Energy balance in turbulent gas-solid channel flow

Abstract

The aim of the present study is to examine the implications of particle additives on the transfer, conversion and dissipation of mechanical energy in a turbulent gas-solid channel flow. To achieve this goal we have performed two-way coupled direct numerical simulations (DNSs) of gas-solid channel flow. Equations for fluid mean flow kinetic energy (KE) and fluid turbulent kinetic energy (TKE) are used in the results analysis. To highlight the influence of particles, the KE budgets were compared with the results of un-laden channel flow, i.e. without any additives. It was found that in the un-laden flow, 57.2% of the energy input was directly dissipated in the mean flow, whereas 40.2% was converted to turbulence through mean shear production before being dissipated by viscous action at small scales. By contrast, in the particle-laden flow, the interaction of the particles and fluid appears in the energy budgets. In the mean-flow energy balance, the mean dissipation accounted for 59.1% of the energy supply. This is comparable with the un-laden flow. However, the energy loss from the mean flow reduced from 40.2% to 13.7%, but was partly compensated by the new sink term (24.7%) which represents negative work done by the particles. The results also suggested that the mean flow loses kinetic energy to particles in the centre region of the channel, whereas it gains energy from the particles in the near-wall region. In the TKE budget, the particles released kinetic energy to the turbulence and this energy is likely obtained from the mean flow. This extra energy supply compensates partially for the substantial reduction of the mean shear production to about 2/3 of the production in the un-laden channel. Ultimately TKE is dissipated by deformation work due to the fluctuating viscous stresses. We concluded that the particles play an intermediary role in the energy transfer and conversion from the mean flow to the turbulence. INTRODUCTION Particle-laden flow is one of the most common twophase flows, which is found both in nature and industry, such as air transport of pollutants, fluidized bed in chemical processes, and dispersion of volcanic ash in the atmosphere. The complexity of the turbulent fluid motion leads to fascinating dynamics of particle suspensions as well as complicated particle-fluid interactions, such as kinetic energy transfer between the solid and gas phases (see Zhao et al. 2013). It is known that the addition of tiny particles can modulate the fluid motion and either augmentation or attenuation of the turbulence has been observed (Balachandar & Eaton 2010, Squires & Eaton 1990). Such phenomena have been widely explored by means of experiments and numerical simulations, such as Squires & Eaton (1990), Pan & Banerjee (1996), Dritselis and Vlachos (2008), Zhao et al. (2010). Kinetic energy budgets are one of the primary tools to examine the turbulent flow. Andersson & Barri (2008) investigated KE transport and conversion in an unladen turbulent plane Couette flow. Mansour et al. (1988) have shown and analysed the Reynolds stress budgets and the turbulent dissipation in a turbulent channel flow. In flows of gas-solid mixtures the suspended solid particles interact with the fluid and make the energy exchange processes more complex than in an unladen channel flow (Balachandar & Eaton 2010). In the presence of particles, a reaction force from each and every particle affects the fluid motion through an extra force term in the NavierStokes equations. The presence of this particle force may give rise to significant modifications of the flow field, both in isotropic turbulence (Squires & Eaton 1990) and in channel flows (Li et al. 2010). In this work the two-way coupled Eulerian-Lagrangian approach is employed to investigate particle suspensions in turbulent channel flow and we mainly focus on the influence of tiny inertial particles on the KE and TKE balance of the particle-laden flow. June 30 July 3, 2015 Melbourne, Australia 9 6C-4