Direct numerical simulation of turbulent heat transfer in annuli: Effect of heat flux ratio

Abstract

Fully developed turbulent flow and heat transfer in a concentric annular duct is investigated for the first time by using a direct numerical simulation (DNS) with isoflux conditions imposed at both walls. The Reynolds number based on the half-width between inner and outer walls, δ = ( r 2 - r 1 ) / 2 , and the laminar maximum velocity is Re δ = 3500 . A Prandtl number Pr = 0.71 and a radius ratio r ∗ = 0.1 were retained. The main objective of this work is to examine the effect of the heat flux density ratio, q ∗ = q 1 / q 2 , on different thermal statistics (mean temperature profiles, root mean square (rms) of temperature fluctuations, turbulent heat fluxes, heat transfer, etc.). To validate the present DNS calculations, predictions of the flow and thermal fields with q ∗ = 1 are compared to results recently reported in the archival literature. A good agreement with available DNS data is shown. The effect of heat flux ratio q ∗ on turbulent thermal statistics in annular duct with arbitrarily prescribed heat flux is discussed then. This investigation highlights that heat flux ratio has a marked influence on the thermal field. When q ∗ varies from 0 to 0.01, the rms of temperature fluctuations and the turbulent heat fluxes are more intense near the outer wall while changes in q ∗ from 1 to 100, lead to opposite trends.