Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session G20: Acoustics III: Thermoacoustics |
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Chair: Thierry Poinsot, CERFACS Room: 2008 |
Monday, November 24, 2014 8:00AM - 8:13AM |
G20.00001: High-fidelity simulations of a standing-wave thermoacoustic-piezoelectric engine Jeffrey Lin, Carlo Scalo, Lambertus Hesselink We have carried out time-domain three-dimensional and one-dimensional numerical simulations of a thermoacoustic Stirling heat engine (TASHE). The TASHE model adopted for our study is that of a standing-wave engine: a thermal gradient is imposed in a resonator tube and is capped with a piezoelectric diaphragm in a Helmholtz resonator cavity for acoustic energy extraction. The 0.51m engine sustains 500Pa pressure oscillations with atmospheric air and pressure. Such an engine is interesting in practice as an external heat engine with no mechanically-moving parts. Our numerical setup allows for both the evaluation of the nonlinear effects of scaling and the effect of a fully electromechanically-coupled impedance boundary condition, representative of a piezoelectric element. The thermoacoustic stack is fully resolved. Previous modeling efforts have focused on steady-state solvers with impedances or nonlinear effects without energy extraction. Optimization of scaling and the impedance for power output can now be simultaneously applied; engines of smaller sizes and higher frequencies suitable for piezoelectric energy extraction can be studied with three-dimensional solvers without restriction. Results at a low-amplitude regime were validated against results obtained from the steady-state solver DeltaEC and from experimental results in literature. Pressure and velocity amplitudes within the cavities match within 2{\%} difference. [Preview Abstract] |
Monday, November 24, 2014 8:13AM - 8:26AM |
G20.00002: A nonlinear framework for the prediction of thermoacoustic oscillations Alessandro Orchini, Matthew Juniper Thermoacoustic oscillations may occur in afterburners and gas turbines because of the interaction of unsteady heat release and acoustic waves. These oscillations lead to structural damage and deteriorate system efficiency. We present a low-order thermoacoustic model for premixed flames that exploits the fact that the main nonlinearity of this instability is due to the unsteady heat release. We describe the flame dynamics using the $G$-equation model, and some of the features of a Low Order ThermoAcoustic Network (LOTAN) to describe, in an efficient way, the system's acoustics. The advantage of the latter approach, with respect to the more diffused Galerkin decomposition of the acoustic equations, is that mean flow effects, temperature variations, and cross sectional area changes of the combustion chamber can be easily included. With the resulting nonlinear network, we can analyze the stability of thermoacoustic systems both in the frequency and time domain, and determine the frequency, amplitude and stability of limit cycle oscillations. In the time domain, we can also predict the location of Neimark-Sacker bifurcations, which lead to quasi-periodic oscillations and more elaborate dynamical behavior. Numerical continuation is proved to be an efficient tool to achieve this goal. [Preview Abstract] |
Monday, November 24, 2014 8:26AM - 8:39AM |
G20.00003: An Acoustically Consistent Investigation of Combustion Instabilities in a Dump Combustor Vijaya Krishna Rani, Sarma Rani An acoustically consistent, linear modal analysis-based analytical method is presented to predict the longitudinal and transverse combustion instabilities in a 2-D cartesian dump combustor. At first, rigorous acoustical analysis is performed. Novel, acoustically consistent jump or matching conditions are developed and applied at the duct cross-sectional interface(s), with distinct forms for the purely axial and non-axial modes. The effects of uniform and non-uniform mean flow, cross-sectional area ratio, as well as of different types of boundary conditions on the duct acoustic modes are investigated. Subsequent to the acoustic analysis, combustion instabilities of a 2-D, cartesian dump combustor are investigated. The instability analysis employs the developed acoustically consistent jump conditions, instead of the conventional mass, momentum, and energy balance-based conditions. Effects of the fluctuating heat-release source term in the acoustic wave equation are incorporated directly into the longitudinal wavenumber, obviating the need for a separate energy matching condition across the flame. A detailed investigation of the parametric space and boundary conditions affecting combustion instabilities is undertaken. [Preview Abstract] |
Monday, November 24, 2014 8:39AM - 8:52AM |
G20.00004: Numerical Study of Energy Conversion of the Taconis Oscillations in an Axisymmetric Closed Tube Katsuya Ishii, Shizuko Adachi, Hiroyuki Hayashi This paper studies spontaneous thermoacoustic oscillations of a helium gas in a closed cylindrical tube by solving the axisymmetric compressible Navier-Stokes equations. The wall temperature of the hot part near both ends (300K) and that of the cold central part (20K) are fixed. Numerical simulations are done for various values of the length ratio of the hot part to the cold part between 0.2 and 5.0. It is found that there are three groups of oscillation states, which are the fundamental mode and the second mode of a standing wave, and the oscillation with a shock wave. The states in each group have distinguished features of the vortical flow field and the temperature distribution. The evolution of the Lagrangian time derivative of entropy is analyzed to understand the energy conversion mechanism which maintains the nonlinear thermoacoustic oscillations. [Preview Abstract] |
Monday, November 24, 2014 8:52AM - 9:05AM |
G20.00005: Nonlinear saturation of thermoacoustic oscillations in annular combustion chambers Giulio Ghirardo, Matthew Juniper Continuous combustion systems such as aeroplane engines can experience self-sustained pressure oscillations, called thermoacoustic oscillations. Quite often the combustion chamber is rotationally symmetric and confined between inner and outer walls, with a fixed number of burners equispaced along the annulus, at the chamber inlet. We focus on thermoacoustic oscillations in the azimuthal direction, and discuss the nonlinear saturation of the system towards 2 types of solutions: standing waves (with velocity and pressure nodes fixed in time and in space) and spinning waves (rotating waves, in clockwise or anti-clockwise direction). We neglect the effect of the transverse velocity oscillating in the azimuthal direction in the combustion chamber, and focus the model on the nonlinear effect that the longitudinal velocity, just upstream of each burner, has on the fluctuating heat-release response in the chamber. We present a low-order analytical framework to discuss the stability of the 2 types of solutions. We discuss how the stability and amplitudes of the 2 solutions depend on: 1) the acoustic damping in the system; 2) the number of injectors equispaced in the annulus; 3) the nonlinear response of the flames. [Preview Abstract] |
Monday, November 24, 2014 9:05AM - 9:18AM |
G20.00006: Multiple space-scale global analysis for hydrodynamic/thermoacoustic instability in low Mach number combustion chambers Luca Magri, Outi Tammisola, Yee Chee See, Matthias Ihme, Matthew Juniper We propose a method to reduce the complexity of the reacting compressible Navier-Stokes equations for global/sensitivity analyses of thermo-acoustic systems. We use multiple space-scale analysis and consider a low Mach number. We assume that reacting hydrodynamic phenomena evolve at small space scales whereas acoustics evolve at larger space scales, a common situation in thermo-acoustics. The reacting hydrodynamics (RH) is governed by the reacting low Mach number equations, and the acoustics (AC) by the reacting Euler equations. The RH feeds into the AC via the heat release by the flame and the AC, in turn, feed back into the RH via the acoustic-pressure gradient (Klein's limit). These two coupling terms enable the thermo-acoustic system to be linearized around time-averaged LES flows and studied as an eigenproblem. We perform global, adjoint and sensitivity analyses, investigating the reciprocal influence of RH/AC interactions and suggest strategies for open-loop control. The analysis is applied to a dump combustor and a complex industrial combustor (Meier's). [Preview Abstract] |
Monday, November 24, 2014 9:18AM - 9:31AM |
G20.00007: Forced response of self-excited thermoacoustic oscillations: lock-in, bifurcations, chaos and open-loop control Karthik Kashinath, Matthew Juniper This study aims to identify synchronization phenomena in thermoacoustics and to explore the possibility of open-loop control of self-excited thermoacoustic oscillations using weak periodic perturbations. We examine the response of a self-excited system of a premixed flame in a duct to harmonic forcing. When the system oscillating periodically is forced, we find that: (i) at low forcing amplitudes, the system responds at the natural and forced frequencies and linear combinations of these; (ii) above a critical forcing amplitude, the system locks into the external forcing; (iii) the bifurcations leading up to lock-in and the critical forcing amplitude required depend on the proximity of the forcing frequency to the natural frequency. When the system oscillating quasi-periodically is forced, we find that (i) if the forcing frequency is the same as one of the two characteristic frequencies of the torus attractor, then lock-in occurs at a critical amplitude via a saddle-node bifurcation; (ii) if the forcing frequency is not equal to either of the two characteristic frequencies of the torus attractor, then the torus breaks down and more elaborate behavior is noticed. When the system oscillating chaotically is forced close to the most dominant frequency in its spectrum, we find that it is possible to establish a stable periodic oscillation. Finally, we find that in some cases low-amplitude forcing can achieve lock-in and the amplitude of oscillations in the system are decreased by up to 70{\%} of the unforced amplitude. [Preview Abstract] |
Monday, November 24, 2014 9:31AM - 9:44AM |
G20.00008: ABSTRACT WITHDRAWN |
Monday, November 24, 2014 9:44AM - 9:57AM |
G20.00009: Engine core noise analysis using an hybrid modeling approach Jeffrey O'Brien, Jeonglae Kim, Matthias Ihme As aircraft engines become progressively quieter through the reduction of jet noise, the acoustic contributions of components upstream of the jet, especially the combustor, must be reduced to produce still quieter engines. Combustion noise can be broken down into two components: direct and indirect noise. Direct noise refers to pressure fluctuations that are generated directly by turbulent combustion, while indirect noise describes acoustics that stem from the interaction between the entropy fluctuations generated inside a combustor and the downstream flow path. This study analyzes the effects of both types of core noise. An LES simulation of a model swirl combustor is performed in order to generate representative pressure and entropy fluctuations which are then fed into a moving-mesh RANS calculation of a high pressure turbine stage. The evolution of these fluctuations through the turbine stage is analyzed and the ''chopping'' effect of the turbine on the fluctuations is characterized. Additionally, the turbine output will be fed into a fully compressible jet noise calculation to assess how the entropy fluctuations are affected by the flow path and alter the acoustic behavior of the jet. [Preview Abstract] |
Monday, November 24, 2014 9:57AM - 10:10AM |
G20.00010: Adjoint sensitivity analysis of thermoacoustic instability in a nonlinear Helmholtz solver Matthew Juniper, Luca Magri Thermoacoustic instability is a persistent problem in aircraft and rocket engines. It occurs when heat release in the combustion chamber synchronizes with acoustic oscillations. It is always noisy and can sometimes result in catastrophic failure of the engine. Typically, the heat release from the flame is assumed to equal the acoustic velocity at a reference point multiplied by a spatially-varying function (the flame envelope) subject to a spatially-varying time delay. This models hydrodynamic perturbations convecting down the flame causing subsequent heat release perturbations. This creates an eigenvalue problem that is linear in the acoustic pressure but nonlinear in the complex frequency, omega. This can be solved as a sequence of linear eigenvalue problems in which the operators are updated with a new value of omega after each iteration. Adjoint methods find the sensitivity of each eigenmode to all the parameters simultaneously and are well suited to thermoacoustic problems because there are a few interesting eigenmodes but many influential parameters. The challenge here is to express the sensitivity of the eigenvalue at the final iteration to an arbitrary change in the parameters of the first iteration. This is a promising new technique for the control of thermoacoustics. [Preview Abstract] |
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