Analytical eddy viscosity models based on the concepts of velocity and length scales are presented: (1) a near-wall eddy viscosity formulation based on an analytical solution for turbulent kinetic energy (TKE); for the outer part, two eddy viscosity formulations namely (2) an exponential-type eddy viscosity profile and (3) an eddy viscosity based on an extension of von Karman’s similarity hypothesis. The eddy viscosity from model (3) is Reτ -independent, while the eddy viscosity from model (2) is Reτ-dependent (where Reτ is the friction Reynolds number). However for large values of Reτ (Reτ > 2000), this model (2) becomes Reτ-independent, and the two coefficients reach asymptotic values. All results are validated by both direct numerical simulation DNS and experimental data in the same range of friction Reynolds numbers, respectively 300<Reτ<5200 for fully-developed turbulent channel flows and 923<Reτ<6139 for open-channel flows. Comparisons with DNS data of eddy viscosity in turbulent channel flows for eight different flow conditions show good agreement. For open-channel flows, an additional correction function related to the damping effect of turbulence near the free surface is used in the outer part. Both models (2) and (3) are similar to the log-wake-modified eddy viscosity profile with different values of the Coles’ parameter, i.e., Π=0.2 for the first model and Π=0.15 for the second model. These values are similar to those found in open-channel flow experiments. The proposed analytical models were validated through computation of mean streamwise velocity profiles, obtained from the resolution of the momentum equation and comparisons to DNS and experimental data. Our method allows for both fully-developed turbulent channel and open-channel flows accurate description of mean streamwise velocity profiles and turbulent shear stress outside the log-law layer, in the viscous and buffer layers and in the outer region. The aim of this study is to provide analytical tools for turbulent flow applications. Different applications of these models including CFD will be presented.
About the Speaker
Rafik Absi is PhD in Fluid Mechanics (2001) from University of Caen Normandy (France) and HDR (Accreditation to supervise research) in Physics (2011) from CY Cergy Paris University (France). He is since 2008 professor and since 2021 Director of Research at ECAM-EPMI Cergy-Pontoise (France). He was expert and member appointed to the committee of specialized experts CES for ANSES French Environment Agency. He was invited 3 times (2010, 2013, 2020) at Tohoku University (Japan) by JSPS 'Japan Society for the Promotion of Science' within the Invitational Fellowship Program for Research in Japan.
Host: Professor Leo Chamorro