Thermoacoustic stabilization of a longitudinal combustor using adjoint methods

Abstract

We construct a low order thermoacoustic network model that contains the most influential physical mechanisms of a thermoacoustic system. We apply it to a laboratory-scale longitudinal combustor that has been found to be thermoacoustically unstable in experiments. We model the flame, which is behind a bluff body, by a geometric level set method. We obtain the thermoacoustic eigenvalues of this configuration and examine a configuration in which six eigenmodes are unstable. We then derive the adjoint equations of this model and use the corresponding adjoint eigenmodes to obtain the sensitivities of the unstable eigenvalues to modifications of the model geometry. These sensitivities contain contributions from changes to the steady base flow and changes to the fluctuating flow. We find that these two contributions have similar magnitudes, showing that both contributions need to be considered. We then wrap these sensitivities within a gradient-based optimization algorithm and stabilize all six eigenvalues by changing the geometry. The required geometry changes are well approximated by the first step in the optimization process, showing that this sensitivity information is useful even before it is embedded within an optimization algorithm. We examine the acoustic energy balance during the optimization process and identify the physical mechanisms through which the algorithm is stabilizing the combustor. The algorithm works by, for each mode, reducing the work done by the flame, while simultaneously increasing the work done by the system on the outlet boundary. We find that only small geometry changes are required in order to stabilize every mode. The network model used in this study deliberately has the same structure as one used in the gas turbine industry in order to ease its implementation in practice. * Now at Norges teknisk-naturvitenskapelige universitet (NTNU);

Thermoacoustic stabilization of combustors with gradient-augmented Bayesian optimization and adjoint models

“…The second test case is taken from Aguilar and Juniper 16 and relates to geometry optimization in a network model of Rama Balachandran’s 10 kW longitudinal combustor built in Cambridge, originally intended for the experimental investigation of the response of turbulent premixed flames to acoustic oscillations. 17 The geometry consists of an inlet duct connected to a plenum with a linearly varying cross section on either end.…”

“…The second involves geometry optimization in a low-order network model of a longitudinal combustor. 16 We compare gradient-augmented BO with BFGS, a standard quasi-Newton optimizer which uses an estimate of the inverse Hessian matrix to improve convergence. Compared to BFGS, we find that the gradient-augmented BO does not get stuck in local optima and requires fewer evaluations of the solver to arrive at more thermacoustically stable configurations.…”

An exceptional point switches stability of a thermoacoustic experiment

“…This model for an unflanged tube exit is widely employed in thermoacoustic studies (Moeck et al. 2009; Kraus, Selle & Poinsot 2018; Mukherjee 2018; Aguilar & Juniper 2020).

Figure 3.Representation of the full thermoacoustic system as an ITA system coupled to an acoustic system.

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Inhibiting the onset of thermoacoustic instability through targeted control of critical regions

“…[9][10][11][12] In another type of passive control method, the linear growth rate of oscillations around the base flow is forced to be negative. Aguilar and Juniper 13 employ a simple network model with sensitivity analysis to comprehend the dynamics of the combustor during thermoacoustic stability. They reported that variations in the base flow must be taken into account in the same manner as variations in the fluctuating flow.…”