Loss Coefficients for Periodically Unsteady Flows in Conduit Components: Illustrated for Laminar Flow in a Circular Duct and a 90 Degree Bend

Losses in a flow through conduit components of a pipe system can be accounted for by head loss coefficients K. They can either be determined experimentally or from numerical solutions of the flow field. The physical interpretation is straight forward when these losses are related to the entropy generation in the flow field. This can be done based on the numerical solutions by the second law analysis (SLA) successfully applied for steady flows in the past. This analysis here is extended to unsteady laminar flow, exemplified by a periodic pulsating mass flow rate with the pulsation amplitude and the frequency as crucial parameters. First the numerical model is validated by comparing it to results for unsteady laminar pipe flow with analytical solutions for this case. Then K-values are determined for the benchmark case of a 90 deg bend with a square cross section which is well-documented for the steady case already. It turns out that time averaged values of K may significantly deviate from the corresponding steady values. The K-values determined for steady flow are a good approximation for the time-averaged values in the unsteady case only for small frequencies and small amplitudes.