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Register a new userKernel-smoothed proper orthogonal decomposition (KSPOD)-based emulation for prediction of spatiotemporally evolving flow dynamics
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Added by
Simon Mak
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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This interdisciplinary study, which combines machine learning, statistical methodologies, high-fidelity simulations, and flow physics, demonstrates a new process for building an efficient surrogate model for predicting spatiotemporally evolving flow dynamics. In our previous work, a common-grid proper-orthogonal-decomposition (CPOD) technique was developed to establish a physics-based surrogate (emulation) model for prediction of mean flowfields and design exploration over a wide parameter space. The CPOD technique is substantially improved upon here using a kernel-smoothed POD (KSPOD) technique, which leverages kriging-based weighted functions from the design matrix. The resultant emulation model is then trained using a dataset obtained through high-fidelity simulations. As an example, the flow evolution in a swirl injector is considered for a wide range of design parameters and operating conditions. The KSPOD-based emulation model performs well, and can faithfully capture the spatiotemporal flow dynamics. The model enables effective design surveys utilizing high-fidelity simulation data, achieving a turnaround time for evaluating new design points that is 42,000 times faster than the original simulation.
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In the present study, we propose a new surrogate model, called common kernel-smoothed proper orthogonal decomposition (CKSPOD), to efficiently emulate the spatiotemporal evolution of fluid flow dynamics. The proposed surrogate model integrates and extends recent developments in Gaussian process learning, high-fidelity simulations, projection-based model reduction, uncertainty quantification, and experimental design, rendering a systematic, multidisciplinary framework. The novelty of the CKSPOD emulation lies in the construction of a common Gram matrix, which results from the Hadamard product of Gram matrices of all observed design settings. The Gram matrix is a spatially averaged temporal correlation matrix and contains the temporal dynamics of the corresponding sampling point. The common Gram matrix synthesizes the temporal dynamics by transferring POD modes into spatial functions at each observed design setting, which remedies the phase-difference issue encountered in the kernel-smoothed POD (KSPOD) emulation, a recent fluid flow emulator proposed in Chang et al. (2020). The CKSPOD methodology is demonstrated through a model study of flow dynamics of swirl injectors with three design parameters. A total of 30 training design settings and 8 validation design settings are included. Both qualitative and quantitative results show that the CKSPOD emulation outperforms the KSPOD emulation for all validation cases, and is capable of capturing small-scale wave structures on the liquid-film surface faithfully. The turbulent kinetic energy prediction using CKSPOD reveals lower predictive uncertainty than KSPOD, thereby allowing for more accurate and precise flow predictions. The turnaround time of the CKSPOD emulation is about 5 orders of magnitude faster than the corresponding high-fidelity simulation, which enables an efficient and scalable framework for design exploration and optimization.
The present study proposes a data-driven framework trained with high-fidelity simulation results to facilitate decision making for combustor designs. At its core is a surrogate model employing a machine-learning technique called kriging, which is combined with data-driven basis functions to extract and model the underlying coherent structures. This emulation framework encompasses key design parameter sensitivity analysis, physics-guided classification of design parameter sets, and flow evolution modeling for efficient design survey. To better inform the model of quantifiable physical knowledge, a sensitivity analysis using Sobol indices and a decision tree are incorporated into the framework. This information improves the surrogate model training process, which employs basis functions as regression functions over the design space for the kriging model. The novelty of the proposed approach is the construction of the model through Common Proper Orthogonal Decomposition, which allows for data-reduction and extraction of common coherent structures. The accuracy of prediction of mean flow features for new swirl injector designs is assessed and the dynamic flowfield is captured in the form of power spectrum densities. This data-driven framework also demonstrates the uncertainty quantification of predictions, providing a metric for model fit. The significantly reduced computation time required for evaluating new design points enables efficient survey of the design space.
An extension of Proper Orthogonal Decomposition is applied to the wall layer of a turbulent channel flow (Re {tau} = 590), so that empirical eigenfunctions are defined in both space and time. Due to the statistical symmetries of the flow, the igenfunctions are associated with individual wavenumbers and frequencies. Self-similarity of the dominant eigenfunctions, consistent with wall-attached structures transferring energy into the core region, is established. The most energetic modes are characterized by a fundamental time scale in the range 200-300 viscous wall units. The full spatio-temporal decomposition provides a natural measure of the convection velocity of structures, with a characteristic value of 12 u {tau} in the wall layer. Finally, we show that the energy budget can be split into specific contributions for each mode, which provides a closed-form expression for nonlinear effects.
The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by three-dimensional direct numerical simulations, is limited owing to its computational complexity. Here, we propose a wavelet-based adaptive version of the POD (the wPOD), in order to overcome this limitation. The amount of data to be analyzed is reduced by compressing them using biorthogonal wavelets, yielding a sparse representation while conveniently providing control of the compression error. Numerical analysis shows how the distinct error contributions of wavelet compression and POD truncation can be balanced under certain assumptions, allowing us to efficiently process high-resolution data from three-dimensional simulations of flow problems. Using a synthetic academic test case, we compare our algorithm with the randomized singular value decomposition. Furthermore, we demonstrate the ability of our method analyzing data of a 2D wake flow and a 3D flow generated by a flapping insect computed with direct numerical simulation.
Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kind of systems. It extends the proper orthogonal decomposition (POD) by introducing time-dependent shifts of the snapshot matrix. The approach, called shifted proper orthogonal decomposition (sPOD), features a determination of the {it multiple} transport velocities and a separation of these. One- and two-dimensional test examples reveal the good performance of the sPOD for transport-dominated phenomena and its superiority in comparison to the POD.
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