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Open Capillary Channel Flows (CCF): Flow Rate Limitation<br />
in a Groove-Channel<br />
D. Haake ∗ , U. Rosendahl ∗ ,A.Grah ∗ and M.E. Dreyer ∗<br />
In the present study forced liquid flows through open capillary channels are investigated<br />
experimentally and numerically under reduced gravity conditions. An open<br />
capillary channel is a structure that establishes a liquid flow path at low Bond numbers.<br />
Thereby the capillary pressure caused by the surface tension force dominates in<br />
comparison to the hydrostatic pressure induced by gravitational or residual accelerations.<br />
The investigated capillary channel is a so called groove, which consists of two<br />
parallel plates with a free surface at one side and a closed geometry at the other side<br />
(see figure 1). In case of steady flow through the channel the capillary pressure of the<br />
free surface balances the differential pressure between the liquid and the surrounding<br />
constant pressure gas phase. Due to convective and viscous momentum transport the<br />
pressure along the flow path decreases and causes the free surface to bend inwards.<br />
The maximum flow rate is achieved when the free surface collapses and gas ingestion<br />
occurs at the channel outlet. This critical flow rate depends on the channel geometry<br />
and the liquid properties. Similarities exists to compressible gas flows in ducts and<br />
open channel flows under terrestrial conditions. Each of these flows is governed by<br />
similar equations. The flow rate of these flows is limited due to choking. The theory<br />
of choked flow predicts a limiting velocity corresponding to a characteristic signal<br />
velocity of the flow. In principle this velocity cannot be exceeded, thus the flow is<br />
limited to a certain value 1 .<br />
The experimental investigations of the open capillary channel flows were performed<br />
in the drop tower of Bremen. For the prediction of the critical flow rate an one<br />
dimensional theoretical model is developed taking into account the entrance pressure<br />
loss and the frictional pressure loss in the channel. We will introduce the experimental<br />
setup and present comparisons of the numerical as well as experimental critical flow<br />
rates and surface contours for different flows.<br />
∗ ZARM, University of Bremen, Germany.<br />
1 Rosendahl et al., J. Fluid Mech. 518, 187-214, (2004).<br />
Q<br />
inlet<br />
y<br />
closed side<br />
z<br />
b<br />
l<br />
outlet<br />
a<br />
x<br />
free<br />
surface<br />
Figure 1: Groove-channel of length l, widthb and gap distance a with flow rate Q.<br />
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