Dottorato in INGEGNERIA AERONAUTICA E SPAZIALE

Titolo della tesi: Low Order Q1D Modeling of Pressure Oscillations in Solid Rocket Motors

This Ph.D. research is focused on the study of pressure oscillations (PO) phenomenon which may occur during the operative time of Solid Rocket Motors (SRMs). Although PO do not usually compromise the final mission goals, they bring about thrust oscillations which may have a severe impact on the overall launcher system. The assessment of pressure oscillations amplitude and time windows of occurrence is thus necessary for the correct characterisation of the dynamic environment affecting launcher and payload. In the current state of the art, two physical phenomena are addressed as driving mechanism for PO onset in modern space launchers SRMs: hydrodynamic instabilities, related to vortex shedding, and thermoacoustic instability, related to aluminum distributed combustion. The first PO source occurs when vortical structures generation and dynamics lock in with chamber acoustics, giving rise to an aeroacoustic feedback loop. The second one arises when aluminum combustion rates fluctuations, produced by the burning droplets, are synchronized with the acoustic field. Thermoacoustic instabilities are thus thought to be a source of PO in SRMs. Pressure oscillations comprehension represents a very challenging task to accomplish. Indeed, the energy scale in which the phenomenon takes place is far weaker compared with the mean flowfield one. Moreover the involved physics is truly complex: an unsteady, multiphase, turbulent flow with heterogeneous combustion processes occurring in elaborated geometries. These issues also pose an obstacle to the investigation of the PO basic phenomenology: lab-scale experiments provide limited and incomplete results, DNS analysis are unthinkable due problem geometry size, whereas lighter CFD approach present high computational costs and modeling efforts. In this context, the research work is focused on the development of a low order Q1D model able to deal with both PO sources in SRMs. As a matter of fact, such formulation is hugely lighter than CFD and, once got over the modeling difficulties, may actually be able to deliver more details than analytical or semi-empirical methods. The novel Q1D methodology is based upon two main models: Aeroacoustically Generated Acoustic Resonance (AGAR) model and ThermoAcoustic Resonance (TAR) model. AGAR model was designed, validated and successfully applied at Department of Mechanical and Aerospace Engineering for the past ten years, mainly being employed for Vega SRMs PO prediction and reconstruction. It was built on a single-phase formulation, considering vortex-shedding phenomena as chief mechanism of PO onset. On the other hand, TAR model addresses uniquely thermoacoustics phenomena and has been wholly designed during the Ph.D. starting from multiphase multidimensional simulations carried out by means of an in-house code. This work aims to provide a detailed description of the two separate Q1D models concerning mathematical and numerical methods, physical fundamentals and the relative approximations. Validation is provided against two different test cases: ONERA C1xb for hydrodynamics instabilities and a numerical pipe-like SRM case regarding thermoacoustics. Finally, the application to an aft-finocyl SRM, namely Vega P80, is reported in order to show the Q1D model capability to recover pressure oscillations phenomenon in a configuration which is thought to present both hydrodynamic and thermoacoustic instabilities.