Large eddy simulation of flows past an array of square cylinders

ABSTRACT

The flows past an array of square cylinders occur in wide range of applications. To study these flows, we conducted three-dimensional large-eddy simulations for flows past an array of the circular shape formed by multiple smaller square cylinders, where the Reynolds number defined by the array diameter was 1994. We conducted simulations with different solid volume fractions (SVFs) of the square cylinder array ($0.3\mathrm{\%}<\mathrm{S}\mathrm{V}\mathrm{F}<21.7\mathrm{\%}$). The effects of these configurations on flow characteristics were analyzed. Periodic drag fluctuation was observed when the SVF was small since the distance between the square cylinder was large, and the vortex shedding occurred with impact from other cylinders. No significant fluctuation in the drag was observed over time when the SVF was large. The minimum distance between the square cylinders was used to measure the degree of vortex shedding and reflect the relationship between the square cylinder position and the drag fluctuation.

Keywords:

• Drag coefficient
• flow–structure interactions
• large eddy simulation
• velocity field
• vorticity shedding

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notation

$d$	=	width of square cylinder
$D$	=	diameter of the array envelope
$U_{\mathrm{\infty }}$	=	free stream velocity
$\mathsf{F}\mathsf{r}$	=	Froude number
g	=	gravitational acceleration
ρ	=	water density
N	=	number of square cylinders inside the array
${\mathsf{R}\mathsf{e}}_{\mathsf{D}}$	=	Reynolds number defined by the envelope diameter
${\mathsf{R}\mathsf{e}}_{\mathsf{d}}$	=	Reynolds number defined by the individual cylinder diameter
${\mathsf{R}\mathsf{e}}_{\mathsf{H}}$	=	Reynolds number defined by the cylinder height
$\mathrm{\Delta }t$	=	time step
$t_0$	=	starting point for data statistics
$\mathrm{\Delta }T$	=	period for data statics
n	=	number of time steps during $\mathrm{\Delta }T$
$F_x^I$	=	drag force on an individual square cylinder
$C_d^I$	=	drag coefficient for an individual cylinder
$C_D^G$	=	total drag coefficient for the whole array
$\overline{C_D^G}$	=	the time-average total drag coefficient
$\overline{C_d^I}$	=	the time-average drag coefficient of an individual square cylinder
$\overline{C_d}$	=	average drag coefficient of an individual cylinder
$\overline{C_d^T}$	=	time-average of $\overline{C_d}$
$S_I$	=	sample standard deviation of $C_d^I$
$S_G$	=	sample standard deviation of $C_D^G$
$S_{\overline{I}}$	=	sample standard deviation of $\overline{C_d}$
$L_m^I$	=	minimum distance between the Ith square cylinder and the Jth surrounding cylinder

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant nos. 51625901 and 51879176]. Jianping Meng is grateful for the support of the Computational Science Centre for Research Communities, and the EPSRC grant EP/T026170/1.