Macro-Scale Effects on Sub-Grid Closures in Gas-Solid Riser Flows

Jun 1, 2018
Solid volume fraction fields across solids loadings and gas Reynolds numbers

Motivation

Sub-grid closures for two-fluid models are traditionally derived at a single scale, but this work demonstrates that flow topology at the system scale strongly affects closure accuracy. Accounting for these effects is essential for predictive industrial riser flow simulations.

Background

Filtered two-fluid formulations of gas-solid fluidized flows require closure models to deal with sub-grid filtered parameters. These closures are derived by filtering the results of meso-scale highly resolved simulations (HRS) with two-fluid modeling, and then applying them on the coarse large-scale simulation (LSS) grid.

Closure strategy: a highly resolved simulation with the two-fluid model and microscopic closures is filtered to provide sub-grid closures for the coarse, large-scale filtered two-fluid model.
Closure strategy: a highly resolved simulation with the two-fluid model and microscopic closures is filtered to provide sub-grid closures for the coarse, large-scale filtered two-fluid model.

The question

Trusting in scale separation, the correlation of filtered parameters has traditionally been performed against meso-scale filtered data only, disregarding any macro-scale effects. In this work, the correctness of that practice is tested — and it fails.

Approach

Two macro-scale parameters associated with flow topology are considered for their effects on the relevant filtered parameters: the average solid volume fraction and the average gas Reynolds number. Highly resolved simulations are filtered while holding each of these macro-scale parameters constant at various levels. The interest is directed toward the dilute conditions typical of riser flows.

Instantaneous solid volume fraction for increasing solids loading (left to right) and increasing gas Reynolds number (top to bottom). The cluster structure — and therefore the sub-grid closure — depends strongly on both macro-scale parameters.
Instantaneous solid volume fraction for increasing solids loading (left to right) and increasing gas Reynolds number (top to bottom). The cluster structure — and therefore the sub-grid closure — depends strongly on both macro-scale parameters.

The drag closure is not scale separated

The drag coefficient correction H, the single most influential sub-grid term, is the clearest evidence of the failure of scale separation. Correlating H against the meso-scale filtered variables alone leaves a systematic spread that is set entirely by the macro-scale state of the flow.

Drag coefficient correction H against the filtered solid volume fraction. (a) Effect of the domain average gas Reynolds number at fixed solids loading; (b) effect of the domain average solid volume fraction at fixed Reynolds number. Curves that should collapse if scale separation held instead fan out by a factor of two or more.
Drag coefficient correction H against the filtered solid volume fraction. (a) Effect of the domain average gas Reynolds number at fixed solids loading; (b) effect of the domain average solid volume fraction at fixed Reynolds number. Curves that should collapse if scale separation held instead fan out by a factor of two or more.

The same holds for the stress closures

The effect is not limited to drag. The filtered solid pressure, which closes the solid-phase momentum equation, shifts by roughly an order of magnitude across the range of macro-scale conditions at an otherwise identical filtered state.

Dimensionless filtered solid pressure against the filtered solid volume fraction. (a) Varying the domain average gas Reynolds number; (b) varying the domain average solid volume fraction. The vertical spread at fixed filtered state is the macro-scale signature that traditional closures ignore.
Dimensionless filtered solid pressure against the filtered solid volume fraction. (a) Varying the domain average gas Reynolds number; (b) varying the domain average solid volume fraction. The vertical spread at fixed filtered state is the macro-scale signature that traditional closures ignore.

Conclusion

Results show that both macro-scale parameters should be accounted for in sub-grid correlations if higher accuracy is to be achieved.

Reference

Mouallem, J., Chavez-Cussy, N., Niaki, S. R. A., Milioli, C. C., and Milioli, F. E.: On the effects of the flow macro-scale over meso-scale filtered parameters in gas-solid riser flows, Chemical Engineering Science, 182, 200-211, 2018. https://doi.org/10.1016/j.ces.2018.02.039

CFD Multiphase Flows Two-Fluid Model Sub-grid Modeling
Joseph Mouallem
Joseph Mouallem
Computational Scientist & Research Software Engineer

Publications

Macro-scale effects over filtered and residual stresses in gas-solid riser flows
Filtered and residual stresses of both phases depend strongly on the macro-scale state of the flow, so sub-grid stress closures cannot be built from meso-scale data alone.
Joseph Mouallem, Seyed R. A. Niaki, Norman Chavez-Cussy, Christian C. Milioli, Fernando E. Milioli
Source Document DOI
On the effects of the flow macro-scale over meso-scale filtered parameters in gas-solid riser flows
Macro-scale flow topology parameters are shown to matter for sub-grid closure of filtered two-fluid models of gas-solid riser flows.
Joseph Mouallem, Norman Chavez-Cussy, Seyed R. A. Niaki, Christian C. Milioli, Fernando E. Milioli
Source Document DOI