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

2015 ◽  
Vol 769 ◽  
pp. 570-589 ◽  
Author(s):  
Swathi M. Mula ◽  
Charles E. Tinney
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Vortex Filament ◽  
Blade Loading ◽  
Correction Technique ◽  
Image Velocimetry ◽  
Bladed Rotor ◽  
The Stability ◽  
Proper Orthogonal ◽  
Helical Mode

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 $C_{T}/{\it\sigma}=0.066$. In-plane 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 ${\it\Gamma}_{1}$ 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.

Reduced-Order Model of a Bladed Rotor With Geometric Mistuning

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Disk ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine (CMM) data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

scholarly journals On the mechanism of trailing vortex wandering

2016 ◽  
Vol 801 ◽  
Author(s):  
Adam M. Edstrand ◽  
Timothy B. Davis ◽  
Peter J. Schmid ◽  
Kunihiko Taira ◽  
Louis N. Cattafesta
Keyword(s):  
Particle Image ◽  
Particle Image Velocimetry Data ◽  
Primary Stability ◽  
Measured Velocity ◽  
Naca0012 Airfoil ◽  
Image Velocimetry ◽  
The Stability ◽  
Proper Orthogonal ◽  
Tunnel Effects ◽  
Helical Mode

The mechanism of trailing vortex wandering has long been debated and is often attributed to either wind-tunnel effects or an instability. Using particle image velocimetry data obtained in the wake of a NACA0012 airfoil, we remove the effect of wandering from the measured velocity field and, through a triple decomposition, recover the coherent wandering motion. Based on this wandering motion, the most energetic structures are computed using the proper orthogonal decomposition (POD) and exhibit a helical mode with an azimuthal wavenumber of $|m|=1$ whose kinetic energy grows monotonically in the downstream direction. To investigate the nature of the vortex wandering, we perform a spatial stability analysis of a matched Batchelor vortex. The primary stability mode is found to be marginally stable and nearly identical in both size and structure to the leading POD mode. The strikingly similar structure, coupled with the measured energy growth, supports the proposition that the vortex wandering is the result of an instability. We conclude that the cause of the wandering is the non-zero radial velocity of the $|m|=1$ mode on the vortex centreline, which acts to transversely displace the trailing vortex, as observed in experiments. However, the marginal nature of the stability mode prevents a definitive conclusion regarding the specific type of instability.

Analysis of Coherent Structures in the Far-Field Region of an Axisymmetric Free Jet Identified Using Particle Image Velocimetry and Proper Orthogonal Decomposition

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
A.-M. Shinneeb ◽  
R. Balachandar ◽  
J. D. Bugg
Keyword(s):  
Particle Image Velocimetry ◽  
Proper Orthogonal Decomposition ◽  
Coherent Structures ◽  
Particle Image ◽  
Axial Direction ◽  
Orthogonal Decomposition ◽  
Far Field ◽  
Field Region ◽  
Image Velocimetry ◽  
Proper Orthogonal

This paper investigates an isothermal free water jet discharging horizontally from a circular nozzle (9mm) into a stationary body of water. The jet exit velocity was 2.5m∕s and the exit Reynolds number was 22,500. The large-scale structures in the far field were investigated by performing a proper orthogonal decomposition (POD) analysis of the velocity field obtained using a particle image velocimetry system. The number of modes used for the POD reconstruction of the velocity fields was selected to recover 40% of the turbulent kinetic energy. A vortex identification algorithm was then employed to quantify the size, circulation, and direction of rotation of the exposed vortices. A statistical analysis of the distribution of number, size, and strength of the identified vortices was carried out to explore the characteristics of the coherent structures. The results clearly reveal that a substantial number of vortical structures of both rotational directions exist in the far-field region of the jet. The number of vortices decreases in the axial direction, while their size increases. The mean circulation magnitude is preserved in the axial direction. The results also indicate that the circulation magnitude is directly proportional to the square of the vortex radius and the constant of proportionality is a function of the axial location.

Analysis of Particle Image Velocimetry Measurements of Natural Convection in an Enclosure Using Proper Orthogonal Decomposition

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Nirmalendu Biswas ◽  
Souvick Chatterjee ◽  
Mithun Das ◽  
Amlan Garai ◽  
Prokash C. Roy ◽  
...  
Keyword(s):  
Particle Image Velocimetry ◽  
Natural Convection ◽  
Velocity Field ◽  
Proper Orthogonal Decomposition ◽  
Particle Image ◽  
Field Measurements ◽  
Orthogonal Decomposition ◽  
Image Velocimetry ◽  
Low Dimensional ◽  
Proper Orthogonal

This work investigates natural convection in an enclosure with localized heating on the bottom wall with a flushed or protruded heat source and cooled on the top and the side walls. Velocity field measurements are done by using 2D particle image velocimetry (PIV) technique. Proper orthogonal decomposition (POD) has been used to create low dimensional approximations of the system for predicting the flow structures. The POD-based analysis reveals the modal structure of the flow field and also allows reconstruction of velocity field at conditions other than those used in PIV study.

Vibratory Parameters of Blades From Coordinate Measurement Machine (CMM) Data

2005 ◽  
Author(s):  
Alok Sinha ◽  
Benjamin Hall ◽  
Brice Cassenti ◽  
Gary Hilbert
Keyword(s):  
Finite Element ◽  
Proper Orthogonal Decomposition ◽  
Natural Frequencies ◽  
Orthogonal Decomposition ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of a procedure to model geometric variations of blades. Specifically, vibratory parameters of blades are extracted from CMM data on an integrally bladed rotor (IBR). The method is based on proper orthogonal decomposition (POD) of CMM data, solid modeling and finite element techniques. In addition to obtaining natural frequencies and mode shapes of each blade on an IBR, statistics of these modal parameters are also computed and characterized. Numerical results are validated by comparison with experimental results.

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