This work aims to improve fuel chamber injectors' performance in turbofan engines, thus implying improved performance and reduction of pollutants. This requires the development of models that allow real-time prediction and improvement of the fuel/air mixture. However, the work carried out to date involves using experimental data (complicated to measure) or the numerical resolution of the complete problem (computationally prohibitive). The latter involves the resolution of a system of partial differential equations (PDE). These problems make difficult to develop a real-time prediction tool. Therefore, in this work, we propose using machine learning in conjunction with (complementarily cheaper) single-phase flow numerical simulations in the presence of tangential discontinuities to estimate the mixing process in two-phase flows. In this meaning we study the application of two proposed neural network (NN) models as PDE surrogate models. Where the future dynamics is predicted by the NN, given some preliminary information. We show the low computational cost required by these models, both in their training and inference phases. We also show how NN training can be improved by reducing data complexity through a modal decomposition technique called higher order dynamic mode decomposition (HODMD), which identifies the main structures inside flow dynamics and reconstructs the original flow using only these main structures. This reconstruction has the same number of samples and spatial dimension as the original flow, but with a less complex dynamics and preserving its main features. The core idea of this work is to test the limits of applicability of deep learning models to data forecasting in complex fluid dynamics problems. Generalization capabilities of the models are demonstrated by using the same NN architectures to forecast the future dynamics of four different two-phase flows.

翻译：本研究旨在提升涡轮风扇发动机中燃料室喷射器的性能，从而改善性能并减少污染物排放。这需要开发能够实时预测并优化燃料/空气混合的模型。然而，目前的研究要么依赖（难以测量的）实验数据，要么需要对完整问题进行数值求解（计算成本过高），后者涉及求解偏微分方程组。这些问题使得开发实时预测工具变得困难。因此，本研究提出将机器学习与（互补性且计算成本更低的）含切向间断的单相流数值模拟相结合，以估算两相流中的混合过程。为此，我们研究了两种所提出的神经网络模型作为偏微分方程替代模型的应用。给定初步信息后，神经网络能预测未来动力学行为。我们展示了这些模型在训练和推理阶段所需的低计算成本。同时，我们还展示了如何通过一种称为高阶动态模态分解的模态分解技术降低数据复杂性来改进神经网络训练——该技术可识别流动力学中的主要结构，并仅利用这些主要结构重构原始流场。重构后的流场与原始流场具有相同的样本数量和空间维度，但动力学复杂度更低且保留其主要特征。本研究的核心思想是探索深度学习模型在复杂流体动力学问题数据预测中的适用性极限。通过使用相同的神经网络架构预测四种不同两相流的未来动力学行为，验证了模型的泛化能力。