# Investigation of Momentum and Heat Transfer in Flow Past Suspensions of Non-Spherical Particles

## Files

## TR Number

## Date

## Authors

## Journal Title

## Journal ISSN

## Volume Title

## Publisher

## Abstract

Investigation of momentum and heat transfer between the fluid and solid phase is critical to the study of fluid-particle systems. Dense suspensions are characterized by the solid fraction (ratio of solid volume to total volume), the particle Reynolds number, and the shape of the particle. The behavior of non-spherical particles deviates considerably from spherical particle shapes which have been studied extensively in the literature. Momentum transfer, to first-order, is driven by drag forces experienced by the particles in suspension, followed by lift and lateral forces, and also through the transmission of fluid torque to the particles. The subject of this thesis is a family of prolate ellipsoidal particle geometries of aspect ratios (AR) 2.5, 5.0 and 10.0 at nominal solid fractions (φ) between 0.1 and 0.3, and suspensions of cylinders of AR=0.25. The nominal particle Reynolds number (Re) is varied between 10 to 200, representative of fluidized beds. Fluid forces and heat transfer coefficients are obtained numerically by Particle Resolved Simulations (PRS) using the Immersed Boundary Method (IBM). The method enables the calculation of the interstitial flow and pressure field surrounding each particle in suspension leading to the direct integration of fluid forces acting on each particle in the suspension.

A substantial outcome of the research is the development of a new drag force correlation for random suspensions of prolate ellipsoids over the full range of geometries and conditioned studied. In many practical applications, especially as the deviation from the spherical shape increases, particles are not oriented randomly to the flow direction, resulting in suspensions which have a mean preferential orientation. It is shown that the mean suspension drag varies linearly with the orientation parameter, which varies from -2.0 for particles oriented parallel to the flow direction to 1.0 for particles normal to the flow direction. This result is significant as it allows easy calculation of drag force for suspension with any preferential orientation.

The heat transfer coefficient or Nusselt number is investigated for prolate ellipsoid suspensions. Significantly, two methods of calculating the heat transfer coefficient in the literature are reconciled and it is established that one asymptotes to the other. It is also established that unlike the drag force, at low Reynolds number the suspension mean heat transfer coefficient is very sensitive to the spatial distribution of particles or local-to-particle solid fractions. For the same mean solid fraction, suspensions dominated by particle clusters or high local solid fractions can exhibit Nusselt numbers which are lower than the minimum Nusselt number imposed by pure conduction on a single particle in isolation. This results from the dominant effect of thermal wakes at low Reynolds numbers. As the Reynolds number increases, the effect of particle clusters on heat transfer becomes less consequential.

For the 0.25 aspect ratio cylinder, it was found that while existing correlations under predicted the drag forces, a sinusoidal function F_(d,θ)=F_(d,θ=0°)+(F_(d,θ=90°)-F_(d,θ=0°) )sin(θ) captured the variation of normalized drag with respect to inclination angle over the range 10≤Re≤300 and 0≤φ≤0.3. Further the mean ensemble drag followed F_d=F_(d,θ=0°)+1/2(F_(d,θ=90°)-F_(d,θ=0°)). It was shown that lift forces were between 20% to 80% of drag forces and could not be neglected in models of fluid-particle interaction forces. Comparing the pitching fluid torque to collision torque during an elastic collision showed that as the particle equivalent diameter, density, and collision velocities decreased, fluid torque could be of the same order of magnitude as collisional torque and it too could not be neglected from models of particle transport in suspensions.