Variable-Mass Dynamics Implementations in Multi-Physics Environment for Reusable Launcher Simulations
Creators: name:  B. GAszLER 
name:   L.E. BRIESE 
name:   P. ACQUATELLA 
name:   P. SIMPLICIO 
name:   S. BENNANI 
name:   M. CASASCO 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: FLIGHT DYNAMICS
GNC
AVIONICS
SIMULATIONS
VALIDATIONS

description: Ongoing demand for launch opportunities has stimulated further development of dedicated launch vehicles and new concepts, mainly due to the large amount of spacecraft that are rapidly increasing in development and production as evidenced in the recent years. Such large market of future satellites and space missions makes these new launcher developments a very competitive environment. However, with these new launch vehicles and concepts comes a new set of challenges that have to be assessed rapidly and with agility. One of the driving challenges in launcher GC design is the strong coupling between different disciplines (GNC, aerodynamics, actuators, structure, etc.), which have a \"multi-physics\" nature. In the current industrial approach, these multi-physics effects are tackled by separate teams using their own tools and GC design is usually based on low-fidelity models that simplify the interactions between disciplines. Enabling a more efficient and accurate modelling of some of the multi-disciplinary interactions mentioned above through the use of a multi-physics modelling approach is believed to be beneficial in expediting the design process, reducing the conservatism in the assumptions used by GC design and, ultimately, improving the launcher performance. In particular, the accurate modelling of time-varying propellant mass dynamics is an essential component during preliminary design studies since it might have an impact on the dynamical simulations that in turn influences the assessment and evaluation of the launcher performance and trade-off across disciplines. In most simulators and studies published or described openly in the literature, variable mass dynamics is usually simplified and considered as a linear relationship of mass flow rate which in turn only affects the mass and moment of inertia while neglecting other fundamental dynamical effects due to the mass variability itself. While this might be a valid assumption for some burn/thrust profiles, angular velocities of the composite launcher are actually damped (e.g. jet damping) or amplified by variable mass dynamical effects during propellant burn. However, such variable-mass dynamical effects have also been addressed in the literature at fundamental levels (via Lagrange and Kane\'s formalism, for instance). In some cases, the derived results can be further simplified depending on the propellant/burn type and geometry, giving rise to simpler (more tractable, easy to implement) equations that might be verified with simple models. It can be easily shown that the variable-mass dynamics in turn have an effect both on the translation and rotational motion of the vehicle during thrust phases. The objective of this paper is therefore to present the implementations of variable-mass dynamics towards the preliminary design and development of a dedicated multi-physics simulator, termed R2M2 (Rapid Reusable Launcher Simulation via Multi-physics Modelling), for multi-actuated vertical take-off vertical landing (VTVL) vehicles. The paper first recapitulates previous investigations on variable-mass dynamics from the relevant literature, including specific descriptions of the dynamical effects during translational and rotational motion, and addresses several questions on how to implement these dynamical effects in a modular fashion with a multi-physics modelling environment. The paper also focuses on showcasing the discrepancies arising when these variable-mass dynamical effects are excluded or not properly taken into account. This, in turn, illustrates potential simulation errors that might have an effect on the overall launcher performance assessment. The implementation is done in MathWorks MATLAB and Simulink together with the multi-physics modelling environment Simscape. One of the advantages of this modelling approach and implementation is that it allows to efficiently capture the main dynamical effects of every subsystem together with their interactions while also enabling the possibility for future GC rapid prototyping and simulation within a single tool. The model implementation and analysis of results is performed using simple yet representative models of different burn types of propellants or engines which are commonly found in launch vehicle configurations. These model implementations are cross-checked with theoretical results from the literature as well as against alternative implementations using the multi-physics and acausal modelling language MODELICA. Furthermore, test cases are performed showing good compliance and similarity of results. Finally, the paper concludes with a short investigation on simulation and solver performance of these variable mass implementations for different types of solvers, integration parameters, and multi-physics environments.