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Stability limits of unsteady open capillary channel flow

Published online by Cambridge University Press:  26 March 2008

ALEKSANDER GRAH ,
DENNIS HAAKE ,
UWE ROSENDAHL ,
JÖRG KLATTE  and
MICHAEL E. DREYER
ALEKSANDER GRAH
Affiliation:
Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, Am Fallturm, Bremen, D-28359, Germany
DENNIS HAAKE
Affiliation:
Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, Am Fallturm, Bremen, D-28359, Germany
UWE ROSENDAHL
Affiliation:
Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, Am Fallturm, Bremen, D-28359, Germany
JÖRG KLATTE
Affiliation:
Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, Am Fallturm, Bremen, D-28359, Germany
MICHAEL E. DREYER
Affiliation:
Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, Am Fallturm, Bremen, D-28359, Germany
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Abstract

This paper is concerned with steady and unsteady flow rate limitations in open capillary channels under low-gravity conditions. Capillary channels are widely used in Space technology for liquid transportation and positioning, e.g. in fuel tanks and life support systems. The channel observed in this work consists of two parallel plates bounded by free liquid surfaces along the open sides. The capillary forces of the free surfaces prevent leaking of the liquid and gas ingestion into the flow.

In the case of steady stable flow the capillary pressure balances the differential pressure between the liquid and the surrounding constant-pressure gas phase. Increasing the flow rate in small steps causes a decrease of the liquid pressure. A maximum steady flow rate is achieved when the flow rate exceeds a certain limit leading to a collapse of the free surfaces due to the choking effect. In the case of unsteady flow additional dynamic effects take place due to flow rate transition and liquid acceleration. The maximum flow rate is smaller than in the case of steady flow. On the other hand, the choking effect does not necessarily cause surface collapse and stable temporarily choked flow is possible under certain circumstances.

To determine the limiting volumetric flow rate and stable flow dynamic properties, a new stability theory for both steady and unsteady flow is introduced. Subcritical and supercritical (choked) flow regimes are defined. Stability criteria are formulated for each flow type. The steady (subcritical) criterion corresponds to the speed index defined by the limiting longitudinal small-amplitude wave speed, similar to the Mach number. The unsteady (supercritical) criterion for choked flow is defined by a new characteristic number, the dynamic index. It is based on pressure balances and reaches unity at the stability limit.

The unsteady model based on the Bernoulli equation and the mass balance equation is solved numerically for perfectly wetting incompressible liquids. The unsteady model and the stability theory are verified by comparison to results of a sounding rocket experiment (TEXUS 41) on capillary channel flows launched in December 2005 from ESRANGE in north Sweden. For a clear overview of subcritical, supercritical, and unstable flow, parametric studies and stability diagrams are shown and compared to experimental observations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 600 , 10 April 2008 , pp. 271 - 289
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Ehrig, R., Nowak, U., Oeverdieck, L. & Deuflhard, P. 1999 Advanced extrapolation methods for large scale differential algebraic problems. In High Performance Scientific and Engineering Computing. Lecture Notes in Computational Science and Engineering, vol. 8 (ed. Bungartz, H.-J., Durst, F. & Zenger, C.), pp. 233–244. Springer.CrossRefGoogle Scholar
Jaekle, D. E. Jr., 1991 Propellant management device conceptual design and analysis: Vanes. AIAA Paper 91-2172, pp. 1–13.CrossRefGoogle Scholar
Landau, L. D. & Lifschitz, E. M. 1959 Fluid Mechanics, Course of Theoretical Physics, vol. 6. Pergamon.Google Scholar
Rosendahl, U. 2007 Über die Grenzen des stationären Flüssigkeitstransportes in offenen Kapillarkanälen. Cuvillier Verlag Göttingen.Google Scholar
Rosendahl, U. & Dreyer, M. E. 2007 Design and performance of an experiment for the investigation of open capillary channel flows. Exps. Fluids 42, 683–696.CrossRefGoogle Scholar
Rosendahl, U., Ohlhoff, A. & Dreyer, M. E. 2004 Choked flows in open capillary channels: theory, experiment and computations. J. Fluid Mech. 518, 187–214.CrossRefGoogle Scholar
Sparrow, E. M. & Lin, S. H. 1964 Flow development in the hydrodynamic entrance region of tubes and ducts. Phys. Fluids 7, 338–347.CrossRefGoogle Scholar
Srinivasan, R. 2003 Estimating zero-g flow rates in open channels having capillary pumped vanes. Intl J. Numer. Meth. Fluids 41, 389–417.CrossRefGoogle Scholar
White, F. 1986 Fluid Mechanics. McGraw Hill.Google Scholar