Modulation of turbulence intensity by heavy finite-size particles in upward channel flow

It has been recognized that, generally, large particles enhance the turbulence intensity, while small particles attenuate the turbulence intensity. However, there has been no consensus on the quantitative criterion for particle-induced turbulence enhancement or attenuation. In the present study, interface-resolved direct numerical simulations of particle-laden turbulent flows in an upward vertical channel are performed with a direct forcing/fictitious domain method to establish a criterion for turbulence enhancement or attenuation. The effects of the particle Reynolds number (Re-p), the bulk Reynolds number (Re-b), the particle size, the density ratio and the particle volume fraction on the turbulence intensity are examined at Re-b = 5746 (i.e. Re-tau = 180.8) and 12 000 (Re-tau = 345.9), the ratio of the particle radius to the half channel width a/H = 0.05-0.15, the density ratio 2-100, the particle volume fraction 0.3%-2.36% and Re-p < 227. Our results indicate that at low Re-p the turbulent intensity across the channel is all diminished; at intermediate Re-p the turbulent intensity is enhanced in the channel centre region and attenuated in the near-wall region; and at sufficiently large Re-p the turbulent intensity is enhanced across the channel. The critical Re-p increases with increasing bulk Reynolds number, particle size and particle-fluid density ratio, while increasing with decreasing particle volume fraction, particularly for the channel centre region. Criteria for enhancement or attenuation are provided for the total turbulence intensity in the channel and the turbulence intensity at the channel centre, respectively, and both are shown to agree well with the experimental data in the literature. The reason for the dependence of the critical particle Reynolds number on the other parameters is discussed.