Extraction of response function from numerical simulations and their use for longitudinal combustion intsbility modeling

The present work focuses on high frequency longitudinal combustion instability, with particular attention to the continuously variable resonance combustor (CVRC) characterized by the variable length of the oxidizer post. The aim of the paper is to reproduce the behavior of the combustor at different lengths of the post, long post configuration, inter- mediate post configuration and short post configuration, LPC, IPC and SPC respectively, using a quasi-1D Eulerian solver. This low-order model requires a suitable response function that, in the present work, is calibrated on the basis of two-dimensional axis-symmetric high fidelity simulations of the most unstable geometrical configuration (IPC). Two re- sponse functions of the velocity time lag family are obtained, the first is extracted from hybrid Reynolds averaged Navier-Stokes - Large eddy simulation (hybrid RANS-LES) or detached eddy simulation (DES) while the second is estimated on the basis of an unsteady Reynolds averaged Navier-Stokes simulation (URANS). The obtained response functions are implemented in the quasi-1D solver, not only for simulating the IPC but also for the SPC and LPC cases, with the intention of investigating the generality of the computed response for the different configurations of CVRC, independently of the length of the oxidizer post. Encouraging results are obtained in this sense, showing that a suitable response function is able to identify stable and unstable regime. © 2017 by Maria Luisa Frezzotti, Francesco Nasuti, Cheng Huang, William E. Anderson