Thermoacoustic systems can oscillate self-excitedly, and often non-periodically, owing to coupling between unsteady heat release and acoustic waves. We study a slot-stabilized two-dimensional premixed flame in a duct via numerical simulations of a G-equation flame coupled with duct acoustics. We examine the bifurcations and routes to chaos for three control parameters: (i) the flame position in the duct, (ii) the length of the duct and (iii) the mean flow velocity. We observe period-1, period-2, quasi-periodic and chaotic oscillations. For certain parameter ranges, more than one stable state exists, so mode switching is possible. At intermediate times, the system is attracted to and repelled from unstable states, which are also identified. Two routes to chaos are established for this system: the period-doubling route and the Ruelle-Takens-Newhouse route. These are corroborated by analyses of the power spectra of the acoustic velocity. Instantaneous flame images reveal that the wrinkles on the flame surface and pinch-off of flame pockets are regular for periodic oscillations, while they are irregular and have multiple time and length scales for quasi-periodic and aperiodic oscillations. This study complements recent experiments by providing a reduced-order model of a system with approximately 5000 degrees of freedom that captures much of the elaborate nonlinear behaviour of ducted premixed flames observed in the laboratory.

This paper explores the mechanism of triggering in a simple thermoacoustic system, the Rijke tube. It is demonstrated that additive stochastic perturbations can cause triggering before the linear stability limit of a thermoacoustic system. When triggering from low noise amplitudes, the system is seen to evolve to self-sustained oscillations via an unstable periodic solution of the governing equations. Practical stability is introduced as a measure of the stability of a linearly stable state when finite perturbations are present. The concept of a stochastic stability map is used to demonstrate the change in practical stability limits for a system with a subcritical bifurcation, once stochastic terms are included. The practical stability limits are found to be strongly dependent on the strength of noise.

Many experimental studies have demonstrated that ducted premixed flames exhibit stable limit cycles in some regions of parameter space. Recent experiments have also shown that these (period-1) limit cycles subsequently bifurcate to period-2 n , quasiperiodic, multiperiodic or chaotic behaviour. These secondary bifurcations cannot be found computationally using most existing frequency domain methods, because these methods assume that the velocity and pressure signals are harmonic. In an earlier study we have shown that matrix-free continuation methods can efficiently calculate the limit cycles of large thermoacoustic systems. This paper demonstrates that these continuation methods can also efficiently calculate the bifurcations from the limit cycles. Furthermore, once these bifurcations are found, it is then possible to isolate the coupled flame-acoustic motion that causes the qualitative change in behaviour. This information is vital for techniques that use selective damping to move bifurcations to more favourable locations in the parameter space. The matrix-free methods are demonstrated on a model of a ducted axisymmetric premixed flame, using a kinematic G-equation solver. The methods find limit cycles and period-2 limit cycles, and fold, period-doubling and Neimark-Sacker bifurcations as a function of the location of the flame in the duct, and the aspect ratio of the steady flame.

No abstract

No abstract

No abstract

No abstract

This paper presents a low-cost method for testing the inflation behaviour of small (< 5m) parachutes at high-altitude and high subsonic Mach numbers. A small and light drop vehicle (11.7kg) was developed and used to test a 2.55m ringslot parachute at a velocity of 210.5m/s (Mach 0.71), an altitude of 22.2km (72, 800ft) and an atmospheric density of 0.056kg/m 3 . Sensors and cameras mass-produced for consumer electronics are used in a custom avionics package because they are small, low-cost, lightweight and low power. Acceleration, rotation rate and dynamic pressure data are recorded at 2kHz, and highspeed video at 300fps, during inflation and descent. The per-launch expendable costs (balloon, helium etc.) are of the order of several thousand pounds (GBP). This provides an extremely cost effective way of testing small parachutes for stability and performance at the design Mach number and appropriate mass ratio.