A piezo-magneto-elastically coupled distributed-parameter model of a bistable piezoelectric cantilever generator is developed by using the generalized Hamilton principle. The influence of the spacing between two adjacent magnets on the static bifurcation characteristics of the system is studied and the range of magnet spacing corresponding to the bistable states is obtained. Numerical and experimental studies are carried out to analyze the bifurcation, response characteristics, and their impact on the electrical output performance under varying external excitations. Results indicate that interwell limit cycle motion of the beam around the two centers corresponds to optimum power output; interwell chaotic motion and multiperiodic motion including intrawell oscillations are less effective. At a given frequency, the phenomena of symmetric-breaking and amplitude-phase modulation are observed with increase of base excitation. Both period-doubling bifurcation and intermittency routes to chaotic motion in the bistable system are found. It can be observed that the power output is not proportional to the excitation level because of the bifurcation behaviours.
Self-excited combustion instabilities of transverse modes were experimentally investigated in a rectangular multi-injector model combustor, operating with the bipropellants O2/CH4. The propellants were injected through a linear array of five oxidizer-centered shear coaxial injectors into the combustor. High-amplitude limit cycles obtained in hot-fire tests were analyzed in detail. Different combustion instability modes, including first and second width modes, were observed in cases with three different injection distribution schemes. Hence, the injection distribution strongly determined the combustion dynamics. One insight can be gained that the stable combustion could be achieved by properly designing the propellants' injection distributions.
This study numerically investigated the thermoacoustic combustion instability characteristics of a scaled rocket combustor based on a hybrid of the Reynolds-averaged Navier–Stokes and large–eddy simulation method. The turbulence–combustion interactions were treated using flamelet generated manifold approach. An unstable case was simulated with detailed reaction mechanisms (GRI-Mech 3.0). The obtained results agree well with experiment data from Purdue University, in terms of pressure oscillations frequency and power spectral density spectrum. The combustion instability mode was identified to be coupled with the first longitudinal acoustic mode of the combustion chamber by dynamic model decomposition method. According to Rayleigh index analysis, the unstable driving source was found to be located near the combustor step, which was further confirmed by time-averaged flow fields. Detailed three-dimensional vortex ring shedding evolutions at the combustor step were tracked with fine time resolution. Results indicate that the combustion instability arises from periodic vortex ring shedding at the combustor step and interacting with the chamber wall. The unburnt reactants were rolled up by the shedding vortex ring, which would not break up until impact with the chamber wall. Therefore, the mixing performance was significantly enhanced, leading to sudden heat release. Consequently, the thermal energy is added to the acoustic field, and the first longitudinal mode is thus reinforced, giving rise to large amplitude axial velocity oscillations which prompt the generation of the new vortex ring. The results of the present investigation will support the design and development of high-performance rocket engines.
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