Direct numerical simulation of a 30R long turbulent pipe flow at Re=3008

Abstract

A direct numerical simulation of a turbulent pipe flow at a high Reynolds number of Re-tau = 3008 over a long axial domain length (30R) was performed. The stream-wise mean velocity followed the power law in the overlap region (y(+) = 90-300; y/R = 0.03-0.1) based on the power law indicator function. The scale separation of the Reynolds shear stresses into two components of small-and large-scale motions (LSMs) revealed that the LSMs in the outer region played an important role in constructing the constant-stress layer and the mean velocity. In the pre-multiplied energy spectra of the streamwise velocity fluctuations, the bimodal distribution was observed at both short and long wavelengths. The k(x)(-1) region associated with the attached eddies appeared in lambda(x)/R = 2-5 and lambda(x)/y = 18-160 at y(+) = 90-300, where the power law was established in the same region. The k(z)(-1) region also appeared in lambda(z)/R = 0.3-0.6 at y(+) = 3 and 150. Linear growth of small-scale energy to large-scale energy induced the k(x)(-1) region at high Reynolds numbers, resulting in a large population of the LSMs. This result supported the origin of very-large-scale motions in the pseudo-streamwise alignment of the LSMs. In the pre-multiplied energy spectra of the Reynolds shear stress, the bimodal distribution was observed without the k(x)(-1) region.