scholarly journals Proper orthogonal and dynamic mode decomposition of sunspot data

2020 ◽  
Vol 379 (2190) ◽  
pp. 20200181 ◽  
Author(s):  
A. B. Albidah ◽  
W. Brevis ◽  
V. Fedun ◽  
I. Ballai ◽  
D. B. Jess ◽  
...  
Keyword(s):  
High Resolution ◽  
Complex Structure ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Cross Sectional ◽  
Wave Dynamics ◽  
Mode Decomposition ◽  
Sunspot Data ◽  
Sectional Shape ◽  
Proper Orthogonal

High-resolution solar observations show the complex structure of the magnetohydrodynamic (MHD) wave motion. We apply the techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) to identify the dominant MHD wave modes in a sunspot using the intensity time series. The POD technique was used to find modes that are spatially orthogonal, whereas the DMD technique identifies temporal orthogonality. Here, we show that the combined POD and DMD approaches can successfully identify both sausage and kink modes in a sunspot umbra with an approximately circular cross-sectional shape. This article is part of the Theo Murphy meeting issue ‘High-resolution wave dynamics in the lower solar atmosphere’.

Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

2020 ◽  
Author(s):  
Christian Amor ◽  
José M Pérez ◽  
Philipp Schlatter ◽  
Ricardo Vinuesa ◽  
Soledad Le Clainche
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Turbulent Wake ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Square Cylinder ◽  
Complex Flow ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

Abstract This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.

scholarly journals Analysis of V-Gutter Reacting Flow Dynamics Using Proper Orthogonal and Dynamic Mode Decompositions

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4886 ◽  
Author(s):  
Yang Yang ◽  
Xiao Liu ◽  
Zhihao Zhang
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Reacting Flow ◽  
Eddy Simulation ◽  
Mode Decomposition ◽  
Wake Instability ◽  
Shedding Frequency ◽  
Proper Orthogonal

The current work is focused on investigating the potential of data-driven post-processing techniques, including proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) for flame dynamics. Large-eddy simulation (LES) of a V-gutter premixed flame was performed with two Reynolds numbers. The flame transfer function (FTF) was calculated. The POD and DMD were used for the analysis of the flame structures, wake shedding frequency, etc. The results acquired by different methods were also compared. The FTF results indicate that the flames have proportional, inertial, and delay components. The POD method could capture the shedding wake motion and shear layer motion. The excited DMD modes corresponded to the shear layer flames’ swing and convect motions in certain directions. Both POD and DMD could help to identify the wake shedding frequency. However, this large-scale flame oscillation is not presented in the FTF results. The negative growth rates of the decomposed mode confirm that the shear layer stabilized flame was more stable than the flame possessing a wake instability. The corresponding combustor design could be guided by the above results.

Analysis of dynamic stall flow field of high bypass fan rotor based on airworthiness certification

2020 ◽  
Vol 234 (11) ◽  
pp. 1757-1769
Author(s):  
Kai Zhang ◽  
AJ Wang
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Field Data ◽  
Decomposition Methods ◽  
Modal Identification ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Complex Flow ◽  
Mode Decomposition ◽  
Proper Orthogonal

In order to ensure flight safety, the stall test is one of the most important steps in the airworthiness certification phase of civil aircraft. The twisted-swept fan is one of the most important components of the high bypass ratio engine. The unsteady flow field of the fan rotor stall condition is obtained by numerical simulation. At the same time, the time series flow field data of the stall condition flow field is acquired. The modal analysis of the unsteady flow field at stall condition was performed using the dynamic mode decomposition and proper orthogonal decomposition methods. Through modal identification of a large number of unsteady flow field data, the eigenvalues and corresponding modal information about the unsteady flow field change process are obtained. Finally, the evolution process of the unsteady flow field of the fan rotor under stall condition is visually demonstrated, and the coherent structures of different scales in the complex flow field under stall condition are revealed.

scholarly journals Recursive dynamic mode decomposition of transient and post-transient wake flows

2016 ◽  
Vol 809 ◽  
pp. 843-872 ◽  
Author(s):  
Bernd R. Noack ◽  
Witold Stankiewicz ◽  
Marek Morzyński ◽  
Peter J. Schmid
Keyword(s):  
Dynamic Mode Decomposition ◽  
Attractive Alternative ◽  
Dynamic Mode ◽  
Cylinder Wake ◽  
Frequency Content ◽  
Mode Decomposition ◽  
Nonlinear Transient ◽  
Galerkin Models ◽  
Nonlinear Transient Dynamics ◽  
Proper Orthogonal

A novel data-driven modal decomposition of fluid flow is proposed, comprising key features of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The first mode is the normalized real or imaginary part of the DMD mode that minimizes the time-averaged residual. The $N$th mode is defined recursively in an analogous manner based on the residual of an expansion using the first $N-1$ modes. The resulting recursive DMD (RDMD) modes are orthogonal by construction, retain pure frequency content and aim at low residual. Recursive DMD is applied to transient cylinder wake data and is benchmarked against POD and optimized DMD (Chen et al., J. Nonlinear Sci., vol. 22, 2012, pp. 887–915) for the same snapshot sequence. Unlike POD modes, RDMD structures are shown to have purer frequency content while retaining a residual of comparable order to POD. In contrast to DMD, with exponentially growing or decaying oscillatory amplitudes, RDMD clearly identifies initial, maximum and final fluctuation levels. Intriguingly, RDMD outperforms both POD and DMD in the limit-cycle resolution from the same snapshots. Robustness of these observations is demonstrated for other parameters of the cylinder wake and for a more complex wake behind three rotating cylinders. Recursive DMD is proposed as an attractive alternative to POD and DMD for empirical Galerkin models, in particular for nonlinear transient dynamics.

scholarly journals From snapshots to modal expansions – bridging low residuals and pure frequencies

2016 ◽  
Vol 802 ◽  
pp. 1-4 ◽  
Author(s):  
Bernd R. Noack
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Operating Conditions ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Simple Method ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Optimality Property ◽  
Proper Orthogonal

Data-driven low-order modelling has been enjoying rapid advances in fluid mechanics. Arguably, Sirovich (Q. Appl. Maths, vol. XLV, 1987, pp. 561–571) started these developments with snapshot proper orthogonal decomposition, a particularly simple method. The resulting reduced-order models provide valuable insights into flow physics, allow inexpensive explorations of dynamics and operating conditions, and enable model-based control design. A winning argument for proper orthogonal decomposition (POD) is the optimality property, i.e. the guarantee of the least residual for a given number of modes. The price is unpleasant frequency mixing in the modes which complicates their physical interpretation. In contrast, temporal Fourier modes and dynamic mode decomposition (DMD) provide pure frequency dynamics but lose the orthonormality and optimality property of POD. Sieber et al. (J. Fluid Mech., vol. 792, 2016, pp. 798–828) bridge the least residual and pure frequency behaviour with an ingenious interpolation, called spectral proper orthogonal decomposition (SPOD). This article puts the achievement of the TU Berlin authors in perspective, illustrating the potential of SPOD and the challenges ahead.

Emulsion Jet in Crossflow Atomization Characteristics and Dynamics

2018 ◽  
Author(s):  
Scott B. Leask ◽  
Vincent G. McDonell ◽  
Scott Samuelsen
Keyword(s):  
High Speed ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Cross Sectional ◽  
Neat Water ◽  
Jet In Crossflow ◽  
Video Recordings ◽  
Mode Decomposition ◽  
Liquid Behavior ◽  
Atomization Characteristics

This work presents the atomization characteristics and dynamics of water-in-heptane (W/H) emulsions injected into a gaseous crossflow. W/H mixtures were tested while varying momentum flux ratios and aerodynamic Weber numbers. Different injector orifice diameters and orifice length-to-diameter ratios were used to test the generality of the results. The atomization properties of W/H mixtures were compared with properties of neat water and neat heptane to evaluate the effect of an emulsion on droplet sizing, cross-sectional stability and dispersion, and jet penetration depth. Liquid dynamics were extracted through analyzing instantaneous spray measurements and dynamic mode decomposition (DMD) on high-speed video recordings of the atomization processes. Correlations were proposed to establish preliminary relationships between fundamental spray processes and test conditions. These correlations allowed for emulsion behavior to be compared with neat liquid behavior. The use of emulsions induces greater spray instability than through using neat liquids, likely due to the difficulty in injecting a stable emulsion. Neat liquid correlations were produced and successfully predicted various spray measurements. These correlations, however, indicate that injector geometry has an effect on spray properties which need to be addressed independently. The emulsions are unable to adhere to the neat liquid correlations suggesting that an increased number of correlation terms are required to adequately predict emulsion behavior.

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