Approximate analytical solution to the problem of cryogenic fuel volume increasing while tank drainage under microgravity conditions


Аuthors

Cherkasov S. G.*, Vasiutichev A. S.**, Moiseeva L. A.***, Gorodnov A. O.****

Keldysh Research Centre, 8, Onezhskaya str., Moscow, 125438, Russia

*e-mail: sgcherkasov@yandex.ru
**e-mail: aleksey.vas@mail.ru
***e-mail: lida.moiseeva@mail.ru
****e-mail: an.ol.gorodnov@gmail.com

Abstract

The article tackles the problem of cryogenic fuel volume increasing while tank drainage under microgravity conditions using a simplified physical model. The presented model is based on equilibrium formulation for the volume of boiling fuel. The Clausius-Clapeyron relation is used to describe the temperature and pressure relation. The homogeneous, «thermodynamic» description is applied for vapor and liquid density. The ideal gas equation of state is used for the fuel vapor. Temperature description in the non-boiled region is more complex due to the micro-accelerations in the course of the spaceflight. This effect leads to natural convection in the fuel volume. The convective flows create fuel temperature stratification in the tank, especially in the near free surface layer. The author proposes a one-dimensional formulation to describe these temperature gradients. The model problem of the fuel rise in a cylindrical tank is being solved by application of the presented formulation for physical processes while drainage. Several analytical solutions to the fuel level and vapor concentration changing in variously heated layer near fuel free surface were obtained. These solutions are obtained for different initial temperature profiles in this overheated fuel layer. Further, the problem of the entire fuel volume including initially homogeneously heated core region and overheated near surface layer was solved analytically. Analysis of the analytical solutions being obtained revealed that the largest contribution to the fuel volume growth was being made by the homogeneously heated fuel core region boiling.

Keywords:

cryogenic fuel, drainage, swelling, zero gravity

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