Curved channel geometry

While the previous studies refer to straight channels exceptionally, microfluidic devices often comprise channels with a curvature. It is therefore helpful to know how hydrodynamic dispersion is modified in a curved channel geometry. This aspect was investigated by Daskopoulos and Lenhoff [155] for ducts of circular cross-... 

Similarly to the structure of the flow fleld, heat transfer has also been studied in curved channel geometries. The complicated branch structure with competing patterns of two and four counter-rotating vortices in channels of square cross section is reflected in the Nusselt number [34]. When plotting the Nusselt number as a function of Dean number, different branches are found corresponding to symmetric and asymmetric secondary flow patterns with two and four vortices. However, the relative difference between the different branches is not very pronounced and should be hard to measure experimentally. For a Dean number of 210 and a Prandtl number of 0.7 a heat-transfer-enhancement factor of about 2.8 was determined, thus showing that curved channels as well as other channels with specific periodically varying cross sections may be used for applications where rapid heat transfer is desired. 

As expected, when the characteristic time for diffusion is much larger than the one for convection aPCm 1), higher deviations between approximate and numerical results are observed, especially for large reaction rates and curved channel geometries. For example, for Da = lO and aPem z = 100 in laminar flows, the relative errors are 12% for circular channels, in comparison with 6% for parallel plates. 

Fig. 7.7 Geometry of a staggered herringbone micromixer (left) and a curved channel to induce Dean Vortexes with corresponding secondary flow patterns (right). Arrow indicates flow [92].

The function /, describing the relationship between concentration and delay time t, is dependent on the dispersion process taking place in the FIA channel and, therefore, on channel geometry, volume, and flow velocity. In the simplest case, that is, absence of chemical reactions, and when the flow channel conforms with the model of one well-stirred tank (cf. Chapter 3), the concentration-time matrix of the falling edge of the curve is described by ... 

The channel geometry of a microfluidic device is commonly characterized by a rectangular curved microchannel. The flow field conditions within such a microchannel have a significant influence upon the performance of the device when... 

When the channel width is about ten times the channel depth, the screw contact area will be reduced by about 10%. However, the cross-sectional area of the screw channel will be reduced by the same percentage. Thus, the net effect will be less beneficial than the curved flight geometry. 

Figure 6 Microfluidic geometries for studies of material properties. (a) Curved channels for shear experiments with an additional radial component, (b) MicroChannel with hyperbolic structure. This device generates a constant strain rate e at the channel centerline. (c) Zig-zag device for periodic deformation patterns.

Currently the standard TRACE code heat transfer (Dittus-Boelter) and fluid pressure drop (Churchill and Moody) correlations are applied to the gas cooler. Use of the Churchill correlation and Moody curves, and mathematical representations of the curves, for calculation of the single-phase friction factor in a variety of flow-channel geometries is a common engineering practice. Information on the TRACE default correlations is available in the TRACE theory manual (Reference 12-9). A surface roughness of 2E-6 m is used with the TRACE single phase friction correlations. In order to match the HB24 pressure drop prediction, additional frictional flow factors are included in the hydraulic model. The TRACE model also includes plenums to provide a location to specify form loss factors for the gas cooler. The heat transfer and pressure drop correlations would have been updated as the cooler design was determined and as test data was collected. 

Figure 2.43 Model geometry for the CFD calculations on flow in curved micro channels (above) and time evolution of two initially vertical fluid lamellae over a cross-section of the channel (below), taken from [139].The secondary flow is visualized by streamlines projected on to the cross-sectional area of the channel. The upper row shows results for fC = 150 and the lower row for K = 300.

Other important targets for DNS are the turbulent flows at Reynolds numbers up to say 10,000 in simple geometries (such as straight channels or curved... 

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