Universal Expression of Tangential Velocity Distribution near Side Wall of a Fully Turbulent Agitated Vessel without Baffles

Abstract

For the turbulent boundary layer at the side wall of an agitated vessel without baffles, new dimensionless variables u⁺⁺ and y⁺⁺ were derived as u_θ⁺(βD/1.7d) and y⁺(βD/1.7d), respectively, instead of the dimensionless variables u_θ⁺ and y⁺ in the universal velocity distribution law. The correlation of the measured tangential velocity at the side wall of an agitated vessel without baffles with u⁺⁺ and y⁺⁺ satisfied the logarithmic expression of the universal velocity distribution law in the range 20 < y⁺⁺ < 70 for the paddle impeller having a larger value of the impeller similarity parameter than 0.1. This meant that the mixing length for an agitated vessel was βD/1.7d times that for a flat plate. Besides the tangential velocity at the turbulent boundary layer edge u_D and the boundary layer thickness y_D were roughly expressed as 0.85(d/D)U_D and 0.030(1.7d/βD)L, respectively.