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124<br />
Flow rate limitation in open capillary channels due to choking<br />
U. Rosendahl ∗ ,M.E.Dreyer ∗ ,A.Grah ∗ and A. Ohlhoff ∗<br />
Our investigations are concerned with flow-rate limitations in open capillary channels<br />
under low-gravity conditions. An open capillary channel is a structure in which<br />
capillary forces enable a free surface flow and essentially influence the flow properties.<br />
Such channels are used in the space technology for positioning and transporting<br />
liquids.<br />
The capillary channel we consider consists of two parallel plates that are connected<br />
to ducts of closed circumference. The open flow path is bounded by two free liquid<br />
surfaces at the sides. Depending on the applied volumetric flow rate, the liquid<br />
pressure decreases in the flow direction due to flow losses. A steady flow is obtained<br />
only for a flow rate Q below the critical value Qcrit. ForQ>Qcrit, the liquid surfaces<br />
collapse at the channel outlet and the flow changes from steady single-phase flow to<br />
unsteady two-phase flow.<br />
The aim of these investigations is to understand the mechanism of the flow rate<br />
limitation. Our thesis is, that the limitation occurs due to a ’choking-effect’, which<br />
is known from compressible gas flows and open channel flows under normal gravity.<br />
The theory of choked flow predicts a limiting velocity corresponding to a characteristic<br />
signal velocity of the flow. Once that this critical velocity is reached the mass flow<br />
is maximum and cannot be increased further. For open capillary channel flows we<br />
expect a limiting velocity defined by the speed longitudinal waves.<br />
The investigations are based on data achieved from sounding rocket experiments<br />
(TEXUS 41, TEXUS EML) which were launched from the ESRANGE in North Sweden.<br />
For the prediction of the flow an one-dimensional theoretical was developed 1 .<br />
The experiment evaluation yields the critical flow rate and the surface profiles in good<br />
accuracy with the theoretical predictions. We can show that the gained differential<br />
equation is of the same structure like the equations of similar compressible gas flows.<br />
Thus,inanalogytotheMachnumberweintroducedaspeedindexdefinedbythe<br />
ratio of the flow velocity and the speed of longitudinal capillary waves as the key<br />
parameter. The numerical computations show that the speed index always tends towards<br />
unity when the flow rate is increased which indicates the influence of choking.<br />
This trend is confirmed by the experimental results.<br />
∗Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, D-28359<br />
Bremen, Germany.<br />
1Rosendahl et al., J. Fluid Mech. 518, 187–214 (2004).
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