# (125a) Dynamics of a Homogeneous Bidisperse Gas-Solid Flow Using Particle-Resolved Direct Numerical Simulation

#### AIChE Annual Meeting

#### 2013

#### 2013 AIChE Annual Meeting

#### Particle Technology Forum

#### Industrial Application of Computational and Numerical Approaches to Particle Flow II

#### Monday, November 4, 2013 - 12:30pm to 12:49pm

Gas-solid flows are commonly found in industrial applications such as fluidized-bed combustion, fluid catalytic cracking, coal gasification processes, and biomass energy generation. Practical applications of gas-solid flows usually involve a polydisperse solid phase and the interphase transfer of momentum and energy through gas-particle and particle-particle interactions is complex, resulting in phenomena such as segregation. Better understanding of the physics governing these interactions leads to more accurate models that can be used to improve computational fluid dynamic (CFD) approaches used in device-scale calculations of engineering problems. These interactions have been systematically studied for ideal systems of monodisperse gas-solid flows both experimentally and numerically [1-7]. However, the gas-particle and particle-particle interactions of polydisperse gas-solid flows is still a subject of active research.

In this study, we use particle-resolved direct numerical simulation (PR-DNS) to study canonical bidisperse gas-solid flow problems that capture the essential interactions in more complex polydisperse systems. We consider a homogeneous bidisperse gas-solid suspension in zero gravity where the mean pressure gradient in the fluid phase balances the average solids drag. Both fixed particle assemblies and freely evolving suspensions are simulated. When all the particles move with the same velocity (zero relative velocity between size classes), we can make a Galiliean-invariant (GI) frame transformation such that the particles are at rest in the new frame. Therefore, the fixed particle simulations are performed with zero velocity assigned to all the particles in both size classes, while the mean fluid velocity is specified. Beetstra et al. [6] expressed a drag law for each particle size class in a bidisperse suspension as the product of a quadratic function in *y*_{α} (the particle diameter of the size class α normalized by the Sauter mean diameter of the bidisperse suspension) and the drag experienced by an equivalent monodisperse suspension. Our drag results from PR-DNS of bidisperse suspensions indicate that the quadratic dependence of the mean drag on normalized particle size class diameter y_{α} is valid, although our simulation results indicate that the correlation proposed by Beetstra et al. [6] is not accurate because it is based on a monodisperse drag law [5, 6] that deviates considerably from the high-resolution monodisperse drag law proposed by Tenneti et al. [7]. Fixed particle simulations of bidisperse simulations as described above have no mean slip between the size classes, and are of limited value because in reality each size class experiences a different mean drag force, leading to relative acceleration and a finite mean slip between size classes.

In the case of freely evolving suspensions it is difficult to access the entire range of mean slip Reynolds numbers in sedimentation problems. This is because in sedimenting suspensions the mean slip Re_{m} is determined by the settling velocity, which is in turn determined by the density ratio and solid volume fraction for a fixed value of gravitational acceleration. Therefore, the simulations of freely evolving suspension undergoing elastic collisions are performed in an accelerating frame of reference [8] so that arbitrary mean slip Reynolds numbers Re_{m} can be accessed over a range of solid volume fractions and solid to gas density ratios. PR-DNS of freely evolving bidisperse suspensions undergoing elastic collisions show that the slip velocity between the two size classes attains a nonzero steady value corresponding to a balance between hydrodynamic and collisional forces for each size class that is determined by the physical parameters of the problem. These simulations allow us to quantify the mean drag on particle size classes as they evolve to the mean slip velocities corresponding to each size class as dictated by the natural dynamics of the problem. The attainment of finite mean slip between size classes implies that a particle flux corresponding to each size class can arise even in the absence of a number density gradient. This has implications for kinetic theories of bidisperse gas-solid flow that require a gradient in the number density of the size class in order to generate a number flux for that size class.

In addition to the mean momentum in the gas and solid phases, we extract the second moment of velocity fluctuations in both gas and solid phases. The kinetic energy associated with the velocity fluctuations in the solid phase, also called the granular temperature, reaches a steady state corresponding to a balance between the hydrodynamic source term and viscous dissipation for each size class in the freely evolving suspension. On the other hand, quantification of kinetic energy in the gas-phase velocity fluctuations, called pseudo-turbulence, reveals that the level of pseudo-turbulence in gas-solid flows of the same total solid volume fraction and mixture Reynolds number are in good agreement, even with equivalent monodisperse gas-solid suspensions reported by Tenneti et al. [9]. The simulations of bidisperse gas-solid flows considered in this study show that at steady state the interphase transfer of turbulent kinetic energy acts as the source of gas-phase velocity fluctuations. This is consistent with the model proposed for monodisperse gas-solid flows [9] modified by a correction factor due to the presence of two size classes in the particle assembly. As long as the correction factor remains close to unity, the monodisperse interphase TKE transfer is retrieved, resulting in the same level of pseudo-turbulence. Therefore, in this regime, the eddy viscosity model proposed by Tenneti et al. [9] is still valid.

In summary, this study gives insights into the physics of gas-solid and solid-solid interactions in bidisperse gas-solid flows that are crucial for developing CFD models for industrial applications.

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9. Tenneti, S., Garg, R., Subramaniam, S., *Quantification of gas–phase velocity fluctuations in statistically homogeneous gas–solid flow using particle–resolved direct numerical simulation.* Submitted to AICHE Journal, 2013.