Hybrid model for the boundary surface between a packed bed and the downstream free flowing gas
In project C6 the large eddy simulation approach will be employed to derive a seamless model of the bed’s free surface in the form of source, respectively sink, terms, to be included in classic RANS simulations, thus correctly accounting for the mixing processes at the interface between the packed bed and the free gas phase. The interface between the dense bed of chemical reacting particles and the gas phase freeboard (free gas phase) downstream of the bed needs special treatment. This is especially always the case when the particles release volatile hydrocarbons, H2 or CO which mix and can react at least partially in the bed but also, for example, in a free gas flame, downstream of the bed together with the air passing which flows through the bed (e.g. volatiles flame downstream of a bed of Pellets on a grate). Hence, it is of paramount importance to gain a better understanding of the transport mechanisms of micro-scale turbulence into the freeboard region, as this is likely to strongly influence scalar mixing and therefore chemical reaction. In funding period (FP) 1, project C6 will focus on packed beds accounting for spherical, non-reacting particles and the freeboard region above the bed. The system of Navier-Stokes equations and appropriate scalar conservation equations will be analysed in the light of first principles and a spatial filtering operator will be defined and applied, such that both the flow field realised in the interstices among the solid particles and the flow in the free gas phase will be encompassed, accurately accounting for the morphology of the packed bed as well as the nature and shape of the particles. The unclosed terms arising from the filtering of the governing equations must vanish identically in case of a fully resolved simulation (Direct Numerical Simulation). This principle will guide the successive steps of the research. The configuration measured in project A1 (Zähringer/Lessig) will be simulated and reference data generated, which will serve a twofold purpose. Firstly, the governing equations will be subjected to filtering and the resulting unclosed terms will be computed exactly a priori from the resolved simulation. Based on this step, functional expression for appropriate closures will be derived. A mathematical quantification of the modelling errors will be also obtained by means of analytical LES-quality criteria. Furthermore, the configuration will be employed to validate the additional, modelled terms appearing in the system of filtered equations in the context of under-resolved simulations such as RANS and VLES. Finally, a scaled-up, virtual experiment will be constructed based on an extension of the configuration considered in project C5 (van Wachem), where the freeboard above the packed bed will also be included in the simulations. The closures derived in project C6 for the dispersion and crossstresses and scalar fluxes at the bed’s free surface will be then made available to project C7 (Scherer/Wirtz).