Abstract We performed simulations of Rayleigh-Benard convection (RBC) for very high Ra number, 10 9 , 10 12 , 10 13 , 10 14 and 10 16 , thus beyond the reach of classical LES, by using an elliptic-relaxation hybrid RANS-LES (ER-HRL) model paired with a compound wall treatment that allows much coarser mesh resolution in the near wall region. The standard switching criterion used in the hybrid RANS-LES modeling based on wall distance is modified and linked to the local turbulence properties in order to sustain the modeled turbulence production in the RBC configuration. The proposed hybrid model successfully predicts the main integral and mean flow features at Ra = 10 9 for which experimental and LES data exists. The Nusselt number obtained is closely following the power law correlation based on 0.307 exponent up to Ra = 10 13 . For higher Ra number, the Nusselt number displays a Ra -scaling behaviour that is consistent with the so-called ultimate regime, where Nu ≈ Ra 1 / 2 . Furthermore, unlike LES, the ER-HRL model provides generally good results even when using a very coarse mesh at high Ra number. The instantaneous three-dimensional fields reveal interesting features of the Rayleigh-Benard convection at very high Ra number such as a strong correlation between instantaneous pressure and temperature fields, a major similarity of the flow structures in the near-wall region to those present in the impinging jet, existence of the superstructures and their tendency to cluster and localise with increasing Ra number. The simulations are performed with an in–house unstructured finite-volume code T-Flows, using second-order-accuracy discretisation schemes for space and time.

Abstract We studied numerically the heat transfer in flow over a rotationally oscillating cylinder at a subcritical Reynolds number ( R e = 1.4 × 10 5 ) that is an order of magnitude higher than previously reported in the literature. This paper is a follow-up of the earlier study of hydrodynamics and drag force in a range of forcing frequencies and amplitudes (Palkin et al., 2018). This time we focus on heat transfer and its correlation with the observed flow field and vortical patterns. Four forcing frequencies f = f e / f 0 = 0 , 1 , 2.5 , 4 for two forcing amplitudes Ω = Ω e D / 2 U ∞ = 1 and 2 are considered, where f0 is the natural vortex-shedding frequency, U∞ the free-stream velocity and D the cylinder diameter. The parametric study was performed by solving three-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) equations closed by a wall-integrated second-moment (Re-stress) model, verified earlier by Large-eddy simulations and experiments in several reference cases including flows over a stagnant, as well as rotary oscillating cylinders at the same Re number. The thermal field, treated as a passive scalar, was obtained from the simultaneous solution of the energy equation, closed by the standard (GGDH) anisotropic eddy-diffusivity model. The computations showed that for the unforced cylinder heat transfer is characterized by very high local rates due to a strong thinning of the thermal boundary layer as a result of the impact and interactions of large coherent structures with the wall. The overall average Nusselt number does not change much for the forced cylinder but its time-averaged, phase-averaged and instantaneous circumferential profiles show some profound differences compared to the stationary cylinder. The distribution of Nu on the back surface becomes more uniform with less frequent occurrence of high values, especially for the higher frequencies f = 2.5 and f = 4 . This is attributed to diminishing of the mean-recirculation zone as well as to the overall suppression of turbulent fluctuations. The rotary oscillation of the cylinder appears potentially efficient in achieving a more uniform circumferential distribution of Nu and avoiding local overheats and hot spots.

We report on a numerical study of the vortex structure modifications and drag reduction in a flow over a rotationally oscillating circular cylinder at a high subcritical Reynolds number, $Re=1.4\times 10^{5}$ . Considered are eight forcing frequencies $f=f_{e}/f_{0}=0.5$ , $1$ , $1.5$ , $2$ , $2.5$ , $3$ , $4$ , $5$ and three forcing amplitudes $\unicode[STIX]{x1D6FA}=\unicode[STIX]{x1D6FA}_{e}D/2U_{\infty }=1$ , $2$ , $3$ , non-dimensionalized with $f_{0}$ , which is the natural vortex-shedding frequency without forcing, $U_{\infty }$ the free-stream velocity, $D$ the diameter of the cylinder. In order to perform a parametric study of a large number of cases ( $24$ in total) with affordable computational resources, the three-dimensional unsteady computations were performed using a wall-integrated (WIN) second-moment (Reynolds-stress) Reynolds-averaged Navier–Stokes (RANS) turbulence closure, verified and validated by a dynamic large-eddy simulations (LES) for selected cases ( $f=2.5$ , $\unicode[STIX]{x1D6FA}=2$ and $f=4$ , $\unicode[STIX]{x1D6FA}=2$ ), as well as by the earlier LES and experiments of the flow over a stagnant cylinder at the same $Re$ number described in Palkin et al. (Flow Turbul. Combust., vol. 97 (4), 2016, pp. 1017–1046). The drag reduction was detected at frequencies equal to and larger than $f=2.5$ , while no reduction was observed for the cylinder subjected to oscillations with the natural frequency, even with very different values of the rotation amplitude. The maximum reduction of the drag coefficient is 88 % for the highest tested frequency $f=5$ and amplitude $\unicode[STIX]{x1D6FA}=2$ . However, a significant reduction of 78 % appears with the increase of $f$ already for $f=2.5$ and $\unicode[STIX]{x1D6FA}=2$ . Such a dramatic reduction in the drag coefficient is the consequence of restructuring of the vortex-shedding topology and a markedly different pressure field featured by a shrinking of the low pressure region behind the cylinder, all dictated by the rotary oscillation. Despite the need to expend energy to force cylinder oscillations, the considered drag reduction mechanism seems a feasible practical option for drag control in some applications for $Re>10^{4}$ , since the calculated power expenditure for cylinder oscillation under realistic scenarios is several times smaller than the power saved by the drag reduction.