IDEA: Artificial neural network models for 11-species air properties at thermochemical equilibrium
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Accurate prediction of high-temperature air properties is essential in many aerodynamic applications under hypersonic flight conditions. Various curve-fit models using piecewise polynomial fittings have been commonly adopted to approximate equilibrium air properties at high temperatures. Several shortcomings including low accuracy, lack of diversity, and discontinuity at curve-fit boundary still remain, causing numerical troubles in computational procedures. To address the issues, IDEA, an open-source C++ library that enables fast and accurate computations of the equilibrium air properties and their first and second derivatives, is newly developed based on the artificial neural network (ANN). IDEA, which stands for the Infinitely Differentiable Equilibrium Air, predicts thermodynamic and transport properties of 11-species (N2, O2 , N, O, NO, NO+, N+, O+, N++, O++, and e-) thermochemical equilibrium air at the temperature range up to 25,000 K and density range from 10^-7 to 10^3 amagats. The training data is constructed from the kinetic molecular theory using the equilibrium constant method with the rigid-rotor, harmonic-oscillator model. As the name suggests, IDEA's models are infinitely differentiable in the application range; thus, they have enhanced convergence in computational fluid dynamics (CFD) when using gradient-based methods. Using a newly developed training process based on the Levenberg–Marquardt algorithm with weighted mean squared error loss, IDEA provides more accurate and diverse property models with much fewer parameters than previous piecewise polynomial fitting models. In addition, the proposed training method offers easy extensions to various property models with different species data. IDEA provides C interfaces that can be used for programs in various computer languages, such as C/C++, Fortran, Python, and MATLAB. IDEA's modeling routines are thread-safe, so they can be safely used for parallel programs without performance loss. The accuracy and enhanced convergence of IDEA is demonstrated via several high-speed flow computations
在高超声速飞行工况下的诸多气动应用中，精准预测高温空气物性至关重要。过往常采用各类基于分段多项式拟合的曲线模型，近似高温环境下的平衡态空气物性。这类模型仍存在精度不足、多样性匮乏以及拟合边界处不连续等缺陷，会在计算流程中引发数值问题。为解决上述问题，本研究基于人工神经网络（Artificial Neural Network, ANN）全新开发了IDEA——一款可快速精准计算平衡态空气物性及其一、二阶导数的开源C++库。IDEA全称为Infinitely Differentiable Equilibrium Air（无限可微平衡空气），可针对包含11种组分（N₂、O₂、N、O、NO、NO⁺、N⁺、O⁺、N⁺⁺、O⁺⁺以及e⁻）的热化学平衡空气，在最高25000 K的温度区间以及10^-7 至 10^3 amagats的密度范围内，预测其热力学与输运物性。其训练数据基于分子动理论，采用平衡常数法结合刚转子-简谐振荡器模型构建得到。正如其名称所示，IDEA的模型在应用区间内具备无限可微性，因此在基于梯度的方法用于计算流体动力学（Computational Fluid Dynamics, CFD）时，可提升收敛性能。通过采用基于莱文贝格-马夸特（Levenberg–Marquardt）算法与加权均方误差损失的全新训练流程，IDEA相较过往的分段多项式拟合模型，可在参数数量大幅更少的前提下，提供精度更高、多样性更强的物性模型。此外，所提出的训练方法可便捷扩展至各类基于不同组分数据的物性模型。IDEA提供C语言接口，可适配C/C++、Fortran、Python以及MATLAB等多种编程语言的程序调用。IDEA的建模子程序具备线程安全性，因此可安全用于并行程序且不会带来性能损耗。通过若干高速流动数值算例，验证了IDEA的精度优势与收敛性能提升效果。
