Bayesian inference of thermodynamic models from vapor flow experiments

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.