LAUSR

Turbulent kinetic energy (TKE) equation based on the Reynolds averaging hypothesis was approximated in the near wall region of turbulent channel flows and an analytical solution for TKE was proposed by Absi for $$y^{ + } < 20$$ (R. Absi, Analytical solutions for the modeled k equation, Trans. ASME: J. Appl. Mech. 75 (2008) 044,501). While, comparisons with DNS data show very good agreement, some of the model approximations employed previously require revision which is the main motivation of this work. We here present an alternate formulation for the smooth near wall TKE budget and propose an improved method of solution. Results are compared against wide range of friction Reynolds numbers, Reτ DNS datasets and found to be in good agreement. Interestingly the proposed improved method reveals that beyond Reτ, = 5200 TKE profiles collapse meaning that the TKE remains independent of Reτ that is consistent with high Reynolds number turbulent characteristics reported in the DNS (Hultmark et. al., Turbulent pipe flow at extreme Reynolds numbers, Phys. Rev. Lett., 108 (2012) 094,501). Although there exist two parameters in the paresent work to be determined empirically from DNS data it is reported that these parameters become empirically free at high turbulent Reynolds numbers, Reτ → ∞.The other interesting aspect of this work is that one of these parameters may be sensitized to other additional effects viz., wall roughness, pressure gradient, magnetic field, etc. One of the potential advantages of these near wall smooth turbulent channel flow analytical solutions is to obviate the need for solving the TKE equation near the smooth wall in the RANS, hybrid RANS/LES closures thus resulting in quicker and accurate engineering computations.