Low order duct acoustic models are a powerful tool to predict and avoid aeroacoustic instabilities like whistling. Such instabilities are important in the development process of many applications as diverse as pipeline networks, mufflers or HVAC systems. We develop a low order network duct acoustic simulation tool called taX, which takes advantage of the Matlab control system toolbox.

The propagation of acoustic perturbations may be modeled by a set of linear, time invariant differential equations. By simplification to one dimensional propagation of acoustic waves, the acoustic system can be modeled by Green's functions describing the transmission of acoustic waves in a network of acoustic elements, as depicted in Figure 1. The scattering of acoustic waves in each of the acoustic elements can be respresented by the scattering matrix, which is the Fourier transformation of the Green's function [1]. We demonstrate that there exists an equivalence between the aeroacoustic system models and commonly used models of control sytem theory. Being aware of this analogy, we have the opportunity to leverage the power of control system theory to solve duct acoustic network problems. Our tool thus takes advantage of efficient implementations provided by the Matlab control system routines [2].

The acoustic models involved may be analytically derived from first principles in continuous time. Further we have a seamless integration of discrete time models obtained by system identification of time series data from LES simulations. For this purpose, the discrete time systems are transformed to continuous time.

We are investigating the thermoacoustic stability of velocity sensitive premixed flames. A causal representation of the flow-flame-acoustic interactions reveals a flame-intrinsic feedback mechanism [3]. The feedback loop as shown in Figure 2 may be described as follows: An upstream velocity disturbance induces a modulation of the heat release rate, which in turn generates an acoustic wave traveling in the upstream direction, where it influences the acoustic velocity and thus closes the feedback loop. The resonances of this feedback dynamics, which are identified as intrinsic eigenmodes of the flame, have important consequences for the dynamics and stability of the combustion process in general and the flame in particular. It is found that the amplification of acoustic power by flame-acoustic interactions can reach very high levels at frequencies close to the intrinsic eigenvalues of the flame-internal feedback mechanism. This is shown rigorously by evaluating the "instability potentiality'' from a balance of acoustic energy fluxes across the flame. Factors of maximum (as well as minimum) power amplification are obtained. Based on the acoustic energy amplification, the small gain theorem is introduced as a stability criterion for the combustion system. It allows to formulate an optimization criterion for the acoustic characteristics of burners and flames without regard of the boundary conditions emerging from the coupling with the combustor and plenum.