Experimental Assessment of Symmetry Induced Higher-Moment Scaling Laws in Turbulent Pipe Flow

Abstract

The total velocity moment scaling law that can be obtained through the symmetry group analysis described by Oberlack et al. (Mech. Eng. Rev., vol. 2, 2015) is assessed using experimental pipe flow velocity measurements previously published in Zimmerman et al. (J. Fluid Mech., vol. 869, 2019, pp. 182–213) and Baidya et al. (J. Fluid Mech., vol. 871, 2019, pp. 377–400). Although the streamwise velocity data are well described by the proposed scaling law, we show that the observed level of agreement is primarily reflective of the role played by the mean velocity rather than of the details of the fluctuations. Indeed, recalculation of moment profiles using Gaussian standardized central moments in place of the measured ones results in very little change, and does not affect the overall quality of agreement. We also show that the influence of the mean makes discrimination between these turbulent and Gaussian total streamwise moment profiles via hotwire anemometry essentially infeasible. Finally, we find that in its present form the proposed scaling law is not suitable to describe the azimuthal total moment profiles using the same coefficients obtained from the streamwise total moment profiles.