## 1 Introduction
The two-phase flow can be predicted by different models, such as the two-fluid model, the drift-flux model, and the homogeneous model [8]. The two-fluid model is the most rigorous approach since each phase is modelled separately with interfacial interactions. Nevertheless, it is rarely applied [9; 10] due to the considerable difficulties linked to the uncertainties in predicting the interfacial interaction terms between the two phases and the mathematical complexity of two sets of conservation equations. The drift-flux model provides a simpler and more reliable alternative to the two-fluid models. This model, employed by [PERSON] et al. [11], simulates the behaviour of the two-phase flow as a whole while considering the relative motion between the two phases. In this way, the model uses one set of three conservation equations for the two-phase mixture and a drift-flux equation. The most commonly used approach is the homogeneous model. The model considers the fluid as a homogeneous mixture and employs a set of three conservation equations [12; 13; 14]. As an example, this model was adopted by [PERSON] et al. [13] to investigate complex problems such as the chill-down of the feed line with a centrifugal turbopump. They adopted a novel finite-volume-based network flow analysis procedure [14] and demonstrated that fluid networks could be used to simulate geometries as complex as those of a turbopump. It should be noted that fluid network solvers use bulk properties averaged over a cross-sectional area and require a set of correlations based on experimental data [15; 16; 17; 18; 19; 20; 21; 22; 23; 24] to accurately determine heat transfer and pressure losses. Therefore, the accuracy of the chosen correlations for the specific application heavily influences the prediction accuracy of the model. Therefore, in order to choose the most suitable correlations, a review of the performance of the different correlations for various fluids and geometries is needed, such as those presented by [PERSON] et al. [25] and [PERSON] et al. [7]. Despite its limitations, the homogeneous model for fluid network solvers offers robustness, fast calculations, and good accuracy for preliminary design studies. Although some research has been carried out on the modelling of the two-phase flow of a pure cryogenic fluid, very little attention has been paid to the role of the mixing of fluid in the presence of phase change. In a previous work [26], the authors developed a thermo-fluid network solver and used it to simulate a pure substance/two-phase flow in a spinning stator-rotor-stator disk [26]. The purpose of this paper was to improve the aforementioned numerical model by adding the capacity to describe the mixing of different fluids (e.g., oxygen and helium). The numerical tool uses a one-dimensional general-purpose finite volume homogeneous model to predict two-phase multi-component flows in cryogenic feeding systems. A finite difference discretization was employed in the mass, the momentum, and the energy conservation equations of fluids and solids in order to predict thermo-fluid transients during the two-phase flow of cryogenic lines. The classical two-phase heat transfer and pressure drop empirical correlations were adapted to multi-component flows using an overall gas fraction. The numerical model was validated on experimental data collected by Avio S.p.A. during the tests on the Dynamic Seal Package (DSP). A simplified cross-section of the test bench is shown in Figure 1. Experimental data for a number of DSP operating conditions were used as a reference in order to validate the tool and to make it available for the design and analysis of new advanced components. In Section 2, the model assumptions and equations are presented, including the conservation equations, the thermodynamic properties, and the pressure drop and heat transfer correlations. Section 3 presents the test setup and its modelling used in the numerical solver.