Turbulent flow of viscoelastic shear-thinning liquids through a rectangular duct: Quantification of turbulence anisotropy

Abstract

We report laser Doppler anemometry (LDA) measurements of mean velocity and turbulence structure for fully-developed turbulent flow through a rectangular duct of aqueous solutions of a xanthan gum and a polyacrylamide both of which are drag-reducing polymer solutions. All three components of the turbulent fluctuations (i.e. the Reynolds normal stresses) have been measured as well as the Reynolds shear stress − ρ u v ¯ . A novel open-slit test-section allows measurement of the component of Reynolds normal stress perpendicular to the duct wall and of the Reynolds shear stress down to values of y +, the distance from the surface in wall units, close to unity. We show that the maximum value of the transverse (or normal) component of turbulence intensity in wall units v ′ M A X + decreases linearly from about unity for zero drag reduction ( DR 1) to about 0.6 at DR 1 = 80% while the lateral component w M A X + is practically independent of DR 1 . For levels of drag reduction below 50% the streamwise component u′ + MAX increases monotonically but for higher levels of drag reduction the trend is less clear. Anisotropy of the turbulence structure is characterised using Pope's modification [S. Pope, Turbulent flows (2000), Cambridge University Press, New York.] of the triangle plot suggested by Lumley [J.L. Lumley, Computational modelling of turbulent flows, Adv. Appl. Mech. 18 (1978) 123–176] and shown to follow closely the line for axisymmetric turbulence. The detailed LDA measurements are supplemented by particle-image velocimetry observations which reveal how drag reduction changes the near-wall streaky structure.