Bayesian quantification of thermodynamic uncertainties in dense gas flows

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. for a dense gas flow over a wing section. Flow thermodynamic conditions are such that the gas thermodynamic behavior strongly deviates from that of a perfect gas. In the aim of assessing the proposed methodology, synthetic calibration data -specifically, wall pressure data-are generated by running the numerical solver with a more complex and accurate thermodynamic model. The statistical model used to build the likelihood function includes a model-form inadequacy term, accounting for the gap between the model output associated to the best-fit parameters, and the true phenomenon. Results show that, for all of the relatively simple models under investigation, calibrations lead to informative posterior probability density distributions of the input parameters and improve the predictive distribution significantly. Nevertheless, calibrated parameters strongly differ from their expected physical values. The relationship between this behavior and model-form inadequacy is discussed.

Robust prediction of dense gas flows under uncertain thermodynamic models

“…Accounting for model-form uncertainty in the statistical calibration is useful to temperate overfitting problems (see [16,18]). Nevertheless, such problems are not completely avoided and the closure parameter posterior distributions have limited validity when used to predict flow configurations far away the one on which they where calibrated.…”

“…Specifically, we first use Bayesian calibration for updating the coefficients of two different EOS, namely the cubic EOS of Peng-Robinson-Strjyek-Vera [9] (PRSV) and the 5th-order virial Martin-Hou EOS [10] (MAH). For that purpose, similarly to [16], we consider pressure data for dense gas flows past an airfoil [31][32][33] characterized by different free-stream thermodynamic conditions. For all the flows, the airfoil geometry and the free-stream Mach number are the same, while the free-stream pressure and temperature may vary, leading to a different thermodynamic behaviour.…”

“…by using statistical inference methodologies [14,15]. In a previous work [16], the present authors used aerodynamic data instead of thermodynamic ones for calibrating the material-dependent coefficients of equations of state (EOS) used to model the thermodynamic behavior of the working fluid. For that purpose, a Bayesian statistical procedure was used to infer on the posterior probability distributions of the closure coefficients associated with three well-known thermodynamic models, given data on the wall pressure distribution for a dense gas flow past an airfoil.…”

Optimal Sensor Placement for the Estimation of Turbulence Model Parameters in CFD

“…Among others, the Bayesian methodology has been applied to the identification of model parameters in structural dynamics [2][3][4][5], molecular dynamics [6][7][8], heat conduction [9], flight dynamics [10], and bioengineering [11]. The Bayesian approach has also been used to estimate the parameter of turbulence models for CFD computations [12][13][14][15][16][17][18].…”

“…Bayesian formulations for the estimation of turbulence model parameters in CFD based on experimental data has been presented in [12][13][14][15][16][17] using Markov-chain Monte Carlo (MCMC) techniques [41][42][43][44] and in Papadimitriou and Papadimitriou [18] using asymptotic approximations. However, the optimal location of the sensors so that the resulting measurements are most informative for the estimation of the turbulence model or other parameters in CFD simulations has not been presented in the literature.…”