Sub-grid models for heat transfer in gas-particle flows with immersed horizontal cylinders

• A subgrid model for heated gas-particle flows was developed.
• The model takes the form of a Nusselt correlation, analogous to single-phase flow.
• Implementation in CFD code is through source terms on the governing energy equations.
• Verification of the model shows good agreement, within ±20% of observed results.

Simulating full-scale heated fluidized bed reactors can provide invaluable insight to the design process. Such simulations are typically computationally intractable due to their complex multi-physics and various length-scales. While it may be possible to simulate some large-scale systems, they require significant computing resources and do not lend themselves well to design optimization methods. To overcome these problems coarse-grid simulations can be used with supplementary constitutive sub-grid models to approximate the unresolved physics. This study details the development, implementation, and verification of a sub-grid model for heat transfer in gas-particle flows with immersed horizontal cylinders. Using the two-fluid model for multiphase flow, small periodic unit-cell domains were simulated over a wide range of flow and geometry conditions. The results were filtered and fit using nonlinear regression to build a Nusselt correlation based on the solids fraction, solids velocity, cylinder geometry (diameter and spacing), and the Peclet number. The proposed model is highly nonlinear and includes power-law contributions from each parameter. The model was verified using a nearly orthogonal experiment design where the input parameters were varied randomly to generate combinations not previously considered. The predicted filtered Nusselt numbers agreed well with the observed (simulated) values. Work is on-going to further expand the capabilities of the model, including 3D simulations, vertical cylinders, and uncertainty quantification.