scholarly journals Flow Structures Identification through Proper Orthogonal Decomposition: The Flow around Two Distinct Cylinders

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 384
Author(s):  
Ângela M. Ribau ◽  
Nelson D. Gonçalves ◽  
Luís L. Ferrás ◽  
Alexandre M. Afonso
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fluid Flows ◽  
Orthogonal Decomposition ◽  
Flow Structures ◽  
Data Set ◽  
Power Law Fluids ◽  
2D Flow ◽  
Periodic Behaviour ◽  
Flow Through ◽  
Proper Orthogonal

Numerical simulations of fluid flows can produce a huge amount of data and inadvertently important flow structures can be ignored, if a thorough analysis is not performed. The identification of these flow structures, mainly in transient situations, is a complex task, since such structures change in time and can move along the domain. With the decomposition of the entire data set into smaller sets, important structures present in the main flow and structures with periodic behaviour, like vortices, can be identified. Therefore, through the analysis of the frequency of each of these components and using a smaller number of components, we show that the Proper Orthogonal Decomposition can be used not only to reduce the amount of significant data, but also to obtain a better and global understanding of the flow (through the analysis of specific modes). In this work, the von Kármán vortex street is decomposed into a generator base and analysed through the Proper Orthogonal Decomposition for the 2D flow around a cylinder and the 2D flow around two cylinders with different radii. We consider a Newtonian fluid and two non-Newtonian power-law fluids, with n=0.7 and n=1.3. Grouping specific modes, a reconstruction is made, allowing the identification of complex structures that otherwise would be impossible to identify using simple post-processing of the fluid flow.

Analysis of Unsteady Flow Structures in a Radial Turbomachine by Using Proper Orthogonal Decomposition

2018 ◽  
Author(s):  
Matthias Witte ◽  
Benjamin Torner ◽  
Frank-Hendrik Wurm
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Mode Shapes ◽  
Flow Structures ◽  
Periodic Flow ◽  
Noise Emission ◽  
Turbulent Flow Field ◽  
Proper Orthogonal

Tonalities in hydro and airborne noise emission are a known problem of turbomachines, wherein the tonalities in the noise spectrum are associated with the different orders of the blade passing frequency (BPF). The proper orthogonal decomposition (POD) method was utilized to find the relationship between the fluctuations in the pressure field at the BPF orders which are the origin of the noise emission and the correlated fluctuations in the turbulent velocity field in terms of coherent, periodic flow structures. In order the provide the input data for the POD analysis, a URANS k-ω-SST scale adaptive simulation (SAS) of the turbulent flow field in a single stage radial pump under part load conditions was performed. Compared to traditional two equation turbulence models this approach is less dissipative and allows the development of small scale turbulence structures and is therefore an appropriate method for this study. In order to compute the POD correlation matrix Sirovich’s “Methods of Snapshots” was applied to the unsteady pressure and velocity fields from the CFD simulation. The discrimination of coherent, periodic flow structures and the incoherent, chaotic turbulence was carried out by analyzing the POD eigenvalue distributions, the POD mode shapes and the spectral properties of the POD time coefficients. Five coupled POD mode pairs were identified in total, which were strictly correlated with the 1st, 2nd, 3rd, 4th and 5th order of the BPF and therefore responsible for the noise emission at these discrete frequencies. The coherent structures were explored on the basis of the spatial POD velocity und pressure mode shapes and in terms of vortical structures after an additional phase averaging. The scope of this study is to introduce an enhanced collection of post processing techniques which are capable of analyzing highly unsteady flow fields from numerical simulations in a better way than is possible by just using traditional techniques like the evaluation of integral or time averaged quantities. The identified coherent flow structures and their associated pressure fluctuations are key elements for a proper comprehension of the internal dynamics of the turbulent flow field in a turbomachine and therefore essential for the understanding of the noise generation processes and the optimization of such machines.

Proper Orthogonal Decomposition for Nonlinear Radiative Heat Transfer Problems

2011 ◽  
Author(s):  
Daryl Hickey ◽  
Luc Masset ◽  
Gaetan Kerschen ◽  
Olivier Bru¨ls
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Large Scale ◽  
Radiative Heat ◽  
Heat Fluxes ◽  
Orthogonal Decomposition ◽  
Compact Representation ◽  
Thermomechanical Model ◽  
Data Set ◽  
Proper Orthogonal ◽  
Fully Coupled

Analysing large scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally very expensive, especially if the number of degrees-of-freedom is high. This paper develops modal reduction techniques for such nonlinear multiphysical systems. The paper focuses on Proper Orthogonal Decomposition (POD), a multivariate statistical method that obtains a compact representation of a data set by reducing a large number of interdependent variables to a much smaller number of uncorrelated variables. A fully coupled, thermomechanical model consisting of a multilayered, cantilever beam is described and analysed. This linear benchmark is then extended by adding nonlinear radiative heat exchanges between the beam and an enclosing box. The radiative view factors, present in the equations governing the heat fluxes between beam and box elements, are obtained with a ray-tracing method. A reduction procedure is proposed for this fully coupled nonlinear, multiphysical, thermomechanical system. Two alternative approaches to the reduction are investigated, a monolithic approach incorporating a scaling factor to the equations, and a partitioned approach that treats the individual physical modes separately. The paper builds on previous work presented previously by the authors. The results are given for the RMS error between either approach and the original, full solution.

scholarly journals Construction of reduced-order models for fluid flows using deep feedforward neural networks

2019 ◽  
Vol 872 ◽  
pp. 963-994 ◽  
Author(s):  
Hugo F. S. Lui ◽  
William R. Wolf
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fluid Flows ◽  
Leading Edge ◽  
Feedforward Neural Networks ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Order Model ◽  
Sparse Regression ◽  
Reduced Order ◽  
Proper Orthogonal

We present a numerical methodology for construction of reduced-order models (ROMs) of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition is applied to reduce the dimensionality of the model and, at the same time, filter the proper orthogonal decomposition temporal modes. The regression step is performed by a deep feedforward neural network (DNN), and the current framework is implemented in a context similar to the sparse identification of nonlinear dynamics algorithm. A discussion on the optimization of the DNN hyperparameters is provided for obtaining the best ROMs and an assessment of these models is presented for a canonical nonlinear oscillator and the compressible flow past a cylinder. Then the method is tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced-order model is able to capture the dynamics of the leading edge stall vortex and the subsequent trailing edge vortex. For the cases analysed, the numerical framework allows the prediction of the flow field beyond the training window using larger time increments than those employed by the full-order model. We also demonstrate the robustness of the current ROMs constructed via DNNs through a comparison with sparse regression. The DNN approach is able to learn transient features of the flow and presents more accurate and stable long-term predictions compared to sparse regression.

Tomographic Reconstruction of Unsteady Fields Using Proper Orthogonal Decomposition

2008 ◽  
Author(s):  
Dhruv Singh ◽  
Atul Srivastava ◽  
K. Muralidhar
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Tomographic Reconstruction ◽  
Three Dimensional ◽  
Concentration Field ◽  
Orthogonal Decomposition ◽  
Gradient Field ◽  
Data Set ◽  
Cylindrical Annulus ◽  
Typical Experiment ◽  
Proper Orthogonal

An algorithm for the reconstruction of unsteady three dimensional concentration field from path-integrated data has been discussed. We propose the use of Proper Orthogonal Decomposition (Karhunen Loe´ve Expansion) to completely decouple the spatial and temporal components of the image sequence (projections) obtained from a typical experiment enabling the analysis of an asynchoronous time-dependent data set. We apply the algorithm to experimental data from a Laser Interferometric study of convection in a cylindrical annulus to capture transients that are invariably faster than the camera speed. The strength of the technique is demonstrated in the reconstruction of the flow field (related to concentration gradients) from model (simulated) Schlieren projections. Tomographic reconstruction based on Convolution Back Projection (CBP) has been coupled with Proper Orthogonal Decomposition to enable the reconstruction of unsteady concentration gradient field from asynchronous projections.

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