Obtaining bifurcation diagrams with a thermoacoustic network model

Linear techniques can predict whether the non-oscillating (steady) state of a thermoacoustic system is stable or unstable. With a sufficiently large impulse, however, a thermoacoustic system can reach a stable oscillating state even when the steady state is also stable. A nonlinear analysis is required to predict the existence of this oscillating state. Continuation methods are often used for this but they are computationally expensive. In this paper, an acoustic network code called LOTAN is used to obtain the steady and the oscillating solutions for a horizontal Rijke tube. The heat release is modelled as a nonlinear function of the mass flow rate. Several test cases from the literature are analysed in order to investigate the effect of various nonlinear terms in the flame model. The results agree well with the literature, showing that LOTAN can be used to map the steady and oscillating solutions as a function of the control parameters. Furthermore, the nature of the bifurcation between steady and oscillating states can be predicted directly from the nonlinear terms inside the flame model. Copyright © 2012 by ASME.

Experimental investigation into parameters governing corner interactions for transonic shock wave/ boundary layer interactions

Experiments were conducted investigating the interaction between a normal shock wave and a corner boundary layer in a constant area rectangular duct. Active corner suction and passive blowing were applied to manipulate the natural corner flows developing in the working section of the Cambridge University supersonic wind tunnel. In addition robust vane micro-vortex generators were applied to the corners of the working section. Experiments were conducted at Mach numbers of M∞=1.4 and 1.5. Flow visualisation was carried out through schlieren and surface oil flow, while static pressures were recorded via floor tappings. The results indicate that an interplay occurs between the corner flow and the centre line flow. It is believed that corner flow separation acts to induce a shock bifurcation, which in turn leads to a smearing of the adverse pressure gradient elsewhere. In addition the blockage effect from the corners was seen to result in a reacceleration of the subsonic post-shock flow. As a result manipulation of the corner regions allows a separated or attached centre line flow to be observed at the same Mach number. Copyright © 2010 by Babinsky, Burton, Bruce.

Triggering in a thermoacoustic system with stochastic noise

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.

Effects of constraint curvature on structural instability: tensile buckling and multiple bifurcations

Bifurcation of an elastic structure crucially depends on the curvature of the constraints against which the ends of the structure are prescribed to move, an effect which deserves more attention than it has received so far. In fact, we show theoretically and we provide definitive experimental verification that an appropriate curvature of the constraint over which the end of a structure has to slide strongly affects buckling loads and can induce: (i.) tensile buckling; (ii.) decreasing- (softening), increasing- (hardening), or constant-load (null stiffness) postcritical behaviour; (iii.) multiple bifurcations, determining for instance two bifurcation loads (one tensile and one compressive) in a single-degree-of-freedom elastic system. We show how to design a constraint profile to obtain a desired postcritical behaviour and we provide the solution for the elastica constrained to slide along a circle on one end, representing the first example of an inflexional elastica developed from a buckling in tension. These results have important practical implications in the design of compliant mechanisms and may find applications in devices operating in quasi-static or dynamic conditions.

Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor

Instability triggering and transient growth of thermoacoustic oscillations were experimentally investigated in combination with linear/nonlinear flame transfer function (FTF) methodology in a model lean-premixed gas turbine combustor operated with CH 4 and air at atmospheric pressure. A fully premixed flame with 10kW thermal power and an equivalence ratio of 0.60 was chosen for detailed characterization of the nonlinear transient behaviors. Flame transfer functions were experimentally determined by simultaneous measurements of inlet velocity fluctuations and heat release rate oscillations using a constant temperature anemometer and OH */CH * chemiluminescence emissions, respectively. The phase-resolved variation of the local flame structure at a limit cycle was measured by planar laser-induced fluorescence of OH. Simultaneous measurements of inlet velocity, OH */CH * emission, and acoustic pressure were performed to investigate the temporal evolution of the system from a stable to a limit cycle operation. This measurement allows us to describe an unsteady instability triggering event in terms of several distinct stages: (i) initiation of a small perturbation, (ii) exponential amplification, (iii) saturation, (iv) nonlinear evolution of the perturbations towards a new unstable periodic state, (v) quasi-steady low-amplitude periodic oscillation, and (vi) fully-developed high-amplitude limit cycle oscillation. Phase-plane portraits of instantaneous inlet velocity and heat release rate clearly show the presence of two different attractors. Depending on its initial position in phase space at infinitesimally small amplitude, the system evolves towards either a high-amplitude oscillatory state or a low-amplitude oscillatory state. This transient phenomenon was analyzed using frequency- and amplitude-dependent damping mechanisms, and compared to subcritical and supercritical bifurcation theories. The results presented in this paper experimentally demonstrate the hypothesis proposed by Preetham et al. based on analytical and computational solutions of the nonlinear G-equation [J. Propul. Power 24 (2008) 1390-1402]. Good quantitative agreement was obtained between measurements and predictions in terms of the conditions for the onset of triggering and the amplitude of triggered combustion instabilities. © 2011 The Combustion Institute.

Progress towards the design and numerical analysis of a 3D microchannel biochip separator

This paper reports the design and numerical analysis of a three-dimensional biochip plasma blood separator using computational fluid dynamics techniques. Based on the initial configuration of a two-dimensional (2D) separator, five three-dimensional (3D) microchannel biochip designs are categorically developed through axial and plenary symmetrical expansions. These include the geometric variations of three types of the branch side channels (circular, rectangular, disc) and two types of the main channel (solid and concentric). Ignoring the initial transient behaviour and assuming that steady-state flow has been established, the behaviour of the blood fluid in the devices is algebraically analysed and numerically modelled. The roles of the relevant microchannel mechanisms, i.e. bifurcation, constriction and bending channel, on promoting the separation process are analysed based on modelling results. The differences among the different 3D implementations are compared and discussed. The advantages of 3D over 2D separator in increasing separation volume and effectively depleting cell-free layer fluid from the whole cross section circumference are addressed and illustrated. © 2011 John Wiley & Sons, Ltd.