High-fidelity emulation of spatiotemporally evolving flow dynamics
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This dissertation utilizes a comprehensive interdisciplinary approach to demonstrate a paradigm for a novel design strategy for new generation engineering. Computational fluid dynamics (CFD), reduced-basis modeling, statistics, uncertainty quantification, and machine learning are employed to develop this strategy. In the real world, designing a new product or device may require months or years. It is therefore crucial to develop more time-efficient strategies for reducing investigation and development costs. Using a rocket engine injector as an example, this dissertation addresses fundamental issues critical to the development of an efficient and robust capability for understanding, analyzing, and predicting fluid dynamics and enhancing the interpretation of physical characteristics for future propulsion systems. The presented work demonstrates recent breakthroughs in modeling and data analytics techniques to substantially improve modeling capabilities at many levels. Due to the high-pressure requirements of cryogenic propellants, such as those of liquid rocket engines, physical experiments are expensive. Furthermore, it is difficult to observe the physical mechanisms of the combustion process via optical diagnostics. High-fidelity CFD, such as large eddy simulations (LES), has been employed for decades to better capture the flowfield and combustion characteristics that occur in rocket engines, but these computationally expensive calculations are impractical for design purposes. A 2D axisymmetric LES case, for instance, can take 6-14 days with 200-350 CPU cores in parallelization, which is extremely costly and time-inefficient. Further, a full-size 3D LES case with the same grid resolution and CPU cores as a 2D case may take over a month to complete. To develop an efficient design strategy for new generation engines, therefore, an interdisciplinary revolution, spanning fields from statistics to engineering, is needed. Taking a swirl injector as a demonstration example, Design of Experiment (DoE) is formulated based on few pivotal geometric design parameters and the corresponding ranges for each of these parameters. Drawing upon prior knowledge of the major contributing geometric parameters, the sample size is determined based on semi-empirical approaches, with a recommended six to ten simulations per design variable. This approach facilitates the design process and reduces the number of total sample points required to efficiently scrutinize the design space. To effectively and efficiently examine the physical mechanisms and dynamic details of instantaneous flow features for a new swirl injector design, serial novel data reduction methods are developed and employed to reduce the data size while keeping dominating physics information. These methods include low-fidelity models such as common proper orthogonal decomposition (CPOD), kernel-smoothed proper orthogonal decomposition (KSPOD), and common kernel-smoothed proper orthogonal decomposition (CKSPOD). The reduced data are used to train the high-fidelity simulation models, and finally a kriging-based emulator is applied to predict the dynamics of the flowfield with various spatiotemporal characteristics, based on the new geometric design of an injector. These representative metamodeling techniques are found to be substantially improved the modeling capabilities at all levels. Recent breakthroughs in modeling and data analytics successfully capture turbulent dynamics in a swirl injector and yield predictions more quickly than high-fidelity simulations. Most notably, CKSPOD, the latest proposed emulator, can achieve a turnaround time 34,000 times faster than LES in evaluating a new design point across 1,000 snapshots with only 10 CPU cores. Furthermore, the presented work conducts uncertainty quantification (UQ) theorems to examine the uncertainties (i.e., the accuracy and precision) of all models. Results of the UQ analysis reveal not only that the proposed models are qualitatively good comparing with simulation but also that they perform quantitatively well for spatiotemporal predictions. The work described in this dissertation produces a suite of multi-fidelity modeling techniques for effective and efficient assessment of the dynamic behaviors of a practical system, with geometric details over a broad range of operating conditions. This approach can also be applied to other engineering systems involving complex turbulence dynamics, nano/micro fluid dynamics, combustion instabilities, manufactory industry, geological exploration, biomedical device invention, medicine, and other fields. It is noted that this dissertation interpolates materials from three published or submitted papers [1-3] by Simon Mak, Chih-Li Sung, C. F. Jeff Wu, Xingjian Wang, Shiang-Ting Yeah, Vigor Yang, Liwei Zhang, and the author of this dissertation (note: all names are listed in alphabetical order by the surnames). Partial results for the CPOD-based emulation of the presented work have been published in JASA and AIAA J. in 2017  and 2018  respectively, with the author of this dissertation as a co-author who contributes most of the preliminary data physical mechanism exploration, data work organization, and partial coding works. Partial research results for the KSPOD in the presented work have been submitted to J. Comp. Phys. in early 2018 and are currently under review, with the author of this dissertation as first author . Meanwhile, partial results for the CKSPOD in the presented work are currently being prepared for submission to J. Comp. Phys. as a first-author paper.