Assessment of performance of subgrid stress models for a LES technique for predicting suppression of turbulence and heat transfer in channel flows under the influence of body forces

Abstract

The main purpose of this work was to assess the performance of subgrid stress models for large eddy simulation (LES) of the flow and heat transfer of a conductive liquid simulating a molten salt (Pr = 4.1) in a square duct under the influence of a transverse magnetic field and an upward flow of air in a vertical heated pipe under a strong influence of buoyancy. An analysis of these problems is important when choosing the most appropriate subgrid-scale LES model for calculating the flows of an electrically conductive liquid under the combined influence of a magnetic field and buoyancy forces. Four subgrid-scale (SGS) models were verified: the Smagorinsky model with damping function (SMP), a coherent structure model (CSM), a WALE model and a hybrid model based on the equation for turbulent kinetic energy (KDES). For magnetohydrodynamic (MHD) flow in the duct, computations were performed in a domain with periodic inlet-exit boundaries and in a domain corresponding to the entrance region of a duct with a transverse magnetic field. Mixed convection of the air in the vertical heated pipe was simulated only in the domain with periodic boundaries. The results are compared with available data of direct numerical simulations (DNS).For MHD flow in the duct, the best predictions of DNS data for the average and fluctuating velocity components at Ha=21.2 and Re=5602 were obtained with the CSM and WALE models. The skin-friction and heat transfer coefficients are well known to have a minimum as Ha increases due to turbulence suppression by the magnetic field. The SMP and KDES models predict a minimum at Hadip≈22, whereas the CSM and WALE models predict a minimum at Hadip≈30 for Re=5602. The DNS data marked these values as the lower and upper boundaries of the complete turbulence suppression region for the same Reynolds number.For mixed convection of the air upward flows in a circular heated pipe at Re=5300, the CSM and WALE models showed weaker suppression of turbulence due to buoyancy forces when compared to the DNS results. The results of calculations of skin-friction and heat transfer coefficients performed with the help of the SMP and KDES models are much more coincident with the DNS data.