Analysis of PIV measurements using modal decomposition techniques, POD and DMD, to study flow structures and their dynamics within a stirred-tank reactor
de Lamotte, Anne; Delafosse, Angélique; Calvo, Sébastienet al.
[en] The present work is a comparative analysis of Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) computed on experimental turbulent velocity fields measured in a 20L-tank stirred by two Rushton impellers at two rotating speeds, N = 150 and 300 rpm. POD identifies flow structures that optimally capture the total kinetic energy of the flow, while DMD identifies structures that significantly contribute to the dynamics of the flow. The experimental data, i.e. the instantaneous radial and axial velocity fields, come from 2-D Particle Image Velocimetry (PIV). The flow motion is turbulent, and it occurs over a wide range of length and time scales, from equipment-dependent large-scale coherent structures to the smallest-scale eddies where energy dissipation takes place. It thus provides an interesting benchmark case for the comparison between POD and DMD, which are based on energy and dynamic analysis, respectively. POD analysis reveals that the most energetic structures are related to the inherent periodic unsteadiness due to the relative motion between the rotating impeller blades and the non-moving baffles. Apart from the mean field, the first most energetic group of modes is related to trailing vortices induced by the Rushton turbines and is associated to a frequency equivalent to the blade passage frequency and its overtones. The second most energetic group of modes is related to vortical structures in the impeller stream and is associated to a frequency equivalent to the rotating speed. DMD analysis identifies flow structures that are found similar to these most energetic modes, although differences appear due to the fact that DMD isolates structures associated to a single frequency and their corresponding growth/decay rate. As in POD, the relative importance of each DMD mode can be estimated using an appropriately defined energy criterion. Comparison of the results from both modal decomposition methods points out their complementarity and their potential for describing the spatial and time characteristics of the flow within a stirred tank.
Disciplines :
Chemical engineering
Author, co-author :
de Lamotte, Anne ; Université de Liège - ULiège > Department of Chemical Engineering > Génie de la réaction et des réacteurs chimiques
Delafosse, Angélique ; Université de Liège - ULiège > Department of Chemical Engineering > Génie de la réaction et des réacteurs chimiques
Calvo, Sébastien ; Université de Liège - ULiège > Department of Chemical Engineering > Génie de la réaction et des réacteurs chimiques
Toye, Dominique ; Université de Liège - ULiège > Department of Chemical Engineering > Génie de la réaction et des réacteurs chimiques
Language :
English
Title :
Analysis of PIV measurements using modal decomposition techniques, POD and DMD, to study flow structures and their dynamics within a stirred-tank reactor
Publication date :
2018
Journal title :
Chemical Engineering Science
ISSN :
0009-2509
eISSN :
1873-4405
Publisher :
Pergamon Press - An Imprint of Elsevier Science, Oxford, United Kingdom
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Aubin, J., Sauze, N.L., Bertrand, J., Fletcher, D., Xuereb, C., Piv measurements of flow in an aerated tank stirred by a down- and an up-pumping axial flow impeller. Exp. Therm. Fluid Sci. 28:5 (2004), 447–456 5th International Conference on Gas-Liquid and Gas-Liquid-Solid Reactor Engineering.
Berkooz, G., Holmes, P., Lumley, J.L., The proper orthogonal decomposition in the analysis of turbulent flows. Ann. Rev. Fluid Mech. 25:1 (1993), 539–575.
Brucato, A., Ciofalo, M., Grisafi, F., Micale, G., Numerical prediction of flow fields in baffled stirred vessels: a comparison of alternative modelling approaches. Chem. Eng. Sci. 53:21 (1998), 3653–3684.
Bujalski, W., Nienow, A., Chatwin, S., Cooke, M., The dependency on scale of power numbers of rushton disc turbines. Chem. Eng. Sci. 42:2 (1987), 317–326.
Chara, Z., Kysela, B., Konfrst, J., Fort, I., Study of fluid flow in baffled vessels stirred by a rushton standard impeller. Appl. Math. Comput. 272:Part 3 (2016), 614–628.
Chatterjee, A., An introduction to the proper orthogonal decomposition. Curr. Sci. 78:7 (2000), 808–817.
Chiti, F., Bakalis, S., Bujalski, W., Barigou, M., Eaglesham, A., Nienow, A.W., Using positron emission particle tracking (PEPT) to study the turbulent flow in a baffled vessel agitated by a rushton turbine: Improving data treatment and validation. Chem. Eng. Res. Des. 89:10 (2011), 1947–1960.
de Lamotte, A., Delafosse, A., Calvo, S., Delvigne, F., Toye, D., Investigating the effects of hydrodynamics and mixing on mass transfer through the free-surface in stirred tank bioreactors. Chem. Eng. Sci. 172 (2017), 125–142.
Deen, N.G., Solberg, T., Hjertager, B.H., Flow generated by an aerated Rushton impeller: two-phase PIV experiments and numerical simulations. Can. J. Chem. Eng. 80:4 (2002), 1–15.
Deglon, D., Meyer, C., CFD modelling of stirred tanks: numerical considerations. Miner. Eng. 19:10 (2006), 1059–1068.
Delafosse, A., Collignon, M.-L., Calvo, S., Delvigne, F., Crine, M., Thonart, P., Toye, D., CFD-based compartment model for description of mixing in bioreactors. Chem. Eng. Sci. 106 (2014), 76–85.
Delafosse, A., Collignon, M.-L., Crine, M., Toye, D., Estimation of the turbulent kinetic energy dissipation rate from 2D-PIV measurements in a vessel stirred by an axial mixel TTP impeller. Chem. Eng. Sci. 66:8 (2011), 1728–1737.
Delafosse, A., Line, A., Morchain, J., Guiraud, P., Les and urans simulations of hydrodynamics in mixing tank: comparison to piv experiments. Chem. Eng. Res. Des. 86:12 (2008), 1322–1330.
Delafosse, A., Morchain, J., Guiraud, P., LinÃl, A., Trailing vortices generated by a rushton turbine: assessment of urans and large eddy simulations. Chem. Eng. Res. Des. 87:4 (2009), 401–411.
Derksen, J., Doelman, M., Van den Akker, H., Three-dimensional LDA measurements in the impeller region of a turbulently stirred tank. Exp. Fluids 27:6 (1999), 522–532.
Ducci, A., Doulgerakis, Z., Yianneskis, M., Decomposition of flow structures in stirred reactors and implications for mixing enhancement. Ind. Eng. Chem. Res. 47:10 (2008), 3664–3676.
Escudié, R., Bouyer, D., Liné, A., Characterization of trailing vortices generated by a rushton turbine. AIChE J. 50:1 (2004), 75–86.
Escudié, R., Liné, A., Experimental analysis of hydrodynamics in a radially agitated tank. AIChE J. 49:3 (2003), 585–603.
Gabriele, A., Nienow, A., Simmons, M., Use of angle resolved PIV to estimate local specific energy dissipation rates for up- and down-pumping pitched blade agitators in a stirred tank. Chem. Eng. Sci. 64:1 (2009), 126–143.
Galletti, C., Brunazzi, E., Yianneskis, M., Paglianti, A., Spectral and wavelet analysis of the flow pattern transition with impeller clearance variations in a stirred vessel. Chem. Eng. Sci. 58:17 (2003), 3859–3875.
Guha, D., Dudukovic, M.P., Ramachandran, P.A., Mehta, S., Alvare, J., CFD-based compartmental modeling of single phase stirred-tank reactors. AIChE J. 52:5 (2006), 1836–1846.
Hasal, P., Fort, I., Kratena, J., Force effects of the macro-instability of flow pattern on radial baffles in a stirred vessel with pitched-blade and rushton turbine impellers. Chem. Eng. Res. Des. 82:9 (2004), 1268–1281.
Hasal, P., Montes, J.-L., Boisson, H.-C., Fořt, I., Macro-instabilities of velocity field in stirred vessel: detection and analysis. Chem. Eng. Sci. 55:2 (2000), 391–401.
Jahoda, M., Moštĕk, M., Kukuková, A., Machoš, V., CFD modelling of liquid homogenization in stirred tanks with one and two impellers using large eddy simulation. Chem. Eng. Res. Des. 85:5 (2007), 616–625.
Joshi, J.B., Nere, N.K., Rane, C.V., Murthy, B.N., Mathpati, C.S., Patwardhan, A.W., Ranade, V.V., CFD simulation of stirred tanks: comparison of turbulence models. Part I: Radial flow impellers. Can. J. Chem. Eng. 89:1 (2011), 23–82.
Joshi, J.B., Tabib, M.V., Deshpande, S.S., Mathpati, C.S., Dynamics of flow structures and transport phenomena, 1. Experimental and numerical techniques for identification and energy content of flow structures. Ind. Eng. Chem. Res. 48:17 (2009), 8244–8284.
Liné, A., Eigenvalue spectrum versus energy density spectrum in a mixing tank. Chem. Eng. Res. Des. 108 (2016), 13–22.
Liné, A., Gabelle, J.-C., Morchain, J., Anne-Archard, D., Augier, F., On POD analysis of PIV measurements applied to mixing in a stirred vessel with a shear thinning fluid. Chem. Eng. Res. Des. 91:11 (2013), 2073–2083.
Machado, M.B., Bittorf, K.J., Roussinova, V.T., Kresta, S.M., Transition from turbulent to transitional flow in the top half of a stirred tank. Chem. Eng. Sci. 98 (2013), 218–230.
Mavros, P., Flow visualization in stirred vessels: a review of experimental techniques. Chem. Eng. Res. Des. 79:2 (2001), 113–127.
Mezic, I., Analysis of fluid flows via spectral properties of the koopman operator. Ann. Rev. Fluid Mech. 45:1 (2013), 357–378.
Montes, J.-L., Boisson, H.-C., Fořt, I., Jahoda, M., Velocity field macro-instabilities in an axially agitated mixing vessel. Chem. Eng. J. 67:2 (1997), 139–145.
Moreau, J., Liné, A., Proper orthogonal decomposition for the study of hydrodynamics in a mixing tank. AIChE J. 52:7 (2006), 2651–2655.
Raju, R., Balachandar, S., Hill, D., Adrian, R., Reynolds number scaling of flow in a stirred tank with Rushton turbine. Part II – Eigen decomposition of fluctuation. Chem. Eng. Sci. 60:12 (2005), 3185–3198.
Rammohan, A., Kemoun, A., Al-Dahhan, M., Dudukovic, M., Characterization of single phase flows in stirred tanks via computer automated radioactive particle tracking (CARPT). Chem. Eng. Res. Des. 79:8 (2001), 831–844.
Ranade, V., Perrard, M., Sauze, N.L., Xuereb, C., Bertrand, J., Trailing vortices of rushton turbine: PIV measurements and CFD simulations with snapshot approach. Chem. Eng. Res. Des. 79:1 (2001), 3–12.
Riet, K.V., Smith, J.M., The trailing vortex system produced by rushton turbine agitators. Chem. Eng. Sci. 30:9 (1975), 1093–1105.
Roussinova, V.T., Kresta, S.M., Weetman, R., Resonant geometries for circulation pattern macroinstabilities in a stirred tank. AIChE J. 50:12 (2004), 2986–3005.
Rowley, C.W., Mezić, I., Bagheri, S., Schlatter, P., Henningson, D.S., Spectral analysis of nonlinear flows. J. Fluid Mech. 641 (2009), 115–127.
Ruhe, A., Rational krylov sequence methods for eigenvalue computation. Linear Algebra Appl. 58:Supplement C (1984), 391–405.
Rutherford, K., Mahmoudi, S., Lee, K., Yianneskis, M., et al. The influence of rushton impeller blade and disk thickness on the mixing characteristics of stirred vessels. Chem. Eng. Res. Des. 74:3 (1996), 369–378.
Sakowitz, A., Mihaescu, M., Fuchs, L., Flow decomposition methods applied to the flow in an IC engine manifold. Appl. Therm. Eng. 65:1–2 (2014), 57–65.
Schmid, P.J., Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656 (2010), 5–28.
Schmid, P.J., Application of the dynamic mode decomposition to experimental data. Exp. Fluids 50:4 (2011), 1123–1130.
Schmid, P.J., Violato, D., Scarano, F., Decomposition of time-resolved tomographic PIV. Exp. Fluids 52:6 (2012), 1567–1579.
Semeraro, O., Bellani, G., Lundell, F., Analysis of time-resolved PIV measurements of a confined turbulent jet using POD and koopman modes. Exp. Fluids 53:5 (2012), 1203–1220.
Sharp, K.V., Adrian, R.J., PIV study of small-scale flow structure around a rushton turbine. AIChE J. 47:4 (2001), 766–778.
Sheng, J., Meng, H., Fox, R., A large eddy piv method for turbulence dissipation rate estimation. Chem. Eng. Sci. 55:20 (2000), 4423–4434.
Sheng, J., Meng, H., Fox, R.O., Validation of CFD simulations of a stirred tank using particle image velocimetry data. Can. J. Chem. Eng. 76:3 (1998), 611–625.
Sirovich, L., Turbulence and the dynamics of coherent structures. I - Coherent structures. Quart. Appl. Math. 45 (1987), 561–571.
Tabib, M.V., Joshi, J.B., Analysis of dominant flow structures and their flow dynamics in chemical process equipment using snapshot proper orthogonal decomposition technique. Chem. Eng. Sci. 63:14 (2008), 3695–3715.
Tissot, G., Cordier, L., Benard, N., Noack, B.R., 2013. Dynamic mode decomposition of PIV measurements for cylinder wake flow in turbulent regime. In: TSFP DIGITAL LIBRARY ONLINE. Begel House Inc.
Tissot, G., Cordier, L., Benard, N., Noack, B.R., Model reduction using dynamic mode decomposition. Compt. Rend. Méc. 342:6–7 (2014), 410–416.
Tu, J.H., Rowley, C.W., Luchtenburg, D.M., Brunton, S.L., Kutz, J.N., On dynamic mode decomposition: theory and applications. J. Comput. Dyn. 1:2 (2014), 391–421.
Wu, H., Patterson, G., Laser-doppler measurements of turbulent-flow parameters in a stirred mixer. Chem. Eng. Sci. 44:10 (1989), 2207–2221.
Zadghaffari, R., Moghaddas, J., Revstedt, J., A mixing study in a double-rushton stirred tank. Comput. Chem. Eng. 33:7 (2009), 1240–1246.
Zhang, Q., Liu, Y., Wang, S., The identification of coherent structures using proper orthogonal decomposition and dynamic mode decomposition. J. Fluids Struct. 49 (2014), 53–72.