Grid-Averaged Lagrangian Equations of Dispersed Phase in Dilute Two-Phase Flow

Abstract

k0 pi i is derived and demonstrated through a well-dee ned test problem of droplet-loading mixing layer. It is shown that accurate predictions of the turbulence kinetic energy of the droplets can be achieved by solving from this set of grid-averaged Lagrangian equations with signie cantly less computational droplets than those of a purely stochasticmodel. The information of the turbulence modulation quantity, which is solved from the grid-averaged Lagrangian transport equation of hu 0u k 0 pii, can also be used to evaluate accurately the source term accounting for the two-phase interaction in the turbulence kinetic energy k transport equation of the carrier e uid, which is important for determining the turbulence characteristics of the carrier e uid. Nomenclature CD = drag coefe cient C3 = turbulence model constant; see Eq. (10) dp = droplet diameter g = gravity K = history-force kernel k = turbulence kinetic energy N = number e ow rate P, Q = values of probability density function Rep = particle Reynolds number Sp, sp = instantaneous and mean time source terms due to turbulence- particle interactions, respectively T = time U, u = instantaneous and mean velocities, respectively hu 0 i u