Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session R5: CFD: Uncertainty Quantification |
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Chair: Daniele Venturi, UC Santa Cruz Room: 104 |
Tuesday, November 24, 2015 12:50PM - 1:03PM |
R5.00001: A new paradigm for variable-fidelity stochastic simulation and information fusion in fluid mechanics Daniele Venturi, Lucia Parussini, Paris Perdikaris, George Karniadakis Predicting the statistical properties of fluid systems based on stochastic simulations and experimental data is a problem of major interest across many disciplines. Even with recent theoretical and computational advancements, no broadly applicable techniques exist that could deal effectively with uncertainty propagation and model inadequacy in high-dimensions. To address these problems, we propose a new paradigm for variable-fidelity stochastic modeling, simulation and information fusion in fluid mechanics. The key idea relies in employing recursive Bayesian networks and multi-fidelity information sources (e.g., stochastic simulations at different resolution) to construct optimal predictors for quantities of interest, e.g., the random temperature field in stochastic Rayleigh-B\'enard convection. The object of inference is the quantity of interest at the highest possible level of fidelity, for which we can usually afford only few simulations. To compute the optimal predictors, we developed a multivariate recursive co-kriging approach that simultaneously takes into account variable fidelity in the space of models (e.g., DNS vs. potential flow solvers), as well as variable-fidelity in probability space. Numerical applications are presented and discussed. [Preview Abstract] |
Tuesday, November 24, 2015 1:03PM - 1:16PM |
R5.00002: Uncertainty Quantification applied to flow simulations in thoracic aortic aneurysms Alessandro Boccadifuoco, Alessandro Mariotti, Simona Celi, Nicola Martini, Maria Vittoria Salvetti The thoracic aortic aneurysm is a progressive dilatation of the thoracic aorta causing a weakness in the aortic wall, which may eventually cause life-threatening events. Clinical decisions on treatment strategies are currently based on empiric criteria, like the aortic diameter value or its growth rate. Numerical simulations can give the quantification of important indexes which are impossible to be obtained through in-vivo measurements and can provide supplementary information. Hemodynamic simulations are carried out by using the open-source tool SimVascular and considering patient-specific geometries. One of the main issues in these simulations is the choice of suitable boundary conditions, modeling the organs and vessels not included in the computational domain. The current practice is to use outflow conditions based on resistance and capacitance, whose values are tuned to obtain a physiological behavior of the patient pressure. However it is not known a priori how this choice affects the results of the simulation. The impact of the uncertainties in these outflow parameters is investigated here by using the generalized Polynomial Chaos approach. This analysis also permits to calibrate the outflow-boundary parameters when patient-specific in-vivo data are available. [Preview Abstract] |
Tuesday, November 24, 2015 1:16PM - 1:29PM |
R5.00003: Uncertainty quantification of box model and CFD predictions for night-time ventilation in Stanford's Y2E2 building Catherine Gorle, Gianluca Iaccarino Robust design of natural ventilation systems remains a challenging task, because the simplifications and assumptions introduced in models that predict natural ventilation performance can result in non negligible uncertainty in the results. The objective of this work is to investigate the predictive capability of two models with very different levels of fidelity: a box model and a CFD simulation. We consider night-flush ventilation in the Y2E2 building and compare the results with available temperature measurements. The box model solves for the average air and thermal mass temperatures, representing heat sources and sinks as integral values. The uncertainty in the input parameters is propagated using a non-intrusive polynomial chaos method. The mean result predicts a too fast cooling rate with a maximum air temperature difference of 0.6K, but the measurements are within the predicted 95{\%} confidence interval. The CFD simulation represents a much higher level of detail in the building model, but it also predicts a too high cooling rate with a maximum air temperature difference of 0.9K. Further work will focus on quantifying the uncertainty in the CFD simulation and on using CFD results to determine inputs for the box model, such as discharge and heat transfer coefficients. [Preview Abstract] |
Tuesday, November 24, 2015 1:29PM - 1:42PM |
R5.00004: Quantifying Model-Form Uncertainties in Reynolds Averaged Navier-Stokes Equations: An Open-Box, Physics-Based, Bayesian Approach Heng Xiao, Jinlong Wu, Jianxun Wang, Rui Sun, Christopher J. Roy For many practical flows, the turbulence models are the most important source of uncertainty in Reynolds-Averaged Navier-Stokes (RANS) predictions. In this work, we develop an open-box, physics-informed Bayesian framework for quantifying the model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to incorporate the prior information with available observation data in a Bayesian framework to posterior distributions of the Reynolds stresses and other quantities of interest. Two representative cases, the flow over periodic hills and the flow in a square duct, are used to evaluate the performance of the proposed framework. Simulation results suggest that the obtained posterior mean has significantly better agreement with the benchmark data compared to the baseline simulation, even with very sparse observations. At most locations, the posterior distribution adequately represents the model-form uncertainties. [Preview Abstract] |
Tuesday, November 24, 2015 1:42PM - 1:55PM |
R5.00005: Model-Form Uncertainty Quantification in RANS Simulation of Wing-Body Junction Flow Jinlong Wu, Jianxun Wang, Heng Xiao Junction flow, known as one of the remaining challenges for computational aerodynamics, occurs when a boundary layer encounters an obstacle mounted on the surface. Previous studies have shown that the RANS models are not capable to provide satisfactory prediction. In this work, a novel open-box, physics-informed Bayesian framework is used to quantify the model-form uncertainties in RANS simulation of junction flow. The first objective is to correct the bias in RANS prediction, by utilizing several observation data. The second one is to quantify the model-form uncertainties, which can enable risk-informed decision-making. To begin with a standard RANS simulation, which is performed on a 3:2 elliptic nose and NACA0020 tail cylinder, uncertainties with empirical prior knowledge and physical constraints are directly injected into the Reynolds stresses term, and the unbiased knowledge from observation data is incorporated by an iterative ensemble Kalman method. Current results show that the bias in the quantities of interest (QoIs) of the RANS prediction, e.g., mean velocity, turbulent kinetic energy, etc, can be significantly corrected by this novel Bayesian framework. The probability density distributions of QoIs show that the model-form uncertainty can be quantified as well. [Preview Abstract] |
Tuesday, November 24, 2015 1:55PM - 2:08PM |
R5.00006: Assessment of the DNS Data Accuracy Using RANS-DNS Simulations Juan D. Colmenares F., Svetlana V. Poroseva, Scott M. Murman Direct numerical simulations (DNS) provide the most accurate computational description of a turbulent flow field and its statistical characteristics. Therefore, results of simulations with Reynolds-Averaged Navier-Stokes (RANS) turbulence models are often evaluated against DNS data. The goal of our study is to determine a limit of RANS model performance in relation to existing DNS data. Since no model can outperform DNS, this limit can be determined by solving RANS equations with all unknown terms being represented by their DNS data (RANS-DNS simulations). In the presentation, results of RANS-DNS simulations conducted using transport equations for velocity moments of second, third, and fourth orders in incompressible planar wall-bounded flows are discussed. The results were obtained with two solvers: OpenFOAM and in-house code for fully-developed flows at different Reynolds numbers using different DNS databases. [Preview Abstract] |
Tuesday, November 24, 2015 2:08PM - 2:21PM |
R5.00007: A fast algorithm for the estimation of statistical error in DNS (or experimental) time averages Paolo Luchini, Serena Russo A standard final step in the DNS (but the same can be said of experimental measurements) of turbulence, is the time- and space-averaging of the instantaneous results in order to give their means or correlations or other statistical properties. These averages are necessarily performed over a finite time and space window, and are therefore more correctly just estimates of the ``true'' statistical averages. The choice of the appropriate window size is most often subjectively based on individual experience, but as subtler statistics enter the focus of investigation, an objective criterion becomes desirable. Classical estimators of the averaging error of finite time series fall in two categories: ``batch means'' algorithms, fast but not very accurate, and ARMA methods, slower because they estimate the complete correlation function to start with. Here a modification of the batch means algorithm will be presented, which retains its speed while removing its biasing error. As a side benefit, an automatic determination of batch size is also included. Examples will be given involving both an artificial time series of known statistics and an actual DNS of turbulence. [Preview Abstract] |
Tuesday, November 24, 2015 2:21PM - 2:34PM |
R5.00008: Turbulence model form uncertainty quantification in OpenFOAM Zengrong Hao, St\'ephanie Zeoli, Laurent Bricteux, Catherine Gorl\'e Reynolds-averaged Navier-Stokes (RANS) simulations with a two-equation linear eddy-viscosity turbulence model remain a commonly used computational technique for engineering design and analysis of turbulent flows. The accuracy of the results is however limited by the inability of the turbulence model to correctly predict the complex flow features relevant to engineering applications. To enable supporting critical design decisions based on these imperfect model results it is essential to quantify the uncertainty related to the turbulence model form and define confidence levels for the results. The objective of this study is the implementation and validation of a previously developed approach for quantifying the uncertainty in RANS predictions of a turbulent flow in the open source code OpenFOAM. The methodology is based on two steps: 1. calculate a marker to determine where in the flow the model is plausibly inaccurate, and 2. perturb the modeled Reynolds stresses in the momentum equations. The perturbations are defined in terms of the decomposed Reynolds stress tensor, i.e., the tensor magnitude and the eigenvalues and eigenvectors of the normalized anisotropy tensor. Results for a square duct and the flow over a wavy wall will be presented for validation of the implementation. [Preview Abstract] |
Tuesday, November 24, 2015 2:34PM - 2:47PM |
R5.00009: Representing Model Inadequacy in Combustion Mechanisms of Laminar Flames Rebecca Morrison, Robert Moser, Todd Oliver An accurate description of the chemical processes involved in the oxidation of hydrocarbons may include hundreds of reactions and thirty or more chemical species. Kinetics models of these chemical mechanisms are often embedded in a fluid dynamics solver to represent combustion. Because the computational cost of such detailed mechanisms is so high, it is common practice to use drastically reduced mechanisms. But, this introduces modeling errors which may render the model inadequate. In this talk, we present a formulation of the model inadequacy in reduced models of combustion mechanisms. Our goal is to account for the discrepancy between the detailed model and its reduced version by incorporating an additive, linear, probabilistic inadequacy model. In effect, it is a random matrix, whose entries are characterized by probability distributions and which displays interesting properties due to conservation constraints. In particular, we investigate how the inclusion of the random matrix affects the prediction of flame speed in a one-dimensional hydrogen laminar flame. [Preview Abstract] |
Tuesday, November 24, 2015 2:47PM - 3:00PM |
R5.00010: Uncertainty Quantification of the Dynamic Mode Decomposition Anthony DeGennaro, Scott Dawson, Clarence Rowley This work explores and quantifies the statistical effect that parameterized uncertainty has on the dynamic mode decomposition (DMD). For the data under consideration, such uncertain parameters could include Reynolds number, geometry, or random sensor/signal noise in the system. The aims of this study are twofold: firstly, to quantify the robustness of the algorithm in terms of pertinent identified quantities (such as DMD modes and eigenvalues), thus expanding upon recent work in this area, and secondly, to present a method for analyzing the underlying dynamic systems from data in an efficient manner. We use polynomial chaos expansions to represent the relevant DMD quantities of interest. This approach can be computationally more efficient than sample-based methods (e.g., Monte Carlo) when the dimensionality of the parameter space is moderate. We demonstrate our methodology on a number of well-studied example systems, including numerical simulations of flow past a circular cylinder. [Preview Abstract] |
Tuesday, November 24, 2015 3:00PM - 3:13PM |
R5.00011: Impact of uncertainties in free stream conditions on the aerodynamics of a rectangular cylinder Alessandro Mariotti, Pejman Shoeibi Omrani, Jeroen Witteveen, Maria Vittoria Salvetti The BARC benchmark deals with the flow around a rectangular cylinder with chord-to-depth ratio equal to 5. This flow configuration is of practical interest for civil and industrial structures and it is characterized by massively separated flow and unsteadiness. In a recent review of BARC results, significant dispersion was observed both in experimental and numerical predictions of some flow quantities, which are extremely sensitive to various uncertainties, which may be present in experiments and simulations. Besides modeling and numerical errors, in simulations it is difficult to exactly reproduce the experimental conditions due to uncertainties in the set-up parameters, which sometimes cannot be exactly controlled or characterized. Probabilistic methods and URANS simulations are used to investigate the impact of the uncertainties in the following set-up parameters: the angle of incidence, the free stream longitudinal turbulence intensity and length scale. Stochastic collocation is employed to perform the probabilistic propagation of the uncertainty. The discretization and modeling errors are estimated by repeating the same analysis for different grids and turbulence models. The results obtained for different assumed PDF of the set-up parameters are also compared. [Preview Abstract] |
Tuesday, November 24, 2015 3:13PM - 3:26PM |
R5.00012: Stochastic sensitivity analysis to grid resolution and modeling in LES of the flow around a rectangular cylinder Maria Vittoria Salvetti, Lorenzo Siconolfi, Alessandro Mariotti Systematic analysis of the impact of discretization and numerical errors in large eddy simulations (LES) of complex flows is a challenging task. We investigate the sensitivity to grid resolution and modeling of LES results for the flow around a 5:1 rectangular cylinder, which is the object of an international benchmark (BARC) collecting experimental and numerical flow realizations. The related flow is complex, being turbulent with separation from the upstream corners and reattachment on the cylinder side and vortex shedding from the rear corners. Significant dispersion of the BARC results was observed, also for LES, and deterministic sensitivity analyses were not conclusive. LES are carried out here by using the spectral element code Nek5000. An explicit quadratic low-pass filter in the modal space is used, characterized by a cut-off value and by a weight function, which provides dissipation of the modes higher than the cut off and acts as a SGS dissipation. The uncertain parameters are the size of the spectral elements in the spanwise direction and the weight of the explicit filter. The impact of the uncertainty in these parameters is evaluated through generalized polynomial chaos. The stochastic variance of the results is compared to the overall dispersion of the BARC results. [Preview Abstract] |
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