SUMMARYIn this paper the 'Moment of Fluid' interface reconstruction method is extended to axisymmetric coordinate. In order to perform this extension, two modifications are applied to the original method. First, a new fluid moment is defined in the axisymmetric coordinate. Second, the remap phase is altered to incorporate the effect of symmetry. The capability of the extended method is assessed by testing its potential to track interfaces through large topology change. Also, the accuracy of the method is compared against widely used Young's method.

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We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed.

We report a novel power-law scaling for the friction factor of incompressible Newtonian fluid flows at extreme Reynolds numbers: f = Ce/Re2/13. The formula is based on a new phenomenology for coherent structures that dominate the momentum exchange in meso-layer regions and scales with the geometric mean δδν, where δν is the viscous length scale and δ is the pipe radius. Comparisons with the experimental data from the Princeton Superpipe and the Hi-Reff Facility at the National Metrology Institute of Japan show excellent agreement for a large range of Reynolds numbers. This work, along with the recent empirical evidence, suggests a possible change in the mechanism of turbulent momentum transfer for pipe flows in extreme Reynolds numbers.

Most discussions in the literature on the friction coefficient of turbulent flows of fluids with complex rheology are empirical. As a rule, theoretical frameworks are not available even for some relatively simple constitutive models. In the present work, a formula is proposed for the evaluation of the friction coefficient of turbulent flows of Bingham fluids. The developments combine a fresh analysis for the description of the microscales of Kolmogorov and the phenomenological turbulence model of Gioia and Chakraborty [G. Gioia and P. Chakraborty, Phys. Rev. Lett. 96, 044502 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.044502]. The resulting Blasius-type friction equation is tested against some experimental data and shows good agreement over a significant range of Hedstrom and Reynolds numbers. Comments on pressure measurements in yielding fluids are made. The limits of the proposed model are also discussed.