Comparison of numerical analysis based on stream functions with experimetal results for the low frequency fluctuations in an agitated vessel

Four independent stream functions which satisfied the boundary conditions w ere presumed for an agitated vessel. Differential equations for the stream functions, which were derived from the Navier Stokes equation, were solved numerically. An analysis of the cross-correlation of the velocity component s showed that the low frequency fluctuations in the flow corresponded to la rge-scale flow patterns over the entire vessel. The correspondence was also observed experimentally. The period of the low frequency motion was about 34 times that oi the external input stream function, which agreed with the value of 20-30 times the blade passage frequency that was found experimenta lly. The increase in the number of the stream functions from 3 to 4 contrib uted to describing the characteristics of the local phenomena in the flow r ather than to changing the dynamics, as was shown bp the results of the fre quency analysis and the mutual correlation function. It was confirmed that this deterministic analysis with the small number of variables was very eff ective to predict the dynamic behavior for the low frequency fluctuations i n an agitated vessel.