Theoretical Approach for the Fast Estimation of the Turbulent Kinematic Viscosity for Internal Flows

Abstract

An analytical expression for turbulent kinematic viscosity (νt), based solely on the hydraulic Reynolds number (Re), was derived and evaluated. The analytical expression is valid for the fast estimation of νt for internal, isotropic, fully developed flows. The expression was compared with experimental and simulation data for air, water, and liquid sodium, and was shown to provide reasonable values for 2100 ≤ Re ≤ 3.6 × 106 and Prandtl number (Pr) range of 0.0107 ≤ Pr ≤ 5.65. In addition, new expressions suitable for the central portion of internal flows, away from the wall, were derived for the turbulent Reynolds number (ReT), showing its relationship to Re, as well as to the ratio of νt and the molecular kinematic viscosity (ν).