Inflow Conditions in Stochastic Eulerian-Lagrangian Calculations of Two-Phase Turbulent Flow

Abstract

The importance of the inlet conditions of the dispersed-phase e uctuating velocity on the analysis associated with the stochastic Lagrangian method, which is commonly used in the simulation of two-phase turbulent e ows, is demonstrated through two well-dee ned problems. One is under the inlet condition of the carrier-phase turbulent kineticenergy kg largerthanthedispersed-phaseturbulentkineticenergy kp.Theotherisassociatedwith kg < <kp.A solution procedureaccounting for the inlet conditions of the e uctuating dispersed-phase velocities in the stochastic Lagrangian calculation is developed. It is also concluded that the unsteady drag coefe cient has to be considered in themodel formulation whenthecondition of theStokesnumberlargerthan O O(101))isencountered intheexamined two-phase turbulent e owe eld. Nomenclature CD = drag coefe cient D = orie ce diameter, 0.64 mm dp = droplet diameter g = gravity K = history-force kernel k = turbulent kinetic energy n = number density, number of droplets per cubic meter P; Q = value of probability density function Rep = droplet Reynolds number r = radial coordinate St = Stokes number, ?p=?r t = time tM = dimensionless time dee ned by Eq. (14) U;u = instantaneous and mean velocities, respectively U = vector form of instantaneous velocity x = axial or streamwise coordinate y = transverse coordinate ®12 = ratio of velocity slips in two neighboring grid cells 1t = time increment 1U = velocity slip, Ug iUp π = viscosity Ω = density ?p;?r = dynamic relaxation time and residence time of droplet, respectively A = factor accounting for deviation from the Stokesian drag Subscripts