Estimation of Boundary Layer Thickness at Side Wall of a Fully Turbulent Agitated Vessel without Baffles

Abstract

The average boundary layer thickness at the side wall of an agitated vessel without baffles, y_D, was estimated from the correlation of the friction factor with the help of the measured universal expression of tangential velocity distribution at a vessel wall. The average boundary layer thickness was independent of the Reynolds number in the turbulent boundary layer range of Re_G > 5000, but it increased with decreasing Reynolds number being inversely proportional to the 1/2 power of a generalized Reynolds number in the laminar boundary layer range of Re_G < 5000. At the turbulent boundary layer of Re_G > 5000, the ratio of the average boundary layer thickness to the vessel radius y_D/(D/2) was in the range of 0.013 to 0.018 for the ratio of impeller to vessel diameters d/D = 0.61 to 0.4. The correlation line of the dimensionless tangential velocity at the boundary layer edge u_D⁺⁺ (≡u_D⁺(βD/md)) vs. the dimensionless boundary layer thickness y_D⁺⁺ (≡y_D⁺(βD/md)) coincided with the universal velocity distribution law for a flat plate for the impellers having a larger impeller similarity parameter X over 0.15, but the former shifted upward from the latter for the impellers having a smaller impeller similarity parameter X below 0.15, although the gradient (du_D⁺⁺/d ln y_D⁺⁺) was the same as that for the universal velocity distribution law.