Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions

Abstract

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pseudo-turbulent fluctuations to the level of gas-phase velocity fluctuations is quantified in initially ‘laminar’ and turbulent flow past fixed random particle assemblies of monodisperse spheres. The pseudo-turbulent kinetic energy $k^{(f)}$ in steady flow is then characterized as a function of solid volume fraction ${\it\phi}$ and the Reynolds number based on the mean slip velocity $\mathit{Re}_{m}$. Anisotropy in the Reynolds stress is quantified by decomposing it into isotropic and deviatoric parts, and its dependence on ${\it\phi}$ and $Re_{m}$ is explained. An algebraic stress model is proposed that captures the dependence of the Reynolds stress on ${\it\phi}$ and $Re_{m}$. Gas-phase velocity fluctuations in freely evolving suspensions undergoing elastic and inelastic particle collisions are also quantified. The flow corresponds to homogeneous gas–solid systems, with high solid-to-gas density ratio and particle diameter greater than dissipative length scales. It is found that for the parameter values considered here, the level of pseudo-turbulence differs by only 15 % from the values for equivalent fixed beds. The principle of conservation of interphase turbulent kinetic energy transfer is validated by quantifying the interphase transfer terms in the evolution equations of kinetic energy for the gas-phase and solid-phase fluctuating velocity. It is found that the collisional dissipation is negligible compared with the viscous dissipation for the cases considered in this study where the freely evolving suspensions attain a steady state starting from an initial condition where the particles are at rest.

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

“…The flow was simulated for two resolutions; the coarsest one was given by N r = 4, N θ = 24, N φ = 48, N 1 = 88, N 2 = 68 and As a fourth validation, the pressure and viscous parts of the drag force on a sphere in the flow past a structured array of spheres were computed and compared to results obtained by Tenneti et al (2011). These authors used an immersed boundary method (second-order accurate direct forcing embedded into a pseudo-spectral computation; the same method was recently used by Mehrabadi et al (2015)). It is remarked that many variants of immersed boundary methods exist and have been validated for flows past multiple particles -see also, for example, Uhlmann (2005), Mark & van Wachem (2008) and Breugem (2012).…”

“…More recently, PR-DNS studies of turbulent flows with multiple solid fixed and moving spherical particles have occurred in the literature: studies of turbulent channel flow (Uhlmann 2008;Picano, Breugem & Brandt 2015) and homogeneous isotropic turbulence (Lucci, Ferrante & Elghobashi 2010;Mehrabadi et al 2015). In all these cases, the flow was not dilute (α 0.01) and the particle diameter was relatively large (approximately 10 wall units in the turbulent channel flows and at least 5η in the homogeneous isotropic cases).…”

“…Thus we consider stationary homogeneous isotropic turbulence modified by an array of stagnant spherical particles, solved by means of body-fitted PR-DNS. This flow case lies in the gap between, on the one hand, body-fitted PR-DNS of turbulent flow around a single fixed small particle (Bagchi & Balachandar 2003;Burton & Eaton 2005) and, on the other, immersed boundary PR-DNS of turbulent flow around many freely moving coarser particles (Uhlmann 2008;Lucci et al 2010;Mehrabadi et al 2015;Picano et al 2015). Burton & Eaton (2005) remarked that the use of fixed particles in homogeneous turbulence could be justified as relevant for turbulence modification by heavy moving particles or particles in microgravity.…”

Development of a gas–solid drag law for clustered particles using particle-resolved direct numerical simulation

“…Therefore, the focus of this study is on the third approach. It has been shown that fixed particle assemblies of high Stokes number particles in PR-DNS are a good approximation to freely evolving suspensions (Xu and Subramaniam, 2010;Tenneti et al, 2011;Mehrabadi et al, 2015), because the time required for the particle configuration to change significantly is much larger than the fluid relaxation timescale.…”

“…The presence of clusters then gives rise to a reduction in the drag force. We have learned from PR-DNS of freely evolving gas-solid suspensions that the rate of work done in maintaining a flow with constant mean slip between the gas and solid phases by means of a constant mean pressure gradient results in the production of velocity fluctuations in both gas and solid phases (Mehrabadi et al, 2015). Therefore, reduction in the local drag force acting on particle clusters leads to local reduction of the amount of power input to the granular temperature.…”