Numerical Simulation of Turbulent Concentric Annular Pipe Flow using One-Dimensional Turbulence (ODT): Part 2: Heat Transfer

Abstract

Turbulent concentric coaxial (annular) pipe flow with passive heat transfer is theoretically analyzed and numerically modeled in an extended parametric range using the stochastic one-dimensional turbulence (ODT) model. ODT provides predictive capabilities by fully resolving viscous, conductive, and turbulent advective transport processes along a representative radial coordinate within a dimensionally reduced and stochastic model formulation. Using a fixed model calibration for moderate and low Prandtl numbers, $Pr=0.71$ and $0.025$, effects of radius ratio, $η=R_{\rm i}/R_{\rm o}$ are investigated up to a highly turbulent flow regime. The analytical expression of the inner wall boundary layer yields a logarithmic law of the wall for the passive temperature. These results suggest that a conventional linear expression is inadequate for representing near-wall low-order statistics in the radial gap, in particular at the cylindrical inner wall. Additionally, the log-law region falls short if curvature and finite Reynolds number effects are not considered. Analytical boundary layer profiles fitting numerical predictions form the basis for heat transfer scaling relations. Heat transfer scalings are parameterized by a Nusselt correlation, which is extended to account for radius ratio effects. The findings demonstrate that the radius ratio has a significant impact on the thermal statistics over the two curved walls and should be considered even at high Reynolds numbers and low Prandtl numbers.