MMAE Seminar - Dr. Hassan Nagib - Advances in the Quest for a Universal Log-law and the Role of Outer Flow and Pressure Gradient in “Canonical” Wall-bounded Turbulent Flows

Armour College of Engineering's Mechanical, Materials & Aerospace Engineering Department will welcome Dr. Hassan Nagib, John T. Rettaliata Distinguished Professor of Mechanical and Aerospace Engineering at the Illinois Institute of Technology, on Wednesday, September 6th, to present his lecture, Advances in the Quest for a Universal Log-law and the Role of Outer Flow and Pressure Gradient in "Canonical" Wall-bounded Turbulent Flows.

Abstract

The trinity of so-called "canonical" wall-bounded turbulent flows, comprising the zero pressure gradient turbulent boundary layer, abbreviated ZPG TBL, turbulent pipe flow and channel/duct flows has continued to receive intense attention as new and more reliable experimental data have become available. Nevertheless, the debate on whether the logarithmic part of the mean velocity profiles, in particular the Kármán constant κ, is identical for these three canonical flows or flow-dependent is still ongoing. In early pipe flow experiments, the emphasis has been on the scaling of the centerline velocity and the friction factor with Reynolds number. As measurement techniques have evolved, attention has shifted towards the "law of the wall" U+ = (1/κwall) ln(y+) + B and its Kármán constant κwall. In the last years the value of κwall in pipes has closely approached the "most popular" value of 0.384 for the zero-pressure-gradient boundary layer (Furuichi et al. (2015), Örlü et al. (2016)) which seemingly supports the claim of Marusic et al. (2013) that κ = 0.39 is universal for pipe flow and zero-pressure-gradient boundary layers. However, the asymptotic matching to the "wake", already discussed by Coles (1956), has not received enough attention. It requires that κwall be the same as κCL in the expression for the centerline velocity U+ = (1/κCL) ln(Reτ ) + C, but κCL has consistently remained larger than 0.42. Only very recently Monkewitz (2017)) has proposed a resolution of this conundrum by introducing a universal internal wall log-law with κint = 0.384 for the range 102 < y+ < 103, followed by an external log-law with κext = κCL for y+ < 0.05Reτ and the wake. The analysis of Monkewitz (2017) for pipe flow was based on the Superpipe data where κext = 0.42. So the question arises whether the difference between κint and κext is statistically significant. The purpose of this contribution is to show that this is indeed the case, as κCL in CICLoPE (Center for International Cooperation in Long Pipe Experiments, in Predappio, Italy) is found to be κCL ≈ 0.446 +/- 0.008. Interestingly, this value is very close to the original κCL = 0.436 of Zagarola & Smits (1998) for the Superpipe and the value of 0.437 found in the first CICLoPE experiments by Fiorini (2017).

Biography

Professor Hassan Nagib is the John T. Rettaliata Distinguished Professor of Mechanical and Aerospace Engineering at the Illinois Institute of Technology, Chicago, Illinois, and the Founding Director of the Institute's Fluid Dynamics Research Center. His field of specialty is in fluid mechanics, turbulent flow and flow management and control. Professor Nagib is the recipient of a number of prestigious honors including being a Fellow of the American Physical Society, the American Association of Advancement of Science, the American Institute of Aeronautics and Astronautics, and the American Society of Mechanical Engineers.