Drag Force

Author: Sajad Khodadadi

Abstract

This research examines the drag 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 drag coefficient among the different drag 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 study of drag force is a fundamental subject in fluid science and is very important in Lagrangian research and the fields of hydrodynamics, aerodynamics, etc. Examples of drag include a component of pure aerodynamic or hydrodynamic force that acts against the direction of motion of a solid object, such as cars (car drag coefficient), airplanes, and boat hulls. Either it acts in the same direction as the solid's geographic motion, as in sails attached to a yacht, or in average directions on the sail depending on the points of the sail, or in the case of the viscous drag of a fluid in a pipe, or the drag force on a stationary pipe, or the velocity of the fluid relative to In sports physics, the drag force is necessary to explain the movement of balls, spears, arrows and frisbees and the performance of runners and swimmers.

2. Methodology

Yang et al [1]. based on Stokes, Goldstein and Osin laws presented different formulas for the drag coefficient. Based on this and according to Young's research, we finally used a relationship to calculate the drag coefficient and examined the accuracy of the drag coefficient.

boundary conditions for the velocity and for the Outlet boundary as zeroGradient Also, the entrance Inlet was uniform 0 and the walls were noSlip.

3. Flow Simulation Results

As we know, the drag force is obtained through equation (1):

\[ F_D = \frac{1}{2} C_D \rho_c (u_c - u_p) |u_c - u_p| \frac{\pi d_p^2}{4} \]

The drag coefficient equation used in the solver is in the form of equation (2):

\[ Re_p > 1000 \rightarrow C_D = \frac{24}{Re_p} \left( 1 + \frac{\frac{3}{16} Re_p}{1 + \frac{\frac{19}{240} Re_p}{1 + \frac{1}{122} Re_p}} \right) + er(Re_p) \]

In the following, the results of our drag coefficient, which we have used in the developed solver, compared to the experimental results of Yang et al[1]., are as follows:

As can be seen from Figure (1), the calculated drag coefficient has a very good agreement with the experimental results. Also, the results of the relationship used in the solver for Reynolds numbers greater than 1000 are in better agreement with the results of experimental research than the relationship in the OpenFoam solver.

Also, the stopping distance was also investigated by Yang's research. The error caused by our numerical solution with Young's results was 0.006, 0.09 and 0.04 for 400, 800 and 132.60 Reynolds, respectively.