BU AREVA PROJETS Titre présentation – Intervenant/réf. - 13 juillet 2017 - p.1
Solid-liquid suspensions in stirred vessels: a correlation to predict the mixing quality based on experimentally validated numerical simulations Corentin MACQUERON Computational Fluid Dynamics Engineer Nancy, July 12th, 2017
BU AREVA PROJETS
Context The mixing quality in a solid-liquid stirred vessel can be a very important parameter for the good functioning of an equipment or an industrial process At ‘low’ speed, some easy-to-use ‘laws’ exist to determine the minimum stirring speed to achieve total suspension of solid particles (Zwietering, 1958, Mersmann, 1998) At ‘high’ speed however, to our knowledge, there is no easy-to-use ‘law’ to determine the required stirring speed to obtain a homogeneous suspension
Engineers must hence rely on experimental mock-ups and/or numerical simulations to determine the required speed to achieve a required degree of homogeneity, which can be difficult and time and money consuming BU AREVA PROJETS
‘Low’ speed: off-bottom and total suspension, but not homogeneous: Zwietering and Mersmann criteria
‘High’ speed: homogeneous suspension: no criterion ?
Objective and methodology In the framework of the AREVA projects, we have to determine the stirring speed to achieve homogeneous solid-liquid suspensions for large tanks (~10 to ~250 m3) and for a large variety of solid particles
We sized our equipments with mock-ups and numerical simulations and we were interested to see if we could construct an easy-to-use ‘law’ to make homogenisation pre-sizing with a simple correlation We validated a solid-liquid tank model by comparison with experimental results and then we ran hundreds of numerical simulations for various solid particles suspensions and we looked if we could build a correlation based on these results We then cross-validated our correlation on different tank and impeller designs
BU AREVA PROJETS
One of our ~250 m3 tank
Experimental setup We made our own mock-ups (Macqueron et al., 2015) but their design was somewhat complicated and we wanted to build a correlation on a more ‘general’ design We hence used the simpler experimental setup of A. Tsz-Chung Mak (1992)
Glass beads (180 µm, 2630 kg/m3) suspended in tap water
Single stage impeller (Np = 1,52, θ = 45°)
Tank diameter T = 0,61 m, D/T = ½, H/T = 1, C/T = ¼
Solid concentration measured with a conductivity probe at different locations at various speeds
Tank and impeller BU AREVA PROJETS
Probe and measurements locations
COMPUTATIONAL FLUID DYNAMICS MODEL CFD model built with ANSYS FLUENT 15.0, ¼ tank (symmetries), ~800 000 cells Steady-state ‘frozen rotor’ simulations Multiphase: Eulerian-Granular approach (solid particles not tracked individually but modelled as a pseudo-continuous phase with fluid-particles and particles-particles interactions) Turbulence: k-ε realizable mixture model with ‘enhanced wall treatment’ (y+ max ~130, y+ average ~35), Diffusion-in-VOF turbulent dispersion force Drag: Gidaspow, Lift: neglected Pressure-velocity: Coupled, space discretisation: QUICK (3rd order)
Tank with ‘reconstructed’ symmetries, mesh with boundary layers and solid volume fraction field BU AREVA PROJETS
MODEL VALIDATION Power number predicted within 4% accuracy Very good reproduction of the solid volume fraction profiles at ‘high’ speeds (above the ‘avoidance of settling’ Mersmann criterion) At ‘low’ speed the results are greatly improved by deactivating the turbulent dispersion force (TDF) This highlights the differences that can appear between ‘low’ and ‘high’ speed physics, as also noted by Tamburini (2014) ‘Low’ speeds are not our ‘zone of interest’ so this is not a limitation for our work
RSD: Relative Standard Deviation (solid volume fraction)
BU AREVA PROJETS
CONFIGURATIONS Once the model was validated, we ran ~250 numerical simulations for various configurations in order to study the evolution of the mixing quality (quantified by the RSD) with the following parameters: ď ľ Stirring speed : ~1 to ~5 times NAS (‘avoidance of settling’ Mersmann criterion) ď ľ Tank diameter : 0,61 m to 6,50 m ď ľ Pitch blade angle : 30°to 45° ď ľ Particle diameter : 40 Âľm to 1000 Âľm
ď ľ Particle density : 2500 kg/m3 to 10 000 kg/m3 ď ľ Average solid volume fraction : ~0,5% to 30% ď ľ Liquid phase viscosity : 4,74.10-4 Pa.s to 1.10-2 Pa.s
RSD formula : đ?‘…đ?‘†đ??ˇ =
1 đ?œ‘đ?‘šđ?‘œđ?‘Ś
1 �
đ?œ‘ đ?‘‰ − đ?œ‘đ?‘šđ?‘œđ?‘Ś
2
��
A suspension is usually considered homogeneous for RSD ≤ 20% (Tamburini, 2012) BU AREVA PROJETS
RESULTS – CORRELATION At first, we tried to correlate our results to physical and nondimensional parameters. Some correlations were good but none was considered sufficient
As a first approach, N/NJS ≈ 1,5, N/NAS ≈ 4,5 or ND/USS ≈ 150 can be used as ‘homogenising’ criteria but dispersion is large
USS : terminal velocity calculated with the Archimedes number (Ar) and the Richardson and Zaki (1954) formula
BU AREVA PROJETS
RESULTS – CORRELATION We hence decided to correlate our results ‘from scratch’ by building our own variables The simulation results are fitted with a reasonable accuracy of Âą10 points of RSD with the following correlation: đ?‘…đ?‘†đ??ˇ = đ?›źđ?›˝ đ?›ž (in %) With: đ?›ź = 603 847,37 đ?›ž = −2,033 đ?›Ľđ?œŒ
đ?›˝ = đ?‘ Ă— đ?‘“1 đ?‘‡ Ă— đ?‘“2 đ??ˇđ?‘? Ă— đ?‘“3 ( ) Ă— đ?‘“4 đ?œ‡ Ă— đ?‘“5 (đ?œ‘) đ?œŒ
0,809
đ?‘“1 đ?‘‡ = đ?‘‡ đ?‘“2 đ??ˇđ?‘? = đ??ˇđ?‘? −0,735 đ?‘“3
đ?›Ľđ?œŒ đ?œŒ
=
đ?›Ľđ?œŒ −0,513 đ?œŒ
đ?‘“4 đ?œ‡ = đ?œ‡ 0,18 đ?‘“5 đ?œ‘ = 69574,98đ?œ‘ 6 − 68045,96đ?œ‘ 5 + 26995,72đ?œ‘ 4 − 5516,34đ?œ‘ 3 + 610,77đ?œ‘ 2 − 33,39đ?œ‘ + 1,36
R2 = 0,96
β ≈ 125-195 can be seen as a reasonable homogenising criterion
BU AREVA PROJETS
RESULTS – TANK AND PARTICLE DIAMETERS The scale-up dependency in T0,809 is close to the one found by Zwietering in T0,85
The dependency in Dp-0,735 is far from the one found by Zwietering in Dp-0,2 This highlights the differences that can appear between ‘low’ and ‘high’ speed physics BU AREVA PROJETS
RESULTS – PARTICLE DENSITY AND LIQUID VISCOSITY The dependency in Δρ/ρ-0,513 is close to the one found by Zwietering in Δρ/ρ-0,45
The dependency in μ0,18 is far from the one found by Zwietering in μ-0,10
This highlights the differences that can appear between ‘low’ and ‘high’ speed physics
BU AREVA PROJETS
RESULTS – AVERAGE SOLID VOLUME FRACTION AND PITCH BLADE ANGLE The ‘bell curve’ effect is somewhat striking and we did not have the opportunity to verify it with experimental results It showed up on every of our configurations, with the maximum RSD always located around φ ~7,5% Volume fraction (f5 is the polynom defined in slide 10)
There seems to be a threshold above which the ‘mixing equivalent viscosity’ (Krieger and Dougherty, 1959) plays a role by ‘thickening’ the suspension
The effects of the pitch blade angle are small on the RSD but large on the Np An optimal design for both the RSD and the dissipated power should be looked for θ (deg) Np (-)
BU AREVA PROJETS
30 ~0,70
35 ~0,95
40 ~1,24
45 ~1,56
RESULTS – CHALLENGING OUR CORRELATION Our correlation was built on a ‘general’ design and we wanted to see how it would perform on other tank and impeller designs (Liu et al., 2013, Macqueron et al., 2015) D/T = ½ (always, same as reference) Downward pumping with baffles
(always, same as reference) 1 to 3 stages 3 to 6 blades H/T : 0,68 to 1,23
Np : 0,62 to 1,92 Dp : 40 µm to 1000 µm
Fitting is still quite good with different designs
T : 0,288 m to 6,50 m ρs : 2500 kg/m3 to 4500 kg/m3 μ : 6,5.10-4 Pa.s to 1,1.10-3 Pa.s
HRB-1 BU AREVA PROJETS
HRB-2
RCB
HRB-3
LIU
RESULTS – NEURAL NETWORK The simulation results can also be fitted with an artificial neural network with an even better accuracy of ±5 points of RSD (https://deep-float.herokuapp.com), based on the Keras Python library (keras.io) 2 layers of 36 neurons and 1 layer of 1 neuron ReLU activation function (Rectified Linear Unit) ADAM optimizer 1000 learning cycles
(~1 minute of calculation on a laptop computer)
RSD (neural network) (%)
Built with the Deep Float online deep learning tool
Learning set Validation set
20% of data kept for validation (blind test) The better performance of the neural network over
the correlation might be due to the fact that the neural network can capture interactions between each parameters whereas the correlation was constructed without any kind of interaction
BU AREVA PROJETS
RSD (CFD model) (%)
CONCLUSION ANSYS FLUENT 15.0 is able to reproduce solid-liquid suspensions in stirred tanks with a very good accuracy above ‘slow’ speeds as defined by the ‘avoidance of settling’ Mersmann criterion Under this criterion, the results are greatly improved (but nos as good as at ‘high’ speeds) by deactivating the turbulent dispersion force
A correlation was built based on the results of ~250 numerical simulations exploring the effects of multiple tank and solid suspension parameters This correlation can predict the mixing quality with a reasonable accuracy for various suspensions and various tank and impeller designs An artificial neural network showed to be even more effective to predict the suspension quality BU AREVA PROJETS
PERSPECTIVES ‘Low’ speed modelling remains a difficult task and an ‘universal’ model working flawlessly across all speeds remains an open question The average solid volume fraction showed a somewhat striking ‘bell curve’ effect that might need experimental validation and theoretical explanation An optimal tank and impeller design, minimizing both the RSD and the dissipated power, could be engineered by experimental and numerical means Our pre-sizing correlation should be challenged on even more different designs and, if required, ‘enriched’ and modified
BU AREVA PROJETS
Acknowledgments The authors would like to thank Ronan Le Gall and GrĂŠgoire Piot from AREVA and Mokhtar Djeddou from the Aix-Marseille University for their helpful contribution and advice
BU AREVA PROJETS
References Chollet, F. (2015). Keras: Deep Learning Library for Theano and TensorFlow. https://keras.io/ Krieger, I. M., Dougherty, T. J. (1959). A mechanism for non-newtonian flow in suspensions of rigid spheres. Transaction of the Society of Rheology, vol. 3, pp.137-152
Liu, L., Barigou, M. (2013). Numerical modelling of velocity field and phase distribution in dense monodisperse solid-liquid suspensions under different regimes of agitation: CFD and PEPT experiments. Chemical Engineering Science, vol. 101, pp. 837-850 Macqueron, C., Fragnaud, S. (2017). Deep Float: An Easy Deep Learning Tool in Your Internet Browser. https://deep-float.herokuapp.com Macqueron, C., William, J., Le Gall, R., Demarthon, R., Piot, G., Ragouilliaux, A. (2015). Waste homogenisation tank: experimental validation of a numerical study. In : Proceedings of Global. Paris: SFEN, paper 5204 Mersmann, A., Werner, F., Maurer, S., Bartosch, K. (1998). Theoretical prediction of the minimum stirrer speed in mechanically agitated suspensions. Chemical Engineering and Processing, vol. 37 (issue 6), pp. 503-510 Richardson, J. F., Zaki, W. N. (1954). Sedimentation and fluidisation: part 1, Transactions of the Institution of Chemical Engineers, vol. 32, pp. 35-41 Tamburini, A., Brucato, A., Cipollina, A., Micale, G., Ciofalo, M. (2012). CFD Predictions of Sufficient Suspension Conditions in Solid-Liquid Agitated Tanks. International Journal of Nonlinear Sciences and Numerical Simulation, vol. 13 (issue 6), pp. 427-443. Tamburini, A., Cipollina, A., Micale, G., Brucato, A., Ciofalo, M. (2014). Influence of drag and turbulence modelling on CFD predictions of solid liquid suspensions in stirred vessels. Chemical Engineering Research and Design, vol. 92 (issue 6), pp. 1045-1063. Tsz-Chung Mak, A. (1992). Solid-liquid mixing in mechanically agitated vessels. PhD. University of London Zwietering, T. N. (1958). Suspending of solid particles in liquid by agitators. Chemical Engineering Science, vol. 8 (Issues 3-4), pp. 244-253.
BU AREVA PROJETS
TERMINOLOGY QUICK RSD TDF Ar C D Dp g H Hb Hod N NAS NJS Np R, r T USS W y+ α, β, γ φ χ μ ρS ρL θ
BU AREVA PROJETS
Quadratic Upstream Interpolation for Convective Kinematics Relative Standard Deviation Turbulent Dispersion Force Archimedes number impeller axis position impeller diameter particle diameter gravity tank height hub height hub diameter stirring speed avoidance of settling Mersman stirring speed just suspended Zwietering stirring speed power number curvature radius tank diameter particle terminal velocity blade width non-dimensional wall distance correlation coefficients average solid volume fraction blade thickness dynamic viscosity particle density liquid density pitch blade angle
(%) (-) (m) (m) (m) (m/s2) (m) (m) (m) (RPM, RPS) (RPM, RPS) (RPM, RPS) (-) (m) (m) (m/s) (m) (-) (-) (m) (Pa.s) (kg/m3) (kg/m3) (°)