scholarly journals Identification of coexisting dynamics in boundary layer flows through proper orthogonal decomposition with weighting matrices

Meccanica ◽  
2021 ◽  
Author(s):  
Matteo Dellacasagrande ◽  
Dario Barsi ◽  
Patrizia Bagnerini ◽  
Davide Lengani ◽  
Daniele Simoni
Keyword(s):  
Experimental Data ◽  
Proper Orthogonal Decomposition ◽  
Fourier Transforms ◽  
Free Stream ◽  
Numerical Test ◽  
Separated Flow ◽  
Orthogonal Decomposition ◽  
Inner Product ◽  
Test Case ◽  
Proper Orthogonal

AbstractA different version of the classic proper orthogonal decomposition (POD) procedure introducing spatial and temporal weighting matrices is proposed. Furthermore, a newly defined non-Euclidean (NE) inner product that retain similarities with the POD is introduced in the paper. The aim is to emphasize fluctuation events localized in spatio-temporal regions with low kinetic energy magnitude, which are not highlighted by the classic POD. The different variants proposed in this work are applied to numerical and experimental data, highlighting analogies and differences with respect to the classic and other normalized variants of POD available in the literature. The numerical test case provides a noise-free environment of the strongly organized vortex shedding behind a cylinder. Conversely, experimental data describing transitional boundary layers are used to test the capability of the procedures in strongly not uniform flows. By-pass and separated flow transition processes developing with high free-stream disturbances have been considered. In both cases streaky structures are expected to interact with other vortical structures (i.e. free-stream vortices in the by-pass case and Kelvin–Helmholtz rolls in the separated type) that carry a significant different amount of energy. Modes obtained by the non-Euclidean POD (NE-POD) procedure (where weighted projections are considered) are shown to better extract low energy events sparse in time and space with respect to modes extracted by other variants. Moreover, NE-POD modes are further decomposed as a combination of Fourier transforms of the related temporal coefficients and the normalized data ensemble to isolate the frequency content of each mode.

scholarly journals Comparative Study on Modal Decomposition Methods of Unsteady Separated Flow in Compressor Cascade

2020 ◽  
Vol 38 (1) ◽  
pp. 121-129
Author(s):  
Jiawei Hu ◽  
Yangang Wang ◽  
Hanru Liu ◽  
Weixiong Chen ◽  
Yong Xu
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Separated Flow ◽  
Decomposition Methods ◽  
High Load ◽  
Orthogonal Decomposition ◽  
Single Frequency ◽  
Compressor Cascade ◽  
Modal Decomposition ◽  
Cascade Flow ◽  
Proper Orthogonal

The present work investigated the vortex structure and fluctuation frequency characteristics generated by boundary layer separation of a high-load compressor cascade using modal decomposition methods. The dominant modes and dynamic behaviors of unsteady flow in the cascade were obtained, and the differences of three modal decomposition methods (Proper Orthogonal Decomposition, Dynamic Mode Decomposition and Spectral Proper Orthogonal Decomposition) in feature recognition of cascade flow were discussed. The results show that:(1) The POD method can accurately extract the dominant spatial structure of the flow field, but the modal coefficients are multi-frequency coupled, which makes the dominant modal characteristics of cascade flow unclear. (2) The standard DMD method can obtain the spatial-temporal single frequency mode of cascade flow, as well as their growth rates and frequencies. However, this method is likely to capture the suboptimal mode of large amplitude with large attenuation rate, and fails to obtain the high-frequency coherent structure, which makes it impossible to obtain the dominant feature with limited mode number. (3) The SPOD method, based on spectral characteristics, can obtain spatial and temporal single frequency modes, and there is no modal screening problem. The use of spectral estimation method (SPOD) reduces the sensitivity to numerical noise. This method can obtain the low-rank behavior of cascade flow, which is helpful to understand cascade flow mechanisms. Therefore, SPOD method is more advantageous for the modal analysis of unsteady separated flow in high-load compressor cascade.

Permuted proper orthogonal decomposition for analysis of advecting structures

2021 ◽  
Vol 930 ◽  
Author(s):  
Hanna M. Ek ◽  
Vedanth Nair ◽  
Christopher M. Douglas ◽  
Timothy C. Lieuwen ◽  
Benjamin L. Emerson
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Convergence Rates ◽  
Separation Of Variables ◽  
Cross Flow ◽  
Orthogonal Decomposition ◽  
Inner Product ◽  
Turbulent Shear ◽  
Jet In Cross Flow ◽  
Flow Capture ◽  
Proper Orthogonal

Flow data are often decomposed using proper orthogonal decomposition (POD) of the space–time separated form, $\boldsymbol {q}'\left (\boldsymbol {x},t\right )=\sum _j a_j\left (t\right )\boldsymbol {\phi }_j\left (\boldsymbol {x}\right )$ , which targets spatially correlated flow structures in an optimal manner. This paper analyses permuted POD (PPOD), which decomposes data as $\boldsymbol {q}'\left (\boldsymbol {x},t\right )=\sum _j a_j\left (\boldsymbol {n}\right )\boldsymbol {\phi }_j\left (s,t\right )$ , where $\boldsymbol {x}=(s,\boldsymbol {n})$ is a general spatial coordinate system, $s$ is the coordinate along the bulk advection direction and $\boldsymbol {n}=(n_1,n_2)$ are along mutually orthogonal directions normal to the advection characteristic. This separation of variables is associated with a fundamentally different inner product space for which PPOD is optimal and targets correlations in $s,t$ space. This paper presents mathematical features of PPOD, followed by analysis of three experimental datasets from high-Reynolds-number, turbulent shear flows: a wake, a swirling annular jet and a jet in cross-flow. In the wake and swirling jet cases, the leading PPOD and space-only POD modes focus on similar features but differ in convergence rates and fidelity in capturing spatial and temporal information. In contrast, the leading PPOD and space-only POD modes for the jet in cross-flow capture completely different features – advecting shear layer structures and flapping of the jet column, respectively. This example demonstrates how the different inner product spaces, which order the PPOD and space-only POD modes according to different measures of variance, provide unique ‘lenses’ into features of advection-dominated flows, allowing complementary insights.

MODEL REDUCTION FOR FLUIDS, USING BALANCED PROPER ORTHOGONAL DECOMPOSITION

2005 ◽  
Vol 15 (03) ◽  
pp. 997-1013 ◽  
Author(s):  
C. W. ROWLEY
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Model Reduction ◽  
Projection Method ◽  
Computational Cost ◽  
Plane Channel ◽  
Orthogonal Decomposition ◽  
Inner Product ◽  
High Dimensional ◽  
Balanced Truncation ◽  
Proper Orthogonal

Many of the tools of dynamical systems and control theory have gone largely unused for fluids, because the governing equations are so dynamically complex, both high-dimensional and nonlinear. Model reduction involves finding low-dimensional models that approximate the full high-dimensional dynamics. This paper compares three different methods of model reduction: proper orthogonal decomposition (POD), balanced truncation, and a method called balanced POD. Balanced truncation produces better reduced-order models than POD, but is not computationally tractable for very large systems. Balanced POD is a tractable method for computing approximate balanced truncations, that has computational cost similar to that of POD. The method presented here is a variation of existing methods using empirical Gramians, and the main contributions of the present paper are a version of the method of snapshots that allows one to compute balancing transformations directly, without separate reduction of the Gramians; and an output projection method, which allows tractable computation even when the number of outputs is large. The output projection method requires minimal additional computation, and has a priori error bounds that can guide the choice of rank of the projection. Connections between POD and balanced truncation are also illuminated: in particular, balanced truncation may be viewed as POD of a particular dataset, using the observability Gramian as an inner product. The three methods are illustrated on a numerical example, the linearized flow in a plane channel.

Experimental Investigation of Transitional Natural Convection in a Cube Using Particle Image Velocimetry—Part II: Turbulence Quantities and Proper Orthogonal Decomposition

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Marios D. Georgiou ◽  
Aristides M. Bonanos ◽  
John G. Georgiadis
Keyword(s):  
Experimental Data ◽  
Experimental Investigation ◽  
Particle Image Velocimetry ◽  
Natural Convection ◽  
Proper Orthogonal Decomposition ◽  
Particle Image ◽  
Orthogonal Decomposition ◽  
Number Range ◽  
Image Velocimetry ◽  
Proper Orthogonal

An experimental investigation of transitional natural convection in an air filled cube was conducted in this research. The characteristic dimension of the enclosure was H = 0.35 m, and data were collected in the middle plane of the cavity. The Rayleigh number range examined was 5.0×107≤Ra≤3.4×108. In Part I, the authors presented the mean velocity profiles in the enclosure and conducted heat transfer measurements on the hot wall. An expression between Nu and Ra numbers was concluded and compared against other correlations available in literature. In the present work, the authors present a complete description of the flow in the enclosure by quantifying the low turbulence regime developed in the cavity. This was accomplished by estimating Reynolds stresses, turbulent kinetic energy, vorticity, and swirling strength. Proper orthogonal decomposition (POD) was employed to analyze the flow fields obtained from the experimental data and retain the most salient features of the flow field. This study attempts to close the gap of available experimental data in the literature and provide experimental benchmark data that can be used to validate CFD codes since the estimated error from particle image velocimetry (PIV) measurements is within 1–2%.

scholarly journals Proper Orthogonal Decomposition–Radial Basis Function Surrogate Model-Based Inverse Analysis for Identifying Nonlinear Burgers Model Parameters From Nanoindentation Data

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Salah U. Hamim ◽  
Raman P. Singh
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Radial Basis Function ◽  
Proper Orthogonal Decomposition ◽  
Basis Function ◽  
Surrogate Model ◽  
Orthogonal Decomposition ◽  
Model Parameters ◽  
Radial Basis ◽  
Proper Orthogonal

This study explores the application of a proper orthogonal decomposition (POD) and radial basis function (RBF)-based surrogate model to identify the parameters of a nonlinear viscoelastic material model using nanoindentation data. The inverse problem is solved by reducing the difference between finite element simulation-trained surrogate model approximation and experimental data through genetic algorithm (GA)-based optimization. The surrogate model, created using POD–RBF, is trained using finite element (FE) data obtained by varying model parameters within a parametric space. Sensitivity of the model parameters toward the load–displacement output is utilized to reduce the number of training points required for surrogate model training. The effect of friction on simulated load–displacement data is also analyzed. For the obtained model parameter set, the simulated output matches well with experimental data for various experimental conditions.

scholarly journals Choice of Measurement Locations of Nonlinear Structures Using Proper Orthogonal Modes and Effective Independence Distribution Vector

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
T. G. Ritto
Keyword(s):  
Experimental Data ◽  
Computational Model ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Nonlinear Structures ◽  
Nonlinear Structure ◽  
Proper Orthogonal Modes ◽  
Distribution Vector ◽  
Proper Orthogonal

This paper proposes a methodology to automatically choose the measurement locations of a nonlinear structure/equipment that needs to be monitored while operating. The response of the computational model (or experimental data) is used to construct the proper orthogonal modes applying the proper orthogonal decomposition (POD), and the effective independence distribution vector (EIDV) procedure is employed to eliminate, iteratively, locations that contribute less for the independence of the target proper orthogonal modes.

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