Critical Velocity in Open Capillary Channel Flows

We investigate forced liquid flows through open capillary channels with free surfaces experimentally. The experiments were performed under low gravity conditions in the Bremen Drop Tower and on board the sounding rocket TEXUS-37. Open capillary channels (vanes) are used in surface tension tanks to transport the propellant and to provide a flow path for the bubble-free liquid supply to the thrusters. Since the free surfaces can only withstand a certain pressure differential between the liquid and ambient, the flow rate in the channel is limited. The maximum flow rate is achieved when the surfaces collapse and gas is ingested into the outlet. Since experimental and theoretical data of this flow rate limitation is lacking, the safety factors for the application of vanes in surface tension tanks must be unnecessary high. The aim of the investigation is to determine the maximum liquid flow rate and the corresponding critical flow velocity. The characteristic nondimensional parameters, OHNESORGE number, and gap ratio, cover a wide range of usual vanes. For the theoretical approach a one-dimensional momentum balance was set up. The numerical solution yields the maximum volume flux and the position of the free surface in good agreement with the experiments.