Direct numerical simulation of a stationary spherical particle in fluctuating inflows

Yuqi Wang,Zhengping Zhu,Lian Shen,Ruifeng Hu

doi:10.1063/5.0076691

Abstract

Fully resolved direct numerical simulations are conducted to study the effects of fluctuating freestream flow on the drag force and wake characteristics of a stationary spherical particle. Sinusoidal fluctuation around a mean value is adopted as the freestream velocity. The interaction between the particle and fluctuating flow is computed by the direct-forcing immersed boundary method. We principally consider the relative difference between the computed mean drag and the drag law of a uniform flow past the particle and the properties of drag fluctuation in different freestream fluctuation directions. For the influence of streamwise fluctuating inflow, the relative mean drag difference increases with the particle Reynolds number. At small or intermediate particle scale ratios, the relative mean drag difference is very close to zero, indicating that the classical drag law can be used in these cases, while a large particle scale ratio can induce a notable increase in the relative mean drag difference at a large particle Reynolds number and high fluctuation intensity. For the transverse fluctuating inflow, generally, there is an evident increase in the mean drag coefficient when the particle scale ratio is small. Compared with the streamwise fluctuation case, the drag fluctuation intensity is a little smaller with the transverse fluctuating inflow. An explicit empirical drag fluctuation law is obtained by fitting the data for streamwise fluctuating inflow. The wake characteristics are also analyzed, and they are found to be strongly dependent on the direction of inflow fluctuation.

Highlights

Particle-laden flow widely exists in nature and engineering applications, such as fluidized bed reactor flow, sediment transport, and dust storm in the atmosphere, as well as the spread of haze pollutants in cities
The empirical drag law based on the instantaneous or average relative velocity can accurately predict the mean drag coefficient obtained from direct numerical simulation (DNS), but the prediction accuracy will decrease with the increase in the particle diameter
The large particle scale ratio (Dp/L = 10) can induce a notable increase in the relative mean drag coefficient difference at a large particle Reynolds number [(e.g., Rep = 200 and 300)] and high fluctuation intensity (I = 0.5), which can reach about 15%

Summary

INTRODUCTION

Particle-laden flow widely exists in nature and engineering applications, such as fluidized bed reactor flow, sediment transport, and dust storm in the atmosphere, as well as the spread of haze pollutants in cities. The results showed that there is no obvious difference between the drag of liquid droplets in turbulence and that of solid spherical particles in uniform laminar flow (empirical drag law) at the same Reynolds number They argued that turbulence has no significant effect on the drag because very little turbulence energy resided at the length scale comparable to the size of droplets, and most of the turbulence energy resided at the length scales larger than the integral scale. The empirical drag law based on the instantaneous or average relative velocity can accurately predict the mean drag coefficient obtained from DNS, but the prediction accuracy will decrease with the increase in the particle diameter They found that the intensity of the fluctuations in the drag and lift forces can be scaled linearly with both the mean drag and freestream turbulence intensity.

Numerical method

Computational setup

Characteristics of mean and fluctuating drag

Vortical structures in the wake

CONCLUSIONS