Abstract
Filtered drag models for coarse-grid, two-fluid model simulations of gas-solid flows in industrial-scale applications have been under investigation for many years [1-5]. These models are designed to capture the effects of unresolved sub-filter-scale flow on the resolved flow.
In the present study, we have performed highly resolved Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations of gas-fluidization of mono-disperse particles with three different diameters (75, 150, 300 mum) in periodic domains at various solid volume fractions. Simulations of this kind are being done by several research groups to learn more about meso-scale structures in gas-particle flows; for example, see [6,7].
We first mapped the Lagrangian results onto the Eulerian field and then filtered them by volume averaging in order to evaluate the sub-filter contribution of Eulerian drag force. We found that the sub-filter contribution of drag force can be captured via a model relating the filtered drag coefficient to the filtered particle volume fraction, the sub-filter scalar variance of solid volume fraction, and the particle Froude number. The sub-filter scalar variance is a measure of the degree of local inhomogeneity of the solid volume fraction within the filter. The Froude number is based on particle diameter, terminal settling velocity, and gravitational acceleration.
As the sub-filter scalar variance of solid volume fraction cannot be obtained from the resolved field, one must develop a closure model or an additional transport equation for it. In this study, we have formulated an algebraic closure for this scalar variance in terms of the filter size and filtered solid volume fraction. Towards this end, we have analyzed the CFD-DEM simulation results and extracted the functional dependence of the sub-filter scalar variance of the solid volume fraction on the filtered volume fraction and filter size to within an unspecified multiplicative constant. It is then proposed that this constant be determined dynamically in coarse simulations by using a scale similarity assumption [8], and a test filter following the approach proposed by Germano et al. [9].
We assessed the accuracy of the model by computing correlation coefficients between model predictions and exact values calculated from mapped results. The correlation coefficients are around 0.7 even for large filter sizes, indicating that the sub-filter contribution is well captured by the model.
As a further study, we plan to implement the proposed model into a two-fluid model in order to assess a posteriori performance of the model.
In the present study, we have performed highly resolved Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations of gas-fluidization of mono-disperse particles with three different diameters (75, 150, 300 mum) in periodic domains at various solid volume fractions. Simulations of this kind are being done by several research groups to learn more about meso-scale structures in gas-particle flows; for example, see [6,7].
We first mapped the Lagrangian results onto the Eulerian field and then filtered them by volume averaging in order to evaluate the sub-filter contribution of Eulerian drag force. We found that the sub-filter contribution of drag force can be captured via a model relating the filtered drag coefficient to the filtered particle volume fraction, the sub-filter scalar variance of solid volume fraction, and the particle Froude number. The sub-filter scalar variance is a measure of the degree of local inhomogeneity of the solid volume fraction within the filter. The Froude number is based on particle diameter, terminal settling velocity, and gravitational acceleration.
As the sub-filter scalar variance of solid volume fraction cannot be obtained from the resolved field, one must develop a closure model or an additional transport equation for it. In this study, we have formulated an algebraic closure for this scalar variance in terms of the filter size and filtered solid volume fraction. Towards this end, we have analyzed the CFD-DEM simulation results and extracted the functional dependence of the sub-filter scalar variance of the solid volume fraction on the filtered volume fraction and filter size to within an unspecified multiplicative constant. It is then proposed that this constant be determined dynamically in coarse simulations by using a scale similarity assumption [8], and a test filter following the approach proposed by Germano et al. [9].
We assessed the accuracy of the model by computing correlation coefficients between model predictions and exact values calculated from mapped results. The correlation coefficients are around 0.7 even for large filter sizes, indicating that the sub-filter contribution is well captured by the model.
As a further study, we plan to implement the proposed model into a two-fluid model in order to assess a posteriori performance of the model.
| Original language | English |
|---|---|
| Title of host publication | 2016 AIChE Annual Meeting |
| Publisher | AIChE |
| ISBN (Print) | 9780816910977 |
| Publication status | Published - 2016 |
| Event | 2016 AIChE Annual Meeting - San Francisco, United States Duration: 13 Nov 2016 → 18 Nov 2016 https://www.aiche.org/conferences/aiche-annual-meeting/2016 |
Conference
| Conference | 2016 AIChE Annual Meeting |
|---|---|
| Country/Territory | United States |
| City | San Francisco |
| Period | 13/11/16 → 18/11/16 |
| Internet address |