Influence of large-scale accelerating motions on turbulent pipe and channel flows

Abstract

Direct numerical simulation data from turbulent pipe and channel flows at$\mathit{Re}_{\unicode[STIX]{x1D70F}}\approx 930$are used to investigate their statistical difference by focusing on large-scale motions (LSMs). The contribution to the bulk production of turbulent kinetic energy shows marked differences in the overlap and core regions. These discrepancies arise from the dominant contributions of the LSMs ($\unicode[STIX]{x1D706}_{x}>3\unicode[STIX]{x1D6FF}$) to the Reynolds shear stress in the channel flow. The spectrum of the net Reynolds shear force reveals that the LSMs accelerate the mean flow in the overlap region. The net force spectrum is further decomposed into the spectra of velocity–vorticity correlations,$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$, which are related to the advective vorticity transport and the change-of-scale effect, respectively. The dominance of large-scale accelerating motions (LSAMs) in the overlap region of the channel flow is due to the contribution of$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$at longer wavelengths ($\unicode[STIX]{x1D706}_{x}>3\unicode[STIX]{x1D6FF}$), The LSAMs are related to the long low-speed regions, and these regions are longer and wider in the channel flow than in the pipe flow. Due to the pipe curvature, the spanwise size of the LSMs is restricted by neighbouring LSMs and the spanwise velocity fluctuations are reduced. The contribution of$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$to the acceleration is prominent in the channel flow, leading to the dominance of the LSAMs associated with the change-of-scale effect.