Numerical Simulation of Turbulent Concentric Annular Pipe Flow using One-Dimensional Turbulence (ODT): Part 1: Momentum Transfer

Abstract

Turbulent concentric coaxial (annular) pipe flow is numerically investigated using a stochastic one-dimensional turbulence (ODT) model as a stand-alone tool. The dimensionally reduced ODT domain enables fully resolved numerical simulations of the flow across the radial gap between the cylindrical inner wall and the cylindrical outer wall. The model is calibrated with available reference data at low bulk Reynolds number $Re_{D_h} = 8900$ for a wide (radius ratio $η= 0.1$) and a moderate ($η= 0.5$) gap. Making use of the model's predictive capabilities, radius ratio and Reynolds number effects are investigated, reaching bulk Reynolds numbers as large as $Re_{D_h}=10^6$. Despite the large $Re_{D_h}$ values reached, spanwise wall-curvature effects remain sensible in the momentum boundary layer. The effects are more pronounced for larger wall curvature and to leading orders restricted to the convex cylindrical inner wall. Wall-curvature corrections to the law of the wall are obtained for both the viscous and Reynolds-stress dominated regions by fitting analytically derived expressions for the flow profile to the stochastic simulation data, demonstrating physical compatibility with Reynolds-averaged Navier--Stokes flow. Second-order and detailed fluctuation statistics demonstrate the permeating and nonlocal influence of spanwise wall curvature on the turbulent boundary layer. Surrogate model output in terms of conditional eddy event statistics reveals that the disparity between the near-inner and near-outer wall turbulence increases with Reynolds number for small radius ratios, suggesting that annular pipe flows require wall-curvature-aware wall models even at very large Reynolds numbers.