The fast and accurate reduced-order modeling of fluidized beds is a challenging task in the field of fluid dynamics, owing to their high dimensionality and nonlinear dynamic behavior. In this study, a nonintrusive reduced order modeling method, the reduced order model based on principal component analysis and bidirectional long short-term memory networks (PBLSTM ROM), was developed to capture complex spatio-temporal dynamics of fluidized beds. By combining principal component analysis and Bidirectional long- short-term memory networks, the PBLSTM ROM effectively extracted dynamic evolution information without any prior knowledge of governing equations, enabling reduced-order modeling of unsteady flow fields. The PBLSTM ROM was validated using the solid volume fraction and gas velocity flow fields of a fluidized bed with immersed tubes, showing superior performance over both the PLSTM and PANN ROMs in accurately capturing temporal changes in the fluidization fields, especially in the region near immersed tubes where severe fluctuations appear. Moreover, the PBLSTM ROM improved the simulation speed by five orders of magnitude compared to traditional computational fluid dynamics simulations. These findings suggest that the PBLSTM ROM presents a promising approach for analyzing the complex fluid flows in engineering practice.

由于流化床的高维性和非线性动态行为，快速、准确的流化床降阶建模是流体动力学领域的一项具有挑战性的任务。在本研究中，开发了一种非侵入式降阶建模方法，即基于主成分分析和双向长短期记忆网络（PBLSTM ROM）的降阶模型来捕获流化床的复杂时空动力学。通过结合主成分分析和双向长短期记忆网络，PBLSTM ROM有效地提取动态演化信息，无需任何控制方程的先验知识，从而实现非定常流场的降阶建模。使用带有浸入管的流化床的固体体积分数和气体速度流场对 PBLSTM ROM 进行了验证，在准确捕获流化场的时间变化方面，特别是在浸入管附近的区域，表现出优于 PLSTM 和 PANN ROM 的性能出现剧烈波动的地方。此外，与传统的计算流体动力学模拟相比，PBLSTM ROM将模拟速度提高了五个数量级。这些发现表明 PBLSTM ROM 为分析工程实践中的复杂流体流动提供了一种有前景的方法。