Direct numerical simulation of turbulent heat transfer in a channel with circular-arc ribs mounted on one wall

Turbulent heat convection in a cooling channel roughened with circular-arc ribs of different pitch-to-height ratios ($P/H=3.0$, 5.0 and 7.5) are studied using direct numerical simulations (DNS). The pitch-to-height ratio effects on turbulent heat transfer are studied through analyses of the first- and second-order statistical moments of the temperature field. It is observed that the local Nusselt number increases remarkably near the rib centre due to the flow impingement on the rib windward side. Furthermore, the overall thermohydraulic efficiency of the whole ribbed channel enhances dramatically as the pitch-to-height ratio $P/H$ increases. Meanwhile, the Reynolds analogy factor on the ribbed wall side decreases with an increasing value of $P/H$, indicating that the effect of heat transfer enhancement is counterbalanced by that of increasing hydraulic losses caused by the ribbed wall. It is found that temperature variance $〈{\theta }^{\prime }{\theta }^{\prime }〉$ weakens under the rib effects, and further decreases with an increasing value of $P/H$. From the transport equation of $〈{\theta }^{\prime }{\theta }^{\prime }〉$, it is seen that both profiles of $〈{\theta }^{\prime }{\theta }^{\prime }〉$ and its production term $P_{\theta }$ exhibit a dual-peak pattern at the midspan between two adjacent ribs, where the first peak near the wall enhances while the second peak in the internal shear layer weakens as the value of $P/H$ increases. The quadrant analysis of heated turbulent motions indicates that hot sweep and cold ejection events dominate turbulent heat fluxes near the ribbed bottom wall. Interestingly, both hot sweep and cold ejection events enhance in the internal shear layer around the rib height. However, this enhancement effect weakens as the value of $P/H$ increases.