@MISC{Glasgow96mixingcalculations, author = {C. Glasgow and A. K. Parrott}, title = {Mixing Calculations in a Rotating Partitioned Pipe}, year = {1996} }

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Abstract

this paper arises from an analysis of the Partitioned-Pipe Mixer (PPM) presented in [24] where an analytical Stokes velocity representation is used as a basis for the computation of three mixing diagnostics: residence time distributions, Poincare sections and material stretching plots. In each case the Lagrangian equation of motion are integrated to compute the trajectories of individual fluid particles, or in the case of the stretching plots, the evolution of infinitesimal line segments. These three diagnostics are shown to provide a fairly complete picture of the mixing mechanisms evident in the PPM mixer. The accuracy to which these diagnostics can be computed is governed by the accuracy of the underlying velocity representation and the particle tracking algorithms which involve numerical integration and additional schemes related to problem specific geometries. In [24] a fairly crude velocity field is used; a more accurate representation, although possible, would have significantly increased the amount of computational effort making the material stretching diagnostics impractical. Mixing mechanisms arising in industrial processes often involve complex geometries and in these cases analytical velocity representations of the required accuracy are neither available nor practical to derive. Moreover, CFD packages have usually already been applied to these problems to obtain either fluid fluxes or node based velocities on some (possibly curvilinear) mesh discretisation. This data can be used to obtain particle trajectories; integration of a low order piecewise polynomial interpolant of the fluxes being a common approach. Higher order representations, although more costly, have the benefit that the computed trajectories are smoother [18, 21] and we would hope that the rep...