Contribution of large-scale motions to the Reynolds shear stress in turbulent pipe flows

다국어 초록 (Multilingual Abstract)

<P><B>Abstract</B></P> <P>Direct numerical simulation data for turbulent pipe flows with <I>Re<SUB>τ</SUB> </I> = 544, 934, and 3008 were used to investigate the contribution of large-scale motions (LSMs) to the Reynolds shear stress. The relationship between viscous force ( <SUP> d 2 </SUP> <SUP> U + </SUP> / d <SUP> y + 2 </SUP> , VF) and turbulent inertia ( d <SUP> ⟨ − <SUP> u ′ </SUP> <SUP> v ′ </SUP> ⟩ + </SUP> / d <SUP> y + </SUP> , TI) results in a transition from the inner length scale to the intermediate length scale in the meso-layer. The acceleration force of the LSMs is balanced by the deceleration force of the small-scale motions (SSMs), which makes the zero TI at the wall-normal location of the maximum Reynolds shear stress (<I>y<SUB>m</SUB> </I> <SUP>+</SUP>). As the Reynolds number increases, the enhanced acceleration force of the LSMs expands the nearly zero TI region. The constant-stress layer is formed in the neighborhood of the zero TI, having the relatively strong VF. For sufficiently high Reynolds number flows, the log law is established beyond the meso-layer due to the fact that VF loses its leading order. The role of the LSMs in the wall-scaling behavior of <I>y<SUB>m</SUB> </I> <SUP>+</SUP> is examined.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Direct numerical simulation data for turbulent pipe flows were used to investigate the contribution of large-scale motions to the Reynolds shear stress. </LI> <LI> The acceleration force of the large-scale motions is balanced by the deceleration force of the small-scale motions. </LI> <LI> For sufficiently high Reynolds number flows, the log law is established beyond the meso-layer. </LI> </UL> </P>