Physical modeling, large scale simulations and experiments have long been recognized as critical for understanding and advancing science and technology. In the field of computational modeling, Uncertainty Quantification can be broadly defined as a tool for identifying, quantifying and reducing uncertainties associated with models, numerical algorithms, experiments and predicted outcomes. In the experimental field, the quantification of measurement uncertainties is well understood and is addressed by classical statistical methods. However, the systematic quantification of uncertainties and the analysis of how they propagate through complex models, is a new area of research in the field of Computational Fluid Dynamics (CFD).One large-scale application, where Uncertainty Quantification might find an important and useful role, is in the design and safety demonstration of Nuclear Reactors. In the design of Nuclear Reactors, knowing the uncertainties related to predictive models is a key point to define the degree of reliability of numerical simulations. In nuclear reactor models, the main sources of uncertainties are: initial and boundary conditions, input parameters, model and geometrical uncertainties. The resulting numerical models are computationally expensive and require the development of models reproducing the system response to determine uncertainties for the quantities of interest. In the present work, Stochastic Computational Fluid Dynamics--based on generalized Polynomial Chaos Expansion (PCE)--is used to simulate the GEneral MIxing eXperiment(GEMIX), carried out at the Paul Scherrer Institute, where uncertainty, arising from boundary conditions and models input parameters, are propagated through the hydrodynamic model. To quantify the uncertainty in the CFD simulations--using the non-intrusive Polynomial Chaos Expansion--seven stochastic variables have been introduced to handle uncertain boundary conditions and the phenomenological coefficients in the k-€ turbulence model. Two random variables were used to describe the inlet conditions and five to describe the turbulence model. The PCE approximates the response of the system in terms of a series of orthogonal polynomials. The orthogonality property of the polynomial basis is then applied to derive suitable expressions for relevant statistical moments (mean and standard deviation) for concentration, turbulence kinetic energy and velocity. From the standard deviation fields, uncertainty bands were computed. Mean PCE values for velocity, turbulence kinetic energy and concentration were compared with experimental measurements at several locations inside the mixing section. The numerical results show good agreement with experiments, which are well bounded by the uncertainty bands obtained from the PCE analysis. From the sensitivity analysis--based on the Sobol decomposition--was determined that the inlet conditions introduce the highest uncertainty to the CFD results.
Modelli fisici, simulazioni su grandi scale ed esperimenti sono da sempre ritenuti come un punto critico per la comprensione ed il progresso scientifico e tecnologico. Nel campo della modellistica computazionale, Uncertainty Quantification può essere definita come uno strumento per identificare, quantificare e ridurre le incertezze associate a modelli, algoritmi numerici, esperimenti e risultati attesi. In ambito sperimentale, la stima delle incertezze è un problema largamente affrontato e compreso tramite l'uso dei metodi statistici classici. Tuttavia, la sistematica quantificazione delle incertezze e l'analisi di come propagano all'interno id modelli complessi è una nuova area di ricerca nel campo della Fluidodinamica Computazionale. Un'applicazione su grande scala, nella quale Uncertainty Quantification può svolgere un ruolo importante e utile, è rappresentata dal design e dalle problematiche legate alla sicurezza dei Reattori Nucleari. Nella concezione dei Reattori Nucleari, la conoscenza delle incertezze legate ai modelli predittivi è un punto chiave al fine di definire il grado di affidabilità delle simulazioni numeriche. Nei modelli riguardanti i reattori nucleari, le principali fonti di incertezza sono: condizioni iniziali e al contorno, parametri d'ingresso, incertezze legate ai modelli matematici ed alle geometrie dei componenti. I modelli numerici ottenuti sono dispendiosi da un punto di vista computazionale ed inoltre necessitano lo sviluppo di modelli capaci di riprodurre la risposta del sistema per determinare le incertezze legate alle variabili d'interesse. Nel presente lavoro, Fluidodinamica Computazionale Stocastica, basata sul generalized Polynomial Chaos Expansion (PCE), è usata per simulare il GEneral MIxing eXperiment (GEMIX), realizzato nell'istituto Paul Scherrer, nel quale le incertezze, derivanti dalle condizioni al contorno e dai parametri d'ingresso del modello, sono propagate attraverso il modello idrodinamico. Per quantificare l'incertezza legata alla simulazione fluidodinamica, usando il metodo non intrusivo del Polynomial Chaos Expansion, sette variabili stocastiche sono state introdotte al fine di maneggiare le incerte condizioni al contorno e i fenomenologici coefficienti presenti nel modello di turbolenza k-ε. Due variabili casuali sono state usate per descrivere le condizioni di ingresso e cinque per descrivere il modello di turbolenza. PCE approssima la risposta del sistema tramite una serie di polinomi ortogonali . L'ortogonalità della base di polinomi è stata applicata per derivare un'adatta espressione per i momenti statistici (valore medio e deviazione standard) per la concentrazione, l'energia cinetica turbolenta e la velocità. Tramite il campo di deviazione standard calcolato sono state generate bande di incertezza. I valori medi ottenuti tramite PCE per velocità, energia cinetica turbolenta e concentrazione sono stati confrontati con le misure sperimentali per differenti posizioni all'interno della mixing section. I risultati numerici concordano con i risultati sperimentali, i quali risultano ben confinati all'interno delle barre d'incertezza valutate tramite Polynomial Chaos Expansion. Tramite un'analisi di sensitività-- basata sulla decomposizione di Sobol-- si è individuato che le condizioni all'ingresso dell'esperimento introducono l'incertezza più grande all'interno della simulazione CFD.
Uncertainty quantification for CFD simulation in turbulent mixing
BUCCIO, ANTONIO
2013/2014
Abstract
Physical modeling, large scale simulations and experiments have long been recognized as critical for understanding and advancing science and technology. In the field of computational modeling, Uncertainty Quantification can be broadly defined as a tool for identifying, quantifying and reducing uncertainties associated with models, numerical algorithms, experiments and predicted outcomes. In the experimental field, the quantification of measurement uncertainties is well understood and is addressed by classical statistical methods. However, the systematic quantification of uncertainties and the analysis of how they propagate through complex models, is a new area of research in the field of Computational Fluid Dynamics (CFD).One large-scale application, where Uncertainty Quantification might find an important and useful role, is in the design and safety demonstration of Nuclear Reactors. In the design of Nuclear Reactors, knowing the uncertainties related to predictive models is a key point to define the degree of reliability of numerical simulations. In nuclear reactor models, the main sources of uncertainties are: initial and boundary conditions, input parameters, model and geometrical uncertainties. The resulting numerical models are computationally expensive and require the development of models reproducing the system response to determine uncertainties for the quantities of interest. In the present work, Stochastic Computational Fluid Dynamics--based on generalized Polynomial Chaos Expansion (PCE)--is used to simulate the GEneral MIxing eXperiment(GEMIX), carried out at the Paul Scherrer Institute, where uncertainty, arising from boundary conditions and models input parameters, are propagated through the hydrodynamic model. To quantify the uncertainty in the CFD simulations--using the non-intrusive Polynomial Chaos Expansion--seven stochastic variables have been introduced to handle uncertain boundary conditions and the phenomenological coefficients in the k-€ turbulence model. Two random variables were used to describe the inlet conditions and five to describe the turbulence model. The PCE approximates the response of the system in terms of a series of orthogonal polynomials. The orthogonality property of the polynomial basis is then applied to derive suitable expressions for relevant statistical moments (mean and standard deviation) for concentration, turbulence kinetic energy and velocity. From the standard deviation fields, uncertainty bands were computed. Mean PCE values for velocity, turbulence kinetic energy and concentration were compared with experimental measurements at several locations inside the mixing section. The numerical results show good agreement with experiments, which are well bounded by the uncertainty bands obtained from the PCE analysis. From the sensitivity analysis--based on the Sobol decomposition--was determined that the inlet conditions introduce the highest uncertainty to the CFD results.| File | Dimensione | Formato | |
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2015_04_BUCCIO.pdf
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https://hdl.handle.net/10589/106782