Heat Transfer and Hydrodynamics in Stirred Tanks with Liquid-Solid Flow Studied by CFD–DEM Method
Abstract
:1. Introduction
2. Model Description
2.1. Fluid Phase
2.1.1. Momentum Equations and Turbulence Model
2.1.2. Energy Equation
2.2. DEM Model
2.3. Interactions in the Multiphase Flow
2.3.1. Interaction between Particles
2.3.2. Interaction between Particles and Fluid
2.3.3. Particle Heat Transfer
2.4. Coupling Scheme
3. Validation and Simulation Setup
3.1. Configuration of Stirred Tank
3.2. Simulation Details
3.3. CFD–DEM Model and Experimental Verification
3.3.1. Heat Model and Flow Pattern Validation
3.3.2. Grid Independence Verification
4. Results and Discussion
4.1. Effects of Particles on Heat Transfer
4.2. Effects of Blade Height on Heat Transfer and Hydrodynamic
4.3. Effects of Baffles on Heat Transfer and Hydrodynamic
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Cp | heat capacity (J/K) |
D | the diameter of stirred tanks (m) |
dp | particle diameter (m) |
E | total energy of fluid (J/kg) |
FD | drag force (N) |
FMag | Magnus lift force (N) |
Fn | normal contact force (N) |
Ft | tangential contact force (N) |
FSaff | Saffman lift force (N) |
fpf | particle-fluid interaction force (N/m3) |
fs | surface tension (N/m3) |
g | acceleration due to gravity (m/s2) |
H | the height of stirred tanks(m) |
h | the height of the blade(m) |
hc | convective heat transfer coefficient (W/m2·K) |
hpf | heat transfer coefficient between the two phases(W/m2·K) |
I | moment of inertia (kg·m2) |
J | diffusion flux (kg/m·s) |
k | thermal conductivity (W/m·K) |
keff | effective thermal conductivity (W/m·K) |
kt | turbulent thermal conductivity (W/m·K) |
Ln | distance between two particles (m) |
m | mass of inertia (kg·m2) |
N | rotating speed of the impeller (rpm) |
P | pressure (Pa) |
Q | heat flux (W/m2) |
Sn | normal stiffness (N/m) |
St | tangential stiffness (N/m) |
Tr | rolling torque (N·m) |
Tt | tangential torque (N·m) |
u | velocity of fluid (m/s) |
V | normal unit vector volume (m3) |
v | liner velocity of particle(m/s) |
Greek letter | |
ε | local volume fraction of fluid |
ρ | density (kg/m3) |
τ | viscous stress tensor (Pa) |
μ | friction coefficient |
α | volume fraction of relevant phase |
ω | angular velocity (rad/s) |
δ | relative error |
σ | variation coefficient |
κq | heat conductivity of fluid (W/m·K) |
Dimensionless Numbers | |
CD | drag force coefficient |
Re | Reynolds number |
Nup | Nussel number |
References
- Mahmud, T.; Haque, J.N.; Roberts, K.J.; Rhodes, D.; Wilkinson, D. Measurements and modelling of free-surface turbulent flows induced by a magnetic stirrer in an unbaffled stirred tank reactor. Chem. Eng. Sci. 2009, 64, 4197–4209. [Google Scholar] [CrossRef]
- Mckeown, R.R.; Wertman, J.T.; Dell’Orco, P.C. Crystallization Design and Scale-Up; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2010. [Google Scholar]
- Bentham, E.J.; Heggs, P.J.; Mahmud, T. CFD modelling of conjugate heat transfer in a pilot-scale unbaffled stirred tank reactor with a plain jacket. Can. J. Chem. Eng. 2019, 97, 573–585. [Google Scholar] [CrossRef]
- Barnoon, P.; Toghraie, D.; Dehkordi, R.B.; Abed, H. MHD mixed convection and entropy generation in a lid-driven cavity with rotating cylinders filled by a nanofluid using two-phase mixture model. J. Magn. Magn. Mater. 2019, 483, 224–248. [Google Scholar] [CrossRef]
- Carcadea, E.; Ingham, D.B.; Stefanescu, I.; Ionete, R.; Ene, H. The influence of permeability changes for a 7-serpentine channel pem fuel cell performance. Int. J. Hydrogen Energy 2011, 36, 10376–10383. [Google Scholar] [CrossRef]
- Gheynani, A.R.; Akbari, O.A.; Zarringhalam, M.; Shabani, G.A.S.; Alnaqi, A.A.; Goodarzi, M.; Toghraie, D. Investigating the effect of nanoparticles diameter on turbulent flow and heat transfer properties of non-Newtonian carboxymethyl cellulose/CuO fluid in a microtube. Int. J. Numer. Methods Heat Fluid Flow 2019, 29, 1699–1723. [Google Scholar] [CrossRef]
- Toghraie, D.; Karami, A.; Afrand, M.; Karimipour, A. Effects of geometric parameters on the performance of solar chimney power plants. Energy 2018, 162, 1052–1061. [Google Scholar] [CrossRef]
- Toghraie, D.; Mahmoudi, M.; Akbari, O.A.; Pourfattah, F.; Heydari, M. The effect of using water/CuO nanofluid and L-shaped porous ribs on the performance evaluation criterion of microchannels. J. Therm. Anal. Calorim. 2019, 135, 145–159. [Google Scholar] [CrossRef]
- Delaplace, G.; Torrez, C.; Leuliet, J.C.; Belaubre, N.; Andre, C. Experimental and CFD Simulation of Heat Transfer to Highly Viscous Fluids in an Agitated Vessel Equipped With a non Standard Helical Ribbon Impeller. Chem. Eng. Res. Des. 2001, 79, 927–937. [Google Scholar] [CrossRef]
- Wang, L.Z.; Zhou, Y.J.; Chen, Z.B. Investigation of Heat Transfer Efficiency of Improved Intermig Impellers in a Stirred Tank Equipped with Vertical Tubes. Int. J. Chem. React. Eng. 2020, 18, 20. [Google Scholar] [CrossRef]
- Perarasu, T.; Arivazhagan, M.; Sivashanmugam, P. Experimental and CFD Heat Transfer Studies of Al2O3- Water Nanofluid in a Coiled Agitated Vessel Equipped with Propeller. Chin. J. Chem. Eng. 2013, 21, 1232–1243. [Google Scholar] [CrossRef]
- Hafezisefat, P.; Esfahany, M.N.; Jafari, M. An experimental and numerical study of heat transfer in jacketed vessels by SiO2 nanofluid. Heat Mass Transf. 2017, 53, 2395–2405. [Google Scholar] [CrossRef]
- Sivashanmugam, P. Numerical studies on heat transfer characteristics of graphite-water microfluid in a coiled agitated vessel. Heat Transf. Asian Res. 2018, 47, 824–834. [Google Scholar] [CrossRef]
- Jayakumar, J.S.; Mahajani, S.M.; Mandal, J.C.; Vijayan, P.K.; Bhoi, R. Experimental and CFD estimation of heat transfer in helically coiled heat exchangers. Chem. Eng. Res. Des. 2008, 86, 221–232. [Google Scholar] [CrossRef]
- Johnson, M.; Al-Dirawi, K.H.; Bentham, E.; Mahmud, T.; Heggs, P.J. A Non-Adiabatic Model for Jacketed Agitated Batch Reactors Experiencing Thermal Losses. Ind. Eng. Chem. Res. 2021, 60, 1316–1325. [Google Scholar] [CrossRef]
- Hosseini, S.; Patel, D.; Ein-Mozaffari, F.; Mehrvar, M. Study of Solid-Liquid Mixing in Agitated Tanks through Computational Fluid Dynamics Modeling. Ind. Eng. Chem. Res. 2010, 49, 4426–4435. [Google Scholar] [CrossRef]
- Visuri, O.; Liiri, M.; Alopaeus, V. Comparison and validation of CFD models in liquid–solid suspensions. Can. J. Chem. Eng. 2011, 89, 696–706. [Google Scholar] [CrossRef]
- Srinivasa, T.; Jayanti, S. An Eulerian/Lagrangian study of solid suspension in stirred tanks. AIChE J. 2007, 53, 2461–2469. [Google Scholar] [CrossRef]
- Zhu, H.P.; Zhou, Z.Y.; Yang, R.Y.; Yu, A.B. Discrete particle simulation of particulate systems: Theoretical developments. Chem. Eng. Sci. 2007, 62, 3378–3396. [Google Scholar] [CrossRef]
- Lain, S.; Broder, D.; Sommerfeld, M.; Goz, M.F. Modelling hydrodynamics and turbulence in a bubble column using the Euler-Lagrange procedure. Int. J. Multiph. Flow 2002, 28, 1381–1407. [Google Scholar] [CrossRef]
- Li, G.H.; Li, Z.P.; Gao, Z.M.; Wang, J.W.; Bao, Y.Y.; Derksen, J.J. Particle image velocimetry experiments and direct numerical simulations of solids suspension in transitional stirred tank flow. Chem. Eng. Sci. 2018, 191, 288–299. [Google Scholar] [CrossRef] [Green Version]
- Kang, Q.Q.; He, D.P.; Zhao, N.; Feng, X.; Wang, J.T. Hydrodynamics in unbaffled liquid-solid stirred tanks with free surface studied by DEM-VOF method. Chem. Eng. J. 2020, 386, 17. [Google Scholar] [CrossRef]
- Tsuji, Y.; Kawaguchi, T.; Tanaka, T. Discrete Particle Simulation of 2-Dimensional Fluidized-Bed. Powder Technol. 1993, 77, 79–87. [Google Scholar] [CrossRef]
- Patil, A.V.; Peters, E.; Kuipers, J.A.M. Comparison of CFD-DEM heat transfer simulations with infrared/visual measurements. Chem. Eng. J. 2015, 277, 388–401. [Google Scholar] [CrossRef]
- Wang, Z.; Liu, M. Semi-resolved CFD-DEM for thermal particulate flows with applications to fluidized beds. Int. J. Heat Mass Trans. 2020, 159, 120150. [Google Scholar] [CrossRef]
- Hobbs, A. Simulation of an aggregate dryer using coupled CFD and DEM methods. Int. J. Comput. Fluid Dyn. 2009, 23, 199–207. [Google Scholar] [CrossRef]
- Sousani, M.; Hobbs, A.M.; Anderson, A.; Wood, R. Accelerated heat transfer simulations using coupled DEM and CFD. Powder Technol. 2019, 357, 367–376. [Google Scholar] [CrossRef]
- Oschmann, T.; Kruggel-Emden, H. A novel method for the calculation of particle heat conduction and resolved 3D wall heat transfer for the CFD/DEM approach. Powder Technol. 2018, 338, 289–303. [Google Scholar] [CrossRef]
- Golshan, S.; Sotudeh-Gharebagh, R.; Zarghami, R.; Mostoufi, N.; Blais, B.; Kuipers, J.A.M. Review and implementation of CFD-DEM applied to chemical process systems. Chem. Eng. Sci. 2020, 221, 35. [Google Scholar] [CrossRef]
- Wu, L.; Gong, M.; Wang, J.T. Development of a DEM-VOF Model for the Turbulent Free-Surface Flows with Particles and Its Application to Stirred Mixing System. Ind. Eng. Chem. Res. 2018, 57, 1714–1725. [Google Scholar] [CrossRef]
- Zhao, N.; Wang, B.; Kang, Q.Q.; Wang, J.T. Effects of settling particles on the bubble formation in a gas-liquid-solid flow system studied through a coupled numerical method. Phys. Rev. Fluids 2020, 5, 24. [Google Scholar] [CrossRef]
- Lu, Y.; Huang, J.; Zheng, P. A CFD-DEM study of bubble dynamics in fluidized bed using flood fill method. Chem. Eng. J. 2015, 274, 123–131. [Google Scholar] [CrossRef]
- Aubin, J.; Fletcher, D.F.; Xuereb, C. Modeling turbulent flow in stirred tanks with CFD: The influence of the modeling approach, turbulence model and numerical scheme. Exp. Therm. Fluid Sci. 2004, 28, 431–445. [Google Scholar] [CrossRef] [Green Version]
- Zhu, H.P.; Zhou, Z.Y.; Yang, R.Y.; Yu, A.B. Discrete particle simulation of particulate systems: A review of major applications and findings. Chem. Eng. Sci. 2008, 63, 5728–5770. [Google Scholar] [CrossRef]
- Shigeto, Y.; Sakai, M. Arbitrary-shaped wall boundary modeling based on signed distance functions for granular flow simulations. Chem. Eng. J. 2013, 231, 464–476. [Google Scholar] [CrossRef]
- Shao, T.; Hu, Y.; Wang, W.; Jin, Y.; Cheng, Y. Simulation of Solid Suspension in a Stirred Tank Using CFD-DEM Coupled Approach. Chin. J. Chem. Eng. 2013, 21, 1069–1081. [Google Scholar] [CrossRef]
- Ai, J.; Chen, J.F.; Rotter, J.M.; Ooi, J.Y. Assessment of rolling resistance models in discrete element simulations. Powder Technol. 2011, 206, 269–282. [Google Scholar] [CrossRef]
- Sun, X.; Sakai, M. Three-dimensional simulation of gas-solid-liquid flows using the DEM-VOF method. Chem. Eng. Sci. 2015, 134, 531–548. [Google Scholar] [CrossRef]
- Micale, G.; Grisafi, F.; Rizzuti, L.; Brucato, A. CFD simulation of particle suspension height in stirred vessels. Chem. Eng. Res. Des. 2004, 82, 1204–1213. [Google Scholar] [CrossRef]
- Wang, S.Y.; Jiang, X.X.; Wang, R.C.; Wang, X.; Yang, S.W.; Zhao, J.; Liu, Y. Numerical simulation of flow behavior of particles in a liquid-solid stirred vessel with baffles. Adv. Powder Technol. 2017, 28, 1611–1624. [Google Scholar] [CrossRef]
- Blais, B.; Bertrand, O.; Fradette, L.; Bertrand, F. CFD-DEM simulations of early turbulent solid-liquid mixing: Prediction of suspension curve and just-suspended speed. Chem. Eng. Res. Des. 2017, 123, 388–406. [Google Scholar] [CrossRef]
- Bohnet, M.; Niesmak, G. Feststoffverteilung in gerührten Suspensionen. Chem. Ing. Tech. 1979, 51, 314–315. [Google Scholar] [CrossRef]
- Xie, L.; Luo, Z.H. Modeling and simulation of the influences of particle-particle interactions on dense solid-liquid suspensions in stirred vessels. Chem. Eng. Sci. 2018, 176, 439–453. [Google Scholar] [CrossRef]
- Blais, B.; Bertrand, F. CFD-DEM investigation of viscous solid-liquid mixing: Impact of particle properties and mixer characteristics. Chem. Eng. Res. Des. 2017, 118, 270–285. [Google Scholar] [CrossRef]
Parameter | Value |
---|---|
Water density (kg/m3) | 1000 |
Water viscosity (kg/m∙s) | 0.001 |
Water heat capacity (J/kg∙K) | 4182 |
Water thermal conductivity (W/m∙K) | 0.6 |
Particle density (kg/m3) | 1200 |
Particle heat capacity (J/kg∙K) | 1000 |
Particle thermal conductivity (W/m∙K) | 20 |
CFD time step (s) | 5 × 10−4 |
DEM time step (s) | 5 × 10−5 |
Coupling time step (s) | 5 × 10−4 |
Convergence criteria | 1 × 10−5 |
Parameter | Particle | Wall | Particle–Particle | Particle–Wall |
---|---|---|---|---|
Particle poisson’s ratio | 0.25 | 0.3 | - | - |
Particle shear modulus/MPa | 1 | 7 × 104 Pa | - | - |
Coefficient of restitution | - | - | 0.3 | 0.2 |
Coefficient of static friction | - | - | 0.5 | 0.5 |
Coefficient of rolling friction | - | - | 0.01 | 0.01 |
Parameter | Value |
---|---|
Particle density (kg/m3) | 2500 |
Fluid heat capacity (J/kg∙K) | 1010 |
Fluid thermal conductivity (W/m∙K) | 0.0242 |
Particle heat capacity (J/kg∙K) | 840 |
Particle thermal conductivity (W/m∙K) | 1.4 |
Fluid viscosity (kg/m∙s) | 2 × 10−5 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Luo, X.; Yu, J.; Wang, B.; Wang, J. Heat Transfer and Hydrodynamics in Stirred Tanks with Liquid-Solid Flow Studied by CFD–DEM Method. Processes 2021, 9, 849. https://doi.org/10.3390/pr9050849
Luo X, Yu J, Wang B, Wang J. Heat Transfer and Hydrodynamics in Stirred Tanks with Liquid-Solid Flow Studied by CFD–DEM Method. Processes. 2021; 9(5):849. https://doi.org/10.3390/pr9050849
Chicago/Turabian StyleLuo, Xiaotong, Jiachuan Yu, Bo Wang, and Jingtao Wang. 2021. "Heat Transfer and Hydrodynamics in Stirred Tanks with Liquid-Solid Flow Studied by CFD–DEM Method" Processes 9, no. 5: 849. https://doi.org/10.3390/pr9050849