Data Assimilation of Steam Flow Through a Control Valve Using Ensemble Kalman Filter

Fang, Peixun; He, Chuangxin; Wang, Peng; Xu, Shijie

doi:10.1115/1.4050799

Cited by 6 publications

(1 citation statement)

References 22 publications

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“…The commonly adopted methodology of DA for fluid mechanics include temporally continuous data assimilation (TCDA) through direct data embedding [1,2,8,9], spatial and Fourier nudging [10,11], Kalman filtering-based methods [3,[12][13][14][15][16][17][18], adjoint-based variational methods [19][20][21][22][23][24], forward sensitivity method [25], etc. Recently, due to the prosperity of the machine-learning techniques [26][27][28][29][30][31][32][33][34], artificial neural networks have also become powerful tools for DA [13,35].…”

Section: Introductionmentioning

confidence: 99%

Temporally sparse data assimilation for the small-scale reconstruction of turbulence

Wang,

Yuan,

Xie

et al. 2022

Preprint

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A temporally sparse data assimilation (TSDA) strategy for direct numerical simulation (DNS) of incompressible isotropic turbulence (HIT) is proposed using large assimilation time steps. It is shown that the time step in the TSDA can be relaxed to a much coarser level (1 ∼ 2 orders larger) than the existing temporally continuous data assimilation (TCDA) while the accuracy is still maintained. Furthermore, the one-step data assimilation (ODA) is analyzed to explore the mechanism of the TSDA. It is shown that the relaxation effect for errors above the assimilation wavenumber k a is responsible for the faster error decaying rate of the TSDA than the TCDA. This relaxation effect is assumed to be related to the errors contained in the large scales. These largescale errors can make the errors in the small scales (large wavenumbers k > k a ) decay slower with the TCDA than the TSDA. This mechanism is further confirmed by incorporating different levels of errors in the large scales of the reference velocity field. The advantage of the TSDA is found to grow with the magnitude of the incorporated errors. Thus, it is potentially more beneficial to adopt the large-step assimilation strategy if the reference data contains non-negligible errors. Finally, an outstanding issue raised in previous works regarding the possibility of recovering the dynamics of sub-Kolmogorov scales using DNS data at Kolmogorov scale resolution is also discussed.

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Section: Introductionmentioning

confidence: 99%

Temporally sparse data assimilation for the small-scale reconstruction of turbulence

Wang,

Yuan,

Xie

et al. 2022

Preprint

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show abstract

Temporally sparse data assimilation for the small-scale reconstruction of turbulence

et al. 2022

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Previous works have shown that the small-scale information of incompressible homogeneous isotropic turbulence (HIT) is fully recoverable as long as sufficient large-scale structures are continuously enforced through temporally continuous data assimilation (TCDA). In the current work, we show that the assimilation time step can be relaxed to values about 1 ∼ 2 orders larger than that for TCDA, using a temporally sparse data assimilation (TSDA) strategy, while the accuracy is still maintained or even slightly better in the presence of non-negligible large-scale errors. The one-step data assimilation (ODA) is examined to unravel the mechanism of TSDA. It is shown that the relaxation effect for errors above the assimilation wavenumber ka is responsible for the error decay in ODA. Meanwhile, The errors contained in the large scales can propagate into small scales and make the high-wavenumber (k>ka) error noise decay slower with TCDA than TSDA. This mechanism is further confirmed by incorporating different levels of errors in the large scales of the reference flow field. The advantage of TSDA is found to grow with the magnitude of the incorporated errors. Thus, it is potentially more beneficial to adopt TSDA if the reference data contains non-negligible errors. Finally, an outstanding issue raised in previous works regarding the possibility of recovering the dynamics of sub-Kolmogorov scales using direct numerical simulation (DNS) data at Kolmogorov scale resolution is also discussed.

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A further investigation on the data assimilation-based small-scale reconstruction of turbulence

2023

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Existing works have shown that the small-scale errors of turbulence can be completely eliminated through data assimilation (DA), provided that all the large-scale Fourier modes below a critical wavenumber $k_c \approx 0.2 \eta^{-1}$ are continuously enforced, where $\eta$ is the Kolmogorov length scale. Here, we further explore the DA-based small-scale reconstruction problem for which the large-scale data is insufficient. Under such conditions, an unexpected artificial jump in the energy spectrum is observed. To alleviate this issue and improve the reconstruction accuracy, several approaches have been attempted, including ensemble averaged assimilation, temporally sparse data assimilation (TSDA) and filtering the penalty term in the assimilation. It is shown that ensemble averaging can tangibly reduce the reconstruction error, but the resulted energy spectrum is invariably lower than the true spectrum; TSDA can effectively remove the jump in the energy spectrum, but the reduction of the reconstruction error is limited; Filtering the penalty term can also rectify the energy spectrum, but it makes the reconstruction error larger. Based on these observations, we re-scale the ensemble averaged solution according to the rectified energy spectrum. Both the energy spectrum and the small-scale reconstruction accuracy have been improved by the re-scaled ensemble average (RES-EA) method. Further, we also test the current approach in the spatial nudging-based reconstruction of turbulence. Again, enhanced predictions are obtained for both the energy spectrum and the instantaneous turbulent field, invariably demonstrating the effectiveness and robustness of the proposed method.

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Data Assimilation of Steam Flow Through a Control Valve Using Ensemble Kalman Filter

Cited by 6 publications

References 22 publications

Temporally sparse data assimilation for the small-scale reconstruction of turbulence

Temporally sparse data assimilation for the small-scale reconstruction of turbulence

Temporally sparse data assimilation for the small-scale reconstruction of turbulence

A further investigation on the data assimilation-based small-scale reconstruction of turbulence

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