Abstract
Several industrial activities require the introduction of mechanical agitation and mixing process in vessels with heated walls. This operation is performed in order to accelerate a certain physical or chemical desired homogeneity. Most of the numerical studies presented for the mixing and mechanical agitation process were based on the enhancement of the hydrodynamic performance and energy consumption, while comparatively less research is carried out on thermal phenomena in the literature. Based on this deficiency, the adoption of computational fluid dynamics (CFD) to study mixed convection in a mechanically stirred tank is the subject of the present paper. The numerical investigation focuses on a 3D unsteady laminar flow in a cylindrical tank equipped with an anchor and filled with an alumina-water nanofluid. The wall of this tank is exposed to a constant hot temperature. However, the anchor, the bottom of the tank and the free surface are assumed adiabatic and the nanofluid has an initial cold temperature. The rotary flow is governed by the equations that describe mixed convection, introducing the buoyancy force in the vertical direction into momentum equations. The Richardson number and the volume fraction of the alumina nanoparticles have been considered as control parameters in order to demonstrate their effect on the thermo-hydrodynamic behavior during the temporal evolution of the thermal state. The numerical results show that the predominant nature of the flow generated by the anchor is no longer tangential in the stirred tank by increasing the Richardson number in the unsteady state. In addition, a relative increase in the average Nusselt number is directly attributed to the increase in buoyancy effects on the one hand, and to the volume fraction of alumina nanoparticles on the other hand.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- C :
-
Anchor off-bottom clearance (m)
- Cp :
-
Specific heat (J kg−1.K−1)
- d :
-
Anchor diameter (m)
- D :
-
Tank diameter (m)
- da :
-
Shaft diameter (m)
- h :
-
Anchor height (m)
- H :
-
Tank height (m)
- k :
-
Thermal conductivity (W m−1 K−1)
- L :
-
Blade length (m)
- n :
-
Normal coordinate (m)
- N :
-
Rotation speed (m)
- Np:
-
Power number (s−1)
- Nu:
-
Average Nusselt number (−)
- P :
-
Pressure (Pa)
- P0:
-
Stirring power (W)
- Pr:
-
Prandtl number (–)
- Q v :
-
Viscous dissipation (s−1)
- r :
-
Radial coordinate (m)
- Re:
-
Reynolds number (–)
- Ri:
-
Richardson number (–)
- t :
-
Time (s)
- T :
-
Temperature (K)
- U, V, W :
-
Cartesian velocity component (m s−1)
- X, Y, Z :
-
Cartesian coordinates (m)
- α :
-
Thermal diffusivity (m2.s−1)
- β :
-
Thermal expansion (K−1)
- φ :
-
Volume fraction (or concentration) (–)
- μ :
-
Dynamic viscosity (kg m−1 s−1)
- θ :
-
Tangential coordinate (rd)
- ρ :
-
Density (kg m−3)
- c:
-
Cold
- f:
-
Base fluid
- h:
-
Hot
- n:
-
Nanofluid
- *:
-
Dimensionless function
References
Ali SKA, Kumar P, Kumar S (2020) Experimental studies of helical coils in laminar regime for mechanically agitated vessel. J Process Mechanical Engineering 234:173–181. https://doi.org/10.1177/0954408919895856
Alliet-Gaubert M, Sardeing R, Xuereb C, Hobbes P, Letellier B, Swaels P (2006) CFD analysis of industrial multi-staged stirred vessels. Chem Eng Process 45:415–427. https://doi.org/10.1016/j.cep.2005.11.003
Ameur H (2016) Effect of some parameters on the performance of anchor impellers for stirring shear-thinning fluids in a cylindrical vessel. J Hydrodyn 28(4):669–675. https://doi.org/10.1016/S1001-6058(16)60671-6
Ameur H (2020) Newly modified curved-bladed impellers for process intensification: Energy saving in the agitation of Hershel-Bulkley fluids. Chem Eng Process Process Intensification 154:108009. https://doi.org/10.1016/j.cep.2020.108009
Ameur H, Bouzit M, Ghenaim A (2015) Numerical study of the performance of multistage Scaba 6SRGT impellers for the agitation of yield stress fluids in cylindrical tanks. J Hydrodyn 27(3):436–442. https://doi.org/10.1016/S1001-6058(15)60501-7
Anil Kumar Naik B, Venu Vinod A (2018) Heat transfer enhancement using non-Newtonian nanofluids in a shell and helical coil heat exchanger. Exp Thermal Fluid Sci 90:132–142. https://doi.org/10.1016/j.expthermflusci.2017.09.013
Baccar M, Mseddi M, Abid MS (2001) Contribution numérique à l’étude hydrodynamique et thermique des écoulements turbulents induits par une turbine radiale en cuve agitée. Int J Therm Sci 40:753–772. https://doi.org/10.1016/S1290-0729(01)01263-7
Benmoussa A, Rahmani L (2018) Numerical Analysis of thermal behavior in agitated vessel with Non-Newtonian fluid. Int. J Multiphys 12:209–220. https://doi.org/10.21152/1750-9548.12.3.209.
Bertrand J, Couderc J (1985) Etude numérique des écoulements générés par une ancre dans le cas de fluides visqueux. Newtonien Ou Pseudoplastiques, Entropie 48:125–126
Bertrand J. (1983). Agitation des fluids visqueux cas de mobiles à pales, d’encre et de barrières. Thèse de doctorat, Istitut nationale polytechnique de Toulouse. URL: http://ethesis.inp-toulouse.fr/archive/00001376/.
Bouanini M, Youcefi A, Rahmani L, Hami O, Mebarki B, Belkacem D (2008) Temporal evolution of the thermal field of a stirred tank in Bingham fluid and laminar inertial regime. Proceedings of CHT-08, ICHMT International Symposium on Advances in Computational Heat Transfer, Marrakech, Morocco. https://doi.org/10.1615/ICHMT.2008.CHT.1240.
Brinkman HC (1952) The viscosity of concentrated suspensions and solutions. J Chem Phys 20:571–581. https://doi.org/10.1063/1.1700493
Choi SUS, Eastman JA (1995) Enhancing thermal conductivity of fluids with nanoparticles, in: D.A. 309 Siginer, H.P. Wang (eds) Developments and Applications of Non-Newtonian 310 Flows, FED-vol. 231/MD-vol. 66, ASME, New York, pp. 99–105.
Daza SA, Prada RJ, Nunhez JR, Castilho GJ (2018) Nusselt number correlation for a jacketed stirred tank using computational fluid dynamics. Can J Chem Eng 97:586–593. https://doi.org/10.1002/cjce.23385
Eastman JA, Phillpot SR, Choi SUS, Keblinski P (2004) Thermal transport in nanofluids. Annu Rev Mater Res 34(1):219–246. https://doi.org/10.1146/annurev.matsci.34.052803.090621
Gammoudi A, Ayadi A, Baccar M (2016) The hydrodynamic and thermal characterization of a yield stress fluid in stirred tanks equipped with simple helical ribbons with two stages. Meccanica. https://doi.org/10.1007/s11012-016-0506-z.
Hami O, Draoui B, Mebarki B, Rahmani L, Bouanini M (2008) Numerical model for laminar flow and heat transfer in an Agitated vessel by inclined blades anchor. Proceedings of cht-08 ICHMT international symposium on advances in computational heat transfer, Marrakech, Morocco. https://doi.org/10.1615/ICHMT.2008.CHT.1270.
Hammami M, Chebbi A, Baccar M (2013) Numerical study of hydrodynamic and thermal behaviors of agitated yield-stress fluid. Mech Industry 14:305–315. https://doi.org/10.1051/meca/2013070
Heidari A (2020) CFD simulation of impeller shape effect on quality of mixing in two-phase gas–liquid agitated vessel. Chin J Chem Eng 28:2733–2745. https://doi.org/10.1016/j.cjche.2020.06.036
Kamla Y, Ameur H, Karas A, Arab I (2020) M Performance of new designed anchor impellers in stirred tanks. Chem Pap 74:779–785. https://doi.org/10.1007/s11696-019-00902-x
Kong X, Qi B, Wei J, Li W, Ding J, Zhang Y (2016) Boiling heat transfer enhancement of nanofluids on a smooth surface with agitation. Heat Mass Transfer 52:2769–2780
Mahir M, El Maakoul A, Khay I, Saadeddine S, Bakhouya M (2021) An investigation of heat transfer performance in an agitated vessel Processes 9:468. https://doi.org/10.3390/pr9030468
Maxwell JC (1881) A Treatise on Electricity and Magnetism, 2nd edn, Oxford University Press, Cambridge, pp. 54.
Mebarki B, Draoui B (2011) Simulation numérique de l’écoulement d’un fluide newtonien : simulation numérique de l’écoulement d’un fluide newtonien dans une cuve agitée par ancre à pales inclinées. Editions universitaires européennes, Sarrebruck, Allemagne, p 75
Metawea R, Zewail T, El-Ashtoukhy E, Hamad IH (2018) Process intensification of the transesterification of palm oil to biodiesel in a batch-agitated vessel provided with mesh screen extended baffles. Energy 158:111–120. https://doi.org/10.1016/j.energy.2018.06.007
Mokhefi A, Bouanini M, Elmir M, Spitéri P (2021a) Effect of an anchor geometry on the hydrodynamic characteristics of a nanofluid in agitated tank. Defect Diffusion Forum 409:179–193. https://doi.org/10.4028/www.scientific.net/DDF.409.179
Mokhefi A, Bouanini M, Elmir M (2021b) Numerical Simulation of Laminar Flow and Heat Transfer of a Non-Newtonian Nanofluid in an Agitated Tank, International Journal of Heat and Technology 39(1):251–261. https://doi.org/10.18280/ijht.390128.
Mokhefi A, Bouanini M, Elmir M, Spitéri P (2021b) effect of the wavy tank wall on the characteristics of mechanical agitation in the presence of an Al2O3-water nanofluid, Metallurgical and Materials Engineering. https://doi.org/10.30544/626.
Nagata S (1975) Heat transfer in agitated vessel. In mixing Principles and applications. Wiley, New York, pp 385–387.
Pak BC, Cho YI (1998) Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, experimental heat transfer. J Thermal Energy Generation Transport Storage Conversion 11(2):151–170. https://doi.org/10.1080/08916159808946559
Pedrosa SMCP, Duarte CG, Nunhez JR (2000) Improving the flow of stirred vessels with anchor type impellers. European Symposium on Computer Aided Process Engineering l0: 403–408. https://doi.org/10.1016/S1570-7946(00)80069-3.
Perarasu VT, Arivazhagan M, Sivashanmugam P (2012) Heat transfer of tio2/water nanofluid in a coiled agitated Vessel with propeller. J Hydrodyn 24(6):942–950. https://doi.org/10.1016/S1001-6058(11)60322-3
Prajapati P, Ein-Mozaffari F (2009) CFD investigation of the mixing of yield-pseudoplastic fluids with anchor impellers. Chem Eng Technol 32(8):1211–1218. https://doi.org/10.1002/ceat.200800511
Rajasekaran E, Kumar B, Muruganandhan R, Raman SV, Nandhini Devi G (2020) CFD simulation of convective heat transfer in vessel with mechanical agitation for milk. J Food Sci Technol 57:3667–3676. https://doi.org/10.1007/s13197-020-04399-1
Sahu AK, Kumar P, Patwardhan A.W (1999). CFD modeling and mixing in stirred tanks. Chem Eng Sci 54 (13–14):2285–2293. https://doi.org/10.1016/S0009-2509(98)00334-0.
Sangare D, Bostyn S, Moscosa-Santillan M, Gökalp I (2021) Hydrodynamics, heat transfer and kinetics reaction of CFD modeling of a batch stirred reactor under hydrothermal carbonization conditions. Energy 219:119635. https://doi.org/10.1016/j.energy.2020.119635
Sheikhzadeh GA, Nazari S (2013) Numerical Study of Natural Convection in a Square Cavity Filled with a, Porous Medium Saturated with Nanofluid. Transport phenomena in nano and micro scales 1(2):138–146. https://www.sid.ir/en/journal/ViewPaper.aspx?id=351864.
Stoller M, Di Palma L, Vuppala S, Verdone N, Vilardi G (2018) Process intensification techniques for the production of nano- and submicronic particles for food and medical applications. Curr Pharm Des 24(21):2329–2338. https://doi.org/10.2174/1381612824666180523125144
Thangavelu P, Mahizhnan A, Palani S (2013) Experimental and CFD heat transfer studies of Al2O3-water nanofluid in a coiled agitated vessel equipped with propeller. Chin J Chem Eng 21(11):1232–1243. https://doi.org/10.1016/S1004-9541(13)60579-0
Věřišova M, Dostal M, Jirout T, Petera K (2015) Heat transfer in a jacketed agitated vessel equipped with multistage impellers. Chemical Papers 69: 690–697. doi/https://doi.org/10.1515/chempap-2015-0080.
Vilardi G, Verdone N (2020) Production of metallic iron nanoparticles in a baffled stirred tank reactor: Optimization via computational fluid dynamics simulation. Particuology 52:83–96. https://doi.org/10.1016/j.partic.2019.12.005
Vilardi G, Stoller M, Di Palma L, Boodhoo K, Verdonem N (2019) Metallic iron nanoparticles intensified production by Spinning Disk Reactor: optimization and fluid dynamics modelling. Chem Eng Process Process Intensification 146:107683. https://doi.org/10.1016/j.cep.2019.107683
Vilardi G, De Caprariis D, Stoller M, Di Palma L, Verdone N (2020) Intensified water denitrification by means of a spinning disk reactor and stirred tank in series: Kinetic modelling and computational fluid dynamics. J Water Process Eng 34:101147. https://doi.org/10.1016/j.jwpe.2020.101147
Vilardi G, Verdone N, Bubbico R (2021) Combined production of metallic-iron nanoparticles: exergy and energy analysis of two alternative processes using Hydrazine and NaBH4 as reducing agents. J Taiwan Inst Chem Eng 118:97–111. https://doi.org/10.1016/j.jtice.2020.11.020
Xuereb C, Poux M, Bertrand J (2006) Agitation et mélange : Aspects fondamentaux et applications industrielles, 1e edn. L’usine nouvelle, Paris
Zakrzewska B, Jaworski Z (2004) CFD modelling of turbulent jacket heat transfer in a Rushton turbine stirred vessel. Chem Eng Technol 27(3):237–242. https://doi.org/10.1002/ceat.200401988
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mokhefi, A., Bouanini, M., Elmir, M. et al. Numerical investigation of mixed convection in an anchor-stirred tank filled with an Al2O3-water nanofluid. Chem. Pap. 76, 967–985 (2022). https://doi.org/10.1007/s11696-021-01914-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11696-021-01914-2