Local turbulent energy dissipation rate in an agitated vessel: New approach to dimensionless definition

Abstract

Using theory of turbulence, particularly using turbulence spectrum analysis, the relations ε^* = ε/(u⁴/ν) = const., v_K/u = const. and Λ/η_K = const. were derived. Assuming that u ∝ (Nd) from this it follows that the widely used dimensionless local turbulent energy dissipation rate defined as ε/((N³d²) is directly proportional to impeller Reynolds number, i.e. ε/((N³d²) ∝ Re, and length scale ratio Λ/d is indirectly proportional to impeller Reynolds number, i.e. Λ/d ∝ Re^–1, in an agitated vessel at high Reynolds number. The relations obtained by turbulence spectrum analysis were used for estimation of local turbulent energy dissipation rates experimentally measured by Ståhl Wernersson and Trägårdh (1998, 1999) covering the range of Re = 87600–910200 and own experimental data covering the range of Re = 50000–189000. The experiments have been performed in tanks of 300 mm and 400 mm in the inner diameter for three different viscosities and for various impeller rotational speeds.