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

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 107 ⩽ Ra ⩽ 109 range, the performance of a T-RANS (using a low-Re three-equation 〈k〉–〈ε〉–〈θ2〉 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 = 109), 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 ⩽ 109) and experimental data for over a ten-decades range of Ra (106 ⩽ Ra ⩽ 2 × 1016). 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.