Modelling effects of flame development on stationary and oscillating premixed turbulent combustion
Abstract: The vast majority of contemporary models of premixed turbulent flames applied to multi-dimensional RANS numerical simulations of combustion in gas turbine engines and aero-engine afterburners focus on fully-developed flames, characterized by fully-developed turbulent diffusivity, thickness, and burning velocity. However, abundant experimental data obtained from statistically stationary premixed flames clearly show that a typical turbulent flame develops as it is convected by mean flow from a stabilization zone. For instance, the mean thickness of a typical premixed turbulent flame grows with the distance from that zone, indicating the development of the flame. The main goal of the work underlying this thesis has been to assess the role played by the flame development in premixed turbulent combustion. Two problems have been specifically addressed, (i) oscillations of a confined premixed turbulent flame, attached to a bluff body, under the influence of prescribed harmonic oscillations of the oncoming flow velocity and (ii) statistically stationary premixed turbulent combustion behind a bluff body in a channel. Both problems have been studied using the same strategy: selection of a well-known and widely-used model as a reference approach, then step-by-step extension to account for the development of turbulent diffusivity, mean flame thickness and speed. In both cases, the submodels of the development of the diffusivity, flame thickness and speed have been based on the same Flame Speed Closure (FSC) model, which has already been validated thoroughly for expanding flames. When studying the flame oscillations, an unsteady one-dimensional kinematic equation with developing flame speed has been solved to determine the flame surface, then the mean flame structure has been reconstructed by adapting the FSC model, and the heat release rate has been integrated over the oscillating flame brush. The results of the simulations, reported in a form of a flame transfer function, which relates the normalized magnitude and phase of the heat release rate oscillations with the normalized magnitude and phase of oncoming flow velocity oscillations at various frequencies of them, show that turbulent flame development markedly affects the flame transfer function. The computed flame transfer functions have been incorporated into the well-known n-? model of longitudinal thermo-acoustic oscillations. The complex frequencies of the oscillations, calculated using the flame transfer functions obtained for fully-developed and developing flames, other things being equal, show that the flame development substantially affects the stability of the combustor studied. The model predicts the frequency of the unstable acoustic mode recorded by Langhorne at Cambridge University, whereas the same model applied to a fully-developed flame yields stable combustion under the conditions of these experiments. Second, statistically stationary premixed turbulent combustion behind a bluff body has been studied within the RANS framework by implementing the FSC model into the CFD code Fluent 6.2. By combining the submodels of developing turbulent diffusivity, flame brush thickness, and burning velocity, the effects of these processes on the mean position, thickness, and structure of the flame have been studied step-by-step by numerically simulating Validation Rig I experiments performed at Volvo Aero Co. Numerical results show that all these processes affect the computed transverse profiles of the Reynolds-averaged combustion progress variable. The profiles of the progress variable computed using the FSC model, which addresses all the abovementioned processes, show the best agreement with the measured profiles as compared with other combustion models used. The main conclusion from the thesis is as follows: Flame development may substantially affect not only expanding but also statistically stationary or oscillating premixed turbulent combustion and this phenomenon should be addressed in numerical simulations of flames in gas turbine engines or aero-engine afterburners.
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