Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition

1999 ◽  
Vol 391 ◽  
pp. 91-122 ◽  
Author(s):  
J. DELVILLE ◽  
L. UKEILEY ◽  
L. CORDIER ◽  
J. P. BONNET ◽  
M. GLAUSER
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Large Scale ◽  
Mixing Layer ◽  
Orthogonal Decomposition ◽  
Plane Mixing Layer ◽  
Large Scale Structures ◽  
The Mean ◽  
Scale Structures ◽  
Turbulent Plane ◽  
Proper Orthogonal

Large-scale structures in a plane turbulent mixing layer are studied through the use of the proper orthogonal decomposition (POD). Extensive experimental measurements are obtained in a turbulent plane mixing layer by means of two cross-wire rakes aligned normal to the direction of the mean shear and perpendicular to the mean flow direction. The measurements are acquired well into the asymptotic region. From the measured velocities the two-point spectral tensor is calculated as a function of separation in the cross-stream direction and spanwise and streamwise wavenumbers. The continuity equation is then used for the calculation of the non-measured components of the tensor. The POD is applied using the cross-spectral tensor as its kernel. This decomposition yields an optimal basis set in the mean square sense. The energy contained in the POD modes converges rapidly with the first mode being dominant (49% of the turbulent kinetic energy). Examination of these modes shows that the first mode contains evidence of both known flow organizations in the mixing layer, i.e. quasi-two-dimensional spanwise structures and streamwise aligned vortices. Using the shot-noise theory the dominant mode of the POD is transformed back into physical space. This structure is also indicative of the known flow organizations.

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.

Turbulent Flows Over Rough Forward Facing Steps

2014 ◽  
Author(s):  
Weijie Shao ◽  
Martin Agelin-Chaab
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Reattachment Length ◽  
Particle Image Velocimetry Technique ◽  
Large Scale Structures ◽  
Image Velocimetry ◽  
The Mean ◽  
Scale Structures ◽  
Scale Turbulence ◽  
Proper Orthogonal

This paper reports an investigation of the effects of rough forward facing steps on turbulent flows. The surfaces of the rough steps were covered with sandpapers. A particle image velocimetry technique was used to conduct measurements at the mid-plane of the test section and at several locations downstream to 68 step heights. A Reynolds number of Reh = 4800 and δ/h = 4.7 were employed, where h is the mean step height and δ is the incoming boundary layer thickness. The results indicate that mean reattachment length decreases with increasing roughness. In addition, the effect of the step roughness decreases with downstream distance. The proper orthogonal decomposition results showed that the step roughness affects even the large scale structures. Furthermore, the reconstructed turbulence quantities suggest that the step roughness suppresses the large scale turbulence.

scholarly journals Characteristics of Large-Scale Structures in Supersonic Planar Mixing Layer with Finite Thickness

2014 ◽  
Vol 6 ◽  
pp. 878679
Author(s):  
Hailong Zhang ◽  
Jiping Wu ◽  
Jian Chen ◽  
Weidong Liu
Keyword(s):  
High Speed ◽  
Large Scale ◽  
Finite Thickness ◽  
Mixing Layer ◽  
Mixing Enhancement ◽  
Laser Scattering ◽  
Large Scale Structures ◽  
Eddy Simulation ◽  
Planar Laser ◽  
Scale Structures

Nanoparticle-based planar laser scattering (NPLS) experiments and large eddy simulation (LES) were launched to get the fine structure of the supersonic planar mixing layer with finite thickness in the present study. Different from the turbulent development of supersonic planar mixing layer with thin thickness, the development of supersonic planar mixing layer with finite thickness is rapidly. The large-scale structures of mixing layer that possess the characters of quick movement and slow changes transmit to downriver at invariable speed. The transverse results show that the mixing layer is strip of right and dim and possess 3D characteristics. Meanwhile the vortices roll up from two sides to the center. Results indicate that the higher the pressure of the high speed side is, the thicker the mixing layer is. The development of mixing layer is restrained when the pressure of lower speed side is higher. The momentum thickness goes higher with the increase of the clapboard thickness. Through increasing the temperature to change the compression can affect the development of the vortices. The present study can make a contribution to the mixing enhancement and provide initial data for the later investigations.

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 Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model

2001 ◽  
Vol 441 ◽  
pp. 67-108 ◽  
Author(s):  
L. UKEILEY ◽  
L. CORDIER ◽  
R. MANCEAU ◽  
J. DELVILLE ◽  
M. GLAUSER ◽  
...  
Keyword(s):  
Dynamical System ◽  
Velocity Field ◽  
Large Scale ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Mixing Layer ◽  
Basis Set ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Low Order

The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by projecting Navier–Stokes equations onto an empirical basis set from the proper orthogonal decomposition (POD) using a Galerkin method. To obtain this low-dimensional set of equations, a truncation is performed that only includes the first POD mode for selected streamwise/spanwise (k1/k3) modes. The initial truncations are for k3 = 0; however, once these truncations are evaluated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedback between the turbulent and mean flows. The results of the numerical simulations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-stream direction. These models also indicated that the events associated with the centre of the mixing layer lead the temporal dynamics. For truncations involving both spanwise and streamwise wavenumbers, the reconstructed velocity field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connect spanwise vortex tubes.

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