Nonlinear phenomena in thermoacoustic systems with premixed flames

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies, amplitudes and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, but can be used to calculate the amplitudes of limit cycles, as well as their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modelled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearised momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state, for single- mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitudedependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, as well as twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact resulting in a larger limit cycle amplitude. Multimode simulations show that in some situations the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Copyright © 2012 by ASME.

An approach to multi-fidelity optimization of aeroengine compression systems

The aerodynamic design of turbomachinery presents the design optimisation community with a number of exquisite challenges. Chief among these are the size of the design space and the extent of discontinuity therein. This discontinuity can serve to limit the full exploitation of high-fidelity computational fluid dynamics (CFD): such codes require detailed geometric information often available only sometime after the basic configuration of the machine has been set by other means. The premise of this paper is that it should be possible to produce higher performing designs in less time by exploiting multi-fidelity techniques to effectively harness CFD earlier in the design process, specifically by facilitating its participation in configuration selection. The adopted strategy of local multi-fidelity correction, generated on demand, combined with a global search algorithm via an adaptive trust region is first tested on a modest, smooth external aerodynamic problem. Speed-up of an order of magnitude is demonstrated, comparable to established techniques applied to smooth problems. A number of enhancements aimed principally at effectively evaluating a wide range of configurations quickly is then applied to the basic strategy, and the emerging technique is tested on a generic aeroengine core compression system. A similar order of magnitude speed-up is achieved on this relatively large and highly discontinuous problem. A five-fold increase in the number of configurations assessed with CFD is observed. As the technique places constraints neither on the underlying physical modelling of the constituent analysis codes nor on first-order agreement between those codes, it has potential applicability to a range of multidisciplinary design challenges. © 2012 by Jerome Jarrett and Tiziano Ghisu.