Macro-instabilities of the Flow Pattern in a Stirred Vessel: Detection and Characterization Using Local Velocity Data

Abstract

Velocity data obtained by laser Doppler velocimetry (LDV) in a flat-bottomed cylindrical stirred vessel (diameter: 300 mm, filling height: 300 mm, working liquids: water and aqueous glycerine, impeller Reynolds number values (Re_M): 750, 1200 and 75000) equipped with four radial baffles and stirred with a pitched blade impeller are analyzed by methods of non-linear analysis. The macro-instability of the flow pattern (MI) was extracted from the experimental data by a combination of the proper orthogonal decomposition (POD) technique and spectral analysis. The relative magnitude of the MI (the fraction of flow total kinetic energy captured by MI) was evaluated and its spatial distribution was determined. The temporal evolution of the MI was constructed from the POD eigenmodes. The chaotic attractors of the macro-instabilities were reconstructed by the method of delays. The embedding dimension was determined by the false nearest neighbor analysis (FNN) method, and the time delay from the first min imum of mutual information. Correlation dimension de and the largest Lyapunov exponents λ_max of the reconstructed attractors
were evaluated. The correlation dimension slightly increases with the increasing Re_M value. The spatial distribution of d_c is quite uniform at all ReM values. The maximum Lyapunov exponent is clearly positive for all analyzed at tractors. Spatial distribution of λ_max is markedly non-uniform and exhibits irregular variations. Possible applications of nonlinear analysis of local velocity data in mixing processes are mentioned.