Determination of head change coefficients for dividing and combining junctions: A method based on the second law of thermodynamics

Losses due to the flow through conduit components in a pipe system can be accounted for by head loss coefficients K. They correspond to the dissipation in the flow field or, in a more general sense, to the entropy generation due to the conduit component under consideration. When only one single mass flow rate is involved, an entropy based approach is straight forward since the flow rate can be used as a general reference quantity. If, however, one mass flow rate is split or two partial flow rates come together like in junctions, a new aspect appears: there is an energy transfer between the single branches that has to be accounted for. It turns out that this energy transfer changes the total head in each flow branch in addition to the loss of total head due to entropy generation. Therefore, appropriate coefficients for junctions should be named as head change coefficients. As an example, the method is applied to laminar flows. Head change coefficients for dividing and combining flows in a T-shape micro-junction are determined for both branches and discussed with respect to their physical meaning. For the combining junction, the special case of engulfment, leading to enhanced mixing in micro-mixers, is also considered. Finally, it is shown, how the newly defined coefficients can be used for the design of a flow network.