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.

In this paper, the performance and emission characteristics of a diesel engine were investigated with varying ratios of tung oil-based biodiesel blends (B10, B20, and B50) and neat diesel under different operating conditions. The experimental results showed that the addition of biodiesel blends had different effects on engine power and torque depending on the blend ratio. B10 displayed a slight increase in power and torque, which increased by 1.9% and 6.6%. At the same time, B20 and B50 showed declines slightly. The fuel consumption rate increased slightly with an increasing percentage of biodiesel added. In general, all the blends exhibited significantly lower emissions of CO, NO_X, HC, and smoke compared to neat diesel. B10 displayed the most notable reduction of CO emissions, with a 42.86% decrease at medium to high loads. NO_X emissions of tung oil-based biodiesel blends were reduced at all load conditions except for B50. In addition, HC emissions were all reduced, especially for B20, which led to a 27.54% reduction at 50% load. Among all the tested blends, B50 showed the greatest decrease in smoke emissions of 38.05% compared to neat diesel at 2000 rpm. The research concluded that using biodiesel fuels from renewable resources, such as tung oil, presents a promising environmentally friendly alternative fuel option.