster-induced turbulence. J. Fluid Mech., 780:578–635, 2015.

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