Session: 12-03-03: Data-Enabled Predictive Modeling, Scientific Machine Learning, and Uncertainty Quantification in Computational Mechanics

Paper Number: 116339

116339 - Solving Flows Across Rotor and Stator Cascades With Local Neural Operator for Computational Fluid Dynamics 

Simulation of complex flow is crucial for the design and optimization of turbomachinery. Recently, new efficient solutions for this problem are provided to replace conventional numerical simulations with the support of deep learning. The primary concern of building a deep learning-based CFD method is to decide the learning problem definition. One approach is to learn the solution of Navier-Stokes equations as functions, represented by physics-informed neural networks (PINNs). Another approach is to learn the solution as operators, i.e., neural operators. It separates the training and the predicting stages of the neural networks, which brings great efficiency when using the pre-trained neural operators to predict the desired solutions offline. Representative frameworks include Fourier neural operator (FNO) and deep operator network (DeepONet). However, before the possible proliferation of the applications, there are still challenges to dealing with the flexibility suiting various computational domains and boundaries. Because some or all problem-specific conditions (e.g., the computational domain, the boundary condition, and the initial condition) are designated in the learning problem definition, one trained neural network can hardly be used in another problem, which limits the scope of application.

 

In this work, we adopt a newly proposed neural operator named local neural operator (LNO), which is built upon a basic observation of nature that, in the domain far from the boundary, the motion of fluids is only related to the fluids in the adjacent areas in a finite time interval. Moreover, this intrinsic law holds regardless of the absolute position or specific state of motion. Hence, it enables LNO to learn the law as a local mapping between the physical fields at two time levels without limitation on any problem-specific conditions, which greatly enhances the reusability of one trained neural network. Concretely, LNO predicts the density, velocity, and temperature of fluid at a moment using the physical fields of the previous moment. The main body of LNO is formed by a physical path with convolutional layers and a spectral path with point-wise linear operations in the spectral space. LNO is trained on a dataset containing periodic flows, which is equivalent to freestream flows in infinite space without being affected by any boundary.

 

This work aims to investigate the ability of LNO to apply in complex and practical tasks, solving the transient flow caused by rotor-stator interaction. This case is challenging because of the moving boundaries and the unsteady pattern of flow. First, we train LNO to learn the compressible dynamic of fluid modeled with the continuity equation, the N-S equation, and the energy equation. Then, the trained LNO is applied as a CFD tool for investigating the rotor-stator interaction phenomena here. To implement the boundary conditions for the trained LNO, constant padding (for far-field boundary) and circular padding (for periodic boundary) are used for the external boundaries, while the solid wall boundary of cascades is treated by immersed boundary method. According to the results, LNO correctly and efficiently captures the fluctuations of velocity fields due to the interaction between the rotor and stator. We further conduct a brief investigation on several cases with different arrangements of cascades. These practices show great flexibility of LNO in tasks with complex geometries, diverse boundaries, and delicate flow patterns, indicating great potential for applications in various scientific research and engineering.

Presenting Author: Ximeng Ye Xi'an Jiaotong University

Presenting Author Biography: Ximeng Ye received the B.S. degree in energy and power engineering from Xi’an Jiaotong University, Xi’an, China, in 2018, where she is currently working toward the Ph.D. degree at School of Energy and Power Enginnering. Her current research interests include the high-order numerical method for computational fluid dynamics and deep learning-based CAE surrogate.

Authors:

Ximeng Ye Xi'an Jiaotong University
Hongyu Li Xi'an Jiaotong University
Guoliang Qin Xi'an Jiaotong University