In the first part of this work, instability is correctly predicted for a Rijke tube with a new two-term acoustic forcing term derived from a one-dimensional flame dynamics model. The new two-term acoustic forcing term, which is comprised of the summation of chemical heat release rate and heat transfer due to convection, correctly predicts instability where older models of acoustic forcing based solely on chemical heat release rate incorrectly predicted stability. This stability analysis correctly predicts the inlet conditions of the instability in addition to the frequency of instability. In the second part of this work, networks of dynamic well-stirred reactors are used to model qualitative behavior observed in turbulent combustion. First a model of dynamic well-stirred reactor is derived, and then several reactors are coupled together by recirculation. The dynamics of the various models are computed and assessed. The models exhibit interesting behavior that has been viewed experimentally including hysteresis and peaking in the dynamic response. / Master of Science

The first part of the thesis focuses on developing a numerical methodology to simulate the acoustic properties of a hybrid liner consisting of a perforated plate, a porous layer and a Helmholtz cavity. Liners are always a standard way to reduce noise in today’s aeroengines, e.g. the fan noise can be reduced effectively through the installation of acoustic liners as wall treatments in the ducts. In order to optimize a liner in the design phase, an accurate and efficient prediction tool is of interests. Hence, a unified Linearized Navier-Stokes equations(LNSE) approach has been implemented in the thesis, combining the LNSE in frequency domain with the fluid equivalent model. The LNSE is applied in the vicinity of the perforated plate to simulate sound propagation including viscous damping effect, and the fluid equivalent model is used to model the sound propagation in the porous material including absorption. The second part of the thesis focuses on the prediction of thermoacoustic instabilities. Thermoacoustic instabilities arise when positive coupling occurs between the flame and the acoustics in the feedback loop, i.e. the flame acts as an amplifier of the disturbances (acoustic or fluid) at a natural frequency of the combustion system. Once the thermoacoustic instabilities occur, it will lead to extremely high noise levels within a relatively narrow frequency range, resulting in a huge damage to the structure of the combustors. Hence, a solution must be found, which breaks the link between the combustion process and the structural acoustics. The numerical prediction of thermoacoustic instabilities in the thesis is performed by two different numerical methodologies. One solves the Helmholtz equation in combination of the flame n − tau model with the low Mach number assumptions, and the other solves the Linearized Navier-Stokes equations in frequency domain with mean flow. The result show that the mean flow has a significant effect on the thermoacoustic instabilities, which is non-negligible when the Mach number reaches to 0.15. / <p>QC 20151221</p> / TANGO

Controlling unsteady combustion induced gas flow fluctuations and the resultant motor vibrations is a very significant step in rocket motor design. It occurs when the unsteady heat release due to combustion happens to feed the acoustic oscillations of the closed duct forming a feed-back system. The resultant vibrations concerned may even lead to total failure of the rocket system unless analysed and tested thoroughly. This thesis aims developing a linear numerical analysis method for the growth rate of instabilities and possible mode shape of a liquid-propelled chamber geometry. In particular, A 3-D Helmholtz code, utilizing Culicks spatial averaging linear iterative method, is developed to find the form of deformed mode shapes iteratively to obtain possible effects of heat source and impedance boundary conditions. The natural mode shape phase is solved through finite volume discretization and the open-source eigenvalue extractor, ARPACK, and its parallel implementation PARPACK. The iterative method is particularly used for analyzing the geometries with complex shapes and essentially for disturbances of small magnitudes to natural mode shapes. The developed tools are tested via two simple cases, a duct with inactive flame and a Rijke tube, used as validation cases for the code particularly with only boundary contribution and heat contribution respectively. A sample 2-D and 3-D liquid-propelled combustion chamber is also analysed with heat sources. After comparing with the expected values, it is eventually proved that the method should be only used for determining the modes instability analysis, as to whether it keeps vibrating or decays. The methodology described can be used as a preliminary design tool for the design of liquid-propellant rocket engine combustors, rapidly revealing only the onset of instabilities.