Proper orthogonal decomposition for the study of hydrodynamics in a mixing tank

Moreau, Julien; Liné, Alain

doi:10.1002/aic.10854

Cited by 23 publications

(21 citation statements)

References 11 publications

(17 reference statements)

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“…Modes 2 and 3 (ϕ 2 and ϕ 3 plotted in Figures b, c) exhibit large rotating structures that are almost symmetric with respect to the plane of the impeller. Mode 4 (Figure d) looks like a flapping jet similar behavior was observed in water . Modes higher than 4 are no longer symmetric and do not seem to represent any organized motion.…”

Section: Resultsmentioning

confidence: 99%

“…This is a classic result when the POD is carried out with the instantaneous velocity fields. Moreau and Liné have shown that POD can be an efficient way to separate the periodic velocity fluctuations induced by the impeller rotation without performing conditional or phase‐averaged measurements. The two following modes (second and third) were shown to reveal large‐scale rotating structures .…”

Section: Theoretical Analysismentioning

confidence: 99%

“…Such local and instantaneous data can be used to estimate large‐scale structures by processing velocities but also small‐scale structures with information on root mean square velocity gradients and vorticity at small scales . The application of data processing methods such as proper orthogonal decomposition (POD) to PIV data enables mean flow, periodic flow induced by the rotation of the impeller, and turbulence to be discriminated …”

Section: Introductionmentioning

confidence: 99%

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Experimental determination of the shear rate in a stirred tank with a non‐newtonian fluid: Carbopol

et al. 2012

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in Wiley Online Library (wileyonlinelibrary.com).The local shear rate generated in a cylindrical tank equipped with a Rushton turbine was investigated using particle image velocimetry in a shear-thinning fluid (Carbopol). This non-Newtonian fluid was used in an attempt to mimic fermentation broths. Three Reynolds numbers corresponding to the transition regime were investigated. The hydrodynamics is analyzed, and the velocity field is decomposed by proper orthogonal decomposition into mean flow, organized motion, and turbulence. Then, the contributions of each flow structure to the total dissipation of kinetic energy are presented. The spatial heterogeneity of shear rate is discussed and a new expression is proposed for shear rate. This work shows that the local shear rate is highly heterogeneous in a tank. Future works will need to focus on other types of stirrer and investigate the effect of scaling up reactors on the shear rate heterogeneity.

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Section: Resultsmentioning

confidence: 99%

Section: Theoretical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Experimental determination of the shear rate in a stirred tank with a non‐newtonian fluid: Carbopol

et al. 2012

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“…This POD methodology allows separating the organized and turbulent motions without the necessity to collect angular phased data . It was also shown by many authors that 2D measurement in a vertical plane enables to extract trailing vortices induced by a Rushton turbine.…”

Section: Pod Processing Of Piv Data and Velocity Reconstructionmentioning

confidence: 99%

Kinetic Energy Transfer between First Proper Orthogonal Decomposition Modes in a Mixing Tank

2017

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Two‐dimensional particle image velocimetry (PIV) was applied to study hydrodynamics in a mixing tank at medium Reynolds numbers. Post‐processing of PIV data was based on proper orthogonal decomposition (POD) which enabled to reconstruct organized motion induced by impeller blades without performing angle‐averaged sampling. Energy transfers between POD modes were analyzed. In particular, a local analysis of the modal interactions was developed in terms of energy transfer between the first mode, i.e., mean flow, and successive modes, i.e., organized motion. Eventually, derivation of transfer of energy between the second mode and fourth or fifth ones reveals a double pulsation.

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“…However, this technique is time‐consuming, and a lot of planes have to be studied to reconstruct the periodically oscillating fields (as a function the plane angle with respect to the blade). Alternatively, a technique named snapshot proper orthogonal decomposition (POD) is applied since it is able to identify periodic structures using nontime resolved PIV data (see Supplementary Materials for more information).…”

Section: Resultsmentioning

confidence: 99%

Hydrodynamic analysis of an axial impeller in a non‐Newtonian fluid through particle image velocimetry

2020

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The rheology of non-Newtonian fluids in agitated vessels is complex making equipment sizing more an art than a science. To increase our understanding and to resolve the data gap for computational fluid dynamics validation, we present a detailed particle image velocimetry study of the hydrodynamics of Carbopol encountered in a 70 L mechanically mixed (A310) tank at three different rotational speeds (100, 250, 500 rpm). Bulk flow visualizations show that the flow field below the impeller is highly influenced by the rheological behavior of the fluid. Moreover, an analysis of the shear rate and viscosity revealed important spatial heterogeneities. An estimation of the Reynolds number classified the rotational speeds as the onset of the transitional regime (100), in the transitional regime (250) and turbulent conditions (500 rpm). This data set consists of local mean and fluctuating velocities at different locations below the impeller, which are available for validation and further study. K E Y W O R D SCarbopol, mechanical mixing, particle image velocimetry, proper orthogonal decomposition, shear rate

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Proper orthogonal decomposition for the study of hydrodynamics in a mixing tank

Cited by 23 publications

References 11 publications

Experimental determination of the shear rate in a stirred tank with a non‐newtonian fluid: Carbopol

Experimental determination of the shear rate in a stirred tank with a non‐newtonian fluid: Carbopol

Kinetic Energy Transfer between First Proper Orthogonal Decomposition Modes in a Mixing Tank

Hydrodynamic analysis of an axial impeller in a non‐Newtonian fluid through particle image velocimetry

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