(482b) An Extension To The Incorporation Model Of Micromixing And Its Use In Estimating The Maximum Angular-Resolved And Azimuthally-Averaged Local Specific Energy Dissipation Rates

Authors: 
Nienow, A., Birmingham University
Assirelli, M., Institute of Chemical and Engineering Sciences
Bujalski, W., Birmingham University
Eaglesham, A., Huntsman Polyurethanes
Wynn, E. J., Fluent Europe Ltd


The Incorporation Model of micromixing first developed conceptually and quantified by Villermaux and co-workers has been extended to cover both higher rates of micromixing (higher mean and local specific energy dissipation rates) and higher reaction rates (by using higher acid concentrations in the iodide-iodate model reaction scheme). The extended model has involved the use of Bader and Deuflhard's semi implicit discretization in the Bulirsch-Stoer method, which is especially suitable for stiff ordinary differential equations. Both exponential and linear rates of incorporation were considered and polynomial equations for three acid concentrations for micromixedness ratios from ~ 1 to ~ 100 were determined. It was shown that though different acid concentrations gave different a values at the same feed position and agitation conditions, the micromixing time estimated from the model was constant (as it should be) with exponential incorporation. With linear incorporation, the micromixing time was much less and not constant and was therefore rejected for further analysis. Subsequently, it was shown that the ratio of the local specific energy dissipation rate to the average was constant at the same reactant feed position except when fed into the region of maximum local specific energy dissipation rate close to the impeller. In this case, the ratio of energy dissipation rates fell with increasing speed as the reactants were swept more rapidly from this region to regions of lower specific energy dissipation rates. By comparing estimates of the ratio from feeding a reactant at equivalent positions with a static pipe and one rotating with the impeller, it was found that the ratio of the maximum local angular resolved specific energy dissipation rate to the ensemble-average was about 2.7 in reasonable agreement with the value of ~3 very recently obtained by Ducci and Yianneskis based on two-point LDA measurements. The absolute value of the ensemble-average value was rather high compared to most recent estimates from LDA or PIV, which may reflect some weakness in the model.