The Reynolds-averaged Navier–Stokes (RANS) models depend on empirical constants to close the Reynolds stress terms. The empirical constants were obtained using experiments conducted at low Reynolds numbers several decades ago. In this paper, we revisit the turbulent viscosity parameter $C_\mu$, based on the stress–intensity ratio $c^2 = {|\overline {uw}|}/{k}$. Here, $\overline {|uw|}$ and $k$ are the absolute values of the Reynolds stress and turbulent kinetic energy, respectively. Through a priori comparisons, we find that the currently accepted value of $C_\mu = 0.09$ does not agree with the latest direct numerical simulation (DNS) and experimental datasets of wall-bounded turbulent planar flows. Therefore, a new value is suggested by averaging $c^2$ in the equilibrium region, where the production ($\mathcal {P}$) of $k$ is within 10 % of the dissipation rate ($\epsilon$), and consequently, $c^4 \approx C_\mu$. We evaluate flows up to friction Reynolds number $Re_\tau \approx 10\,000$ and find that with increasing $Re_\tau$, $C_\mu$ approaches a value of 0.06, which is almost 50 % lower than the prevalent value of 0.09. Finally, we perform an a priori test with the new (proposed) value of $C_\mu = 0.06$ to show that the estimated turbulent viscosity $\nu _T$ for wall-bounded flows is in much closer agreement with the exact (DNS) values than when $\nu _T$ is estimated using $C_\mu = 0.09$.

The flow and heat transfer characteristics over a single dimple and an array of staggered dimples have been investigated using the Reynolds Averaged Navier-Stokes (RANS) approach. The objective is to determine how reliably RANS models can predict this type of complex cooling flows. Three classes of low-Reynolds number RANS models have been employed to represent the turbulence. These included a linear Eddy Viscosity Model (EVM), a Non-Linear Model (NLEVM) and a Reynolds Stress transport Model (RSM). Variants of the k-ε model have been used to represent the first two categories. Steady and time-dependent simulations have been carried out at a bulk Reynolds number of around 5,000 with dimple print diameter to channel height ratios of D/H = 1.0, 2.0 and ratios of dimple depth to channel height of δ/H = 0.2, 0.4. The linear EVM and the RSM tested both produce symmetric circulations in the dimples, while the NLEVM produces an asymmetric pattern. The mean velocity profiles predicted numerically are generally in good agreement with the data. The main flow characteristics are reproduced by the RANS models, but some predictive deviations from available data point to the need for further investigations. All models report an overall enhancement in heat transfer levels when using dimples in comparison to those of a plane channel.

Progress is reported on the modelling, via RANS closures, of two swirling turbulent flows important in aeronautics: the trailing wing-tip vortex and the flow in rotor-stator cavities. For the former the decay of the vortex is only well captured at second-moment level while, for the latter, an unsteady flow computation brings out large-scale organized structures, with the number of structures varying with cavity aspect ratio and Reynolds number, a result qualitatively in accord with experiment.