Interior corner flow theory and its application to the satellite propellant management device design

In 1931, Onsager proposed a variational principle which has become the base of many kinetic equations for non-equilibrium systems. We have been showing that this principle is useful in obtaining approximate solutions for the kinetic equations, but our previous method has a weakness that it can be justified, strictly speaking, only for small incremental time. Here we propose an improved method which does not have this drawback. The new method utilizes the integral proposed by Onsager and Machlup in 1953, and can tell us which of the approximate solutions is the best solution without knowing the exact solution. The new method has an advantage that it allows us to determine the steady state in non-equilibrium system by a variational calculus. We demonstrate this using three examples, (a) simple diffusion problem, (b) capillary problem in a tube with corners, and (c) free boundary problem in liquid coating, for which the kinetic equations are written in second or fourth order partial differential equations..

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“…(See also Ref. [23] for the application.) Here we use the same model as theirs, and solve the problem using Onsager principle.…”

Section: Finger Flow In a Square Tubementioning

confidence: 99%

Application of the Onsager-Machlup integral in solving dynamic equations in nonequilibrium systems

Doi

Zhou

et al. 2019

Phys. Rev. E

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“…Theoretical expressions of capillary ows in different shapes of corners are also derived (Weislogel et al, 1998(Weislogel et al, , 2005Chen et al, 2006;Li et al, 2012;Li et al, 2015;Wu et al, 2018). The interior corner ow theory is adopted to design the PMD, and it's validated by drop tower experiments (Wei et al, 2011). The mathematical models of capillary rise between plates were established and the effects of different forces are discussed in detail (Dreyer et al, 1994;Chen et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

Study on liquid reorientation in tank models aboard the Chinese Space Station

Chen,

et al. 2024

Preprint

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Propellant tanks provide non-entrained propellant for thrusters of satellites, which plays an important role in space mission. And the fluid transfer efficiency of tanks is the key to supply non-entrained propellant. An experiment cabin containing two different scaled tank models are designed and experiments of liquid reorientation under microgravity are carried out in the Chinese Space Station. Experiment results present the high liquid transportation efficiency of the two kinds of propellant management devices. Finite element models of the two tank models are established and verified by simulation matching with experiments. Furthermore, methylhydrazine is adopted to carry out more simulation analysis by considering different liquid contact angles and surface tension, and numerical results show smaller liquid contact angle and bigger surface tension can increase liquid flow speed. This research can provide theory and data support for the design of plate type tanks.

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“…Nowadays, the interest in capillary problems is still open, and a fairly large number of papers connected to the capillary rise of fluid in corners of liquid reservoirs under microgravity have been published recently [34][35][36][37][38][39][40][41][42], amongst others. The problem is of great interest from the scientific and technical point of view, and recently a capillary experiment has been performed on the International Space Station (ISS), which dealt with partially open channels aiming to determine the critical flow rate-limiting conditions above which the free surface collapses ingesting bubbles [43,44].…”

Section: Introductionmentioning

confidence: 99%

Surface tension and microgravity

et al. 2014

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The behaviour of confined liquids on board an orbiting spacecraft is mainly driven by surface tension phenomena, which cause an apparently anomalous response of the liquid when compared with the behaviour that can be observed on an Earth laboratory provided that the amount of liquid is high enough. The reason is that in an orbiting spacecraft the different inertial forces acting on the bulk of the liquid are almost zero, causing thus capillary forces to be the dominant ones. Of course, since gravity forces are proportional to the liquid volume, whereas surface tension forces are proportional to the liquid surface, there are situations on Earth where capillarity can be the dominant effect, as it happens when very small volume liquid samples are considered. However, work with small size samples may require the use of sophisticated optical devices. Leaving aside the neutral buoyancy technique, a way of handling large liquid interfaces is by using drop towers, where the sample falls subjected to the action of Earth's gravity. This approach is suitable when the characteristic time of the problem under consideration is much smaller than the drop time. In this work the transformation of an out-of-use chimney into a drop tower is presented. Because of the miniaturization, hardiness and low cost of current electronic devices, a drop tower can be used as an inexpensive tool for undergraduate students to experimentally analyse a large variety of surface tension driven phenomena.

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Interior corner flow theory and its application to the satellite propellant management device design

Cited by 11 publications

References 10 publications

Application of the Onsager-Machlup integral in solving dynamic equations in nonequilibrium systems

Application of the Onsager-Machlup integral in solving dynamic equations in nonequilibrium systems

Study on liquid reorientation in tank models aboard the Chinese Space Station

Surface tension and microgravity

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