Local Turbulent Energy Dissipation Rate in an Agitated Vessel: Experimental and Turbulence Scaling

Abstract

The hydrodynamics and the flow field in an agitated vessel were measured using 2-D time resolved particle image velocimetry (2-D TR PIV). The experiments were carried out in fully baffled cylindrical flat bottom vessels 300 and 400 mm in inner diameter. The 300 mm inner diameter tank was agitated by a Rushton turbine 100 mm in diameter, and the 400 mm inner diameter tank was agitated by a Rushton turbine 133 mm in diameter. Three liquids of different viscosities were used as the agitated liquid: (i) distilled water (ν = 9.35 × 10^–7 m²/s), (ii) a 28 vol % aqueous solution of glycol (ν = 2 × 10^–6 m²/s), and (iii) a 43 vol % aqueous solution of glycol (ν = 3 × 10^–6 m²/s). The velocity fields were measured at an impeller rotation speed in the range from 300 to 850 rpm, which covers the Reynolds number range from 50000 to 189000. This means that fullydeveloped turbulent flow was reached. The experiments were performed to investigate the applicability of the following relations: ε* = ε/(u⁴/ν) = const, vK/u = const, Λ/ηK = const, τ_Λ/τ_K = const, ε* = ε/((Nd)4/ν) = const, Λ/d ∝ Re^–1, ηK/d ∝ Re^–1, vK/(Nd) = const, Nτ_Λ ∝ R^–1, Nτ_K ∝ Re^–1, and ε/(Nq) ∝ Re. These formulas were theoretically derived in our previous work, using turbulence theory, in particular, using turbulence spectrum analysis. The correctness of the proposed relations is investigated by statistical hypothesis testing.