| description abstract | A methodology is presented to model noncompact thermoacoustic phenomena using reducedorder models (ROMs) based on the linearized Navier–Stokes equations (LNSEs). The method is applicable to geometries with a complex flow field as in a gas turbine combustion chamber. The LNSEs, and thus the resulting ROM, include coupling effects between acoustics and mean fluid flow and are hence capable of describing propagation and (e.g., vortical) damping of the acoustic fluctuations within the considered volume. Such an ROM then constitutes the main building block for a novel thermoacoustic stability analysis method via a loworder hybrid approach. This method presents an expansion to stateoftheart loworder stability tools and is conceptually based on three core features: First, the multidimensional and volumetric nature of the ROM establishes access to account spatial variability and noncompact effects on heatrelease fluctuations. As a result, it is particularly useful for highfrequency phenomena such as screech. Second, the LNSE basis grants the ROM the capability to reconstruct complex acoustic performances physically accurate. Third, the formulation of the ROM in statespace allows convenient access to the frequency and time domain. In the time domain, nonlinear saturation mechanisms can be included, which reproduce the nonlinear stochastic limit cycle behavior of thermoacoustic oscillations. In order to demonstrate and verify the ROM's underlying methodology, a test case using an orificetube geometry as the acoustic volume is performed. The generation of the ROM of the orifice tube is conducted in a twostep procedure. As the first step, the geometrical domain is aeroacoustically characterized through the LNSE in frequency domain and discretized via the finite element method (FEM). The second step concerns the actual derivation of the ROM. The highorder dynamical system from the LNSE discretization is subjected to a modal reduction as order reduction technique. Mathematically, this modal reduction is the projection of the highorder (N∼ 200,000) system into its truncated left eigenspace. An order reduction of several magnitudes (ROM order: Nr∼ 100) is achieved. The resulting ROM contains all essential information about propagation and damping of the acoustic variables, and efficiently reproduces the aeroacoustic performance of the orifice tube. Validation is achieved by comparing ROM results against numerical and experimental benchmarks from LNSE–FEM simulations and test rig measurements, respectively. Excellent agreement is found, which grants the ROM modeling approach full eligibility for further usage in the context of thermoacoustic stability modeling. This work is concluded by a methodological demonstration of performing stability analyses of noncompact thermoacoustic systems using the herein presented ROMs. | |
