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In this thesis, detailed uncertainty quantification studies focusing on the closure coefficients of eddy-viscosity turbulence models for several flows using two CFD solvers have been performed. Three eddy viscosity turbulence models considered are: the one-equation Spalart-Allmaras (SA) model, the two-equation Shear Stress Transport (SST) k-[omega] model, and the one-equation Wray-Agarwal (WA) model. OpenFOAM and ANSYS Fluent are used as flow solvers. Uncertainty quantification analyses are performed for subsonic flow over a flat plate, subsonic flow over a backward-facing step, and transonic flow past an axisymmetric bump. In the case of flat plate, coefficients of pressure, lift, drag, and skin friction are considered to be the output quantities of interest. In case of the backward-facing step, these quantities are considered along with the separation bubble size. In case of an axisymmetric transonic bump, the drag coefficient, lift coefficient, separation point and reattachment point are considered. In addition to these four quantities, global uncertainty is employed on every node in the flow for Reynolds shear stress to determine which areas of the flow the closure coefficients contribute most to the uncertainty. Uncertainty quantification is conducted using DAKOTA developed by Sandia National Laboratories using stochastic expansions based on non-intrusive polynomial chaos. All closure xii coefficients are treated as epistemic uncertain variables, each defined by a specified range. The influence of the closure coefficients on output quantities is assessed using the global sensitivity analysis based on variance decomposition. This yields Sobol indices which are used to rank the contributions of each constant. A comparison of the Sobol indices between the turbulence models, flow cases, and flow solvers is conducted. This research identifies closure coefficients for each turbulence model that contribute significantly to uncertainty in the model predictions; this information can then be used to improve the prediction capability of the models in separated flow region by a more judicious choice of the closure coefficients.
"The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) [kappa]-[omega] Model, and the Menter Shear-Stress Transport Model. The FUN3D code developed by NASA Langley Research Center and the BCFD code developed by The Boeing Company were used as the flow solvers. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. Two studies were performed in this work. The main study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows. A case study demonstrated that the RAE 2822 sensitivity results of the main study are independent of the flow solver and of the computational grid topology and resolution"--Abstract, page iii.
The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.
Shock wave-boundary-layer interaction (SBLI) is a fundamental phenomenon in gas dynamics that is observed in many practical situations, ranging from transonic aircraft wings to hypersonic vehicles and engines. SBLIs have the potential to pose serious problems in a flowfield; hence they often prove to be a critical - or even design limiting - issue for many aerospace applications. This is the first book devoted solely to a comprehensive, state-of-the-art explanation of this phenomenon. It includes a description of the basic fluid mechanics of SBLIs plus contributions from leading international experts who share their insight into their physics and the impact they have in practical flow situations. This book is for practitioners and graduate students in aerodynamics who wish to familiarize themselves with all aspects of SBLI flows. It is a valuable resource for specialists because it compiles experimental, computational and theoretical knowledge in one place.
This book introduces design techniques developed to increase the safety of aircraft engines, and demonstrates how the application of stochastic methods can overcome problems in the accurate prediction of engine lift caused by manufacturing error. This in turn addresses the issue of achieving required safety margins when hampered by limits in current design and manufacturing methods. The authors show that avoiding the potential catastrophe generated by the failure of an aircraft engine relies on the prediction of the correct behaviour of microscopic imperfections. This book shows how to quantify the possibility of such failure, and that it is possible to design components that are inherently less risky and more reliable. This new, updated and significantly expanded edition gives an introduction to engine reliability and safety to contextualise this important issue, evaluates newly-proposed methods for uncertainty quantification as applied to jet engines. Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines will be of use to gas turbine manufacturers and designers as well as CFD practitioners, specialists and researchers. Graduate and final year undergraduate students in aerospace or mathematical engineering may also find it of interest.
"A mixed aleatory (inherent) and epistemic (model-form) uncertainty quantification (UQ) analysis method was applied to a computational fluid dynamics (CFD) modeling problem of synthetic jet actuators. A test case, (Case 3, flow over a hump model with synthetic jet actuator control) from the CFDVAL2004 workshop was selected to apply the Second-Order Probability framework implemented with a stochastic response surface obtained from Quadrature-Based Non-Intrusive Polynomial Chaos (NIPC). Three uncertainty sources were considered: (1) epistemic uncertainty in turbulence model, (2) aleatory uncertainty in free stream velocity and (3) aleatory uncertainty in actuation frequency. Uncertainties in both long-time averaged and phase averaged quantities were quantified using a fourth order polynomial chaos expansion (PCE). Results were compared with experimental data available. A global sensitivity analysis with Sobol indices was utilized to rank the importance of each uncertainty source to the overall output uncertainty. The results indicated that for the long-time averaged separation bubble size, the uncertainty in turbulence model had a dominant contribution, which was also observed in the long-time averaged skin friction coefficients at three selected locations. For long-time averaged pressure coefficient, the contributions from free stream velocity and turbulence model are depending on the locations. The mixed UQ results for phase averaged x-velocity distributions at three selected locations showed that the 95% confidence intervals (CI) could generally envelope the experimental data. The Sobol indices showed that near the wall, the turbulence model had a main influence on the x-velocity, while approaching the main stream, the uncertainty in free stream velocity became a larger contributor. The uncertainty in frequency was found to have a very small contribution to both long-time averaged and phase averaged quantities with the range of variance considered"--Abstract, leaf iii
Surrogates are used to mitigate the aggregate cost of simulation needed to perform a comprehensive uncertainty quantification (UQ) analysis. A realistic uncertainty analysis of any engineering system involves a large number of uncertainties, and as a result, the surrogates take inputs in a high dimensional space. We investigate surrogates that take the form of a truncated Legendre polynomial series, from which the coefficients associated to each polynomial basis function must be estimated. High dimensional estimation is a known instance of the curse of dimensionality, and for sufficiently "complex'" functions, an unsolved problem. In order to break the curse, we assume the function to be approximated is sparse in the Legendre polynomials and employ the machinery of l-1-regularized regression. We make three contributions under this theme. Firstly, we present a novel approach to choosing sample (design) points and show that it yields lower estimation error over a broad range of functions compared to existing sampling approaches. Secondly, we give a novel sparse estimator that effectively uses (partial) derivative information for estimation and show empirically that estimation using derivatives can be more efficient than function values if the derivatives are sparser than the function. Thirdly, we show that by exploiting the best k-term approximation} property of l-1-methods, we can quickly identify the most signfiicant uncertainties and reduce the dimensionality of the input space accordingly. We conclude by demonstrating the efficacy of these methods in a UQ analysis of a notional vertical axis wind turbine design.
During the last decade, research in Uncertainty Quantification (UC) has received a tremendous boost, in fluid engineering and coupled structural-fluids systems. New algorithms and adaptive variants have also emerged.This timely compendium overviews in detail the current state of the art of the field, including advances in structural engineering, along with the recent focus on fluids and coupled systems. Such a strong compilation of these vibrant research areas will certainly be an inspirational reference material for the scientific community.