# (55a) Modeling Gas--Solid Heat Transfer Using Particle-Resolved Direct Numerical Simulation

- Conference: AIChE Annual Meeting
- Year: 2013
- Proceeding: 2013 AIChE Annual Meeting
- Group: Particle Technology Forum
- Session:
- Time:
Monday, November 4, 2013 - 8:30am-8:52am

Gas–solid heat transfer is important in many emerging technologies such as carbon-neutral energy generation using biomass, chemical looping combustion, and CO_{2} capture. Computational Fluid Dynamics (CFD) simulations of multiphase flow are increasingly being used as an efficient alternative to experiments for process and design optimization, because experiments are often costly and time-consuming. The averaged equations governing mass, momentum, and energy that are solved in multiphase CFD simulations require models for the average interphase transfer of momentum and energy between different phases. Specifically, the averaged fluid temperature equation from two–fluid theory contains the three unclosed terms: (i) average gas–solid heat transfer, (ii) divergence of average heat flux in the fluid phase, which includes axial conduction in the fluid phase, and (iii) transport of temperature-velocity covariance. In this work, we use Particle-resolved Direct Numerical Simulations (PR–DNS) to develop models for gas–solid heat transfer, axial conduction in the fluid phase, and transport of temperature-velocity covariance.

Preliminary results for gas--solid heat transfer using PR—DNS have been obtained using the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM) [1]. Tenneti *et al.* studied a canonical problem of heat transfer in a steady flow through a homogeneous fixed assembly of spherical particles and showed that mean fluid temperature changes along the streamwise direction due to fluid heating or cooling by particles. Therefore, although the hydrodynamic problem is statistically homogeneous, the directional nature of the mean flow and fluid heating renders the thermal problem statistically *inhomogeneous*. It has been shown [2] that obtaining surface statistics from PR—DNS of gas-solid flow in inhomogeneous problems is a significant challenge. The difficulty is that averaged interphase exchange terms calculated from spatially varying surface statistics converge much more slowly with the number of realizations than in the statistically homogeneous case [2]. To alternate this difficulty, Tenneti *et al.* formulated a *thermally fully*–*developed* gas–solid heat transfer problem in the same canonical setup using a thermal similarity condition. The thermal similarity condition enabled simulation of the statistically inhomogeneous thermal transport problem in steady flow past a statistically homogeneous assembly of fixed particles in periodic domains. Based on the PR--DNS results, Tenneti *et al.* showed that fluid heating can change the average fluid temperature on very small length scales for high volume fraction and low Reynolds number.

Building on this previous work of Tenneti *et al.,* we verify fundamental assumptions in the averaged fluid temperature equation and develop models for gas–solid heat transfer. Local statistical homogeneity of the average fluid temperature that is assumed in the two–fluid averaged equations is investigated by developing an exponentially decaying model for the bulk fluid temperature from PR–DNS data. We develop a length scale criterion that determines the validity of the locally homogeneous average fluid temperature assumption as a function of solid volume fraction and Reynolds number.

In the range of validity of the two–fluid averaged equation formulation, the unclosed terms in the averaged fluid temperature equation are quantified and modeled using PR–DNS results. We demonstrate that using the bulk fluid temperature is the correct choice to compute average interphase heat transfer in gas–solid flow rather than using the average fluid temperature. PR–DNS results show that axial conduction in the fluid phase that is often neglected in existing one-dimensional models cannot be neglected for Re_{m}< 10. Finally, the transport of temperature-velocity covariance that is often neglected in CFD simulations is computed and modeled from PR–DNS data. It is found that this term is non-negligible since the average transport of temperature-velocity covariance is about 30%-70% of the average convective term in the averaged temperature equation. This study shows how PR–DNS can be used to evaluate fundamental assumptions underlying averaged continuum models for heat and mass transfer in gas--solid flow, and that models can be developed for interphase heat transfer, axial conduction in the fluid phase, and the transport of temperature-velocity covariance.

References

- Tenneti S, Sun B, Garg R, Subramaniam S. 2013. Role of fluid heating in dense gas–solid flow as revealed by particle–resolved direct numerical simulation. Intl. J. Heat Mass Transfer 58:471–479
- Xu Y, Subramaniam S. 2010. Effect of particle clusters on carrier flow turbulence: A direct numerical simulation study. Flow, Turbulence and Combustion 85:735–761. 10.1007/s10494-010-9298-8

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