Self-sustained thermoacoustic oscillations as observed in low-emission combustion- involved gas turbines and aero-engines involve complicated thermal fluid–acoustics interaction and rich nonlinear dynamics. Such pulsating oscillations are known as thermoacoustic instability. When it occurs, large-amplitude limit cycle oscillations (LCOs) of thermodynamic parameters are frequently observed. These LCOs could cause overheating, flame flashback, and even engine failures. Thus it is critical to understand and predict the generation mechanisms and nonlinear dynamics behaviours, and then develop corresponding control approaches to prevent or control the onset of such instabilities. In this work, we develop and extend the classical van der Pol oscillators by integrating a physics-informed neural networks (PINNs) algorithm with a modelled nonlinear Rijke-type thermoacoustic combustor. The theoretical Rijke tube system (with Galerkin expansion and modified King's law implemented) and a CFD simulation model are applied to provide ‘training/calibration data’ for the extended van der Pol (EVDP)-PINNs model. The optimized EVDP oscillators are confirmed to be capable of capturing the key nonlinear characteristics by comparing the transient growth behaviours of thermodynamic perturbations and LCO amplitude and frequency. Further investigations are conducted to obtain Hopf bifurcation and amplitude death (AD) characteristics. Comparison is then made to the coupled EVDP systems. Quite similar Hopf bifurcation features, but differences in regions of AD, are observed. In general, we demonstrate an applicable approach to intelligently ‘learn’ a nonlinear thermoacoustic system and to create reliable EVDP oscillator systems, which have great potential to contribute to the development and testing of control approaches, such as the coupling described in this work, which may replace costly experimental tests.

Consider the flow through a channel with grooved edges on one (or both) side(s). If heating is applied to the boundaries, thermal drift is the flow generated by the interaction of the groove and heating patterns. It is known that, if one side of a channel is smooth while the other is grooved, the application of heating forms a so-called ‘thermal drift engine’. Two thermal drift engines are activated if both surfaces are grooved, and these may reinforce or oppose each other. Carefully choosing these engines can lead to an intensification of the thermal drift. The interplay of two drift engines is explored using a horizontal slot with grooves that have a sinusoidal profile with a prescribed wavenumber $\alpha $. It is shown that the strength of the flow decreases proportional to $\alpha $ as $\alpha \to 0$ and proportional to ${\alpha ^{ - 1}}$ as $\alpha \to \infty $. We determine the value of $\alpha $ corresponding to the strongest flow and characterize how the conclusions should be modified if a uniform heating component is added to the heating pattern.

The measurement of lift on symmetrically shaped obstacles immersed in low Reynolds number flow is the quintessential way to signal odd viscosity. For flow past cylinders, such a lift force does not arise if incompressibility and no-slip boundary conditions are fulfilled, whereas for spheres, a lift force has been found in Stokes flow, which is valid for cases where the Reynolds numbers are negligible and convection can be ignored. When considering the role of convection at low but non-zero Reynolds numbers, two hurdles arise, the Whitehead paradox and the breaking of axial symmetry, which are overcome by the method of matched asymptotic expansions and the Lorentz reciprocal theorem, respectively. We also consider the case where axial symmetry is preserved because the translation of the sphere is aligned with the axis of chirality of odd viscosity. We find that while lift vanishes, the interplay between odd viscosity and convection gives rise to a stream-induced torque.