Reynolds Number Dependence of Velocity Structure Functions in a Turbulent Pipe Flow

Abstract

Low-order moments of the increments δu andδv where u and v are the axial and radial velocity fluctuations respectively, have been obtained using single and X-hot wires mainly on the axis of a fully developed pipe flow for different values of the Taylor microscale Reynolds numberR λ. The mean energy dissipation rate〉e〈 was inferred from the uspectrum after the latter was corrected for the spatial resolution of the hot-wire probes. The corrected Kolmogorov-normalized second-order structure functions show a continuous evolution withR λ. In particular, the scaling exponentζ v , corresponding to the v structure function, continues to increase with R λ in contrast to the nearly unchanged value of ζ u . The Kolmogorov constant for δu shows a smaller rate of increase with R λ than that forδv. The level of agreement with local isotropy is examined in the context of the competing influences ofR λ and the mean shear. There is close but not perfect agreement between the present results on the pipe axis and those on the centreline of a fully developed channel flow.