Macroscopic turbulent kinetic energy budget in flow through a wall-bounded compact bank of cylinders

Abstract

The flow in devices, such as heat exchangers, can be idealized as turbulent flow past an array of regularly spaced obstacles. Engineering calculations in such devices are easily handled if the flow can be represented by its volume-average quantities. This paper reports an investigation into the volume-averaged flowfield in a regular array of cylinders of finite height in crossflow at two Reynolds numbers (ReD). The investigation is based on scale-resolving computations and is thus the first to analyze the true form of the macroscopic turbulent kinetic energy (TKE) conservation law in the presence of macroscopic shear. Volume-averaging is performed parallel to the end walls in order to obtain profiles of macroscopic flow quantities. In inner coordinates, the macroscopic velocity profiles are similar to the canonical turbulent channel flow profiles, but with different values of the von Kármán constant and log-law y-intercept. The volume-averaged TKE is defined so as to include contributions from both the macroscopic and microscopic components of the flow. While the macroscopic TKE profile is very different to that of channel flow, the macroscopic TKE budget terms are remarkably similar. One notable exception is that the production rate stays large throughout the domain rather than attenuating rapidly after a near-wall peak. An extension to a widely used macroscopic turbulence model is proposed, which enables it to match the volume-averaged TKE production rate predicted by the large eddy simulations.