On the Relevance of Closures Laws for Momentum, Heat and Mass Transfer in Gas-Particle Suspensions

Nowadays, computer simulations allow us to develop closures for momentum, heat, and mass transfer rates on different levels: first, one can use Direct Numerical Simulations (DNS, [1,2]) of fluid flow in the interstices of dense particle beds to determine, e.g., the forces acting on individual particles. Second, one can use highly-resolved Eulerian-Eulerian, or Eulerian-Lagrangian (EL) approaches to quantify the effect of structure formation in these suspensions [3,4]. Naturally, the question arises which of these closures dominates the predictions of the overall performance of a full scale device like a fluidized bed. Unfortunately, this question has not been answered with sufficient rigor yet.

In the present contribution we give a tentative answer to this question with a focus on polydisperse systems, as well as wet fluidized beds. In part I we present results of DNS to quantify particle-based heat transfer rates in dense bi-disperse suspensions (see Figure). Specifically, we highlight that existing correlations developed for monodisperse systems cannot give a precise estimate of the heat transfer rate. Also, we determine critical Peclet numbers (as a function of the particle concentration) for which heat transfer rates are extremely fast – in these systems the exact form of the closure for the heat transfer rate will not influence the overall dynamics of the system.

Part II is devoted to full-physics simulations of heat and mass transport in wet fluidized beds with continuous droplet injection. We analyze (i) the deposition rate of droplets on the particles, (ii) the evaporation rate of droplets suspended in air, as well as (iii) evaporation from droplets deposited on the particle surface. By systematically de-activating individual closures for these phenomena, we (i) explore their relative importance, and (ii) give guidance for the future improvements of these closures.

Last, we summarize recent developments in the field of computational tools for the simulation and analysis of dense suspension flow which were heavily influenced by Prof. Sundaresan’s ideas. Specifically, we present the latest version of the CFDEM® EL simulator, which has been significantly upgraded by the inclusion of cutting-edge models for momentum, heat and mass transfer. Also, we detail on some applications of the filtering tool “CPPPO”: this tool should help researchers and engineers to follow the footprints of Prof. Sundaresan, and apply his seminal ideas to a variety of challenges in the field.

Figure: Direct numerical simulation of heat transfer in a bi-disperse gas-particle suspension in a fully periodic cuboid. Dimensionless velocity (left panel) and temperature fields (right panel; the overall particle volume fraction is 0.35, the Reynolds number is 250, and the Prandtl number is 1).

References

[1] W. Holloway, J. Sun, S. Sundaresan, Effect of microstructural anisotropy on the fluid–particle drag force and the stability of the uniformly fluidized state, J. Fluid Mech. 713 (2012) 27–49.

[2] B. Sun, S. Tenneti, S. Subramaniam, Modeling average gas–solid heat transfer using particle-resolved direct numerical simulation, Int. J. Heat and Mass Trans. 86 (2015) 898–913.

[3] K. Agrawal, W. Holloway, C. C. Milioli, F. E. Milioli, S. Sundaresan, Filtered models for scalar transport in gas–particle flows, Chem. Eng. Sci. 95 (2013) 291–300.

[4] S. Radl, S. Sundaresan, A drag model for filtered Euler-Lagrange simulations of clustered gas-particle suspensions, Chem. Eng. Sci. 117 (2014) 416-425.