Equilibrium Physics in Particulate Flow
Open Access
- Author:
- Parkhill, Alexander Earl
- Graduate Program:
- Aerospace Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- None
- Committee Members:
- Mario F Trujillo, Thesis Advisor/Co-Advisor
- Keywords:
- Stokes drag
droplet
particle
Lagrangian tracking
Two-phase flow
equilibrium
tracer - Abstract:
- Dynamic equilibrium for particles in one-way momentum coupled flow is studied. The basis for evaluating the particle velocity is a Stokes drag law with gravity that represents a simplified variant of the equation of motion for a rigid sphere (Maxey and Riley 1983). The equilibrium condition, whereby the sum of the forces on the particle is zero, provides an opportunity to reduce computational cost in simulating large numbers of particles. It is shown that the primary parameter that governs deviation from equilibrium is the product of the particle time constant and the maximum eigenvalue of the velocity gradient tensor. This parameter is proposed as a redefinition of the Stokes number for particulate flow. The new Stokes number's effectiveness in predicting departures from equilibrium is demonstrated mathematically and numerically. The analytical conclusions derived from studying the behavior of a particle under a local flow field are supported by simulations in a variety of analytical flow fields. The Lagrangian analysis presented here stands in contrast to many Eulerian formulations presented in the literature, and several limitations involved in using Eulerian techniques are revealed. The Lagrangian solutions presented clarify the physical mechanisms for a particle entering and exiting equilibrium. These solutions are also intended to be used in nonequilibrium situations, avoiding the stiff computational problem of standard particle evolution.