Stochastic models for the prediction of individual particle trajectories in one dimensional turbulence flows

Abstract

This dissertation presents the development of a method for integrating two-phase flow into the vector formulation of the One Dimensional Turbulence model (ODT). The novel ODT model is an unsteady turbulent flow simulation model implemented on a one-dimensional domain, representing flow evolution as observed along a line of sight through a 3D turbulent flow. Overturning motions representing individual eddies are implemented as instantaneous rearrangement events. They obey applicable conservation laws and emulate the multiplicative increase of strain and decrease of length scales associated with the turbulent cascade. Eddy occurrences are random, with likelihoods proportional to a local measure of shear kinetic energy. These events punctuate conventional time advancement of viscous transport. In the present study, the ODT configuration used to simulate turbulent channel flow is augmented by a representation of particles coupled to the fluid by a drag law, with one-way coupling. It is straightforward to implement this drag coupling using the vector wall-normal fluid velocity profile evolved by ODT, but motion (displacement by eddy events) and velocity are distinct in ODT, so this procedure violates physical requirements such as correct representation of the marker-particle limit. Instead, a particle-eddy interaction mechanism is introduced. ODT eddies are instantaneous, so this interaction is defined by integrating the drag law over the lifetime of the corresponding physical eddy, but applying the resulting particle location and velocity change at the instant of eddy occurrence. A subtraction procedure is used to prevent double-counting of particle-eddy interaction due to subsequent viscous time advancement over the same time interval. The net outcome is a particle-eddy interaction that obeys correct limiting behaviors and transitions smoothly between these limits. This formulation introduces a free parameter that multiplies a scaling estimate of the eddy lifetime. Numerical simulations were run with turbulent friction Reynolds numbers ranging from 180 to 1395. Validation was achieved by comparing (1) wall-normal profiles of particle statistics with DNS, LES, and experiments; (2) wall deposition for particles from the inertial range of (Stokes number) 0.3 <= Tau+ <= 55,000 to DNS, LES, and experiments; (3) the non-inertial, Brownian Motion, regime was demonstrated by comparison with experiments and DNS.