Modelica Stage Separation Dynamics Modeling for End-to-End Launch Vehicle Trajectory Simulations

Abstract

Stage separation dynamics modeling is a critical capability of future launchers preparatory studies. The development of stage separation frameworks integrable in end-to-end launch vehicle trajectory simulations have been presented in the relevant literature but none profiting from the object-oriented and equation-based acausal modeling properties of MODELICA. The objective of this paper is therefore to present such an approach to this problematic. Based on the Constraint Force Equation (CFE) methodology, two case studies to evaluate the proposed approach are considered. Results demonstrate that the approach corresponds very well with the physics behind separation. In addition, we found easiness of implementation of the method within a single environment such as DYMOLA, demonstrating the benefits of an integrated approach.

Proceedings of the 2nd Japanese Modelica Conference Tokyo, Japan, May 17-18, 2018

“…Each stage is connected to the next stage with separation components. As long as the boolean signal is defined as false the stages remain connected and they are separated if otherwise (see (Acquatella B. and Reiner, 2014)). The mass flow rate and thrust magnitude for each stage are obtained from MATLAB files using multi-dimensional time-dependent interpolation tables to include a realistic modeling challenge since import and interpolation of external engine or aerodynamic datasets have to be performed very often in design studies.…”

“…In recent developments, launch vehicle multibody models were obtained which use time-and state-dependent conditional statements to characterize the variable system structure, as presented in (Acquatella B., 2016). Also, separation models as introduced in (Acquatella B. and Reiner, 2014) can be used to fulfill the requirements for a fixed number of states and equations during the overall simulation by defining a connectivity condition between separated components and continuously simulating all components even after separation. These kind of models and methods are used within end-to-end simulations, which consider the multibody dynamics of all separated and connected launch vehicle components simultaneously as shown in Figure 1(a).…”

“…Since all forces are applied only vertically in the bodies' z-direction according to a flat world assumption, this drift error should be ideally zero as can be seen by the results of the sequential simulation models. The resulting drift of the multibody parts after separation is caused by the acceleration residual at separation time, which in turn is caused by the Baumgarte stabilization solution during joint body motion whose accuracy is sensitive to computational erros as mentioned in (Acquatella B. and Reiner, 2014).…”

Modeling and simulation of dynamically constrained objects for limited structurally variable systems in Modelica

“…There are also examples in the field of aeronautics, such as the structural changes during runtime in the area of stage separation (Acquatella and Reiner 2014) or for in orbit construction of orbital platforms (Reiner 2022).…”

“…This work builds on the previous work of (Acquatella and Reiner 2014) and (Reiner 2022) to make it usable in a wider range of applications, and shows how robot tool changers can be modeled using the proposed technique. We present a new solution for the modeling and simulation of structurally variable systems in Modelica.…”