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.

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.

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.

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