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Recent Advances in Overlap Region of Wall-Bounded Turbulence

Time: Mon 2024-03-11 10.30 - 11.30

Location: Faxén, Teknikringen 8

Participating: Prof. Hassan Nagib, ILLINOIS TECH (IIT)

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Abstract: Utilizing the three-pronged approach of experimental measurements, computational results (DNS) and matched asymptotic analysis, we have reexamined the three canonical wall-bounded turbulent flows of pipe, channel and zero pressure gradient boundary layer. Detailed and systematic study confirmed the non-universality of the Kármán constant (k) reported in 2008 by Nagib, H. M. & Chauhan, K. A. “Variations of von Kármán coefficient in canonical flows,” Phys. Fluids 20, 101518. Recentley, a new matching approach also revealed an inner-outer overlap consisting of a superposition of log-law and a linear term, as detailed in paper by Monkewitz, P. A. & Nagib, H. M. “The hunt for the Kármán “constant” Revisited,” J. Fluid Mechanics, vol. 967, A15, 2023. DOI: .

A similar linear term was suggested by Afzal & Yajnik, J. Fluid Mech. (1973 & 1970) and Luchini (2017) Phys. Rev. Lett. 118, 224501. In our results, we find that the coefficients of both terms are dependent on the pressure gradient of the flow. A new and robust method is devised to simultaneously determine the coefficients of the log and linear terms, in pressure driven flows at currently accessible Reynolds numbers, and yields k values that are consistent with the k values deduced from the Reynolds number dependence of centerline velocities.

After many decades of experience with “canonical” wall-bounded turbulent flows, we recognize fully developed pipe flow as the ideal flow to compare computations and experiments. With collaborators at several universities, we have conducted experiments, with \(Re_\tau\)  up to 33,000, and DNS for pipe flow at \(Re_\tau\) = 550 & 1,000, with several resolutions, and extended Eddy Turnover Times (ETT) of up to 200. New criteria for resolution and an existing criterion for convergence of DNS are being developed and confirmed, respectively. We find that higher resolution DNS and longer computational times are required for wall-bounded turbulence, compared to values commonly used. Finally, the impact of the new combined log-law and linear term on Textbooks, Lecture Notes, RANS Codes and Turbulence Models will be highlighted.

Finally, we utilized experimental data obtained under various favorable and adverse pressure gradients in the NDF wind tunnel at IIT and the MTL wind tunnel at KTH, to extract the parameters of the "Log-Linear" overlap region in pressure gradient boundary layers. The Kármán “coefficient” \(\kappa\), the slope of the linear component of the overlap region \(S_0\) and the constant \(B_0\) are presented as functions of the pressure-gradient parameter \(\beta\), and compared to trends from ZPG boundary layers, and fully developed channel and pipe flows that are in equilibrium.

Bio: Professor Nagib is the John T Rettaliata Endowed Professor of Mechanical and Aerospace Engineering at the ILLINOIS TECH (IIT), Chicago, Illinois, and was 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. At ILLINOIS TECH, he served as MMAE Department Chair, Dean of Armour College, Academic Vice President, and Chief Scientist for IIT Research Institute (IITRI). Professor Nagib is the recipient of several 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. From his base institute for over half a century, he has been a visiting faculty on several occasions at Stanford University, Caltech, KTH, EPFL, Friedrich-Alexander University, Erlangen, and Tewkesbury Fellow, in Department. of Mechanical Engineering at University of Melbourne.