• Journal of computational fluids engineering
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• v.9 no.4
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• pp.20-33
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• 2004

In this study a stretching-mapping method is proposed for calculating the materials' stretching exponents, which are to be used in quantification of the mixing effect. In this method, the mapping tensor associated with the deformation of each fluid material is first obtained. Then deformations of a lot of materials are obtained by applying the mapping tensor. The local stretching rates and their space-average values are next computed with the mapped deformations. Application to a simple time-periodic flow within a cavity shows that the method is indeed effective compared with the conventional method; i.e. the mapping method is fast and yields the same results as the conventional one.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.1-13
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• 2005

Fluid flows within microchannels are characterized by low Reynolds numbers. Therefore the effect of mixing is a crucial factor in design of the channels. Since the action of the electro-osmotic or magnetic forces used in the mixing enhancement is usually periodic in the three-dimensional channel configuration, use of the various concepts of chaotic advection is reasonable in the quantification of the stirring effect. In this paper, the details of the method of material-stretching mapping is explained. The actual application of the method to the screw extruder is also presented.

• Journal of computational fluids engineering
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• v.9 no.4
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• pp.55-63
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• 2004

The three-dimensional Stokes flow within a staggered screw channel is obtained by using a finite volume method. The geometry is intended to mimic the single screw extruder having staggered arrangement of flights. The flow solution is then subjected to the analysis of the stirring performance. In the analysis of the stirring performance, the stretching-mapping method developed by the author is employed for calculating the materials' stretching exponents, which are to be used in quantification of the mixing effect. The numerical results Indicate that the staggered geometry gives indeed far much better stirring-performance than the standard (nonstaggered) flight geometry. It was also shown that care must be given to the selection of the basis planes for evaluating the local stretching rate, and it turns out that the best method (H-method) has its basis plane just on the half way between the past and future evolution of fluid particles subjected to the defromation. In evaluating the stretching exponent, the expansion ratio must be considered which is one of the characteristic differences of the actual three-dimensional flows from the two-dimensionmal counterparts. The larger axial pressure-difference causes in general the smaller stirring performance while the flow rate is increased. The smaller channel length also increases the stirring performance.