Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session M29: CFD: Uncertainty Quantification and Error Estimation |
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Chair: Gianluca Iaccarino, Stanford University Room: F150 |
Tuesday, November 22, 2016 8:00AM - 8:13AM |
M29.00001: Structural Uncertainties in RANS Models: Reynolds Stress Transport contra Eddy Viscosity Frameworks Aashwin Mishra, Wouter Edeling, Gianluca Iaccarino A vast majority of turbulent flow studies, both in academia and industry, utilize Reynolds Averaged Navier Stokes based models. There are different RANS modeling frameworks to select from, depending on their complexity and computational requirements, such as eddy viscosity based models, second moment closures, etc. While the relative strengths and weaknesses of each modeling paradigm (vis-a-vis their predictive fidelity, realizability, etc) are roughly established for disparate flows, there are no extant comparative estimates on the relative uncertainty in their predictions. In this investigation, we estimate the structural uncertainty inherent to different RANS modeling approaches for select internal flows. This involves comparisons between models conforming to the same framework, and, across different modeling frameworks. We establish, compare, analyze and explicate the model inadequacy for flows such as in parallel, curved, converging and diverging channels for different models. One of the novel facets of this study involves the estimation of the structural uncertainties of established Reynolds Stress Transport models, and, contrasting these against simpler eddy viscosity models. [Preview Abstract] |
Tuesday, November 22, 2016 8:13AM - 8:26AM |
M29.00002: Error estimation and adaptivity for transport problems with uncertain parameters Onkar Sahni, Jason Li, Assad Oberai Stochastic partial differential equations (PDEs) with uncertain parameters and source terms arise in many transport problems. In this study, we develop and apply an adaptive approach based on the variational multiscale (VMS) formulation for discretizing stochastic PDEs. In this approach we employ finite elements in the physical domain and generalize polynomial chaos based spectral basis in the stochastic domain. We demonstrate our approach on non-trivial transport problems where the uncertain parameters are such that the advective and diffusive regimes are spanned in the stochastic domain. We show that the proposed method is effective as a local error estimator in quantifying the element-wise error and in driving adaptivity in the physical and stochastic domains. We will also indicate how this approach may be extended to the Navier-Stokes equations. [Preview Abstract] |
Tuesday, November 22, 2016 8:26AM - 8:39AM |
M29.00003: The Contribution of Statistical Errors in DNS Data Quantified with RANS-DNS Simulations Svetlana V. Poroseva, Elbert Jeyapaul, Scott M. Murman, Juan D. Colmenares F. In RANS-DNS simulations, the Reynolds-averaged Navier-Stokes (RANS) equations are solved, with all terms but molecular diffusion being represented by the data from direct numerical simulations (DNS). No turbulence modeling is involved in such simulations. Recently, we demonstrated the use of RANS-DNS simulations as a framework for uncertainty quantification in statistical data collected from DNS. In the current study, contribution of the statistical error in the DNS data uncertainty is investigated using RANS-DNS simulations. Simulations of the Reynolds stress transport were conducted in a planar fully-developed turbulent channel flow at Re $=$ 392 (based on the friction velocity) using DNS data collected at seven averaging times. The open-source CFD software OpenFOAM was used in RANS simulations. Budgets for the Reynolds stresses were obtained from DNS performed using a pseudo-spectral (Fourier/Chebyshev-tau) method. [Preview Abstract] |
Tuesday, November 22, 2016 8:39AM - 8:52AM |
M29.00004: Uncertainty Quantification for atmospheric flows: natural terrain and urban area applications Clara Garc\'Ia-S\'anchez, Catherine Gorl\'e Modeling Atmospheric Boundary Layer (ABL) flows is an important concern for a wide range of applications, including the assessment of air quality and wind energy resources. The complexity of these ABL flows, whether in urban areas or over natural terrain, still poses a challenge for Reynolds-averaged Navier-Stokes models. In the present research, the effect of uncertainties in the inflow boundary conditions on the prediction of the flow patterns is investigated, considering two test cases for which field measurements are available: the Askervein Hill experiment (natural terrain) and the Joint Urban 2003 campaign (urban environment). The uncertainty in the inflow boundary conditions is represented by three uncertain parameters, and a non-intrusive polynomial chaos method is used to propagate these uncertainties to the quantities of interest, namely the prediction of the velocity at the locations of the different measurement stations. The results highlight some differences between ABL flows over natural terrain and those in an urban environment, in particular regarding the influence of the different uncertain parameters on the prediction of the velocity field. The implications for evaluating the effect of inflow uncertainties in these different types of ABL flows will be discussed. [Preview Abstract] |
Tuesday, November 22, 2016 8:52AM - 9:05AM |
M29.00005: Stochastic optimization algorithm for inverse modeling of air pollution Kyongmin Yeo, Youngdeok Hwang, Xiao Liu, Jayant Kalagnanam A stochastic optimization algorithm to estimate a smooth source function from a limited number of observations is proposed in the context of air pollution, where the source-receptor relation is given by an advection-diffusion equation. First, a smooth source function is approximated by a set of Gaussian kernels on a rectangular mesh system. Then, the generalized polynomial chaos (gPC) expansion is used to represent the model uncertainty due to the choice of the mesh system. It is shown that the convolution of gPC basis and the Gaussian kernel provides hierarchical basis functions for a spectral function estimation. The spectral inverse model is formulated as a stochastic optimization problem. We propose a regularization strategy based on the hierarchical nature of the basis polynomials. It is shown that the spectral inverse model is capable of providing a good estimate of the source function even when the number of unknown parameters (m) is much larger the number of data (n), m/n > 50. [Preview Abstract] |
Tuesday, November 22, 2016 9:05AM - 9:18AM |
M29.00006: Assessment of accuracy of CFD simulations through quantification of a numerical dissipation rate J.A. Domaradzki, G. Sun, X. Xiang, K.K. Chen The accuracy of CFD simulations is typically assessed through a time consuming process of multiple runs and comparisons with available benchmark data. We propose that the accuracy can be assessed in the course of actual runs using a simpler method based on a numerical dissipation rate which is computed at each time step for arbitrary sub-domains using only information provided by the code in question (Schranner et al., 2015; Castiglioni and Domaradzki, 2015). Here, the method has been applied to analyze numerical simulation results obtained using OpenFOAM software for a flow around a sphere at Reynolds number of 1000. Different mesh resolutions were used in the simulations. For the coarsest mesh the ratio of the numerical dissipation to the viscous dissipation downstream of the sphere varies from 4.5\% immediately behind the sphere to 22\% further away. For the finest mesh this ratio varies from 0.4\% behind the sphere to 6\% further away. The large numerical dissipation in the former case is a direct indicator that the simulation results are inaccurate, e.g., the predicted Strouhal number is 16\% lower than the benchmark. Low numerical dissipation in the latter case is an indicator of an acceptable accuracy, with the Strouhal number in the simulations matching the benchmark. [Preview Abstract] |
Tuesday, November 22, 2016 9:18AM - 9:31AM |
M29.00007: Predicting night-time natural ventilation in Stanford's Y2E2 building using an integral model in combination with a CFD model Giacomo Lamberti, Catherine Gorle' Natural ventilation can significantly reduce energy consumption in buildings, but the presence of uncertainty makes robust design a challenging task. We will discuss the prediction of the natural ventilation performance during a 4 hour night-flush in Stanfordâ€™s Y2E2 building using a combination of two models with different levels of fidelity: an integral model that solves for the average air and thermal mass temperature and a CFD model, used to calculate discharge and heat transfer coefficients to update the integral model. Uncertainties are propagated using polynomial chaos expansion to compute the mean and 95\% confidence intervals of the quantities of interest. Comparison with building measurements shows that, despite a slightly to fast cooling rate, the measured air temperature is inside the 95\% confidence interval predicted by the integral model. The use of information from the CFD model in the integral model reduces the maximum standard deviation of the volume-averaged air temperature by ~20\% when compared to using literature-based estimates for these quantities. The heat transfer coefficient resulting from the CFD model was found to be within the literature-based interval initially assumed for the integral model, but the discharge coefficients were found to be different. [Preview Abstract] |
Tuesday, November 22, 2016 9:31AM - 9:44AM |
M29.00008: Quantifying the Discrepancy in RANS Modeling of Reynolds Stress Eigenvectors System Jinlong Wu, Roney Thompson, Jianxun Wang, Luiz Sampaio, Heng Xiao Reynolds-Averaged Navier-Stokes (RANS) equations are the dominant tool for engineering design and analysis applications involving wall bounded turbulent flows. However, the modeled Reynolds stress tensor is known to be a main source of uncertainty, comparing to other sources like geometry, boundary conditions, etc. Recently, several works have been conducted with the aim to quantify the uncertainty of RANS simulation by studying the discrepancy of anisotropy and turbulence kinetic energy of the Reynolds stress tensor with respect to a reference database obtained from DNS. On the other hand, the eigenvectors system of Reynolds stress tensor is less investigated. In this work, a general metric is proposed to visualize the discrepancy between two eigenvectors systems. More detailed metrics based on the Euler angle and the direction cosine are also proposed to quantify the discrepancy of eigenvectors systems. The results show that even a small discrepancy of the eigenvectors of the Reynolds stress can lead to a drastically different mean velocity field, demonstrating the importance of quantifying this kind of uncertainty/error. Furthermore, the Euler angle and the direction cosine are compared for the purpose of uncertainty quantification and machine learning, respectively. [Preview Abstract] |
Tuesday, November 22, 2016 9:44AM - 9:57AM |
M29.00009: Modeling of stochastic dynamics of time-dependent flows under high-dimensional random forcing Hessam Babaee, George Karniadakis In this numerical study the effect of high-dimensional stochastic forcing in time-dependent flows is investigated. To efficiently quantify the evolution of stochasticity in such a system, the dynamically orthogonal method is used. In this methodology, the solution is approximated by a \emph{generalized} Karhunen-Loeve (KL) expansion in the form of $\mathbf{u}(\mathbf{x},t;\omega) = \overline{\mathbf{u}}(\mathbf{x},t) + \sum_{i=1}^{N} \mathbf{y}_i(t; \omega) \mathbf{u}_i(\mathbf{x},t)$, in which $\overline{\mathbf{u}}(\mathbf{x},t) $ is the stochastic mean, the set of $\mathbf{u}_i(\mathbf{x},t)$'s is a deterministic orthogonal basis and $\mathbf{y}_i(t; \omega)$'s are the stochastic coefficients. Explicit evolution equations for $\overline{\mathbf{u}}$, $\mathbf{u}_i$ and $\mathbf{y}_i$ are formulated. The elements of the basis $\mathbf{u}_i(\mathbf{x},t)$'s remain orthogonal for all times and they evolve according to the system dynamics to capture the energetically dominant stochastic subspace. We consider two classical fluid dynamics problems: (1) flow over a cylinder, and (2) flow over an airfoil under up to one-hundred dimensional random forcing. We explore the interaction of intrinsic with extrinsic stochasticity in these flows. [Preview Abstract] |
Tuesday, November 22, 2016 9:57AM - 10:10AM |
M29.00010: Parameter Estimation for a Turbulent Buoyant Jet Using Approximate Bayesian Computation Jason D. Christopher, Nicholas T. Wimer, Torrey R. S. Hayden, Caelan Lapointe, Ian Grooms, Gregory B. Rieker, Peter E. Hamlington Approximate Bayesian Computation (ABC) is a powerful tool that allows sparse experimental or other ``truth'' data to be used for the prediction of unknown model parameters in numerical simulations of real-world engineering systems. In this presentation, we introduce the ABC approach and then use ABC to predict unknown inflow conditions in simulations of a two-dimensional (2D) turbulent, high-temperature buoyant jet. For this test case, truth data are obtained from a simulation with known boundary conditions and problem parameters. Using spatially-sparse temperature statistics from the 2D buoyant jet truth simulation, we show that the ABC method provides accurate predictions of the true jet inflow temperature. The success of the ABC approach in the present test suggests that ABC is a useful and versatile tool for engineering fluid dynamics research. [Preview Abstract] |
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