Computational fluid dynamics (CFD) has been widely used to simulate turbulent flows. Although an increased availability of computational resources has enabled high-fidelity simulations (e.g. large eddy simulation and direct numerical simulation) of turbulent flows, the Reynolds-Averaged Navier-Stokes (RANS) equations based models are still the dominant tools for industrial applications. However, the predictive capability of RANS models is limited by potential inaccuracies driven by hypotheses in the Reynolds stress closure. With the ever-increasing use of RANS simulations in mission-critical applications, the estimation and reduction of model-form uncertainties in RANS models have attracted attention in the turbulence modeling community. In this work, I focus on estimating uncertainties stemming from the RANS turbulence closure and calibrating discrepancies in the modeled Reynolds stresses to improve the predictive capability of RANS models. Both on-line and off-line data are utilized to achieve this goal. The main contributions of this dissertation can be summarized as follows: First, a physics-based, data-driven Bayesian framework is developed for estimating and reducing model-form uncertainties in RANS simulations. An iterative ensemble Kalman method is employed to assimilate sparse on-line measurement data and empirical prior knowledge for a full-field inversion. The merits of incorporating prior knowledge and physical constraints in calibrating RANS model discrepancies are demonstrated and discussed. Second, a random matrix theoretic framework is proposed for estimating model-form uncertainties in RANS simulations. Maximum entropy principle is employed to identify the probability distribution that satisfies given constraints but without introducing artificial information. Objective prior perturbations of RANS-predicted Reynolds stresses in physical projections are provided based on comparisons between physics-based and random matrix theoretic approaches. Finally, a physics-informed, machine learning framework towards predictive RANS turbulence modeling is proposed. The functional forms of model discrepancies with respect to mean flow features are extracted from the off-line database of closely related flows based on machine learning algorithms. The RANS-modeled Reynolds stresses of prediction flows can be significantly improved by the trained discrepancy function, which is an important step towards the predictive turbulence modeling. / Ph. D. / Turbulence modeling is a critical component in computational fluid dynamics (CFD) simulations of industrial flows. Despite the significant growth in computational resources over the past two decades, the time-resolved high-fidelity simulations (e.g., large eddy simulation and direct numerical simulation) are not feasible for engineering applications. Therefore, the small-scale turbulent velocity fluctuations have to resort to the time-averaging modeling. Reynolds-averaged Navier-Stokes (RANS) equations based turbulence models describe the averaged flow quantities for turbulent flows and are believed to be the dominant tools for industrial applications in coming decades. However, for many practical flows, the predictive accuracy of RANS models is largely limited by the model-form uncertainties stemming from the potential inaccuracies in the Reynolds stress closure. As RANS models are used in the design and safety evaluation of many mission-critical systems, such as airplanes and nuclear power plants, properly estimating and reducing these model uncertainties are of significant importance. In this work, I focus on estimating uncertainties stemming from the RANS turbulence closure and calibrating discrepancies in the modeled Reynolds stresses to improve the predictive capability of RANS models. Several data-driven approaches based on stateof-the-art data assimilation and machine learning algorithms are proposed to achieve this goal by leveraging the use of on-line and off-line high-fidelity data. Numerical simulations of several canonical flows are used to demonstrate the merits of the proposed approaches. Moreover, the proposed methods also have implications in many fields in which the governing equations are well understood, but the model uncertainties come from unresolved physical processes.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/77035 |
| Date | 05 April 2017 |
| Creators | Wang, Jianxun |
| Contributors | Aerospace and Ocean Engineering, Xiao, Heng, Ma, Lin, Roy, Christopher J., Weiss, Robert |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
Page generated in 0.0018 seconds