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.

Study on vortex shedding mode on the wake of horn/ridge ice contamination under high-Reynolds conditions

2019 ◽  
Vol 233 (13) ◽  
pp. 5045-5056
Author(s):  
Shufan Hu ◽  
Chen Zhang ◽  
Hong Liu ◽  
Fuxin Wang
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Vortex Shedding ◽  
Large Scale ◽  
Vortex Motion ◽  
Simulation Method ◽  
Orthogonal Decomposition ◽  
Detached Eddy Simulation ◽  
Dynamic Features ◽  
Large Scale Vortex ◽  
Proper Orthogonal

This paper studied the unsteadiness of vortex motion produced by a three-dimensional wing section with horn/ridge ice contamination. Using improved delayed detached eddy simulation method, multi-scale vortex and their associated flow structures were successfully captured. Results have shown a diversity of unsteadiness scales at different time series, including shear layer instability, vortex pairing, co-rotating and breaking up. Proper orthogonal decomposition was then introduced to extract the characteristic vortex shedding modes with scheduling the eigenvalues λi from large to small. The dominate and secondary proper orthogonal decomposition modes under horn ice condition were displayed, which could be illustrated as fluctuations near recirculation zone, and large-scale vortex shedding/reattaching motion, respectively. The proper orthogonal decomposition modal characteristics for ridge ice showed that vortex scales varied from large to small. The trajectory of large-scale vortex reattaching and co-rotating exist simultaneously with the pressure peak and recover, which also verified the association of proper orthogonal decomposition modes with different scales of vortices. Future works would be presented on demonstration of the complex structures and the dynamic features in such flow.

scholarly journals Dynamics of Large Scale Turbulence in Finite-Sized Wind Farm Canopy Using Proper Orthogonal Decomposition and a Novel Fourier-POD Framework

Energies ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1660
Author(s):  
Tanmoy Chatterjee ◽  
Yulia T. Peet
Keyword(s):  
Power Generation ◽  
Proper Orthogonal Decomposition ◽  
Large Scale ◽  
Wind Farm ◽  
Wind Farms ◽  
Orthogonal Decomposition ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Pod Analysis ◽  
Proper Orthogonal

Large scale coherent structures in the atmospheric boundary layer (ABL) are known to contribute to the power generation in wind farms. In order to understand the dynamics of large scale structures, we perform proper orthogonal decomposition (POD) analysis of a finite sized wind turbine array canopy in the current paper. The POD analysis sheds light on the dynamics of large scale coherent modes as well as on the scaling of the eigenspectra in the heterogeneous wind farm. We also propose adapting a novel Fourier-POD (FPOD) modal decomposition which performs POD analysis of spanwise Fourier-transformed velocity. The FPOD methodology helps us in decoupling the length scales in the spanwise and streamwise direction when studying the 3D energetic coherent modes. Additionally, the FPOD eigenspectra also provide deeper insights for understanding the scaling trends of the three-dimensional POD eigenspectra and its convergence, which is inherently tied to turbulent dynamics. Understanding the behaviour of large scale structures in wind farm flows would not only help better assess reduced order models (ROM) for forecasting the flow and power generation but would also play a vital role in improving the decision making abilities in wind farm optimization algorithms in future. Additionally, this study also provides guidance for better understanding of the POD analysis in the turbulence and wind farm community.

Studying the Stabilization Dynamics of Swirling Partially Premixed Flames by Proper Orthogonal Decomposition

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Christophe Duwig ◽  
Sébastien Ducruix ◽  
Denis Veynante
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Gas Turbines ◽  
Large Scale ◽  
Vortex Breakdown ◽  
Premixed Flames ◽  
Combustion Process ◽  
Orthogonal Decomposition ◽  
Partially Premixed Flames ◽  
Partially Premixed ◽  
Proper Orthogonal

Environmental regulations are continuously pushing lower emissions with an impact on the combustion process in gas turbines (GTs). As a consequence, GT combustors operate in very lean regimes (i.e., at relatively low temperature) to reduce NOx formation. Unfortunately, stabilization becomes a challenge for these lean premixed flames. The extremely unsteady dynamics of swirl stabilized flames present crucial issues and this investigation aim is understanding the interaction of swirl stabilization with large coherent fluctuations inherent to vortex breakdown. The investigation utilizes a simplified cylindrical model combustor consisting of a premixing tube discharging in a larger combustion chamber. Fuel and swirling air are separately injected in the mixing tube so that a partially premixed swirling jet encounters vortex breakdown and allows the partially premixed flame to stabilize. The aforementioned extreme sensitivity of lean partially premixed flames challenges any investigation either for measuring, simulating, or post-processing the case of interest. In this paper, the problem is addressed using large eddy simulation (LES) and planar laser induced fluorescence. The LES data are used to follow the fuel air/mixing along with the fuel combustion evidencing large-scale dynamics. These dynamics are further investigated using proper orthogonal decomposition to identify the role of the premixing stage and of the precessing vortex core in the flame behavior.

Proper Orthogonal Decomposition Analysis of Non-Swirling Turbulent Stratified and Premixed Methane/Air Flames

2014 ◽  
Author(s):  
M. Mustafa Kamal ◽  
Christophe Duwig ◽  
Saravanan Balusamy ◽  
Ruigang Zhou ◽  
Simone Hochgreb
Keyword(s):  
Flow Field ◽  
Proper Orthogonal Decomposition ◽  
High Speed ◽  
Large Scale ◽  
Bluff Body ◽  
Decomposition Analysis ◽  
Orthogonal Decomposition ◽  
Stereoscopic Particle Image Velocimetry ◽  
Large Scale Flow ◽  
Proper Orthogonal

This paper reports proper orthogonal decomposition (POD) analyses for the velocity fields measured in a test burner. The Cambridge/Sandia Stratified Swirl Burner has been used in various studies as a benchmark for high resolution scalar and velocity measurements, for comparison with numerical model prediction. Flow field data was collected for a series of bluff-body stabilized premixed and stratified methane/air flames at turbulent, globally lean conditions (ϕ = 0.75) using high speed stereoscopic particle image velocimetry (HS-SPIV). In this paper, a modal analysis was performed to identify the large scale flow structures and their impact on the flame dynamics. The high speed PIV system was operated at 3 kHz to acquire a series of 4096 sequential flow field images both for reactive and non-reactive cases, sufficient to follow the large-scale spatial and temporal evolution of flame and flow dynamics. The POD analysis allows identification of vortical structures, created by the bluff body, and in the shear layers surrounding the stabilization point. In addition, the analysis reveals that dominant structures are a strong function of the mixture stratification in the flow field. The dominant energetic modes of reactive and non-reactive flows are very different, as the expansion of gases and the high temperatures alter the unstable modes and their survival in the flow.

scholarly journals Proper orthogonal decomposition analysis and modelling of large-scale flow reorientations in a cubic Rayleigh–Bénard cell

2019 ◽  
Vol 881 ◽  
pp. 23-50 ◽  
Author(s):  
Laurent Soucasse ◽  
Bérengère Podvin ◽  
Philippe Rivière ◽  
Anouar Soufiani
Keyword(s):  
Boundary Layer ◽  
Proper Orthogonal Decomposition ◽  
Large Scale ◽  
Orthogonal Decomposition ◽  
Mean Flow ◽  
Large Scale Circulation ◽  
Large Scale Flow ◽  
Proper Orthogonal ◽  
Rayleigh Benard ◽  
Reorientation Process

This paper investigates the large-scale flow reorientations of Rayleigh–Bénard convection in a cubic cell using proper orthogonal decomposition (POD) analysis and modelling. A direct numerical simulation is performed for air at a Rayleigh number of $10^{7}$ and shows that the flow is characterized by four quasi-stable states, corresponding to a large-scale circulation lying in one of the two diagonal planes of the cube with a clockwise or anticlockwise motion, with occasional brief reorientations. Proper orthogonal decomposition is applied to the joint velocity and temperature fields of an enriched database which captures the statistical symmetries of the flow. We found that each quasi-stable state consists of a superposition of four spatial modes representing three types of structures: (i) a mean-flow mode consisting of two stacked counter-rotating torus-like structures; (ii) two large-scale two-dimensional rolls (pair of degenerated modes) which form large-scale diagonal rolls when combined together; and (iii) an eight-roll mode that transports fluid from one corner to the other and strengthens the circulation along the diagonal. In addition, we identified three other modes that play a role in the reorientation process: two boundary-layer modes (pair of degenerated modes) that connect the core region with the horizontal boundary layers and one mode associated with corner rolls. The symmetries of the different POD modes are discussed, as well as their temporal dynamics. A description of the reorientation process in terms of POD modes is provided and compared with other modal approaches available in the literature. Finally, Galerkin projection is used to derive a POD-based reduced-order model. Unresolved modes are accounted for in the model by an extra dissipation term and the addition of noise. A seven-mode model is able to reproduce the low-frequency dynamics of the large-scale reorientations as well as the high-frequency dynamics associated with the large-scale circulation rotation. Linear stability analysis and sensitivity analysis confirm the role of the boundary-layer modes and the corner-rolls mode in the reorientation process.

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