Lift Force

Author: Sajad Khodadadi

Abstract

This research examines the Lift force on a particle using a compressible solver in OpenFoam software. Also, in this research, according to the previous researches, we have chosen the best formula for the Lift coefficient among the different Lift coefficients and used the developed solver. In the end, the simulation results confirm the correctness of our OpenFoam solver compared to the experimental results.

1. Introduction

The lift force applied to a particle is due to the velocity gradients in the velocity field of the main phase. The Saffman lift force is more significant for larger particles. Also, a particle moving in a shear field experiences Saffman lift perpendicular to its direction of movement. The effect of the lift force caused by inertia in the viscous flow surrounding a particle is fundamentally different from the aerodynamic lift force.

2. Methodology

The geometry used is a channel with dimensions of 20m length and 1m width. The flow is laminar and the problem is similar to Couette flow with a moving upper wall and a stationary lower wall. Also, we have used the article of Saffman et al [1]. and Dandy et al [2].

For this channel, the grid used is 20×100 and the results are given below. It should be noted that networking has been done for three types of networks, 1500, 2000, 3000 cells.

3. Flow Simulation Results

In the research of Saffman et al [1], the lift force is expressed as equation (1):

\[ F_{\text{lift (saff)}} = 1.61 \rho_v^{1/2} d^2 (u^f - u^p) \left| \frac{du^f}{dy} \right|^{1/2} \, \text{sgn}\left( \frac{du^f}{dy} \right) \]

For different tests, we change the speed on the wall, which results in a flow with different speed gradients. Now it is possible to obtain and check the changes of the lift coefficient for constant \( \alpha \) and different Reynolds numbers. The desired particle is released near the bottom wall and the interphase communication is one-way. Also, the continuous phase is air and its viscosity is 0.00001 m²/s.

The results of the validation can be seen in Figure (1), which has a very good agreement with the results of Saffman. We can also see that with the increase of particle Reynolds number, the particle lift coefficient decreases and for Reynolds number greater than 40, the lift coefficient value remains constant.

In the following, we compared the obtained values of the lift force through the developed solver with the analytical values. It was observed that the values correspond very much and the lift force sub-model used in the solver works completely correctly.