Curvature influence on flow and heat transfer in a concentric annulus: Conventional and sensitized Reynolds stress modeling study

Abstract

A computational study was carried out on turbulent flow in a concentric annular pipe with a Reynolds number of $R{e}_{D_h}=8900$, subjected to double-sided uniform wall heating with a heat flux ratio of $q^{\ast }=q_{outer}^{\prime \prime }/q_{inner}^{\prime \prime }=1$. The computations were performed over a range of curvature parameters, that is radius ratio of $R_{inner}/R_{outer}=0.5$, 0.1, and 0.01, implying an increased difference in transverse curvature between the inner convex and outer concave pipe walls. The turbulence is modeled by a conventional differential near-wall Reynolds stress model (RSM) and its eddy-resolving version. The latter model represents an extension of the conventional formulation that accounts for turbulence fluctuations within the sensitized Reynolds-averaged Navier–Stokes (RANS) computational framework. The RSM’s eddy-resolving capability is achieved by introducing an additional production term in the scale-determining transport equation to selectively enhance turbulence production, in accordance with the Scale-Adaptive Simulation strategy. The thermal field is modeled using the classical gradient diffusion approach to heat flux, considering different formulations of the corresponding diffusion coefficient. The respective results for the mean flow and thermal field properties and the associated second-order statistics are analyzed in detail along with the available reference DNS data for a weaker transverse curvature influence corresponding to $\alpha \ge 0.1$. While this influence is not as strong at the outer concave wall, where the near-wall behavior of all flow variables resembles that of fully-developed flow in a pipe, the mean flow and thermal properties, as well as the associated turbulence correlations, depart noticeably from equilibrium conditions at the inner convex wall. This is particularly dramatic as the radius ratio decreases to $\alpha =0.01$, further enhancing the transverse curvature effects in terms of strengthening the asymmetry of all flow quantity profiles toward the inner annulus wall consistent with turbulence production suppression and turbulence anisotropy weakening.