Abstract The present work concerns the inference of the coefficients of fluid-dependent thermodynamic models, applicable to complex molecular compounds with non-ideal effects. The main objective is to numerically assess the potential of using experimental measurements of some expansion flows to infer the model parameters. The Bayesian formulation incorporates uncertainties in the flow conditions and measurement errors and compares the measurements with the predictions of Computational Fluid Dynamics (CFD) simulations which depend on the parameter values. The resulting parameters posterior distribution is sampled using a Markov-Chain Monte-Carlo method. Polynomial-Chaos (PC) surrogates substitute the CFD predictions in the definition of the Bayesian posterior, in order to alleviate the computational burden of solving multiple CFD problems. We rely on synthetic data i.e., generated numerically, to assess the potential of expansion flow experiments. Using synthetic data prevents experimental bias, enables the control of model errors (thermodynamic and flow models) and permits the measurement of quantities in conditions that would be hardly achievable in practice. We test three expansion flows with increasing non-ideal effects. Our analyses reveal that the considered experiments have limited potential for the inference of the thermodynamic coefficients. Measuring the temperature, in addition to pressure, improves the posterior knowledge of the specific heat ratio, but other parameters remain highly uncertain. Also, the selection of an expansion condition yielding higher non-ideal effects somehow improves the inference, but the trend is limited, and experimenting with these conditions may be challenging. Our work also supports the use of Bayesian analysis with synthetic data to investigate, analyze, and design new experiments in the future.

中文翻译：

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来自蒸汽流实验的热力学模型的贝叶斯推断

摘要 目前的工作涉及流体相关热力学模型系数的推断，适用于具有非理想效应的复杂分子化合物。主要目标是数值评估使用一些膨胀流的实验测量来推断模型参数的潜力。贝叶斯公式包含流动条件和测量误差中的不确定性，并将测量结果与依赖于参数值的计算流体动力学 (CFD) 模拟的预测进行比较。使用马尔可夫链蒙特卡罗方法对所得参数后验分布进行采样。多项式混沌 (PC) 代理替代了贝叶斯后验定义中的 CFD 预测，以减轻解决多个 CFD 问题的计算负担。我们依靠合成数据，即数字生成，来评估膨胀流实验的潜力。使用合成数据可以防止实验偏差，可以控制模型误差（热力学和流动模型），并允许在实践中几乎无法实现的条件下测量数量。我们测试了三个具有增加的非理想效果的扩展流。我们的分析表明，所考虑的实验推断热力学系数的潜力有限。除了压力外，测量温度可以提高比热比的后验知识，但其他参数仍然高度不确定。此外，选择产生更高非理想效果的扩展条件在某种程度上改善了推理，但趋势有限，在这些条件下进行试验可能具有挑战性。我们的工作还支持使用贝叶斯分析和合成数据来调查、分析和设计未来的新实验。