張量基底類神經網路應用於通過後向階流場之紊流模型

Abstract

本研究旨在開發一基於機器學習的紊流模型，延續前人的研究採用張量基底神經網路，透過擴展張量基底神經網路的輸入特徵，以提高模型在紊流建模中的準確性。過去的張量基底神經網路使用了5個張量不變性作為輸入特徵，這5個輸入特徵皆與平均流場有關。然而，我們認為單純依靠這些與平均流場相關的特徵無法充分準確地預測整個流場，因此我們引入一新的概念，考慮流場中的幾何效應，而流線函數和速度位勢是與流場的幾何特徵相關的量，它們能夠描述流場的全域特徵。因此，我們在原有的張量不變性輸入層中添加了流線函數和速度位勢作為額外的輸入特徵。本研究選擇後向階流場作為應用案例，並使用ANSYS FLUENT求解器生成了不同雷諾數 (Re_h=424, 441, 458) 的流場案例，我們將Re_h=424和458 這兩組流場資訊用於張量基底神經網路的訓練，以預測Re_h=441的案例。在先驗測試(priori test)中本研究所預測的雷諾應力藉由平均預測的結果消除了過度擬合的問題，然而雖無法與大尺度渦流模擬模型(LES)模擬的結果完全相同，但其大致變化的趨勢都能有效地捕捉到，而在後驗測試(posteriori test)中，本文藉由神經網路所預測的雷諾應力透過雷諾平均納維爾-斯托克斯模型(RANS)求解器計算而得到的平均流場與大尺度渦流模擬模型(LES)模擬的結果非常接近，像是通過階梯後的回流區或是自由流等流場特徵，藉由加入流線函數和速度位勢作為額外的輸入，本文成功地提高張量基底神經網路在紊流建模中的準確性。

The aim of this study is to develop a machine learning-based turbulence modeling, building upon previous research using tensor-basis neural network (TBNN), to enhance the accuracy of the model in turbulence modeling by extending the input features of TBNN. Previous research has utilized TBNN with five tensor invariants as input features, all related to the mean flow field. However, relying solely on these mean flow-related features may insufficient for accurately predict the entire flow field. Therefore, we introduce a new concept by considering the geometric effects in the flow field. Stream function and velocity potential are quantities associated with the geometric features of the flow field, which can describe global characteristics of the flow. To enhance the accuracy of TBNN in turbulent flow modeling, we incorporate the stream function and velocity potential as additional input features in the tensor invariant input layer. In this study, we focus on turbulent flows over the backward-facing step as the application case, and flow field cases with different Reynolds number (Re_h=424, 441, 458) are generated using the ANSYS FLUENT solver. We employ the flow information from Re_h=424 and 458 to train the TBNN model for predicting the case at Re_h=441. In the priori test, the predicted Reynolds stresses effectively eliminate the problem of overfitting by averaging the predicted results. While the predicted Reynolds stresses cannot exactly match the results of LES simulations, they capture the overall trends reasonably well. In the posteriori test, the average flow field obtained from the Reynolds stress predicted by the neural network through RANS solver is very close to the results of LES simulation. The flow features, such as recirculation region or free stream region, are accurately captured. By incorporating streamline function and velocity potential as additional inputs, this study successfully improves the accuracy of TBNN in turbulence modeling.