Reduced Fidelity Analysis of Combustion Instabilities Using Flame Transfer Functions in a Nonlinear Euler Solver

Gowtham Manikanta Reddy Tamanampudi, Purdue University

Abstract

Combustion instability, a complex phenomenon observed in combustion chambers is due to the coupling between heat release and other unsteady flow processes. Combustion instability has long been a topic of interest to rocket scientists and has been extensively investigated experimentally and computationally. However, to date, there is no computational tool that can accurately predict the combustion instabilities in full-size combustors because of the amount of computational power required to perform a high-fidelity simulation of a multi-element chamber. Hence, the focus is shifted to reduced fidelity computational tools which may accurately predict the instability by using the information available from the high-fidelity simulations or experiments of single or few-element combustors. One way of developing reduced fidelity computational tools involves using a reduced fidelity solver together with the flame transfer functions that carry important information about the flame behavior from a high-fidelity simulation or experiment to a reduced fidelity simulation.To date, research has been focused mainly on premixed flames and using acoustic solvers together with the global flame transfer functions that were obtained by integrating over a region. However, in the case of rockets, the flame is non-premixed and distributed in space and time. Further, the mixing of propellants is impacted by the level of flow fluctuations and can lead to non-uniform mean properties and hence, there is a need for reduced fidelity solver that can capture the gas dynamics, nonlinearities and steep-fronted waves accurately. Nonlinear Euler equations have all the required capabilities and are at the bottom of the list in terms of the computational cost among the solvers that can solve for mean flow and allow multi-dimensional modeling of combustion instabilities. Hence, in the current work, nonlinear Euler solver together with the spatially distributed local flame transfer functions that capture the coupling between flame, acoustics, and hydrodynamics is explored.In this thesis, the approach to extract flame transfer functions from high-fidelity simulations and their integration with nonlinear Euler solver is presented. The dynamic mode decomposition (DMD) was used to extract spatially distributed flame transfer function (FTF) from high fidelity simulation of a single element non-premixed flame. Once extracted, the FTF was integrated with nonlinear Euler equations as a fluctuating source term of the energy equation. The time-averaged species destruction rates from the high-fidelity simulation were used as the mean source terms of the species equations.Following a variable gain approach, the local species destruction rates were modified to account for local cell constituents and maintain correct mean conditions at every time step of the nonlinear Euler simulation. The proposed reduced fidelity model was verified using a Rijke tube test case and to further assess the capabilities of the proposed model it was applied to a single element model rocket combustor, the Continuously Variable Resonance Combustor (CVRC), that exhibited self-excited combustion instabilities that are on the order of 10% of the mean pressure. The results showed that the proposed model could reproduce the unsteady behavior of the CVRC predicted by the high-fidelity simulation reasonably well.

Degree

Ph.D.

Advisors

Anderson, Purdue University.

Subject Area

Acoustics|Energy|Mechanical engineering

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