Flow temporal reconstruction from non-time-resolved data part I: mathematic fundamentals

Legrand, Mathieu; Nogueira, J.; Lecuona, A.

doi:10.1007/s00348-011-1111-5

Cited by 55 publications

(29 citation statements)

References 16 publications

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“…However, since there is still a dispersion of points around the centre of the plot and the related spatial modes are in quadrature, it was decided to fit a 1 (t) and a 3 (t) with a pair of trigonometric functions, such that the temporal coefficients could be reordered in phase (see Fig. 12b) following an approach similar to that proposed by Van Oudheusden et al (2005) and Legrand et al (2011).…”

Section: Characterisation Of the Symmetric Statementioning

confidence: 99%

Evolution of the bi-stable wake of a square-back automotive shape

2017

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Square-back shapes are popular in the automotive market for their high level of practicality. These geometries, however, are usually characterised by high drag and their wake dynamics present aspects, such as the coexistence of a long-time bi-stable behaviour and short-time global fluctuating modes that are not fully understood. In the present paper, the unsteady behaviour of the wake of a generic square-back car geometry is characterised with an emphasis on identifying the causal relationship between the different dynamic modes in the wake. The study is experimental, consisting of balance, pressure, and stereoscopic PIV measurements. Applying wavelet and cross-wavelet transforms to the balance data, a quasi-steady correlation is demonstrated between the forces and bi-stable modes. This is investigated by applying proper orthogonal decomposition to the pressure and velocity data sets and a new structure is proposed for each bi-stable state, consisting of a hairpin vortex that originates from one of the two model's vertical trailing edges and bends towards the opposite side as it merges into a single streamwise vortex downstream. The wake pumping motion is also identified and for the first time linked with the motion of the bi-stable vortical structure in the streamwise direction, resulting in out-of-phase pressure variations between the two vertical halves of the model base. A phase-averaged low-order model is also proposed that provides a comprehensive description of the mechanisms of the switch between the bi-stable states. It is demonstrated that, during the switch, the wake becomes laterally symmetric and, at this point, the level of interaction between the recirculating structures and the base reaches a minimum, yielding, for this geometry, a 7% reduction of the base drag compared to the time-averaged result.

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Section: Characterisation Of the Symmetric Statementioning

confidence: 99%

Evolution of the bi-stable wake of a square-back automotive shape

2017

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“…Other authors have contributed with exhaustive explanations on the mathematics behind POD and its application to the analysis of turbulent flows [21][22][23]. For this reason the analysis procedure is only briefly described in the present work.…”

Section: Proper Orthogonal Decomposition (Pod) To Identify Coherent Smentioning

confidence: 99%

“…In light of the vast amounts of data generated by modern measurements, it is essential to further develop and foment the use of exploratory data analysis techniques that can summarize the available information. Proper Orthogonal Decomposition (POD), also known in different fields as Principal Component Analysis (PCA) or Empirical Mode Decomposition (EMD), is known to be a suitable tool to study coherent structures in turbulent flows [21][22][23][24][25]. Recent work by Lengani et al [26] have further improved current vortex identification methodologies [22,23] by incorporating a polynomial fit of the velocity fluctuations to better extract the coherent characteristics of the velocity field.…”

Section: Introductionmentioning

confidence: 99%

“…Proper Orthogonal Decomposition (POD), also known in different fields as Principal Component Analysis (PCA) or Empirical Mode Decomposition (EMD), is known to be a suitable tool to study coherent structures in turbulent flows [21][22][23][24][25]. Recent work by Lengani et al [26] have further improved current vortex identification methodologies [22,23] by incorporating a polynomial fit of the velocity fluctuations to better extract the coherent characteristics of the velocity field. These ideas have been recently applied by Berrino and coauthors to study the effects of confinement in a double swirl nozzle [27], proving the potential of the technique to extract the embedded coherent structures in combustor flows and obtain their phase characteristics.…”

Section: Introductionmentioning

confidence: 99%

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Isothermal coherent structures and turbulent flow produced by a gas turbine combustor lean pre-mixed swirl fuel nozzle

Gomez-Ramirez

Ekkad

Moon³

et al. 2017

Experimental Thermal and Fluid Science

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The steady and unsteady isothermal fluid dynamics generated by an industrial low emission, lean premixed, fuel swirl nozzle designed by Solar Turbines Incorporated were investigated in this study. The experiments were carried out in a model optical can combustor operating at atmospheric pressures. Non-time resolved, planar Particle Image Velocimetry (PIV) measurements were taken at Reynolds numbers with respect to the nozzle throat diameter of ~50 000, ~100 000, and ~180 000. The time-averaged velocity fields were approximately self-similar, with the highest mass flow exhibiting a central recirculation zone (CRZ) with a slightly larger diameter. The results were analyzed using a methodology based on Proper Orthogonal Decomposition (POD) to extract the periodic structures in the flow and obtain the underlying stochastic turbulence field. This distinction between stochastic and coherent fluctuations is critical to properly model combustor flows. Coherent flow instabilities such as the precessing vortex core (PVC) and the propagation of axial/radial vortices were observed to significantly contribute to the mixing between the nozzle exit flow and the recirculated mass flow. Over 30% of the total fluctuation (difference between instantaneous and time-averaged velocity fields) kinetic energy was attributed to coherent structures throughout the inner shear layer between the swirling jet exiting the nozzle and the CRZ. Stochastic variability was prevalent close the liner wall and throughout the combustor domain after the swirling jet impinged on the wall, with <20% of the total fluctuation attributed to coherent structures. The normalized coherent and stochastic flow fields were also approximately self-similar with Reynolds number.

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“…POD has been used for reconstructing the low-dimensional model in a variety of disciplines, looking for maximising flow energy with the first few modes of the decomposition. [30] The large-scale structure can be reconstructed from the PIV measurement by snapshot POD. For handling numerical data over large domain by POD, the method of snapshots of Sirovich [31] is most appropriate.…”

Section: Introductionmentioning

confidence: 99%

Study on the flow structure and its effects on the interaction and formation of cryogenic taylor bubbles by PIV technique and POD analysis

et al. 2013

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The flow structures around continuous cryogenic Taylor bubbles in the concentric glass tube with different diameters were investigated using particle image velocimetry (PIV) technique under various inclination angles. Optical distortions produced by tube curvature and the refractive index differences between tube and fluid were corrected using ray tracing method. Based on the PIV results, the proper orthogonal decomposition (POD) method was used to investigate the effect of flow structure on the interaction of Taylor bubbles through the large‐scale turbulent structures of POD modes. Four best‐fitted curves for Taylor bubble interaction for different inclination angles were represented. A correlation for Taylor bubble formation was developed with the consideration of turbulence suppression, tube inner diameter, fluid properties, inclination angle, etc. The results demonstrate that the minimum stable distance attains the smallest value at θ=60∘. The correlation for Taylor bubble formation shows good agreement with the experimental data both in the present study and from its references.

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Flow temporal reconstruction from non-time-resolved data part I: mathematic fundamentals

Cited by 55 publications

References 16 publications

Evolution of the bi-stable wake of a square-back automotive shape

Evolution of the bi-stable wake of a square-back automotive shape

Isothermal coherent structures and turbulent flow produced by a gas turbine combustor lean pre-mixed swirl fuel nozzle

Study on the flow structure and its effects on the interaction and formation of cryogenic taylor bubbles by PIV technique and POD analysis

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