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http://hdl.handle.net/10985/10073
Bayesian quantification of thermodynamic uncertainties in dense gas flows
MERLE, Xavier; CINNELLA, Paola
A Bayesian inference methodology is developed for calibrating complex equations of state used in numerical fluid flow solvers. Precisely, the input parameters of three equations of state commonly used for modeling the thermodynamic behavior of so-called dense gas flows, – i.e. flows of gases characterized by high molecular weights and complex molecules, working in thermodynamic conditions close to the liquid-vapor saturation curve–, are calibrated by means of Bayesian inference from reference aerodynamic data 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 func-tion 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 infor-mative 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.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/100732015-01-01T00:00:00ZMERLE, XavierCINNELLA, PaolaA Bayesian inference methodology is developed for calibrating complex equations of state used in numerical fluid flow solvers. Precisely, the input parameters of three equations of state commonly used for modeling the thermodynamic behavior of so-called dense gas flows, – i.e. flows of gases characterized by high molecular weights and complex molecules, working in thermodynamic conditions close to the liquid-vapor saturation curve–, are calibrated by means of Bayesian inference from reference aerodynamic data 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 func-tion 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 infor-mative 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
http://hdl.handle.net/10985/15563
Robust prediction of dense gas flows under uncertain thermodynamic models
MERLE, Xavier; CINNELLA, Paola
A Bayesian approach is developed to quantify uncertainties associated with the thermodynamic models used for the simulation of dense gas flows, i.e. flows of gases characterized by complex molecules of moderate to high molecular weight, in thermodynamic conditions of the general order of magnitude of the liquid/vapor critical point. The thermodynamic behaviour of dense gases can be modelled through equations of state with various mathematical structures, all involving a set of material-dependent coefficients. For several organic fluids of industrial interest abundant and high-quality thermodynamic data required to specify such coefficients are hardly available, leading to undetermined levels of uncertainty of the equation output. Additionally, the best choice for the kind of equation of state (mathematical form) to be used is not always easy to determine and it is often based on expert opinion. In other terms, equations of state introduce both parametric and model-form uncertainties, which need to be quantified to make reliable predictions of the flow field. In this paper we propose a statistical inference methodology for estimating both kinds of uncertainties simultaneously. Our approach consists of a calibration step and a prediction step. The former allows to infer on the parameters to be input to the equation of state, based on the observation of aerodynamic quantities like pressure measurements at some locations in the dense gas flow. The subsequent prediction step allows to predict unobserved flow configurations based on the inferred posterior distributions of the coefficients. Model-form uncertainties are incorporated in the prediction step by using a Bayesian model averaging (BMA) approach. This consists in constructing an average of the predictions of various competing models weighted by the posterior model probabilities. Bayesian averaging also provides a useful tool for making robust predictions from a set of alternative calibration scenarios (Bayesian model-scenario averaging or BMSA). The proposed methodology is assessed for a class of dense gas flows, namely transonic flows around an isolated airfoil, at various free-stream thermodynamic conditions in the dense-gas region.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/155632019-01-01T00:00:00ZMERLE, XavierCINNELLA, PaolaA Bayesian approach is developed to quantify uncertainties associated with the thermodynamic models used for the simulation of dense gas flows, i.e. flows of gases characterized by complex molecules of moderate to high molecular weight, in thermodynamic conditions of the general order of magnitude of the liquid/vapor critical point. The thermodynamic behaviour of dense gases can be modelled through equations of state with various mathematical structures, all involving a set of material-dependent coefficients. For several organic fluids of industrial interest abundant and high-quality thermodynamic data required to specify such coefficients are hardly available, leading to undetermined levels of uncertainty of the equation output. Additionally, the best choice for the kind of equation of state (mathematical form) to be used is not always easy to determine and it is often based on expert opinion. In other terms, equations of state introduce both parametric and model-form uncertainties, which need to be quantified to make reliable predictions of the flow field. In this paper we propose a statistical inference methodology for estimating both kinds of uncertainties simultaneously. Our approach consists of a calibration step and a prediction step. The former allows to infer on the parameters to be input to the equation of state, based on the observation of aerodynamic quantities like pressure measurements at some locations in the dense gas flow. The subsequent prediction step allows to predict unobserved flow configurations based on the inferred posterior distributions of the coefficients. Model-form uncertainties are incorporated in the prediction step by using a Bayesian model averaging (BMA) approach. This consists in constructing an average of the predictions of various competing models weighted by the posterior model probabilities. Bayesian averaging also provides a useful tool for making robust predictions from a set of alternative calibration scenarios (Bayesian model-scenario averaging or BMSA). The proposed methodology is assessed for a class of dense gas flows, namely transonic flows around an isolated airfoil, at various free-stream thermodynamic conditions in the dense-gas region.Sensitivity of Supersonic ORC Turbine Injector Designs to Fluctuating Operating Conditions
http://hdl.handle.net/10985/15321
Sensitivity of Supersonic ORC Turbine Injector Designs to Fluctuating Operating Conditions
BUFI, Elio Antonio; CINNELLA, Paola; MERLE, Xavier; CINNELLA, Paola
The design of an efficient organic rankine cycle (ORC) expander needs to take properly into account strong real gas effects that may occur in given ranges of operating conditions, which can also be highly variable. In this work, we first design ORC turbine geometries by means of a fast 2-D design procedure based on the method of characteristics (MOC) for supersonic nozzles characterized by strong real gas effects. Thanks to a geometric post-processing procedure, the resulting nozzle shape is then adapted to generate an axial ORC blade vane geometry. Subsequently, the impact of uncertain operating conditions on turbine design is investigated by coupling the MOC algorithm with a Probabilistic Collocation Method (PCM) algorithm. Besides, the injector geometry generated at nominal operating conditions is simulated by means of an in-house CFD solver. The code is coupled to the PCM algorithm and a performance sensitivity analysis, in terms of adiabatic efficiency and power output, to variations of the operating conditions is carried out.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/153212015-01-01T00:00:00ZBUFI, Elio AntonioCINNELLA, PaolaMERLE, XavierCINNELLA, PaolaThe design of an efficient organic rankine cycle (ORC) expander needs to take properly into account strong real gas effects that may occur in given ranges of operating conditions, which can also be highly variable. In this work, we first design ORC turbine geometries by means of a fast 2-D design procedure based on the method of characteristics (MOC) for supersonic nozzles characterized by strong real gas effects. Thanks to a geometric post-processing procedure, the resulting nozzle shape is then adapted to generate an axial ORC blade vane geometry. Subsequently, the impact of uncertain operating conditions on turbine design is investigated by coupling the MOC algorithm with a Probabilistic Collocation Method (PCM) algorithm. Besides, the injector geometry generated at nominal operating conditions is simulated by means of an in-house CFD solver. The code is coupled to the PCM algorithm and a performance sensitivity analysis, in terms of adiabatic efficiency and power output, to variations of the operating conditions is carried out.Bayesian quantification of thermodynamic uncertainties in dense gas flows
http://hdl.handle.net/10985/8640
Bayesian quantification of thermodynamic uncertainties in dense gas flows
MERLE, Xavier; CINNELLA, Paola
A Bayesian inference methodology is developed for calibrating complex equations of state used in numerical fluid flow solvers. Precisely, the input parameters of three equations of state commonly used for modeling the thermodynamic behavior of so-called dense gas flows, – i.e. flows of gases characterized by high molecular weights and complex molecules, working in thermodynamic conditions close to the liquid-vapor saturation curve–, are calibrated by means of Bayesian inference from reference aerodynamic data 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 rue 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.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/86402014-01-01T00:00:00ZMERLE, XavierCINNELLA, PaolaA Bayesian inference methodology is developed for calibrating complex equations of state used in numerical fluid flow solvers. Precisely, the input parameters of three equations of state commonly used for modeling the thermodynamic behavior of so-called dense gas flows, – i.e. flows of gases characterized by high molecular weights and complex molecules, working in thermodynamic conditions close to the liquid-vapor saturation curve–, are calibrated by means of Bayesian inference from reference aerodynamic data 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 rue 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.Bayesian model-scenario averaged predictions of compressor cascade flows under uncertain turbulence models
http://hdl.handle.net/10985/23746
Bayesian model-scenario averaged predictions of compressor cascade flows under uncertain turbulence models
DE ZORDO-BANLIAT, Maximilien; MERLE, Xavier; DERGHAM, Grégory; CINNELLA, Paola
The Reynolds-Averaged Navier-Stokes (RANS) equations represent the computational workhorse for engineering design, despite their numerous flaws. Improving and quantifying the uncertainties associated with RANS models is particularly critical in view of the analysis and optimization of complex turbomachinery flows. In this work, we use Bayesian inference for assimilating data into RANS models for the following purposes: (i) updating the model closure coefficients for a class of turbomachinery flows, namely a compressor cascade; (ii) quantifying the parametric uncertainty associated with closure coefficients of
RANS models and (iii) quantifying the uncertainty associated with the model structure and the choice of the calibration dataset based on an ensemble of concurrent models and calibration scenarios. Inference of the coefficients of three widely employed RANS models is carried out from high-fidelity LES data for the NACA65 V103 compressor cascade [1, 2]. Posterior probability distributions of the model coefficients are collected for various calibration scenarios, corresponding to different values of the flow angle at inlet.
The Maximum A Posteriori estimates of the coefficients differ from the nominal values and depend on the scenario. A recently proposed Bayesian mixture approach, namely, Bayesian Model-Scenario Averaging (BMSA) [3, 4], is used to build a prediction model that takes into account uncertainties associated with alternative model forms and with sensitivity to the calibration scenario. Stochastic predictions are presented for the turbulent flow around the NACA65 V103 cascade at mildly and severe off-design conditions. The results show that BMSA generally yields more accurate solutions than the baseline RANS
models and succeeds well in providing an estimate for the predictive uncertainty intervals, provided that a sufficient diversity of scenarios and models is included in the mixture.
Wed, 01 Apr 2020 00:00:00 GMThttp://hdl.handle.net/10985/237462020-04-01T00:00:00ZDE ZORDO-BANLIAT, MaximilienMERLE, XavierDERGHAM, GrégoryCINNELLA, PaolaThe Reynolds-Averaged Navier-Stokes (RANS) equations represent the computational workhorse for engineering design, despite their numerous flaws. Improving and quantifying the uncertainties associated with RANS models is particularly critical in view of the analysis and optimization of complex turbomachinery flows. In this work, we use Bayesian inference for assimilating data into RANS models for the following purposes: (i) updating the model closure coefficients for a class of turbomachinery flows, namely a compressor cascade; (ii) quantifying the parametric uncertainty associated with closure coefficients of
RANS models and (iii) quantifying the uncertainty associated with the model structure and the choice of the calibration dataset based on an ensemble of concurrent models and calibration scenarios. Inference of the coefficients of three widely employed RANS models is carried out from high-fidelity LES data for the NACA65 V103 compressor cascade [1, 2]. Posterior probability distributions of the model coefficients are collected for various calibration scenarios, corresponding to different values of the flow angle at inlet.
The Maximum A Posteriori estimates of the coefficients differ from the nominal values and depend on the scenario. A recently proposed Bayesian mixture approach, namely, Bayesian Model-Scenario Averaging (BMSA) [3, 4], is used to build a prediction model that takes into account uncertainties associated with alternative model forms and with sensitivity to the calibration scenario. Stochastic predictions are presented for the turbulent flow around the NACA65 V103 cascade at mildly and severe off-design conditions. The results show that BMSA generally yields more accurate solutions than the baseline RANS
models and succeeds well in providing an estimate for the predictive uncertainty intervals, provided that a sufficient diversity of scenarios and models is included in the mixture.Sparse Bayesian Learning of Explicit Algebraic Reynolds-Stress models for turbulent separated flows
http://hdl.handle.net/10985/23747
Sparse Bayesian Learning of Explicit Algebraic Reynolds-Stress models for turbulent separated flows
CHERROUD, Soufiane; MERLE, Xavier; CINNELLA, Paola; GLOERFELT, Xavier
A novel Sparse Bayesian Learning (SBL) framework is introduced for generating parsimonious stochastic algebraic stress closures for the Reynolds-Averaged Navier–Stokes (RANS) equations from high-fidelity data. The models are formulated as physically-interpretable frame-invariant tensor polynomials and built from a library of candidate functions. By their stochastic formulation, the learned model coefficients are described by probability distributions and are therefore equipped with an intrinsic measure of uncertainty. The SBL framework is used to derive customized stochastic closure models for three separated flow configurations, characterized by different geometries but similar Reynolds number. The resulting SBL models are then propagated through a CFD solver for all three configurations. The results show significantly improved predictions of velocity profiles and friction coefficient in the separation / reattachment region in comparison with a baseline LEVM (namely, k-ω SST model), for training as well as for test cases. In all cases, the computed uncertainty intervals encompass reasonably well the reference data. Furthermore, the stochastic outputs enable a global sensitivity analysis with respect to the model terms selected by the algorithm, thus providing insights in view of further improvements of EARSM-type corrections.
Thu, 01 Dec 2022 00:00:00 GMThttp://hdl.handle.net/10985/237472022-12-01T00:00:00ZCHERROUD, SoufianeMERLE, XavierCINNELLA, PaolaGLOERFELT, XavierA novel Sparse Bayesian Learning (SBL) framework is introduced for generating parsimonious stochastic algebraic stress closures for the Reynolds-Averaged Navier–Stokes (RANS) equations from high-fidelity data. The models are formulated as physically-interpretable frame-invariant tensor polynomials and built from a library of candidate functions. By their stochastic formulation, the learned model coefficients are described by probability distributions and are therefore equipped with an intrinsic measure of uncertainty. The SBL framework is used to derive customized stochastic closure models for three separated flow configurations, characterized by different geometries but similar Reynolds number. The resulting SBL models are then propagated through a CFD solver for all three configurations. The results show significantly improved predictions of velocity profiles and friction coefficient in the separation / reattachment region in comparison with a baseline LEVM (namely, k-ω SST model), for training as well as for test cases. In all cases, the computed uncertainty intervals encompass reasonably well the reference data. Furthermore, the stochastic outputs enable a global sensitivity analysis with respect to the model terms selected by the algorithm, thus providing insights in view of further improvements of EARSM-type corrections.