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.

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 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.

scholarly journals Comparison of the Atmospheric 200 hPa Jet’s Analyses between Proper Orthogonal Decomposition and Advanced Dynamic Mode Decomposition Method

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Mei Gao ◽  
Xiao-Qun Cao ◽  
Bai-Nian Liu ◽  
Zi-Hang Han ◽  
Shi-Cheng Hou ◽  
...  
Keyword(s):  
Decomposition Method ◽  
Jet Flow ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Reduced Order Models ◽  
Dynamic Information ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

In this paper, a frequently employed technique named the sparsity-promoting dynamic mode decomposition (SPDMD) is proposed to analyze the velocity fields of atmospheric motion. The dynamic mode decomposition method (DMD) is an effective technique to extract dynamic information from flow fields that is generated from direct experiment measurements or numerical simulation and has been broadly employed to study the dynamics of the flow, to achieve a reduced-order model (ROM) of the complex high dimensional flow field, and even to predict the evolution of the flow in a short time in the future. However, for standard DMD, it is hard to determine which modes are the most physically relevant, unlike the proper orthogonal decomposition (POD) method which ranks the decomposed modes according to their energy content. The advanced modal decomposition method SPDMD is a variant of the standard DMD, which is capable of determining the modes that can be used to achieve a high-quality approximation of the given field. It is novel to introduce the SPDMD to analyze the atmospheric flow field. In this study, SPDMD is applied to extract essential dynamic information from the 200 hPa jet flow, and the decomposed results are compared with the POD method. To further demonstrate the extraction effect of POD/SPDMD methods on the 200 hPa jet flow characteristics, the POD/SPDMD reduced-order models are constructed, respectively. The results show that both modal decomposition methods successfully extract the underlying coherent structures from the 200 hPa jet flow. And the DMD method provides additional information on the modal properties, such as temporal frequency and growth rate of each mode which can be used to identify the stability of the modes. It is also found that a fewer order of modes determined by the SPDMD method can capture nearly the same dynamic information of the jet flow as the POD method. Furthermore, from the quantitative comparisons between the POD and SPDMD reduced-order models, the latter provides a higher precision than the former, especially when the number of modes is small.

scholarly journals Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Brenton T. Hall ◽  
Ching-Shan Chou ◽  
Jen-Ping Chen
Keyword(s):  
Memory Storage ◽  
Dynamic Mode Decomposition ◽  
Dynamics Simulation ◽  
Dynamic Mode ◽  
Compressor Rotor ◽  
Reduction Techniques ◽  
Mode Decomposition ◽  
Proper Orthogonal ◽  
Diffusion Simulation ◽  
Local Research

Partial Differential Equation simulations can produce large amounts of data. These datasets are very slow to transfer, for example, from an off-site supercomputer to a local research facility. There have been many model reduction techniques that have been proposed and utilized over the past three decades. Two of the most popular techniques are the Proper Orthogonal Decomposition and Dynamic Mode Decomposition. Nonuniform Dynamic Mode Decomposition (NU-DMD) is one of the newest techniques as it was introduced in 2015 by Guéniat et al. In this paper, the NU-DMD’s mathematics are explained in detail, and three versions of the NU-DMD’s algorithm are outlined. Furthermore, different numerical experiments were performed on the NU-DMD to ascertain its behavior with respect to errors, memory usage, and computational efficiency. It was shown that the NU-DMD could reduce an advection-diffusion simulation to 6.0075% of its original memory storage size. The NU-DMD was also applied to a computational fluid dynamics simulation of a NASA single-stage compressor rotor, which resulted in a reduced model of the simulation (using only three of the five simulation variables) that used only about 4.67% of the full simulation’s storage with an overall average percent error of 8.90%. It was concluded that the NU-DMD, if used appropriately, could be used to possibly reduce a model that uses 400 GB of memory to a model that uses as little as 18.67 GB with less than 9% error. Further conclusions were made about how to best implement the NU-DMD.

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