In this work, we develop a 2D numerical model of a Y-shaped bifurcating combustor with a Helmholtz resonator attached. Propane (${\mathrm{C}}_3{\mathrm{H}}_8$) is fueled and burnt with air by applying single-step eddy dissipation combustion model and $k-ϵ-$RNG turbulence model for simplicity. To validate the numerical findings, experimental measurements are conducted on a bifurcating Y-shaped thermoacoustic combustor with an off-design Helmholtz resonator implemented. It is found that the frequency and amplitude of the dominant mode as experimentally measured agree well with the numerical results. Further agreement is obtained between numerically and theoretically predicted mode-shapes. With the model validated, it is applied to gain insights on the entropy generation and nonlinearity of the pulsating oscillations and the flow fluctuations across the resonator neck. It is found that the nonlinearities are originated in the unsteady heat release rate of the premixed propane flame, and the mass flow rate across the resonator neck. In addition, the rate of the entropy production depends strongly on the temperature fluctuations. Approximately 99% of the entropy production rate involves with the temperature oscillations. Furthermore, it is non-uniformly distributed along the combustor. In addition, the energy conversion rate between total heat release rate and the acoustical energy production rate is less than 0.0001%. Finally, the production of ${\mathrm{CO}}_2$ is increased exponentially, and then reduced gradually in the axial flow direction. In general, the present work provides a low-cost numerical tool of a bifurcating thermoaocustic system. It could be applied to predict the acoustic signature of the combustor and to examine and evaluate the performance of the Helmholtz resonator on attenuating self-sustained thermoacoustic oscillations.

在这项工作中，我们开发了一个附有亥姆霍兹共振器的 Y 形分叉燃烧室的二维数值模型。丙烷 (${\mathrm{C}}_{\mathrm{3个}}{\mathrm{H}}_{\mathrm{8个}}$）通过应用单步涡耗散燃烧模型以空气为燃料并燃烧，并且$k-\epsilon -$为简单起见，RNG 湍流模型。为了验证数值研究结果，对带有非设计亥姆霍兹共振器的分叉 Y 形热声燃烧器进行了实验测量。发现实验测量的主模的频率和振幅与数值结果吻合得很好。在数值和理论预测的振型之间获得了进一步的一致性。通过验证模型，它可用于深入了解脉动振荡的熵产生和非线性以及谐振器颈部的流动波动。发现非线性源于预混丙烷火焰的不稳定放热率和谐振器颈部的质量流量。此外，熵产生的速率在很大程度上取决于温度波动。大约 99% 的熵产生率与温度振荡有关。此外，它沿着燃烧器不均匀地分布。此外，总热释放率与声能产生率之间的能量转换率小于0.0001%。最后，制作${\mathrm{一氧化碳}}_{\mathrm{2个}}$呈指数增加，然后沿轴向流动方向逐渐减小。总的来说，目前的工作提供了一种低成本的分叉热声系统数值工具。它可用于预测燃烧器的声学特征，并检查和评估亥姆霍兹共振器在衰减自持热声振荡方面的性能。