Modelling and Identification of Technically Premix Flame Dynamics
Motivation
Due to the stringent norms on emissions, gas turbine manufacturers have adopted the lean burn combustion concept. Unfortunately, lean combustion systems are prone to thermo-acoustic instabilities, an unfavorable two-way-coupling of the unsteady heat release with perturbations of velocity, swirl and equivalence ratio, which may compromise engine life. Therefore prediction of thermo-acoustic behavior of the system during design phase is of primary importance. The dynamic response of a flame to perturbations can be simulated with transient LES and the input-output-relation is identified as the Flame Transfer Function (FTF), a so called LES-SI approach. Reduced order models determined with system identification can only be as accurate as the time series data that they are deduced from. Therefore the LES must properly resolve the flame dynamics, which requires a suitable combustion model, mesh and case setup, model structure and excitation signals.
The identification procedure must be robust, accurate and efficient. Two methods distinguished by the base type of the excitation signal are common, i.e. mono frequent and broad band excitation. Mono frequent excitation gives accurate estimates but only at the respective forcing frequency. Sampling the frequency range of interest fine enough would be too expensive. Broad band excitation and SI resolves a frequency range but with limited accuracy. Neither of them is suited on its own for a predictive identification. The fusion of both strategies via a machine learning approach called Multi Fidelity Gaussian Process can retain the strengths of each method and avoid their weaknesses. The FTF is determined as the most likely function considering all data sets through a maximum likelihood approximator. Therein the global trend of the function is provided by the broad band part and its accuracy and certainty is greatly increased near the mono frequent excitation frequencies. Only a few mono frequent training samples are required for the resulting function to satisfy the accuracy and uncertainty bounds on the whole frequency range. This greatly reduces the effort compared to pure mono frequent excitation. Further the accuracy compared to broad band excitation is greatly increased.
In industrial applications a perfect premixing is often not achieved leading to spatial and temporal mixture inhomogeinities and a so called technically premixed case. These may arise from too short mixing lengths and/or acoustically compliant fuel injection systems coupled to Acoustic Boundary Conditions (ABCs). ABCs often depend on the operating condition of the whole machine and are therefore only estimated. Only a Multi-Input-Single-Output (MISO) model structure allows to describe the flame dynamics independently of ABCs. In a MISO model all input channels are ideally forced with uncorrelated signals to minimize the simulated time necessary for identification. All parts of the process chain must be adapted to the MISO structure.
Objectives and Strategy
Case setup and Mesh: In OpenFOAM the correct choice of numerical schemes and solvers is of utmost importance for the reliability, accuracy and efficiency of the LES. The correct choice depends on mesh base type, combustion model and solver, and the often neglected cluster system. The performance of different mesh base types are another often overlooked aspect. For complex geometries, often tetrahedral or split hex based meshes are preferred but polyhedral meshes may perform better in terms of consistency, accuracy and efficiency. Within this project an optimal choice will be evaluated for each test case.
Turbulent Combustion Model: A turbulent combustion model must comprise two major parts, a turbulence chemistry interaction model and a chemistry model. Turbulence chemistry interaction may be resolution of species (with artificial thickening), flame surface density, stochastic fields and various PDF methods. A chemistry model may be tabulated or of Arrhenius type with a full or reduced chemistry mechanism. Additional flame thickening is often possible. A vast number of combinations has arisen in literature. Within this project promising candidates like the LDTFM and FSDM will be evaluated based on FTF, mean and rms quantities for perfectly and technically premixed flames.
System Identification: MFGP is a promising candidate for a reliable and efficient identification of the FTF but has not been tested in the LES-SI context. Further the procedure must be extended for MISO structure. Several identification techniques are tested for SISO and MISO model structure and compared to experimental measurements.
Acknowledgement
Financial support has been provided by the German Research Foundation (DFG) under grant number PO710/20-1, whose support is gratefully acknowledged. This project is carried out in collaboration with the Institute for Thermodynamics, Bundeswehr University Munich, whose coorporation is highly appreciated.