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In this paper, we utilize a recently proposed analytical/semi-analytical method to study the effect of the cross-sectional shape on the diffusion-free residence time distribution (RTD) in fully developed laminar flow of a Newtonian fluid. The diffusion-free RTD is obtained for elliptical channels of arbitrary aspect ratio, for a family of moon-shaped channels, and for an equilateral triangular channel. The nondimensional RTDs for these channel cross-sections are compared and the influence of the channel shape is found to be rather small. The RTDs can well be approximated by a simple convection model which involves the non-dimensional first appearance time, which represents the ratio between the mean and maximum velocity of the laminar flow, as only parameter. A comparison with recently published results for rectangular channels of arbitrary aspect ratio shows that the one-parameter convection model is unsuited for rectangular channels and a second parameter is required. A first attempt toward the development of such a two-parameter convection model is undertaken, which would then allow predicting the diffusion-free RTD of fully developed laminar flow in straight channels of arbitrary cross-sectional shape.

There is a considerable interest within both academia and industry to develop improved computational fluid dynamic methods for gas-liquid flows in bubble columns in order to support their scale-up and optimal design. One main model limitation in current Eulerian two-fluid and multi-fluid models concerns adequate closure relations for turbulence in bubble-driven flows. This article highlights some special features of bubble-induced turbulence, discusses shortcomings of common concepts for closure of the liquid phase turbulence kinetic energy equation and presents an approach for development and validation of improved models. Some problematic issues related to the direct numerical simulation of bubble swarms in narrow bubble columns are also discussed.

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