Damping Of Acoustic Oscillations Research Articles

Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors

This paper analyzes transversal thermoacoustic oscillations in an experimental gas turbine combustor utilizing dynamical system theory. Limit-cycle acoustic motions related to the first linearly unstable transversal mode of a given 3D combustor configuration are modeled and reconstructed by means of a low-order dynamical system simulation. The source of nonlinearity is solely allocated to flame dynamics, saturating the growth of acoustic amplitudes, while the oscillation amplitudes are assumed to always remain within the linearity limit. First, a reduced order model (ROM) which reproduces the combustor's modal distribution and damping of acoustic oscillations is derived. The ROM is a low-order state-space system, which results from a projection of the linearized Euler equations (LEE) into their truncated eigenspace. Second, flame dynamics are modeled as a function of acoustic perturbations by means of a nonlinear transfer function. This function has a linear and a nonlinear contribution. The linear part is modeled analytically from first principles, while the nonlinear part is mathematically cast into a cubic saturation functional form. Additionally, the impact of stochastic forcing due to broadband combustion noise is included by additive white noise sources. Then, the acoustic and the flame system is interconnected, where thermoacoustic noncompactness due to the transversal modes' high frequency (HF) is accounted for by a distributed source term framework. The resulting nonlinear thermoacoustic system is solved in frequency and time domain. Linear growth rates predict linear stability, while envelope plots and probability density diagrams of the resulting pressure traces characterize the thermoacoustic performance of the combustor from a dynamical systems theory perspective. Comparisons against experimental data are conducted, which allow the rating of the flame modes in terms of their capability to reproduce the observed combustor dynamics. Ultimately, insight into the physics of high-frequency, transversal thermoacoustic systems is created.

Influence of Scaling Rules on the Loss of Acoustic Energy

The damping of acoustic oscillations in two different design concepts of rocket engine demonstrators is assessed. Both engines represent different scaling strategies for subscale demonstrators. In this context, one major question is which of the two designs are less prone to combustion instabilities. Different methods are presented to show the influence of geometry on the loss of acoustic energy. The decay coefficient is determined, which accounts for the overall loss of acoustic energy independent of the physical mechanism. The admittance at the intersection of the combustion chamber and nozzle is evaluated. The acoustic flux is calculated and divided into different kinds of contributions. In this regard, the importance of the relation between pure acoustic transport and convective transport is emphasized. It shows that the pure acoustic transport is directed into the combustion chamber.However, its fraction of acoustic energy is compensated by the convective transported acoustic energy,which is convected out of the thrust chamber. Thus, the overall acoustic energy in the system is decaying. The two designs show different damping characteristics for different modes. The photoscaled design is less stable for longitudinal modes but more stable for transverse modes. The first transverse mode in the Mach-scaled design is barely damped.