LES, T-RANS and hybrid simulations of thermal convection at high Ra numbers

Abstract The paper reports on application of different approaches to the simulations of thermal convection at high Rayleigh ( Ra ) numbers. Based on new well-resolved LES in 10 7  ⩽  Ra  ⩽ 10 9 range, the performance of a T-RANS (using a low- Re three-equation 〈 k 〉–〈 e 〉–〈 θ 2 〉 ASM/AFM subscale model) and a hybrid approach (utilizing the concept of “seamless” RANS/LES merging) have been compared. Targeting accurate predictions of heat transfer at very high Ra numbers, the near-wall behaviour of the subscale turbulence contributions is analyzed in details. Whilst the application of the conventional LES on a coarse grid resulted in huge underprediction of the Nusselt number (50% at Ra  = 10 9 ), thanks to a well-tuned subscale model, the T-RANS results showed excellent agreement for heat transfer with both the fine-resolved LES (for Ra  ⩽ 10 9 ) and experimental data for over a ten-decades range of Ra (10 6  ⩽  Ra  ⩽ 2 × 10 16 ). The visible absence of the fine-scale motion in the T-RANS, however, means that the T-RANS will perform poorly in flows where there are no strong large-scale forcing, as, e.g., in a side-heated vertical channel. In order to sensitize the T-RANS approach to high-frequency instabilities, different ways of hybrid RANS/LES merging based on “seamless” approach have been investigated. It is demonstrated that the hybrid approach is capable of capturing a significantly larger portion of the fine-structure spectrum than is possible with T-RANS, whilst also returning accurate predictions of heat transfer and turbulence statistics.