When they occur, azimuthal thermoacoustic oscillations can detrimentally affect the safe operation of gas turbines and aeroengines. We develop a real-time digital twin of azimuthal thermoacoustics of a hydrogen-based annular combustor. The digital twin seamlessly combines two sources of information about the system (i) a physics-based low-order model; and (ii) raw and sparse experimental data from microphones, which contain both aleatoric noise and turbulent fluctuations. First, we derive a low-order thermoacoustic model for azimuthal instabilities, which is deterministic. Second, we propose a real-time data assimilation framework to infer the acoustic pressure, the physical parameters, and the model and measurement biases simultaneously. This is the bias-regularized ensemble Kalman filter (r-EnKF), for which we find an analytical solution that solves the optimization problem. Third, we propose a reservoir computer, which infers both the model bias and measurement bias to close the assimilation equations. Fourth, we propose a real-time digital twin of the azimuthal thermoacoustic dynamics of a laboratory hydrogen-based annular combustor for a variety of equivalence ratios. We find that the real-time digital twin (i) autonomously predicts azimuthal dynamics, in contrast to bias-unregularized methods; (ii) uncovers the physical acoustic pressure from the raw data, i.e., it acts as a physics-based filter; (iii) is a time-varying parameter system, which generalizes existing models that have constant parameters, and capture only slow-varying variables. The digital twin generalizes to all equivalence ratios, which bridges the gap of existing models. This work opens new opportunities for real-time digital twinning of multi-physics problems.

翻译：当方位热声振荡发生时，会严重影响燃气轮机和航空发动机的安全运行。我们开发了基于氢的环形燃烧室方位热声系统的实时数字孪生。该数字孪生无缝融合了关于系统的两类信息：（i）基于物理的低阶模型；（ii）来自麦克风的原始稀疏实验数据，其中包含随机噪声和湍流脉动。首先，我们推导了方位不稳定性的确定性低阶热声模型。其次，我们提出了一种实时数据同化框架，用于同时推断声压、物理参数以及模型和测量偏差，即带偏差正则化的集合卡尔曼滤波（r-EnKF），并找到了该优化问题的解析解。第三，我们提出了一种储层计算器，用于推断模型偏差和测量偏差以闭合同化方程。第四，我们构建了实验室氢基环形燃烧室在不同当量比下的方位热声动力学实时数字孪生。研究发现，该实时数字孪生（i）能够自主预测方位动力学行为，这与无偏差正则化的方法形成对比；（ii）从原始数据中提取物理声压，即充当基于物理的滤波器；（iii）是一个时变参数系统，突破了仅包含常数参数且仅捕捉缓变变量的现有模型。该数字孪生可推广至所有当量比，弥补了现有模型的空白。本工作为多物理场问题的实时数字孪生开辟了新途径。