Thesis title: Characterization of the behavior of cryogenic propellants in tanks
With the introduction of cryogenic propellant combinations for space engines, there has been an increasing interest in the study of the behavior of the propellant in the tanks in which it is stored. This study can be carried out in two ways. The first approach involves both the dynamic behavior of the propellant, i.e. the sloshing analysis, and the thermo-fluid-dynamic behavior, which are analyzed as coupled phenomena. Conversely, in the second approach, the two phenomena are studied separately. In this thesis, the second approach has been used, and only the thermo-fluid-dynamic characterization of the behavior of cryogenic propellant in tanks has been carried out, since a consolidated reduced order activity on the sloshing analysis is already present in the literature.
Cryogenic propellants, having a very low boiling point, are subject to phase transitions even when exposed to very low heat leaks. As a result, the pressure raises inside a closed non-venting tank. Moreover, the tanks, especially those belonging to the upper stages of space launchers, are subjected to time-varying heat leaks and gravity levels during their operating life. The thermo-fluid-dynamics characterization mainly aims at estimating the evolutions of tank pressure, of the local fluid temperatures, of the phase change rate, and of the propellant location (in the case of reduced gravity). All these analyses, are necessary in order to guarantee the reliability and safety of a tank operation (feed turbopumps with propellant at appropriate temperature and pressure conditions, guarantee that only liquid drains from the tank outlet, ensure that only vapor comes out of the venting valve, etc.).
Due to the cost and complexity associated with the experiments, numerical tools of various levels of complexity have been implemented over the years to carry out the thermo-fluid-dynamic characterization. The first approach is characterized by the use of reduced order models. The latter allow quick estimates of the main observables, and, therefore, represent an engineering tool necessary in the case when a large number of parametric analyses has to be carried out, as in an industrial design process. The second approach involves Computational Fluid Dynamics (CFD) simulations. These last allow to perform more accurate analyses than the previous approach, and to study the complex physical phenomena at play. However, the drawback of CFD simulations is
the elevated computational cost with respect to the reduced order models.
The aim of this study is twofold. On the one hand, a suitable zero-dimensional model has been developed, implemented in Matlab, and successfully verified through the comparison with the results of a one-dimensional code developed by NASA (see Chap. 2). Later, it has been used to simulate two tank characteristic operating conditions, for which experimental data were also available. A ground-based self-pressurization experiment in a small-scale liquid N2 tank (see Chap. 4) and a ground-based active-pressurization experiment in a different small-scale liquid N2 tank (see Chap. 5). On the other hand, the aim of the study has been the development of a state-of-the-art CFD methodology (see Chap. 3), capable of estimating the main thermo-fluid-dynamic observables, and to study the main physical phenomena at play inside tanks of various species of cryogenic propellant, and characterized by different operating conditions. The proposed methodology has
been successfully validated through the comparison with the experimental data of three benchmark test cases, characterized by different propellants, geometries, and operating conditions. This has been done in order to develop a computational tool which guarantees reliability during most of the operating life of the tank. Moreover, for the various validation test cases, different physical and numerical models and parameters have been tested, in order to find the ones which allow the best reproduction of a particular operating condition, as well as the optimal parameters in terms of the trade-off between accuracy and computational time. The three validation test cases which have been simulated are:
• A ground-based liquid N2 self-pressurization test case, inside a small-scale tank (see Chap. 4).
• A ground-based liquid N2 active-pressurization test case, inside a small-scale tank (see Chap. 5).
• A self-pressurization test case carried out in the liquid H2 tank of the second stage of the Saturn IB AS-203 vehicle, while it was into circular low Earth orbit (see Chap. 6).
Then, the validated CFD methodology has been used to carry out a parametric study on the gravity level. In particular, four gravity levels, from normal gravity (g_E = 9.81 m/s^2), until the reduced gravity of 10^−3 g_E have been considered. This study has been performed using the same geometry, fluid, and operating conditions of the first validation test case. The parametric study has allowed to see the effect of the gravity level on the pressurization behavior, phase change, and liquid-ullage interface shape.
Finally, the developed, and repeatedly validated zero-dimensional model and CFD methodology have demonstrated to allow to perform, with different level of detail, the thermo-fluid-dynamics characterization of the behavior of cryogenic propellant, under most of the operating conditions of interest for tank design.