FULLY DEVELOPED FLOW IN TWISTED TAPES: A MODEL FOR MOTIONLESS MIXERS

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Abstract
The fully developed flow fields in twisted tapes for arbitrary aspect ratios were found via a transformation to a non-orthogonal coordinate system. A streamfunction formulation permitted the removal of the transverse pressure field. The method presented allows for non zero Reynolds numbers and offers some computational advantages over previous methods. Results for aspect ratios between 0.1 to 6.4 and Re =0 show that the mixing action is not a strong function of the aspect ratio. Comparisons between Re =0 and Re = 2.5 at an aspect ratio of 1.6 show a small effect upon the transverse circulation. The equations were stable up to Re = 7.5 for aspect ratio 1.6. The aspect ratio strongly influenced the stability of the equations. An optimal design for a motionless mixer was obtained by maximizing the percentage deformation obtained per unit pressure. Optimization parameters were aspect ratio and amount of twist per clement. The optimum mixer has an aspect ratio of 0.5 and 90 degrees of twist per element. The standard Kenics configuration has an aspect ratio of 1.6 and 180 degrees of twist. Efficiency is approximately doubled at the proposed optimum. Tapes of finite thickness (t = 0.125 R) were also studied and show the same general behavior as the infinitely thin tape. The thickness of the tape decreases the cross sectional area for flow and gives a corresponding increase in pressure drop.

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