ON THE PERFORMANCE OF DIFFERENT RANS BASED MODELS TO DESCRIBE THE TURBULENT FLOW IN AN AGITATED VESSEL USING NON-STRUCTURED GRIDS AND PIV VALIDATION

Alonzo-Garcia, Alejandro; Mendoza-Escamilla, Víctor X.; Martinez-Delgadillo, Sergio A.; Gonzalez-Neria, Israel; Gutiérrez-Torres, Claudia del C.; Jiménez-Bernal, José A.

doi:10.1590/0104-6632.20190361s20180091

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Process Systems Engineering • Braz. J. Chem. Eng. 36 (1) • Jan-Mar 2019 • https://doi.org/10.1590/0104-6632.20190361s20180091 copy

ON THE PERFORMANCE OF DIFFERENT RANS BASED MODELS TO DESCRIBE THE TURBULENT FLOW IN AN AGITATED VESSEL USING NON-STRUCTURED GRIDS AND PIV VALIDATION

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The performances of the Standard κ-ε, RNG, Realizable, κ-ω and RSM turbulence models to describe the behavior of the flow in agitated tank reactors were evaluated. Because most of these tanks have complex geometries, structured meshing schemes are not a practical alternative in engineering. Two particular unstructured meshing schemes composed of either Cartesian Cut-Cell (CC) or Tetrahedral elements were tested in domains larger than 3 million cells. In this work, the blade thickness, which is usually disregarded, was accounted for. The performance of the turbulence models was validated by PIV measurements. A strong dependence on the grid size and the power number was found, with CC grids having good agreement with grids > 3.6 Million. The pumping number was independent of the cell number and the values agree with experimental data. The Realizable model resolved with a tetrahedral grid presented the overall best performance.

Key words:
Agitated tank; Pitched blade turbine, Cut-Cell; RANS; Tetrahedral cells; PIV

Authors	Impeller	Re ×10³	Approach and model	# Elements ×10³	Blade thickness	Parameters
Jaworski and Zakrzewska (2002) Jaworski, Z. and Zakrzewska, B., Modelling of the Turbulent Wall Jet Generated by a Pitched Blade Turbine Impeller, Chemical Engineering Research and Design , 80, 846-854 (2002). https://doi.org/10.1205/026387602321143381 https://doi.org/10.1205/0263876023211433...	PBT	22.5	MRF Standard κ-ε RNG Realizable Chen-Kim RSM	112 (hexahedral)	No	Mean velocities TKE
Aubin et al. (2004)Aubin, J., Fletcher, D.F. and Xuereb, C., Modeling Turbulent Flow in Stirred Tanks with CFD: The influence of the Modeling Approach, Turbulence Model and Numerical Scheme, Experimental Thermal and Fluid Sciences, 28, 431-445 (2004). https://doi.org/10.1016/j.expthermflusci.2003.04.001 https://doi.org/10.1016/j.expthermflusci...	Rushton	45	MRF, SM Standard κ-ε RNG	155 (hexahedral)	No	Mean velocities TKE
Yeoh et al. (2004)Yeoh, S.L., Papadakis, G. and Yianneskis, M., Numerical Simulation of Turbulent Flow Characteristics in a Stirred Vessel Using the LES and RANS Approaches with the Sliding=Deforming Mesh Methodology, Chemical Engineering Research and Design , 82, 834-848 (2004). https://doi.org/10.1205/026387604159675 https://doi.org/10.1205/026387604159675...	Rushton	40	SM Standard κ-ε	490 (hexahedral)	Yes	Mean velocities TKE, Dissipation
Murthy and Joshi (2008)Murthy, B.N. and Joshi, J.B., Assessment of Standard k - ε, RSM and LES Turbulence Models in a Baffled Stirred Vessel Agitated by Various Impeller Designs, Chemical Engineering Science , 63, 5468-5495 (2008). https://doi.org/10.1016/j.ces.2008.06.019 https://doi.org/10.1016/j.ces.2008.06.01...	PBT, Rushton, Hydrofoil	45	SM Standard κ-ε RSM	575 (hexahedral)	No	Mean velocities TKE
Coroneo et al. (2011)Coroneo, M., Montante, G., Paglianti, A. and Magelli, F., CFD Prediction of Fluid Flow and Mixing in Stirred Tanks: Numerical Issues About the RANS Simulations, Computers & Chemical Engineering, 35, 1959-1968 (2011). https://doi.org/10.1016/j.compchemeng.2010.12.007 https://doi.org/10.1016/j.compchemeng.20...	Rushton	29	MRF Standard κ-ε	270-6600 (hexahedral)	No	Mean velocities TKE, Dissipation
Joshi et al. (2011a)Joshi, J.B., Nere, N.K., Rane, C. V., Murthy, B.N., Mathpati, C.S., Patwardhan, A.W. and Ranade, V. V., CFD simulation of Stirred Tanks: Comparison of Turbulence Models. Part I: Radial Flow Impellers, Canadian Journal of Chemical Engineering , 89, 23-82 (2011a). https://doi.org/10.1002/cjce.20446 https://doi.org/10.1002/cjce.20446...	Rushton	45	MRF, SM, and others Standard κ-ε RNG Chen-Kim RSM	85 (MRF) 100 (SM) (hexahedral)	No	Mean velocities TKE, dissipation
Joshi et al. (2011bJoshi, J.B., Nere, N.K., Rane, C. V., Murthy, B.N., Mathpati, C.S., Patwardhan, A.W. and Ranade, V. V., CFD Simulation of Stirred Tanks: Comparison of Turbulence Models (Part II: Axial Flow Impellers, Multiple Impellers and Multiphase Dispersions), Canadian Journal of Chemical Engineering , 89, 754-816 (2011b). https://doi.org/10.1002/cjce.20465 https://doi.org/10.1002/cjce.20465...	PBT		MRF SM Standard κ-ε RNG RSM	320 (hexahedral)	No	Mean velocities TKE, dissipation
Singh et al. (2011)Singh, H., Fletcher, D.F. and Nijdam, J.J., An Assessment of Different Turbulence Models for Predicting Flow in a Baffled Tank Stirred with a Rushton Turbine, Chem. Eng. Sci. 66, 5976-5988 (2011). https://doi.org/10.1016/j.ces.2011.08.018 https://doi.org/10.1016/j.ces.2011.08.01...	Rushton		SM Standard κ-ε k-ω SST k-ω SST-CC SAS-SST RSM	2.13 M (hexahedral)	No	Mean velocities, TKE, dissipation
Lane (2017Lane, G.L., Improving the Accuracy of CFD Predictions of Turbulence in a Tank Stirred by a Hydrofoil Impeller, Chemical Engineering Science , 169, 188-211 (2017). https://doi.org/10.1016/j.ces.2017.03.061 https://doi.org/10.1016/j.ces.2017.03.06...	A310 Hydrofoil		SM Standard κ-ε k-ω SST k-ω SST-CC DES	3-28 M Hybrid	Yes	Mean velocities, TKE, dissipation

Grid	Zone 1 × 10⁶	Zone 2 × 10⁶	Total Cells × 10⁶	MRF-Zone 1 ε (W/kg)	Zone 2 ε (W/kg)	Total ε (W/kg)	Blade cell spacing (mm)	Iteration time (s)
CC 0.7 M	0.11	0.57	0.68	0.044 (33 %)	0.090	0.134	1.5	1
CC 1.1 M	0.21	0.90	1.11	0.048 (32 %)	0.100	0.149	0.5	1.2
CC 3.6 M	1.07	2.50	3.57	0.115 (49 %)	0.122	0.237	0.25	4.5
CC 6.2 M	2.77	3.42	6.19	0.099 (48 %)	0.110	0.208	0.225	7.5
T 0.9 M	0.27	0.62	0.89	0.053 (38 %)	0.085	0.138	2.000	1
T 1.7 M	0.64	1.02	1.66	0.058 (37 %)	0.099	0.156	1.000	1.7
T 3.3 M	1.38	1.88	3.26	0.066 (40 %)	0.100	0.166	0.375	3.4
T 6.1 M	1.42	4.71	6.13	0.073 (42 %)	0.100	0.173	0.225	6.7

Algorithm	CC			Tetrahedral
Model	N_p-ε	N_p	N_q	N_p-ε	N_p	N_q
STD	x	✔	✔	x	✔	✔
RNG	x	x	✔	x	✔	✔
RNG α=0.07	x	x	✔	x	✔	x
REA	✔	✔	✔	x	✔	✔
k-ω	✔	✔	✔	x	✔	✔
k-ω SST	x	✔	✔	x	✔	✔
RSM	x	x	✔	x	✔	x

Cartesian Meshing
	V_a				V_r				κ				ε/N³D²				(%)
	l_d1	l_d2	l_r1	l_r2	l_d1	l_d2	l_r1	l_r2	l_d1	l_d2	l_r1	l_r2	l_d1	l_d2	l_r1	l_r2	(%)
STD	✔	✔	✔	x	x	✔	✔	✔	x	x	x	x	x	x	x	x	38
RNG	✔	x	x	x	x	x	x	✔	x	x	✔	✔	x	x	✔	x	31
REA	✔	✔	✔	x	✔	✔	✔	✔	x	x	✔	✔	x	x	✔	x	63
k-ω	✔	✔	✔	x	x	✔	✔	✔	x	x	x	✔	x	x	x	x	44
RSM	✔	x	✔	x	x	x	x	✔	x	x	x	✔	x	x	✔	x	31
Tetrahedral Meshing
	V_a				V_r				κ				ε/N³D²				(%)
	l_d1	l_d2	l_r1	l_r2	l_d1	l_d2	l_r1	l_r2	l_d1	l_d2	l_r1	l_r2	l_d1	l_d2	l_r1	l_r2	(%)
STD	✔	✔	✔	x	x	✔	✔	✔	x	x	x	✔	x	x	x	x	44
RNG	✔	✔	✔	✔	x	✔	x	✔	x	x	✔	✔	x	x	x	x	50
REA	✔	✔	✔	✔	✔	✔	✔	✔	✔	x	✔	✔	✔	x	✔	x	81
k-ω	✔	✔	✔	✔	✔	✔	x	✔	x	x	✔	✔	x	x	✔	x	63
RSM	✔	✔	x	x	x	x	x	✔	x	x	✔	✔	x	x	✔	x	38

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[1] Corresponding author: Sergio A. Martinez-Delgadillo - E-mail: samd@correo.azc.uam.mx