Classical and snapshot forms of the POD technique applied to a helical vortex filament

Mula, Swathi M.; Tinney, Charles E.

doi:10.2514/6.2014-3257

Cited by 6 publications

(6 citation statements)

References 32 publications

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“…When compared with the spatial modes obtained using the snapshot POD method (which also does not force axisymmetry), the general features of the first few most energetic modes were essentially the same (Mula & Tinney 2014).…”

Section: (42)mentioning

confidence: 76%

A study of the turbulence within a spiralling vortex filament using proper orthogonal decomposition

Mula

Tinney

2015

J. Fluid Mech.

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The stability and turbulence characteristics of a vortex filament emanating from a single-bladed rotor in hover are investigated using proper orthogonal decomposition (POD). The rotor is operated at a tip chord Reynolds number and tip Mach number of 218 000 and 0.23, respectively, and with a blade loading of C T /σ = 0.066. Inplane components of the velocity field (normal to the axis of the vortex filament) are captured by way of two-dimensional particle image velocimetry with corrections for vortex wander being performed using the Γ 1 method. The first POD mode alone is found to encompass nearly 75 % of the energy for all vortex ages studied and is determined using a grid of sufficient resolution to avoid numerical integration errors in the decomposition. The findings reveal an equal balance between the axisymmetric and helical modes during vortex roll-up, which immediately transitions to helical mode dominance at all other vortex ages. This helical mode is one of the modes of the elliptic instability. The spatial eigenfunctions of the first few Fourier-azimuthal modes associated with the most energetic POD mode is shown to be sensitive to the choice of the wander correction technique used. Higher Fourier-azimuthal modes are observed in the outer portions of the vortex and appeared not to be affected by the choice of the wander correction technique used.

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Section: (42)mentioning

confidence: 76%

A study of the turbulence within a spiralling vortex filament using proper orthogonal decomposition

Mula

Tinney

2015

J. Fluid Mech.

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“…Compounding this lack of clarity is the inconsistent and incompatible use of the terms 'classical POD' and 'snapshot POD'. Some authors use these terms to refer to the methods we are calling spectral and space-only POD, respectively (e.g., Hellström & Smits, 2014;Mula & Tinney, 2014;George, 2017). Others use the name 'classical POD' to refer to space-only POD and 'snapshot POD' to refer to a particular computational shortcut for computing space-only POD modes (e.g., Hilberg et al, 1994;Pinier et al, 2007;Cordier & Bergmann, 2008).…”

Section: Introductionmentioning

confidence: 99%

Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis

2018

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We consider the frequency domain form of proper orthogonal decomposition (POD) called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space-time POD problem for statistically stationary flows and leads to modes that each oscillate at a single frequency. This form of POD goes back to the original work of Lumley (Stochastic tools in turbulence, Academic Press, 1970), but has been overshadowed by a space-only form of POD since the 1990s. We clarify the relationship between these two forms of POD and show that SPOD modes represent structures that evolve coherently in space and time while space-only POD modes in general do not. We also establish a relationship between SPOD and dynamic mode decomposition (DMD); we show that SPOD modes are in fact optimally averaged DMD modes obtained from an ensemble DMD problem for stationary flows. Accordingly, SPOD modes represent structures that are dynamic in the same sense as DMD modes but also optimally account for the statistical variability of turbulent flows. Finally, we establish a connection between SPOD and resolvent analysis. The key observation is that the resolvent-mode expansion coefficients must be regarded as statistical quantities to ensure convergent approximations of the flow statistics. When the expansion coefficients are uncorrelated, we show that SPOD and resolvent modes are identical. Our theoretical results and the overall utility of SPOD are demonstrated using two example problems: the complex Ginzburg-Landau equation and a turbulent jet.

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“…As can be observed in the Fig.16, the vorticity increases with the addition of each fluctuation mode. The first reconstruction covers 33% of the total energy and affects essentially the radial position of the core vortex that has been moved from 0.796 R to 0.808 R. The addition of the second fluctuating mode induces a displacement of core vortex in the axial direction from 0.738 R to 0.727 R. The mode 3 and 4 are clearly responsible for the elliptical deformation of vortex structure as confirmed by Mula and Tinney (2014) in the case of a propeller rotor.…”

Section: Fig 13 Radial Tip Vortex Velocity: (A) Vortex Age 60° (B)mentioning

confidence: 78%

Experimental Investigation of Tip Vortex Meandering in the Near Wake of a Horizontal-Axis Wind Turbine

Dahmouni¹,

Oueslati²,

Nasrallah³

2017

JAFM

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The aerodynamic optimization of horizontal axis wind turbine has became one of the most important challenge in the renewable energy field. Over the past few years, many researchers have drawn more attention to the physical processes of the wind energy conversion and precisely the identification of the main causes of energy losses. This paper presents an experimental investigation of near wake dynamics for a model horizontal axis wind turbine in a wind tunnel. The coherent structures downstream of the rotor were studied for different tip speed ratios using the Particle Image Velocimetry (PIV) technique. The influence of the tip vortex meandering was discussed and analyzed using the Proper Orthogonal Decomposition (POD) method. The high-energy modes show that radial meandering is the most energetic source of perturbation in each tip vortex sub-region. The energy fraction of these modes increase gradually during the development of the helical tip vortex filament, which confirm the growth of vortex wandering amplitude in the near wake.

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Classical and snapshot forms of the POD technique applied to a helical vortex filament

Cited by 6 publications

References 32 publications

A study of the turbulence within a spiralling vortex filament using proper orthogonal decomposition

A study of the turbulence within a spiralling vortex filament using proper orthogonal decomposition

Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis

Experimental Investigation of Tip Vortex Meandering in the Near Wake of a Horizontal-Axis Wind Turbine

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