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Eulerian steady state solution of boiling curve for impinging water jet on moving hot metal plate

  • Gaurav Abhay Kulkarni
  • Ashok Kumar Nallathambi
  • Eckehard Specht
Original
  • 25 Downloads

Abstract

This paper proposes a method for obtaining boiling curve from experimental temperature measurement for an impinging water stream on the moving hot plate without using the inverse method. Using infrared thermography, temperature profiles on the back side of the moving hot metal sheet were measured. On the front side, water impinges on the hot region and induces pre-cooling in the dry region. This experimental setup can be treated as an impinging region of the DC casting. Once the Eulerian steady state is reached, temperature profiles can be approximated as a single curve using Boltzmann function. With this function, energy balance is conducted, including the advection term to obtain the boiling curve. It is observed that the obtained boiling curve is similar to the boiling curve obtained from inverse solution.

Keywords

Heat transfer analysis Jet impingement quenching DC casting Boiling curve Wetting front 

Notes

Acknowledgments

The authors wishes to acknowledge the financial support provided by the Graaduiertenkolleg-1554 (GKMM) through the German Research Foundation (DFG).

References

  1. 1.
    Sengupta J, Cockcroft SL, Maijer DM, Wells MA, Larouche A (2004) On the development of a three-dimensional transient thermal model to predict ingot cooling behavior during the start-up phase of the direct chill-casting process for an AA5182 aluminium alloy ingot. Metall and Mater Trans B 35B:523–540CrossRefGoogle Scholar
  2. 2.
    Weckman DC, Niessen P (1982) A numerical simulation of the D C continuous casting process including nucleate boiling heat transfer. Metall Trans B 13B:593–602CrossRefGoogle Scholar
  3. 3.
    Bakken JA, Bergström T (1986) Heat transfer measurements during DC casting of aluminium part i : Measurement technique. J Light Met 3:883–889Google Scholar
  4. 4.
    Jensen EK, Johansen S, Bergström T, Bakken JA (1986) Heat transfer measurements during DC casting of aluminium part ii: Results and verification for extrusion ingots. J Light Met 3:891–896Google Scholar
  5. 5.
    Drezet JM, Rappaz M, Grün GU, Gremaud M (2000) Dertermination of thermophysical properties and boundary conditions of direct chill-cast aluminium alloys using inverse methods. Metall and Mater Trans A 31A:1627–1634CrossRefGoogle Scholar
  6. 6.
    Elias E, Yadigarogul G (1977) A general one-dimensional model for conduction-controlled rewetting of a surface. Nucl Eng Des 42-2:185–194CrossRefGoogle Scholar
  7. 7.
    Experimental investigation of circular free-surface jet impingement quenching: Transient hydrodynamics and heat transfer, Experimental Thermal and Fluid Science 35 - 7Google Scholar
  8. 8.
    Implementation of one and three dimensional models for heat transfer coeffcient identification over the plate cooled by the circular water jets, Heat Mass Transfer 54 - 8Google Scholar
  9. 9.
    Local heat transfer from a hot plate to a water jet, Heat Mass Transfer 39Google Scholar
  10. 10.
    Wells MA, Li D, Cockcroft SL (2001) Influence of surface morphology, water flow rate and sample thermal history on the boiling-water heat transfer during direct-chill casting of commercial aluminum alloys. Metall and Mater Trans B 32B:929–939CrossRefGoogle Scholar
  11. 11.
    Nallathambi AK, Specht E (2009) Estimation of heat flux in array of jets quenching using experimental and inverse finite element method. J Mater Process Technol 209:5325–5332CrossRefGoogle Scholar
  12. 12.
    Mozumder AK, Monde M, Woodfield PL (2005) Delay of wetting propagation during jet impingement quenching for a high temperature surface. Int J Heat Mass Transf 48:5395–5407CrossRefGoogle Scholar
  13. 13.
    Mitsutake Y, Monde M (2001) Heat transfer during transient cooling of high temperature surface with an impinging jet. Heat Mass Transf 37:321–328CrossRefGoogle Scholar
  14. 14.
    Akmal M, Omar AMT, Hamed MS (2008) Experimental investigation of propagation of wetting front on curved surfaces exposed to an impinging water jet. Int J Microstruct Mater Prop 3:645–681Google Scholar
  15. 15.
    Effect of surface thickness on the wetting front velocity during jet impingement surface cooling, Heat Mass Transfer 53Google Scholar
  16. 16.
    Beck JV, Blackwell B, St-Clair CR (1985) Inverse heat conduction - ill-posed problems. Wiley, New YorkzbMATHGoogle Scholar
  17. 17.
    Monde M (2000) Analytical methods in inverse heat transfer problem using laplace transform technique. Int J Heat Mass Transf 43:3965–3975CrossRefzbMATHGoogle Scholar
  18. 18.
    Ijaz UZ, Khambampati AK, Kim MC, Kim S, Kim KY (2007) Estimation of time-dependent heat flux and measurement bias in two-dimensional inverse heat conduction problems. Int J Heat Mass Transf 50:4117–4130CrossRefzbMATHGoogle Scholar
  19. 19.
    Deng S, Hwang Y (2006) Applying neural networks to the solution of forward and inverse heat conduction problems. Int J Heat Mass Transf 49:4732–4750CrossRefzbMATHGoogle Scholar
  20. 20.
    Huang CH, Wu HH (2006) An inverse hyperbolic heat conduction problem in estimating surface heat flux by conjugate gradient method. J Phys D Appl Phys 39:4087–4096CrossRefGoogle Scholar
  21. 21.
    Xue QW, Yang HT (2005) Conjugate gradient method for the hyperbolic inverse heat conduction problem with multi-variables. Chin J Comput Phys 22:417–424Google Scholar
  22. 22.
    Groß S, Soemers M, Mhamdi A, Al Sibai F, Reusken A, Marquardt W, Renz U (2005) Identification of boundary heat fluxes in a falling film experiment using high resolution temperature measurements. Int J Heat Mass Transf 48:5549–5562CrossRefGoogle Scholar
  23. 23.
    Gradeck M, Quattara JA, Rémy B, Maillet D (2012) Solution of an inverse problem in the hankel space – infrared thermography applied to estimation of a transient cooling flux. Exp Thermal Fluid Sci 36:56–64CrossRefGoogle Scholar
  24. 24.
    Caron E, Wells MA (2009) Secondary cooling in the direct-chill casting of magnesium alloy az31. Metall and Mater Trans B 40B:585–595CrossRefGoogle Scholar
  25. 25.
    Opstelten IJ, Rabenberg JM (2016) Determination of the thermal boundary conditions during aluminum dc casting from experimental data using inverse modeling. Light Metals 3:665–671Google Scholar
  26. 26.
    Hnizdil M, Chabicovsky M, Raudensky M (2015) Influence of the impace angle and pressure on the spray cooling of vertically moving hot steel surfaces. Mater Technol 49:333–336Google Scholar
  27. 27.
    Physical metallurgy of direct chill casting of aluminum alloys, CRC Press 49Google Scholar
  28. 28.
    Alam U, Krol J, Specht E, Schmidt J (2008) Enhancement and local regulation of metal quenching using atomized spray. J ASTM Int 5:1–10.  https://doi.org/10.1520/JAI101805 CrossRefGoogle Scholar
  29. 29.
    Agrawal MK, Sahu SK (2013) Analysis of conduction-controlled rewetting of a hot surface by variational method. Heat Mass Transf 49:963–971.  https://doi.org/10.1007/s00231-013-1139-6 CrossRefGoogle Scholar
  30. 30.
    Yamanouchi A (1968) Effect of core spray cooling in transient state after loss of coolant accident. J Nucl Sci Technol 5(11):547–558.  https://doi.org/10.1080/1881124819689732513 CrossRefGoogle Scholar
  31. 31.
    Filipovic J, Incropera F P, Viskanta R (1995) Rewetting temperatures and velocity in a quenching experiment. Exp Heat Transfer 8:257–270CrossRefGoogle Scholar
  32. 32.
    Kraushaar H, Jeschar R, Heidt V, Jensen E, Schneider W (1995) Correlation of surface temperatures and heat transfer by D C casting of aluminium ingots, Light Metals (Warrendale PA), pp 1055–1059Google Scholar
  33. 33.
    Grandfield J, Hoadley A, Instone S (1997) Water cooling in direct chill casting: Part 1, boiling theory and control, Light Metals (Warrendale PA), pp 691–700Google Scholar
  34. 34.
    Wiskel J, Cockcroft S (1996) Heat-flow-based analysis of surface crack formation during the start-up of the direct chill casting process: Part ii experimental study of an aa5182 rolling ingot. Metall and Mater Trans B 27 (1):129–137CrossRefGoogle Scholar
  35. 35.
    Watanabe Y, Hayashi N (1996) Light metals 1996, anaheim, ca. In: Hale W (ed). TMS, Warrendale, pp 979–984Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Gaurav Abhay Kulkarni
    • 1
  • Ashok Kumar Nallathambi
    • 1
  • Eckehard Specht
    • 1
  1. 1.Institute of Fluid Dynamics and ThermodynamicsOtto von Guericke University MagdeburgMagdeburgGermany

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