Direct Numerical Simulations of Temporally Decelerating Turbulent Pipe Flows

Abstract

Direct numerical simulations of temporally decelerating turbulent pipe flows are performed to examine the effects of temporal deceleration on the turbulence characteristics. The temporal decelerations are applied with three different values of the decelerating parameter f = |d U (b) /dt| based on the bulk mean velocity (U (b) ) to introduce weak, mild and strong decelerations, and the flow rates for all cases are linearly decreased with time. In order to highlight the variation of the turbulent statistics for an unsteady flow, five independent simulations of steady flows are conducted along with the Reynolds number. An inspection of the mean velocity profiles shows that the log law in the overlap region is established with a slight downward shift for the weakly decelerating flow, whereas this is not the case for the strong decelerating flow. A comparison of the Reynolds stress profiles between the unsteady and steady flows displays that the turbulence is highly intensified with an increase of f due to the enhanced vortical structures and that the radial propagation of the turbulence is delayed. An analysis of the turbulent production term of the Reynolds stress budget equation shows that frozen of the strong second-quadrant Reynolds shear stress event plays an important role in delaying the response of the turbulent energy with a decrease of the Reynolds number, leading to an increase in the Reynolds stress. In addition, spectral decomposition of the streamwise Reynolds normal stress into small- and large-scale components reveals that the enhanced turbulence throughout the entire flow for unsteady flows is a direct consequence of the delay of strong large-scale structures, although small-scale structures throughout the wall layer adjust rapidly to temporal deceleration.