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Stress fields of solid flow in a model blast furnace

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Abstract

The computational fluid dynamics–discrete element method approach, supported by an averaging technique, has been employed to quantitatively investigate the stress distributions of solid flow in a model blast furnace (BF). The results indicate that large normal stresses are mainly observed in the lower central part of the BF, whilst small normal stresses in the vicinity of the raceway. In the upper part, the vertical normal stress varies little horizontally in the central region but reduces a bit near the wall, whereas the horizontal normal stress has a relatively uniform distribution on the whole cross section. The shear stress has its largest magnitude in two symmetrical regions close to the stagnant zone. The couple stress can be ignored except for the regions close to the walls. The stress and couple stress are both affected by gas flow rate. In particular, increasing gas flow rate will decrease the magnitude of the stress and couple stress. The internal friction coefficient is not dependent on the inertial number for the solid flow in a BF, but it may rely on the inertial number in some specific flow regions for the cases without gas and with low gas flow rates.

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References

  1. Yagi J.I.: Mathematical modelling of the flow of four fluids in a packed bed. ISIJ Int. 33, 619–639 (1993). doi:10.2355/isijinternational.33.619

    Article  Google Scholar 

  2. Dong X.F., Yu A.B., Yagi J.I., Zulli P.: Modelling of multiphase flow in a blast furnace: Recent developments and future work. ISIJ Int. 47, 1553–1570 (2007). doi:10.2355/isijinternational.47.1553

    Article  Google Scholar 

  3. Khodak L., Borisov Y.: Velocity and pressure distributions of moving granular materials in a model of a shaft kiln. Powder Technol. 4, 187–194 (1970/1971). doi:10.1016/0032-5910(71)80034-7

    Article  Google Scholar 

  4. Takahashi H., Komatsu N.: Cold model study on burden behaviour in the lower part of blast furnace. ISIJ Int. 33, 655–663 (1993). doi:10.2355/isijinternational.33.655

    Article  Google Scholar 

  5. Inada T., Matsukura Y., Yaeda M., Matsumura S.I., Komatsu S., Yamamoto T., Onishi M.: Behavior of stress field in packed bed of Kokura No. 2 Blast Furnace during filling and after blow-in. ISIJ Int. 43, 1376–1383 (2003). doi:10.2355/isijinternational.43.1376

    Article  Google Scholar 

  6. Zhang S.J., Yu A.B., Zulli P., Wright B., Tuzun U.: Modelling of the solids flow in a blast furnace. ISIJ Int. 38, 1311–1319 (1998). doi:10.2355/isijinternational.38.1311

    Article  Google Scholar 

  7. Takahashi H., Kawai H., Suzuki Y.: Analysis of stress and buoyancy for solids flow in the lower part of a blast furnace. ISIJ Int. 57, 215–226 (2002)

    Google Scholar 

  8. Zaimi S.A., Akiyama T., Guillot J.B., Yagi J.I.: Validation of a blast furnace solid flow model using reliable 3-D experimental results. ISIJ Int. 40, 332–341 (2000). doi:10.2355/isijinternational.40.332

    Article  Google Scholar 

  9. Zhou Z.Y., Yu A.B., Zulli P.: A simplified mathematical model for gas–solid flow in a blast furnace. Prog. Comput. Fluid Dyn. 4, 39–45 (2004). doi:10.1504/PCFD.2004.003786

    Article  Google Scholar 

  10. Zaimi S.A., Akiyama T., Guillot J.B., Yagi J.I.: Sophisticated multi-phase multi-flow modelling of the blast furnace. ISIJ Int. 40, 322–331 (2000). doi:10.2355/isijinternational.40.322

    Article  Google Scholar 

  11. Jackson R.: The Dynamics of Fluidized Particles. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  12. Tsuji Y., Kawaguchi T., Tanaka T.: Discrete particle simulation of 2-dimensional fluidized-bed. Powder Technol. 77, 79–87 (1993). doi:10.1016/0032-5910(93)85010-7

    Article  Google Scholar 

  13. Xu B.H., Yu A.B.: Numerical simulation of the gas–solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics. Chem. Eng. Sci. 52, 2785–2809 (1997). doi:10.1016/S0009-2509(97)00081-X

    Article  Google Scholar 

  14. Zhu H.P., Zhou Z.Y., Yang R.Y., Yu A.B.: Discrete particle simulation of particulate systems: Theoretical developments. Chem. Eng. Sci. 62, 3378–3396 (2007). doi:10.1016/j.ces.2006.12.089

    Article  Google Scholar 

  15. 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. 63, 5728–5770 (2008). doi:10.1016/j.ces.2008.08.006

    Article  Google Scholar 

  16. Latzel M., Luding S., Herrmann H.J.: Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell. Granul. Matter 2, 123–135 (2000). doi:10.1007/s100350000048

    Article  Google Scholar 

  17. Zhu H.P., Yu A.B.: Averaging method of granular materials. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66, 021302 (2002). doi:10.1103/PhysRevE.66.021302

    ADS  Google Scholar 

  18. Zhou Z.Y., Zhu H.P., Yu A.B., Wright B., Pinson D., Zulli P.: Discrete particle simulation of solid flow in a model blast furnace. ISIJ Int. 45, 1828–1837 (2005). doi:10.2355/isijinternational.45.1828

    Article  Google Scholar 

  19. Zhou Z.Y., Zhu H.P., Yu A.B., Wright B., Zulli P.: Discrete particle simulation of gas–solid flow in a blast furnace. Comput. Chem. Eng. 32, 1760–1772 (2008). doi:10.1016/j.compchemeng.2007.08.018

    Article  Google Scholar 

  20. Katayama K., Wakabayashi S., Inada T., Takatani K., Yamaoka H.: Stress analysis of the packed bed in blast furnace. Tetsu-to-Hagane 83, 91–96 (1997)

    Google Scholar 

  21. Nouchi T., Sato T., Sato M., Takeda K., Ariyama T.: Stress field and solid flow analysis of coke packed bed in blast furnace based on DEM. ISIJ Int. 45, 1426–1431 (2005). doi:10.2355/isijinternational.45.1426

    Article  Google Scholar 

  22. Zhu H.P., Yu A.B.: The effects of wall and rolling resistance on the couple stress of granular materials in vertical flow. Phys. A-Stat. Mech. Its Appl. 325, 347–360 (2003). doi:10.1016/S0378-4371(03)00143-2

    Article  MATH  ADS  MathSciNet  Google Scholar 

  23. Xu B.H., Yu A.B., Chew S.J., Zulli P.: Numerical simulation of the gas–solid flow in a bed with lateral gas blasting. Powder Technol. 109, 13–26 (2000). doi:10.1016/S0032-5910(99)00223-5

    Article  Google Scholar 

  24. Di Felice R.: The voidage function for fluid–particle interaction systems. Int. J. Multiph. Flow 20, 153–159 (1994). doi:10.1016/0301-9322(94)90011-6

    Article  MATH  Google Scholar 

  25. Cundall P.A., Strack O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29, 47–65 (1979)

    Article  Google Scholar 

  26. Patankar S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere, New York (1980)

    MATH  Google Scholar 

  27. Zhu H.P., Yu A.B.: Steady-state granular flow in a 3D cylindrical hopper with flat bottom: macroscopic analysis. Granul. Matter 7, 97–107 (2005). doi:10.1007/s10035-004-0191-9

    Article  MATH  Google Scholar 

  28. Moreea S.B.M., Nedderman R.M.: Exact stress and velocity distributions in a cohesionless material discharging from a conical hopper. Chem. Eng. Sci. 51, 3931–3942 (1996). doi:10.1016/0009-2509(96)00248-5

    Article  Google Scholar 

  29. Gremaud, P.A., Matthews, J.V., Shearer, M.: Similarity solutions for granular materials in hoppers. In: Bona J., Saxton K., Saxton R. (eds.) Nonlinear PDE’s, Dynamics, and Continuum Physics, Contemporary Mathematics, vol. 255, pp. 79–95. AMS, Providence (2000)

  30. Potapov A.V., Campbell C.S.: Computer simulation of hopper flow. Phys. Fluids 8, 2884–2894 (1996). doi:10.1063/1.869069

    Article  MATH  ADS  Google Scholar 

  31. Jop P., Forterre Y., Pouliquen O.: A constitutive law for dense granular flows. Nature 441, 727–730 (2006). doi:10.1038/nature04801

    Article  ADS  Google Scholar 

  32. Luding S.: The effect of friction on wide shear bands. Particul. Sci. Technol. 26, 33–42 (2008). doi:10.1080/02726350701759167

    Article  Google Scholar 

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Authors and Affiliations

  1. Lab for Simulation and Modelling of Particulate Systems, School of Materials Science and Engineering, University of New South Wales, Sydney, NSW, 2052, Australia

    H. P. Zhu, Z. Y. Zhou & A. B. Yu

  2. BlueScope Steel Research Laboratories, P.O. Box 202, Port Kembla, NSW, 2505, Australia

    P. Zulli

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  1. H. P. Zhu
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  3. A. B. Yu
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  4. P. Zulli
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Correspondence to H. P. Zhu.

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Zhu, H.P., Zhou, Z.Y., Yu, A.B. et al. Stress fields of solid flow in a model blast furnace. Granular Matter 11, 269–280 (2009). https://doi.org/10.1007/s10035-008-0123-1

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  • DOI: https://doi.org/10.1007/s10035-008-0123-1

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