Spatially-Averaged Models for Heat Transfer in Gas-Solid Flows
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
2018 AIChE Annual Meeting
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
While for small scale fluidised beds, simulation is quite feasible, the occurring physical phenomena cannot be fully numerically analysed in large scale reactors yet, due to a large range of involved scales. In fluidised bed reactors of several meters, the smallest stable structures are usually only several particle diameters wide. However, the unresolved heterogeneous structures have a significant influence on the flow properties. The velocity fluctuations around particle clusters give rise to turbulence, i.e. cluster induced turbulence. An overestimation of the gas-solid drag force by not accounting for this turbulence leads to an overestimation of the bed expansion.
A model accounting for the unresolved terms can be derived by spatially averaging the kinetic theory based two-fluid model equations. The filtered gas-solid drag can be, for example, approximated by the filtered drag coefficient times the the sum of the difference of the filtered slip velocityties and corrected by the a drift velocity. The drift velocity can be seen as the gas-phase velocity fluctuations seen by the particles. Additionally, it is also shown, that the filtered drag force depends on the turbulent kinetic energies of both phases, as well as strongly on bulk density fluctuations. Closures for the turbulent kinetic energies and the bulk density fluctuations are derived.
Finally, filtered energy equations are derived. The effective filtered heat transfer coefficient divided by the filtered solid volume fraction is approximated by its zeroth order Taylor series expansion about the filtered variables. This gives rise to a similar construct as the drift velocity. That is that the temperature difference between both phases is corrected by a drift temperature stemming from phase averaging. Closure models are derived for this drift temperature, as well as for the other unresolved terms in the filtered equations for the thermal energy balance are derived.
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