Rotating Detonation Engines (RDEs) are a type of pressure-gain combustion system based on detonation waves traveling around a cylindrical combustion chamber igniting the fresh gases. Compared to classical combustors, detonative combustion offers an increment in thermodynamic efficiency of the engine due to rapid heat release and lower entropy rise. The development of this technology could bring more compact and efficient combustors with applications to energy generation, aviation, and rocket propulsion.
The objective of the present work is to develop a robust set up to simulate an RDE employing the DLR TAU code to obtain physical solutions to investigate the flow field within the engine and its performance. The impact of different modeling decisions and their influence on the flow physics shall be addressed.
First, a set of 1D shock tube simulations have been conducted to evaluate the best solver parameters to capture detonation dynamics. Later, results of 2D simulations based on a test case from literature were performed and the modeling decisions were re-evaluated for this more realistic case. Lastly, two different 3D simulations have been performed and compared with the respective experimental results.
The results showed that a resolution of 200 microns was enough in 2D simulations to capture the main flow features. Moreover, the chosen chemical reaction mechanism was from Ó Conaire et al. 2004, and the upwind flux that performed the best was the AUSMDV (Wada et al. 1994) solver. Moreover, the time step employed was of the order of ten to the power of minus eight seconds. Different inlet boundary conditions were studied, finding the Dirichlet type more suitable to uncouple injection and detonation dynamics. In addition, different ignition strategies were evaluated, proving that the strategies were successful and achieved a stable mode of operation.
This work presents a robust set up to perform 2D and 3D RDE simulations employing the DLR TAU code. It also provides many insights into the impact of different modeling decisions on the flow field and evolution of the engine performance.

Modeling plankton communities has been an import topic in mathematical biology for quite some time. Previous research mostly comes in two flavors. On one hand we have large global models, which try and recreate measured data, but often lose track of what are the root causes of phenomena. On the other hand we have smaller models, where the (mathematical) reasoning behind phenomena are tried to be understood, but they lose some of their applicability. We try to bridge the gap between these two, by exploring how far results after simplification carry over to a more general case. We do this by investigating a size structured plankton model as proposed by (Poulin & Franks, 2010). We first simplify the interaction between phyto- and zooplankton, for which we are able to find analytical stationary solutions. Using numerical methods we are able to show stable stationary and limit cycle behavior. Furthermore we are able to show how much diversity remains, and how this is linked to the analytical solutions. Then we are able to show that these structures remain in place after allowing more complex interactions, and identify how far this remains true. Using this knowledge we are able to give quick insights into more complex models.

Vibrations in engineering structures can lead to severe instabilities, especially under low-frequency excitations that traditional linear isolators cannot effectively suppress. To address this, quasi-zero stiffness (QZS) vibration isolators, known for their high-static-low-dynamic stiffness properties, have gained increasing attention. This report investigates the reflection and absorption characteristics of a nonlinear string with a QZS mechanism applied as a boundary condition. The model is considered, and the governing equations are derived and nondimensionalized. Using regular perturbation methods and the method of multiple time scales, analytical solutions are obtained and evaluated. The analysis distinguishes between cases where the oblique springs are extended or compressed. It is found that with compressed springs, when the vertical damping coefficient is below unity, the system is counterintuitively stable. Furthermore, the inclusion of oblique dampers leads to unphysical energy growth. These phenomena are attributed to the singular nature of the system’s dynamics and the limitations of the chosen multiple time scale method. The results indicate that the current model does not fully capture the effects of the oblique springs and dampers, underscoring the need for further investigation into the system’s asymptotic expansions. Moreover, exploring second-order dynamics and external forcing could provide a deeper understanding of the system’s complex behaviour.