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Simulation of circulating flow in an annular channel for production of titanium pigment through the chloride process

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The mixing uniformity of the feeding gas TiCl4 and oxygen is the main characteristic of an oxidation reactor, which is a key equipment in titanium pigment production. Therefore, the fluid dynamic behavior of the feeding gas (TiCl4) in an annular channel, which affects the mixing uniformity, should be investigated thoroughly. According to the geometry of the annular channel, a realizable three-dimensional κε turbulence model was developed in this study. To verify the model, the calculated results were compared with data published in the literature. The errors were 1.73% and 3.33% for radii of 175 and 215 mm, respectively, thereby validating the model. Using the developed model, the flow characteristics of TiCl4 in an oxidation reactor with a tangential inlet were investigated. The results showed that, with an increase in the circumferential angle of the annular channel, the velocity first increased and then decreased, with a maximum value at a circumferential angle of 60°. The inlet Reynolds numbers and hole density of the jet ring had slight effects on the dimensionless pressure distribution in the annular channel. With an increase in the flow flux or a decrease in the diameter of the inlet pipe, the pressure curve became smoother, indicating that a homogeneous distribution of the feeding gas could be obtained.

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  1. Abdullah N, Kamarudin SK (2015) Titanium dioxide in fuel cell technology: an overview. J Power Sources 278:109–118

  2. Akroyd J, Smith AJ, Shirley R, Mcglashan LR, Kraft M (2011) A coupled CFD-population balance approach for nanoparticle synthesis in turbulent reacting flows. Chem Eng Sci 66(17):3792–3805

  3. Asami T, Honda I, Ueyama A (2013) Numerical analysis of the internal flow in an annular flow channel type oil damper. J Fluids Eng 136(3):1–8

  4. Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, Cambridge

  5. Bird RB, Stewart WS, Lightfoot EN (2006) Transport phenomena, 2nd edn. Wiley, New York (Chap. 5)

  6. Buddhiraju VS, Runkana V (2012) Simulation of nanoparticle synthesis in an aerosol flame reactor using a coupled flame dynamics–monodisperse population balance model. J Aerosol Sci 43(1):1–13

  7. By RR, Lakshminarayana B (1995) Measurement and analysis of static pressure field in a torque converter pump. J Fluids Eng 117(3):473–478

  8. Cheng Y, Ye AW, Liu F, Wei F (2006) Numerical simulation of swirling flows in oxidation reactors for TiO2 manufacture. China Part 4(3–4):108–113

  9. Daisuke O, Taro H, Mitsuharu M (2013) Three-dimensional normal shock-wave/boundary-layer interaction in a diffuser. ASME J Fluids Eng 135(4):041105

  10. Driel BV, Artesani A, Berg KJVD (2018) New insights into the complex photoluminescence behaviour of titanium white pigments. Dyes Pigm 155:285

  11. Guardoa A, Coussiratb M, Larrayoza MA, Recasensa F, Egusquizab E (2005) Influence of the turbulence model in CFD modeling of wall-to-fluid heat transfer in packed beds. Chem Eng Sci 60(6):1733–1742

  12. Im JH, Song SJ (2015) Mixing and entrainment characteristics in circular short ejectors. J Fluids Eng 137(5):051103–051103-10

  13. Jiang Z, Vijay M (2000) Near wall measurements for a turbulent impinging slot jet (data bank contribution). J Fluids Eng 123(1):112–120

  14. Johannessen T, Patsinis SE, Livbjerg H (2001) Computational analysis of coagulation and coalescence in the flame synthesis of titania particles. Powder Technol 118(3):242–250

  15. Karagozian AR (2010) Transverse jets and their control. Prog Energy Combust Sci 36(5):531–553

  16. Kartaev EV, Emel’kin VA, Ktalkherman MG, Kuz’min VI, Aul’chenko SM, Vashenko SP (2014) Analysis of mixing of impinging radial jets with crossflow in the regime of counter flow jet formation. Chem Eng Sci 119:1–9

  17. Lauridsen CB, Sanyova J, Simonsen KP (2014) Analytical study of modern paint layers on metal knight shields: the use and effect of Titanium white. Spectrochim Acta Part A Mol Biomol Spectrosc 124(8):638–645

  18. Liang Y, Qiao B, Wang TJ, Gao H, Yu K (2016) Effect of porous films on the lights reflectivity of pigmentary titanium dioxide particles. Appl Surf Sci 387:581–587

  19. Lu ZM, Li CZ, Cong DZ, Gu HC, Liu HL, Hu Y (2000) The mass variable flow and pressure distribution in a gas distributor. J East China Univ Sci Technol 26(4):362–366

  20. Lu ZM, Li CZ, Cong DZ (2001) Prediction of the pressure distribution of mass variable flow in a circle distributor. J East China Univ Sci Technol 27(6):623–625

  21. Mahmoud MHH (2012) Effective separation of iron from titanium by transport through TOA supported liquid membrane. Sep Purif Technol 84:63–71

  22. Mansoor A, Fatimah A, Marzie R (2018) Preparation of titanium dioxide nanostructure from ilmenite through sulfate-leaching process and solvent extraction by D2EHPA. J Iran Chem Soc 15(11):2533–2540

  23. Manuel JG, Juan PB, Rafael GT, Federico V (2014) A review of the production cycle of tiatnium dioxide pigment. Mater Sci Appl 5(7):441–452

  24. Middlemas S, Fang ZZ, Fan P (2013) Life cycle assessment comparison of emerging and traditional titanium dioxide manufacturing processes. Hydrometallurgy 108–132:107–113

  25. Middlemas S, Fang ZZ, Fan P (2015) A new method for production of titanium dioxide pigment. J Clean Prod 89:137–147

  26. Nguyen TD, Souad H (2015) PIV measurements in a turbulent wall jet over a backward-facing step in a three-dimensional, non-confined channel. Flow Meas Instrum 42:26–39

  27. Sauret E, Vallet I (2006) Near-wall turbulent pressure diffusion modeling and influence in three-dimensional secondary flows. J Fluids Eng 129(5):634–642

  28. Schild A, Gutsch A, Mühlenweg H, Patsinis SE (1999) Simulation of nanoparticle production in premixed aerosol flow reactors by interfacing fluid mechanics and particle dynamics. J Nanopart Res 1(2):305–315

  29. Shih TH, Liou WW, Shabbir A, Yang Z, Zhu J (1995) A new kε eddy-viscosity model for high Reynolds number turbulent flows-model development and validation. Comput Fluids 24(3):227–238

  30. Singh R, Raman V (2012) Two-dimensional direct numerical simulation of nanoparticle precursor evolution in turbulent flames using detailed chemistry. Chem Eng J 207–208:794–802

  31. Sung Y, Raman V, Fox RO (2011) Large-eddy-simulation-based multiscale modeling of TiO2 nanoparticle synthesis in aturbulent flame reactor using detailed nucleation chemistry. Chem Eng Sci 66(19):4370–4381

  32. Zhang SM (2000) A cold model experimental study of titanium pigment. Paint Coat Ind 30(5):20–22

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This work is financially supported by the National Natural Science Foundation of China (21566015), the Applied Basic Research Projects of Yunnan (2018FD134).

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Correspondence to Yan-qing Hou.

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Yu, C., Zhou, Y., Li, Y. et al. Simulation of circulating flow in an annular channel for production of titanium pigment through the chloride process. Braz. J. Chem. Eng. (2020).

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  • Oxidation reactor
  • Chloride process
  • Annular channel
  • Fluid dynamics
  • Dimensionless pressure