Very large-scale computation of very small-scale motions in a fully developed pipe flow

Abstract

Local isotropy theory is examined using direct numerical simulation in a fully developed pipe flow at two Reynolds numbers Reτ=1285.6 and 684.8. The approach to local isotropy is assessed with reference to the two Kolmogorov classical equations for longitudinal and transverse velocity structure functions. The results for the second-order longitudinal structure functions in both the dissipative and inertial ranges indicate an improved agreement with the local isotropy hypothesis as the centreline is approached. However, the transverse structure functions satisfy isotropy neither in the dissipative range or in the inertial range. The distribution of the longitudinal and transverse structure functions also shows a substantial Reynolds number dependance in the logarithmic region of the flow and beyond. The results for the third-order longitudinal structure function demonstrate an increased Reynolds number influence, and a deteriorating tendency to local isotropy for large separations. Contour images of axial velocity differences in the dissipative and inertial ranges have exhibited interesting patterns in relation to those of the instantaneous axial velocity. Finally, the results obtained in this investigation are in very good agreement with other published experimental and numerical data on channel and duct flows. Copyright © 2010 John Wiley & Sons, Ltd.