LES of incompressible heat and fluid flows past a square cylinder at high Reynolds numbers

Abstract

This paper presents large eddy simulation (LES) results of incompressible heat and fluid flows around a square cylinder (SC) at zero incident angle at high Reynolds numbers (Re) in the range from 1.25×10⁵ to 3.5×10⁵. LES results are obtained on the basis of swirling strength based sub-grid model, and a higher order upwind scheme developed with respect to the Taylor expansion. It was found that, for the zero incident SC wake flows at a Reynolds number in the range {Re₅ = Re/10⁵ ∈ [1.25, 3.5]}, the Strouhal number equals to 0.1079, completely independent of the Reynolds number; the coefficient of drag is around 1.835 with an uncertainty of about 1.9%, almost non-sensitive to the Re. When Re is beyond 3.0×10⁵, the time-averaged peak value of sub-grid viscosity is over 340, implying that the role of sub-grid model is crucial in some regions where vortex motion is active and vortex interaction is intense. The time–spanwise (t-z) averaged sub-grid viscosity ratio profiles and the profiles of fluctuations of the sub-grid viscosity ratio and velocity components at four locations downstream of the SC are presented. The fields of the t-z averaged sub-grid viscosity ratio, and the instantaneous fields of streamwise and spanwise vorticities are also reported and discussed. The predicted mean Nusselt number is compared with empirical correlations, revealing that swirling strength based LES has its potential in predicting natural and industrial flows.

Keywords:

• square cylinder wake flow
• sub-grid viscosity ratio
• incompressible heat and fluid flows
• swirling strength
• vortex interaction

Acknowledgements

We thank the anonymous referees for their invaluable suggestions and Dr. J.L. Niu working at PolyU of Hong Kong for his helpful private communications.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is financially supported by NSFC [grant number 11372303] and the Research Grant Council of HKSAR [grant numbers PolyU 5109/10E and B-Q21J].