This paper describes the CFD modelling of a reactor operating in the nuclear industry using LES approach. The reactor consists of an unbaffled stirred tank reactor in which plutonium precipitation reactions are carried out. The flow generated in such a precipitator is complex and there is very little information available in the literature about unbaffled reactors stirred with magnetic rod. That is why a hydrodynamic modelling has been developed using computational fluid dynamics (CFD) in order to get accurate description of mixing phenomena inside the precipitator and therefore to be able to predict the solid particle properties. Due to the strong turbulence anisotropy, the turbulence transport simulation is achieved by a large eddy simulation (LES) approach which gives unsteady solutions. The numerical simulations are performed in 3D using the Trio_U code developed at the Commissariat à l'énergie Atomique. The predictive performances of the modelling are analysed through a mixing phenomena study. Both experimental and numerical studies are performed. This work shows how hydrodynamics inside the reactor can have a noticeable effect on the precipitate properties and how LES modelling is a very effective tool for the process control. 1. Introduction Owing to the manipulation of radioactive materials at large scale, nuclear industry has to implement reactors with unusual design. An unbaffled magnetic rod-stirred reactor thus has been developed in the spent nuclear fuel reprocessing industry for use as a precipitator [1, 2]. Precipitation reactions being very fast are well known to be highly sensitive to mixing effects. That is why an accurate knowledge of the hydrodynamics inside the reactor is particularly essential to control the quality of the solid particles formed, on the one hand, and to develop a global modelling of the precipitation process, on the other hand. Flows in stirred unbaffled vessels have not been widely discussed in the literature, unlike stirred baffled vessels, because they are less frequently used in processes [2–4]. Their mixing performance is significantly lower due to the predominance of the tangential velocity over the axial and radial velocity components. Without counterimpellers, however, fluid rotation leads to the formation of a vortex that distorts the free surface; some applications can take advantage of this vortex. In the precipitator considered here, this configuration limits scaling by maintaining potentially adhering particles away from the walls and thus facilitates maintenance procedures that are particularly
References
[1]
P. Auchapt and A. Ferlay, “Appareil à effet vortex pour la fabrication d'un procédé,” Patent FR 1 556 996, 1981.
[2]
T. Mahmud, J. N. Haque, K. J. Roberts, D. Rhodes, and D. Wilkinson, “Measurements and modelling of free-surface turbulent flows induced by a magnetic stirrer in an unbaffled stirred tank reactor,” Chemical Engineering Science, vol. 64, no. 20, pp. 4197–4209, 2009.
[3]
P. Armenante, C. C. Chou, and R. B. Hemrajani, “Comparison of experimental and numerical velocity distribution profiles in an unbaffled mixing vessel provided with a pitched-blade turbine,” IChemE Symposium Series, vol. 136, pp. 349–356, 1994.
[4]
M. Kagoshima and R. Mann, “Development of a networks-of-zones fluid mixing model for an unbaffled stirred vessel used for precipitation,” Chemical Engineering Science, vol. 61, no. 9, pp. 2852–2863, 2006.
[5]
S. Nagata, N. Yoshioka, and T. Yokoyama, “Studies on the power requirement of mixing impellers,” Memoirs of the Faculty of Engineering, Kyoto University, vol. 17, pp. 175–185, 1955.
[6]
H. Hartmann, J. J. Derksen, and H. E. A. van den Akker, “Macroinstability uncovered in a Rushton turbine stirred tank by means of LES,” AIChE Journal, vol. 50, no. 10, pp. 2383–2393, 2004.
[7]
B. N. Murthy and J. B. Joshi, “Assessment of standard k—ε{lunate}, RSM and LES turbulence models in a baffled stirred vessel agitated by various impeller designs,” Chemical Engineering Science, vol. 63, no. 22, pp. 5468–5495, 2008.
[8]
A. Delafosse, A. Line, J. Morchain, and P. Guiraud, “LES and URANS simulations of hydrodynamics in mixing tank: comparison to PIV experiments,” Chemical Engineering Research and Design, vol. 86, no. 12, pp. 1322–1330, 2008.
[9]
J. J. Derksen, M. S. Doelman, and H. E. A. van den Akker, “Three-dimensional LDA measurements in the impeller region of a turbulently stirred tank,” Experiments in Fluids, vol. 27, no. 6, pp. 522–532, 1999.
[10]
J. Derksen and H. E. A. van den Akker, “Large eddy simulations on the flow driven by a Rushton turbine,” AIChE Journal, vol. 45, no. 2, pp. 209–221, 1999.
[11]
R. Alcamo, G. Micale, F. Grisafi, A. Brucato, and M. Ciofalo, “Large-eddy simulation of turbulent flow in an unbaffled stirred tank driven by a Rushton turbine,” Chemical Engineering Science, vol. 60, no. 8-9, pp. 2303–2316, 2005.
[12]
S. L. Yeoh, G. Papadakis, and M. Yianneskis, “Determination of mixing time and degree of homogeneity in stirred vessels with large eddy simulation,” Chemical Engineering Science, vol. 60, no. 8-9, pp. 2293–2302, 2005.
[13]
H. S. Yoon, S. Balachandar, and M. Y. Ha, “Large eddy simulation of flow in an unbaffled stirred tank for different Reynolds numbers,” Physics of Fluids, vol. 21, no. 8, Article ID 085102, 2009.
[14]
B. Chapelet-Arab, L. Duvieubourg, G. Nowogrocki, F. Abraham, and S. Grandjean, “U(IV)/Ln(III) mixed site in polymetallic oxalato complexes. Part III: structure of Na[Yb(C2O4)2(H2O)]·3H2O and the derived quadratic series (NH4+)1-x[Ln1-xUx (C2O4)2(H2O)]·(3+x) H2O, Ln？=？Y, Pr-Sm, Gd, Tb,” Journal of Solid State Chemistry, vol. 179, no. 12, pp. 4029–4036, 2006.
[15]
R. Perry and C. Chilton, Chemical Engineer’s Handbook, McGraw-Hill, New York, NY, USA, 5th edition, 1973.
[16]
S. B. Pope, Turbulent Flows, Cambridge University Press, Cambridge, UK, 2000.
[17]
Y. Benarafa, O. Cioni, F. Ducros, and P. Sagaut, “RANS/LES coupling for unsteady turbulent flow simulation at high Reynolds number on coarse meshes,” Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 23-24, pp. 2939–2960, 2006.
[18]
C. Calvin and P. Emonot, “The Trio_U project: a parallel CFD 3-dimensional code,” in Proceedings of the Scientific Computing in Object-Oriented Parallel Environments (ISCOPE '97), Y. Ishikawa, R. R. Oldehoeft, J. Reynders, and M. Tholburn, Eds., Lecture Notes in Computer Science, pp. 169–176, Springer, Marina del Rey, Calif, USA, December 1997.
[19]
C. Calvin, O. Cueto, and P. Emonot, “An object-oriented approach to the design of fluid mechanics software,” Mathematical Modelling and Numerical Analysis, vol. 36, no. 5, pp. 907–921, 2002.
[20]
http://www-trio-u.cea.fr/.
[21]
B. Mathieu, O. Lebaigue, and L. Tadrist, “Dynamic contact line model applied to single bubble growth,” in Proceedings of the 41st European Two-Phase Flow Group Meeting, Trondheim, Norway, 2003.
[22]
E. A. Fadlun, R. Verzicco, P. Orlandi, and J. Mohd-Yusof, “Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations,” Journal of Computational Physics, vol. 161, no. 1, pp. 35–60, 2000.
[23]
B. Mathieu, “A 3D parallel implementation of the front-tracking method for two-phase flows and moving bodies,” in Proceedings of the 177ème Session Société Hydrotechnique de France, Advances in the Modelling Methodologies of Two-Phase Flows, Lyon, France, November 2004.
[24]
F. Nicoud and F. Ducros, “Subgrid-scale stress modelling based on the square of the velocity gradient tensor,” Flow, Turbulence and Combustion, vol. 62, no. 3, pp. 183–200, 1999.
[25]
S. Nagata, K. Yamamoto, and M. Ujhara, “Studies on the power requirement of mixing impellers,” Memoirs of the Faculty of Engineering, Kyoto University, pp. 336–349, 1958.
[26]
J. Jeong and F. Hussain, “On the identification of a vortex,” Journal of Fluid Mechanics, vol. 285, pp. 69–94, 1995.
[27]
R. Escudié and A. Liné, “Analysis of turbulence anisotropy in a mixing tank,” Chemical Engineering Science, vol. 61, no. 9, pp. 2771–2779, 2006.
[28]
N. Lamarque, B. Zoppé, O. Lebaigue, Y. Dolias, M. Bertrand, and F. Ducros, “Large-eddy simulation of the turbulent free-surface flow in an unbaffled stirred tank reactor,” Chemical Engineering Science, vol. 65, no. 15, pp. 4307–4322, 2010.
[29]
A. Le Lan and H. Angelino, “Etude du vortex dans les cuves agitées,” Chemical Engineering Science, vol. 27, no. 11, pp. 1969–1978, 1972.
[30]
M. Bertrand-Andrieu, E. Plasari, and P. Baron, “Determination of nucleation and crystal growth kinetics in hostile environment—application to the tetravalent uranium oxalate U(C2O4)2· 6H2O,” Canadian Journal of Chemical Engineering, vol. 82, no. 5, pp. 930–938, 2004.
[31]
S. Lalleman, M. Bertrand, and E. Plasari, “Physical simulation of precipitation of radioactive element oxalates by using the harmless neodymium oxalate for studying the agglomeration phenomena,” Journal of Crystal Growth, vol. 342, no. 1, pp. 42–49, 2012.
