Loss Coefficients in Microelbows

Abstract

The goal of this study was to determine laminar pressure loss coefficients for flow in microelbows with circular and trapezoidal cross-sections. Flow conditions and pressure losses in these elbows are of interest in microfluidic devices, in porous media, and in other types of microfluidic networks. The literature focuses almost exclusively on loss coefficients due to turbulent flow in macroelbows with very little data on laminar flow in macroelbows. The pressure loss coefficients determined in this study are intended to aid in realistic simulation of existing laminar flow networks or the design of these networks. This study focused on an elbow of constant cross-section with inlet and outlet tubes of sufficient length so as to allow fully developed laminar flow at the entrance to the elbow and at the outlet tube exit. For the circular elbow, both the ratio of elbow radius to inner diameter and inlet Reynolds number were allowed to vary over the ranges of 0.5—10.5 and 1—2500, respectively. The laminar pressure loss coefficients were determined by simulating incompressible flow over the range of geometries and Reynolds numbers in the commercial CFD software FLUENT. The pressure and velocity distributions in the inlet and outlet tubes were averaged at multiple upstream and downstream positions, and were then used to extrapolate the loss coefficient due to the elbow. The results showed that the loss coefficient for larger ratios tended to be higher, in some cases in excess of 100, at low Reynolds number flows, but as the flow approached the transitional regime, the loss coefficients leveled out to roughly their accepted turbulent values of between 0.4 and 1.0. These results show good qualitative and quantitative agreement with limited laminar elbow experimental data available for macroelbows. For the trapezoidal elbows the loss coefficient levels off to about two for Reynolds numbers greater than 100.