| Summary: | In this dissertation, a 2D domain decomposition technique (DDT) is developed based on an overset method coupling a nonlinear solver with a linearized Euler solver. The nonlinear solver can account for complex physics such as turbulence, combustion, and thermoacoustics, whereas the linear domain is based on a low dispersion and dissipation scheme to convect waves accurately. Multiple problems are investigated in this thesis, namely acoustic wave generation and scattering in internal and external flows, convection driven thermal plume, isothermal turbulent jet flow, and thermoacoustic instabilities induced by heater and chemical reacting flow. First, extension of DDT to 2D was validated with 1D published results and theoretical solutions. For 2D inviscid flow cases, the internal and external flow simulations, converging-diverging nozzle in subsonic and supersonic flow regimes and transonic flow over supercritical airfoil were conducted, respectively. Simulation results have demonstrated that higher overlap ratio between linear and nonlinear regions is encouraged to propagate the acoustic waves with less dissipation and dispersion errors. Moreover, substantial cost-savings of 84% and 51% were observed when DDT was used for converging-diverging nozzle simulations in subsonic and supersonic flow regimes, respectively. Additionally, implementation of DDT in external flow simulation has eliminated the unsteady perturbation observed in fully nonlinear far-field region and allows proper wave scattering, interference, and Doppler effect to be observed. For 2D viscous flow, a thermal plume under convective flow condition was simulated as a canonical study of thermoacoustic problem. Results demonstrate the feasibility of DDT in capturing not only the frequency of vortex shedding, but also the heat release rate fluctuation, while reducing approximately 13% of computational hours as compared to fully nonlinear simulations. Hence, more complex thermoacoustic DDT simulations are possible. DDT was then extended into 3D to get high-fidelity acoustic generation results for an isothermal turbulent jet case. Preliminary results for the 3D case demonstrate cost-saving of 16% however technical challenges remain unsolved. Extension of complex nonlinear simulation to include thermoacoustic for chemically reaching flows was performed for a Rijke tube test case. The thermoacoustic instability was assessed by evaluating the standard and extended Rayleigh criteria. In this thesis, only the nonlinear domain was considered as extension to DDT will be addressed in future work. Numerical results show that both chemically non-reacting and reacting simulations compare well with theoretical models and qualitatively with experimental measurements, respectively. Both assessment criteria are correctly indicating the state of thermoacoustic instability in all Rijke tube simulations. The nonlinear solver, therefore, is capable for high-fidelity acoustic generation via thermoacoustic means.
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