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Swirling-strength based large eddy simulation of turbulent flow around single square cylinder at low Reynolds numbers

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Abstract

In view of the fact that large scale vortices play the substantial role of momentum transport in turbulent flows, large eddy simulation (LES) is considered as a better simulation model. However, the sub-grid scale (SGS) models reported so far have not ascertained under what flow conditions the LES can lapse into the direct numerical simulation. To overcome this discrepancy, this paper develops a swirling strength based the SGS model to properly model the turbulence intermittency, with the primary characteristics that when the local swirling strength is zero, the local sub-grid viscosity will be vanished. In this paper, the model is used to investigate the flow characteristics of zero-incident incompressible turbulent flows around a single square cylinder (SC) at a low Reynolds number range Re ∈ [103, 104]. The flow characteristics investigated include the Reynolds number dependence of lift and drag coefficients, the distributions of time-spanwise averaged variables such as the sub-grid viscosity and the logarithm of Kolmogorov micro-scale to the base of 10 at Re = 2 500 and 104, the contours of spanwise and streamwise vorticity components at t = 170. It is revealed that the peak value of sub-grid viscosity ratio and its root mean square (RMS) values grow with the Reynolds number. The dissipation rate of turbulent kinetic energy is larger near the SC solid walls. The instantaneous factor of swirling strength intermittency (FSI) exhibits some laminated structure involved with vortex shedding.

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Abbreviations

A :

matrix expression of velocity gradient ∇ u

a ij :

element of matrix A

B :

spanwise length of square cylinder (m)

C μ :

artificially defined constant in Eq. (1)

d :

cross-sectional side length of SC (m)

f I :

factor of swirling strength intermittency

k :

turbulent kinetic energy

p :

pressure (Pa)

Re :

Reynolds number (du in/ν)

Re 3 :

representative for Re (Re/103)

t :

time(s)

u :

velocity vector (m/s) (u, v, w)

u in :

incoming flow speed (m/s)

x :

coordinate vector (m) (x, y, z)

x u , x d :

parameters for computational-domain (m)

y b , y d :

parameters for computational-domain (m)

δ :

harmonically averaged grid interval (m)

δ i :

gridintervalinx i direction (m)

Δ t :

timestep(s)

ɛ :

dissipation rate of turbulent kinetic energy

∈:

infinitesimal for accuracy representation

λ ci :

swirling strength (1/s)

λ :

eigenvalue of ∇ u (λ cr + iλ ci )

ρ :

fluid density (kg/m3)

ν :

fluid kinematic viscosity (m2/s)

ν s :

sub-grid viscosity (m2/s)

ν sr :

viscosity ratio (ν s/ν)

(ν sr)pm :

time-averaged (ν sr)peak

(ν sr)′p :

root mean square of(ν sr)peak

(ν sr)peak :

peak value of ν sr

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Authors and Affiliations

  1. Faculty of Engineering Science, University of Science and Technology of China, Hefei, 230026, P. R. China

    Zuo-jin Zhu  (朱祚金) & Ying-lin Li  (李应林)

  2. Faculty of Construction and Environment, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, P. R. China

    Zuo-jin Zhu  (朱祚金) & Jian-lei Niu  (牛建磊)

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  1. Zuo-jin Zhu  (朱祚金)
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  2. Jian-lei Niu  (牛建磊)
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Correspondence to Zuo-jin Zhu  (朱祚金).

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Project supported by the National Natural Science Foundation of China (No. 11372303)

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Zhu, Zj., Niu, Jl. & Li, Yl. Swirling-strength based large eddy simulation of turbulent flow around single square cylinder at low Reynolds numbers. Appl. Math. Mech.-Engl. Ed. 35, 959–978 (2014). https://doi.org/10.1007/s10483-014-1847-7

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