Speaker
Description
Cryogenic propellant management in micro-gravity environment has become of a primordial importance for the development of future space transportation systems. Upper stages are required to operate during long coasting phases, in order to allow for multiple payloads injections. Even small overheats can induce nucleate boiling in the saturated liquid, thus inducing overpressures in the tank, obliging to vent the gas and thus inducing a waste of propellant. Moreover, in order to sub-cool the propellant prior to engine ignition, a common approach consists in reducing the pressure in the tank, thus inducing cavitation in the liquid, that is bubble creation and growth induced by the pressure decrease. The same issues are encountered for in space depot that are expected to play an important role for in space exploration. Cryogenic propellants must be stored for several weeks/months, and pressure cycles could be employed to sub-cool the propellant before the fuel transfer. There is clearly a necessity to study the phenomena associated with phase change induced by temperature and pressure variations in a micro-gravity environment in order to increase the understanding and develop suitable guidelines allowing a proper tank design.
The peculiarity of the problem is that phase change phenomena are driven by temperature gradients at the interfaces and capillary effects at the contact line: small scales drive bubbles growth and their impact at the tank scale in terms of heat transfer and pressure increase. From a numerical point of view, direct numerical simulation (DNS) solvers are needed in order to study these phenomena at the bubble scale. The goal of this presentation is to show some recent developments that have been carried on the DIVA code for the DNS of bubbles growth induced either by overheat or pressure decrease [1-2].
First, a parametric study of a bubble nucleated in a subcooled liquid, under micro-gravity conditions will be presented. The simulation in the fluid domain is coupled with a temperature field resolution in the solid wall. Contact angles and Jacob numbers have been varied in order to extract a correlation for the diameter and the Nusselt number. However, these simulations have been limited to high contact angles (greater than 30°) and small wall thermal conductivity because of the lack of a model for the micro-region. Indeed, cryogens are wettable fluids characterized by very low microscopic contact angles. For a bubble nucleated over a superheated wall, micro-regions are expected to be formed at the contact line for such fluids: over an extension of the order of hundreds of nanometers, the contact angle varies between the microscopic and apparent values. This induces a variation of the local interface temperature and has a strong impact on the phase change mass flow rate. The micro-region cannot be simulated and need to be modeled. The numerical challenge consists in introducing a proper sub-grid model for the micro-region while maintaining suitable numerical properties of the solver, including numerical convergence and energy balances.
Finally, the presentation will end with an overview of the compressible solver development allowing the simulation of phase change induced either by temperature or pressure variation. Indeed, when it comes to phase change induced by pressure variations, the numerical challenge consists in including the proper thermodynamic description of the system (liquid, vapour and interface), coupling the pressure and temperature variations, and being able to describe both rapid and slow pressure variations. This will be shown on some examples of bubbles cavitation under different pressure temporal variation rates.
[1] Urbano, Tanguy and Colin, Int. J. of Heat and Mass Trans.,143, pp 118521 (2019)
[2] Urbano, Bibal and Tanguy, J. Comp. Fluids, 456, pp. 111034 (2022)
| Keywords | nucleate boiling; cavitation; micro-region; direct numerical simulation; |
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