Session G4: Acoustics III: Thermoacoustics

Analytical Model for Axial-Azimuthal Thermoacoustic Modes in an Annular Combustor

Recent advances in theoretical models for azimuthal modes have highlighted their potential in accurately capturing the physics with minimal cost when compared to detailed simulations. Such models for annular combustors have considered multiple burners, effects of the plenum as well as effects of azimuthal mean flow to name a few. However, in all these models, only the azimuthal modes have been considered and as such cannot capture axial-azimuthal coupling of modes. In this paper, we consider an extension of these models by considering the axial extent of the annular combustor with a generic impedance boundary condition at the combustor exit. The inclusion of the axial mode is of practical relevance to combustors where axial-azimuthal modal coupling controls the Thermoacoustic instability of the system.   

Generation of indirect combustion noise by compositional inhomogeneities

The generation of indirect combustion noise in nozzles and turbine stages is commonly attributed to temperature inhomogeneities and vorticity fluctuations. Here, compositional inhomogeneities in a multi-component gas mixture are shown to produce indirect noise both theoretically and numerically. The chemical potential function is introduced as an additional acoustic source mechanism. The contribution of the compositional noise is compared to the entropy noise and direct noise by considering subsonic, supersonic and shocked nozzles downstream of the combustor exit. It is shown that the compositional noise is dependent on the local mixture composition and can exceed entropy noise for fuel-lean conditions and supersonic/shocked nozzle flows. This suggests that compositional indirect combustion noise may require consideration with the implementation of advanced combustion concepts in gas turbines, including low-emissions combustors, high-power-density engine cores, or compact burners.   

LES Investigation of Core Noise Mechanisms inside a Combustor-Nozzle System

The aim of the work is to expand knowledge of core noise physics through the study of a representative aviation-type combustor with converging-diverging nozzle attached to the exhaust. First, a fully compressible LES of the entire flowpath is performed and validated against experimental measurements. From this calculation, the time history of the flow is sampled in a plane near the nozzle entrance to construct a library of representative fluctuations that are potential precursors to the direct & indirect noise observed at the nozzle outlet. This data is then used as an inflow for a series of separate nozzle simulations in which fluctuations in pressure, temperature ("hot spots"), and mixture composition are imposed separately to isolate their effect on the emitted noise. This methodology allows quantitative investigation of core-noise physics that lower-order models do not, including: the effect of non-linearity of high-amplitude perturbations, superposition of forcing types, the impact of the spatial structure of the perturbations, and the restriction to low-frequency perturbations and calorically perfect gas assumption. The calculations also represent the first time variations in mixture composition have been shown to induce downstream noise in a high-fidelity, 3D simulation.   

Bulk viscosity effects on ultrasonic thermoacoustic instability

We have carried out unstructured fully-compressible Navier--Stokes simulations of a minimal-unit traveling-wave ultrasonic thermoacoustic device in looped configuration. The model comprises a thermoacoustic stack with 85\% porosity and a tapered area change to suppress the fundamental standing-wave mode. A bulk viscosity model, which accounts for vibrational and rotational molecular relaxation effects, is derived and implemented via direct modification of the viscous stress tensor, $\tau_{ij} \equiv 2 \mu \left[S_{ij} + \frac{\lambda}{2\mu} \frac{\partial u_k }{\partial x_k} \delta_{ij} \right]$, where the bulk viscosity is defined by $\mu_b \equiv \lambda + \frac{2}{3}\mu$. The effective bulk viscosity coefficient accurately captures acoustic absorption from low to high ultrasonic frequencies and matches experimental wave attenuation rates across five decades. Using pressure-based similitude, the model was downscaled from total length $L=2.58$ m to $0.0258$ m, corresponding to the frequency range $f=242$ -- $24200$ Hz, revealing the effects of bulk viscosity and direct modification of the thermodynamic pressure. Simulations are carried out to limit cycle and exhibit growth rates consistent with linear stability analyses, based on Rott's theory.   

Nonlinear modeling of thermoacoustically driven energy cascade

We present an investigation of nonlinear energy cascade in thermoacoustically driven high-amplitude oscillations, from the initial weakly nonlinear regime to the shock wave dominated limit cycle. We develop a first principle based quasi-1D model for nonlinear wave propagation in a canonical minimal unit thermoacoustic device inspired by the experimental setup of Biwa et al. (JASA, 2011). Retaining up to quadratic nonlinear terms in the governing equations, we develop model equations for nonlinear wave propagation in the proximity of differentially heated no-slip boundaries. Furthermore, we discard the effects of acoustic streaming in the present study and focus on nonlinear energy cascade due to high amplitude wave propagation. Our model correctly predicts the observed exponential growth of the thermoacoustically amplified second harmonic, as well as the energy transfer rate to higher harmonics causing wave steepening. Moreover, we note that nonlinear coupling of local pressure with heat transfer reduces thermoacoustic amplification gradually thus causing the system to reach limit cycle exhibiting shock waves. Throughout, we verify the results from the quasi-1D model with fully compressible Navier-Stokes simulations.   

Gas dynamics of heat-release-induced waves in supercritical fluids: revisiting the Piston Effect

We investigate a gasdynamic approach to the modeling of heat-release-induced compression waves in supercritical fluids. We rely on highly resolved one-dimensional fully compressible Navier-Stokes simulations of CO$_2$ at pseudo-boiling conditions in a closed duct inspired by the experiments of Miura \textit{et al.}, \textit{Phys. Rev. E}, vol. 74, 2006. Near-critical fluids exhibit anomalous variations of thermodynamic variables taken into account by adopting the Peng-Robinson equation of state and Chung's Method. An idealized heat source is applied, away from the boundaries, resulting in the generation of compression waves followed by contact discontinuities bounding a region of hot expanding fluid. For higher heat-release rates such compressions are coalescent with distinct shock-like features (i.e. non-isentropicity and propagation Mach numbers measurably greater than unity) and a non-uniform post-shock state, not present in ideal gas simulations, caused by the highly nonlinear equation of state. Thermoacoustic effects are limited to: (1) a one-way/one-time thermal-to-acoustic energy conversion, and (2) cumulative non-isentropic bulk heating due to the resonating compression waves, resulting in what is commonly referred to as the Piston Effect.   

The nature of combustion noise: Stochastic or chaotic?

Combustion noise, which refers to irregular low-amplitude pressure oscillations, is conventionally thought to be stochastic. It has therefore been modeled using a stochastic term in the analysis of thermoacoustic systems. Recently, however, there has been a renewed interest in the validity of that stochastic assumption, with tests based on nonlinear dynamical theory giving seemingly contradictory results: some show combustion noise to be stochastic while others show it to be chaotic. In this study, we show that this contradiction arises because those tests cannot distinguish between noise amplification and chaos. We further show that although there are many similarities between noise amplification and chaos, there are also some subtle differences. It is these subtle differences, not the results of those tests, that should be the focus of analyses aimed at determining the true nature of combustion noise. Recognizing this is an important step towards improved understanding and modeling of combustion noise for the study of thermoacoustic instabilities.   

Forced synchronization of thermoacoustic oscillations in a ducted flame

Forced synchronization is a process in which a self-excited system subjected to external forcing starts to oscillate at the forcing frequency $f_f$ in place of its own natural frequency $f_n$. There are two motivations for studying this in thermoacoustics: (i) to determine how external forcing could be used to control thermoacoustic oscillations, which are harmful to many combustors; and (ii) to better understand the nonlinear interactions between self-excited hydrodynamic and thermoacoustic oscillations. In this experimental study, we examine the response of a ducted premixed flame to harmonic acoustic forcing, for two natural states of the system: (1) a state with periodic oscillations at $f_1$ and a marginally stable mode at $f_2$; and (2) a state with quasiperiodic oscillations at two incommensurate frequencies $f_1$ and $f_2$. When forcing the periodic state, we find that the forcing amplitude required for lock-in increases linearly with $|f_f-f_1|$ and that the marginally stable mode becomes excited when $f_f\approx f_2$. When forcing the quasiperiodic state, we find that the system locks into the forcing when $f_f\approx f_1$ or $f_2$ or $1/2(f_1+f_2)$. These findings should lead to improved control of periodic and aperiodic thermoacoustic oscillations in combustors.   

Numerical Study of Energy Conversion in the Taconis Oscillations by Tracing Fluid Particles

Temporal evolution of physical properties of spontaneous thermoacoustic oscillations of a helium gas in a closed cylindrical tube is obtained by solving the axisymmetric compressible Navier-Stokes equations. The ratio of the wall temperature of the hot part near both ends to that of the cold central part is 15. We trace fluid particles which start from various points in a closed tube for a fundamental mode oscillation of a standing wave and a second mode oscillation. Work done by the fluid particles is numerically estimated. Fluid particles drift in the closed tube while oscillating. Work done by fluid particles moving in a hot region during one cycle is negative in both excitation modes. Displacement of fluid particles moving in the finite temperature gradient region is large. They do not give a cyclic transformation in a pressure-volume diagram. Work done by fluid particles moving near the tube axis from the cold part to the hot part is positive. Work done by fluid particles moving in a cold region during one cycle is positive but the amount of the work is smaller than that in the hot region.