TY - JOUR

T1 - Velocity distribution functions for a bidisperse, sedimenting particle-gas suspension

AU - Kumaran, V.

AU - Tsao, H. K.

AU - Koch, D. L.

N1 - Funding Information:
Acknowledgements--The authors thank James T. Jenkins for many helpful discussions. This work was supported by grant CTS-885 7565 from the National Science Foundation Fluids, Particulates and Hydraulics Program. The numerical calculations were performed using the Corneli National Supercomputer Facility, which is supported by the NSF and IBM Corporation.

PY - 1993/8

Y1 - 1993/8

N2 - The velocity distribution function of a dilute bidisperse particle-gas suspension depends on the relative magnitudes of the viscous relaxation time, τv, and the time between successive collisions, τv. The The distribution functions in the two asymptotic limits, τc ≪ τv and τv ≪ τc, which were analysed previously are qualitatively very different. In the former limit, the leading-order distributions are Gaussian distributions about the mean velocity of the suspension, whereas in the latter case the distributions for the two species are singular at their respective terminal velocities. Here, we calculate the properties of the suspension for intermediate values of τv/τc by approximating the distribution function as a composite Gaussian distribution. This distribution reduces to a Gaussian distribution in the limit τv ≪ τc, in agreement with previous asymptotic analysis. In the intermediate regime, however, the composite Gaussian has a non-zero skewness, which is a salient feature of the distribution in the limit τv ≪ τc. We have also performed numerical calculations using the direct-simulation Monte Carlo method. The approximate values for the moments of the velocity distribution obtained using the composite Gaussian compare well with the full numerical solutions for all values of τv/τc.

AB - The velocity distribution function of a dilute bidisperse particle-gas suspension depends on the relative magnitudes of the viscous relaxation time, τv, and the time between successive collisions, τv. The The distribution functions in the two asymptotic limits, τc ≪ τv and τv ≪ τc, which were analysed previously are qualitatively very different. In the former limit, the leading-order distributions are Gaussian distributions about the mean velocity of the suspension, whereas in the latter case the distributions for the two species are singular at their respective terminal velocities. Here, we calculate the properties of the suspension for intermediate values of τv/τc by approximating the distribution function as a composite Gaussian distribution. This distribution reduces to a Gaussian distribution in the limit τv ≪ τc, in agreement with previous asymptotic analysis. In the intermediate regime, however, the composite Gaussian has a non-zero skewness, which is a salient feature of the distribution in the limit τv ≪ τc. We have also performed numerical calculations using the direct-simulation Monte Carlo method. The approximate values for the moments of the velocity distribution obtained using the composite Gaussian compare well with the full numerical solutions for all values of τv/τc.

KW - fluidized bed

KW - kinetic theory

KW - sedimentation

UR - http://www.scopus.com/inward/record.url?scp=0027643343&partnerID=8YFLogxK

U2 - 10.1016/0301-9322(93)90094-B

DO - 10.1016/0301-9322(93)90094-B

M3 - 期刊論文

AN - SCOPUS:0027643343

SN - 0301-9322

VL - 19

SP - 665

EP - 681

JO - International Journal of Multiphase Flow

JF - International Journal of Multiphase Flow

IS - 4

ER -