Phd in AERONAUTICS AND SPACE ENGINEERING

Thesis title: Low Order Modeling Approach to Longitudinal and Transverse Combustion Instability in Liquid Rocket Engines

High frequency combustion instability in liquid propellant rocket engines arises from the coupling between unsteady heat release rate and acoustics of the combustor. If unpredicted, such kind of instability can often result in the rapid destruction of the engine. From the numerical point of view, two different ways exist to approach the subject: the so-called high-fidelity and low-order models. The former ones, such as LESs or DESs, are capable of giving lots of information on the flow field but still struggle to give an accurate prediction of combustion instability, which would make experiments unnecessary. Moreover, they require a huge computational and economical effort that is prohibitive during the development phases of a new engine. Low-order models, on the other hand, require a larger modeling effort to include suitable laws capable of capturing the physics of the problem, but they are usually fast and cheap in terms of computations and data storage and, as a consequence, in terms of financial requirements. For such reason they deserve attention to be paid in the research community, since a predictive low-order model could represent an useful design tool. The approach which has been developed and is presented in this thesis is a brand new formulation belonging to the family of low-order models. The formulation novelty lies in the simplified heat release to acoustics coupling function, the so- called response function, which is realized here by means of the modeling of the shear-coaxial injector dynamics. In particular, the fuel mass flow rate injected by the elements is linked to the acoustic field here, in the place of linking directly the acoustics to an energy source term, as commonly done in the literature. In order to implement such low-order model a new one-dimensional injector solver is developed from scratch and it is used to solve one-dimensional problems. After that, such solver is even more interestingly used as a “tool” to solve the injectors flow fields within an existing in-house CFD solver, in order to deal with multi-dimensional instability problems. The employed set of equations is Eulerian and a simplified single step chemical mechanism is adopted to solve combustion. The model testing is performed onto two different test-cases, namely the Con- tinuously Variable Resonant Combustor (CVRC) and the Transverse Instability Combustor (TIC), both designed and assembled at Purdue University, IN, USA. CVRC is a single injector system affected by longitudinal combustion instability, while TIC is a multi-element test-engine affected by transverse instability. Prelimi- nary linear acoustics analyses are performed on both systems in order to validate the solver. After that, since the low-order model employs several free parameters, different sensitivity analyses are carried out to assess their role and to set them properly. Such analyses showed how the most part of the free parameters employed in the formulation is in fact negligible, while few of them are important. Finally, the self-excited behaviors of CVRC and TIC are simulated. Outcomes are satisfactorily: the model is capable to predict the high frequency oscillating behaviors of both CVRC and TIC within a low error threshold, provided an appropriate model tuning, which is however independent of the use of external data coming from experiments or other more detailed simulations.