(378b) 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.