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Surface oscillations of liquid nitrogen under microgravity<br />
M. Stief ∗ andM.E.Dreyer ∗<br />
Thefreesurfacebehaviorhasalwaysbeenamatterofconcernforspaceapplications<br />
involving the handling of fluids. Special needs arise if the fluid handling involves<br />
large quantities of cryogenic fluids like liquid hydrogen or oxygen as used in the upper<br />
stage of rockets.<br />
To overcome this lack of knowledge experiments have been performed at the droptower<br />
in Bremen to investigate the surface oscillations of liquid nitrogen (LN2) upon<br />
sudden change of gravity acceleration. The oscillations were observed inside the axisymmetric<br />
configuration of a right circular cylinder with diameter D. The circular<br />
cylinder is filled with LN2 up to the height h and the liquid is initially quiescent.<br />
Thefreesurfaceformsaflatinterfaceduetotheinitialaccelerationofkzi = 9.81<br />
m/s2 along the symmetry axis z of the cylinder. With the release of experiment setup<br />
inside the drop tower the whole system undergoes a sudden change of the acceleration<br />
from kzi to kz ≈ 1.0 · 10−6 m/s2 and the free surface is initiated to search its new<br />
equilibrium configuration.<br />
To perform the experiment with LN2 under isothermal and ambient pressure conditions<br />
the described experimental setup required to be at cryogenic temperatures in<br />
the range of 75-80 K. This was achieved by integrating the experiment inside a bath<br />
cryostat with two vacuum insulation shields.<br />
For the surface oscillation upon sudden reduction of gravity two characteristic time<br />
domains can be identified. During the initial time domain a wave is traveling from<br />
the wall of the cylinder towards the center of the free surface. The influence of the<br />
first time domain can be shown by the Morton number which expresses the ratio of<br />
the viscous time scale tpvLc = νρLc/σ and convective time scale tpuLc = σ/ρk3 1/4. zi<br />
This yields to a Morton number of Mo = kziµ 4 /ρσ31/4 .<br />
The second time domain is characterized by the Ohnesorge number which is<br />
expressing the global behavior of the free surface oscillation. The Ohnesorge also<br />
derives from the ratio of convective to viscous time scale but in this case with the<br />
radius R = D/2 of the container as the characteristic length scale (where for the<br />
initial time domain the capillary length scale Lc = (σ/ρkzi) 1/2 has been found). This<br />
leads to the expression Oh = ν2ρ/σL 1/2 for the Ohnesorge number.<br />
With the use of liquid nitrogen we are able to investigate the free surface oscillation<br />
down to a Ohnesorge of Oh ≈ 3.0 · 10−4 where previous experiments1 with<br />
conventional liquids could only cover the range down to Oh = 0.98 · 10−3 .<br />
A series of experiments have been performed to investigate the main characteristic<br />
of the surface reorientation like maximum displacement zcp, timeforthefirstoscillation<br />
tcp and the oscillation frequency ω. The optical observation of the free surface<br />
also revealed the feature of the formation of a liquid layer at the cylinder wall during<br />
the reorientation process.<br />
∗ ZARM - University of Bremen, Am Fallturm, 28359 Bremen, Germany.<br />
1 M. Michaelis et al., PAMM (Proceedings in Applied Mathematics and <strong>Mechanics</strong>), 2, (2003).<br />
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