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Energy-Beam redistribution and absorption in a drilling or welding cavity

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Abstract

Energy redistributed and absorbed in the cavity produced by a high-intensity beam during drilling and welding is systematically and quantitatively investigated. The incident energy flux is assumed to be a realistic Gaussian distribution, and the cavity is idealized by a paraboloid of revolution having both specular and diffuse reflectivities. By using a Monte Carlo method, the results show that the energy absorbed by the cavity wall deviates markedly from the Gaussian distribution. Effects of the cavity depth-to-opening radius ratio, absorptivity, and specular reflectivity on the absorbed energy are presented. A comparison of incident energy fluxes of uniform and Gaussian distributions is also made.

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Abbreviations

b :

local Cartesian coordinate, as shown in Fig. 2

f :

focal distance = ĝ/r0, as shown in Fig. 3(a)

g :

function describing cavity surface = ĝ/r0, as shown in Fig. 2

g’ :

dg/dr

h :

cavity depth = ĥ/r0

i, j, k:

Cartesian coordinate vectors

n:

local Cartesian coordinate vector, as shown in Fig. 2

N b :

number of energy bundles

N e :

subdivisions of incident flux in a ring element

N r :

number of ring elements

q :

incident flux, as defined in Eq. [3]

q a :

dimensionless energy flux absorbed by cavity wall

Q :

beam power

r :

radial coordinate =r/r 0

R:

position vector = R/r0

R ij , Rij :

magnitude and directional vector of energy bundle,R ij =R ij /r 0, Rij = Rij/r0, as shown in Fig. 2

R′ ij , R’ij :

magnitude and direction of specularly reflected rayR′ ij =R′ ij /r 0, R′ij = R′ij/r0, as shown in Fig. 2

r0 :

cavity opening radius

r s :

a critical radius = rs/r0, as illustrated in Fig. 3(a)

t:

local Cartesian coordinate vector, as shown in Fig. 2

x, y, z :

Cartesian coordinates,x = x/r0,y = ŷ/r0,z = ž/r 0, as shown in Fig. 2

α, α o :

absorptivity and apparent absorptivity defined in Eq. [4]

θ:

angle, as shown in Fig. 2

p d,p s :

diffuse and specular reflectivity

σ :

energy distribution parameter = σ/ro

ϕ :

angle, as shown in Fig. 2

^:

dimensional quantity

′:

angles defined in local Cartesian coordinates, as shown in Fig. 2

i :

originating point

j :

striking point

References

  1. P.S. Wei and L.R. Chiou:ASME J. Heat Transfer, 1988, vol. 110, pp. 918–23.

    Article  Google Scholar 

  2. W.H. Giedt and L.N. Tallerico:Weld. J., 1988, vol. 67, pp. 299-s–304-s.

    Google Scholar 

  3. P.S. Wei, T.H. Wu, and Y.T. Chow:ASME J. Heat Transfer, 1990, vol. 112, pp. 163–69.

    Article  Google Scholar 

  4. Y. Arata:Plasma, Electron and Laser Beam Technology, ASM, Metals Park, OH, 1986, pp. 217–25.

    Google Scholar 

  5. C.E. Albright:Trends in Welding Research in the United States, S.A. David, ed., ASM, Metals Park, OH, 1982, pp. 653–65.

    Google Scholar 

  6. E.M. Sparrow:ASME J. Heat Transfer, 1962, vol. 84, pp. 283–93.

    Google Scholar 

  7. E.M. Sparrow and V.K. Jonsson:J. Appl. Mech., 1963, vol. 85, pp. 237–44.

    Google Scholar 

  8. E.M. Sparrow, E.R.G. Eckert, and V.K. Jonsson:ASME J. Heat Transfer, 1962, vol. 84, pp. 294–300.

    Google Scholar 

  9. R.A. Seban:ASME J. Heat Transfer, 1962, vol. 84, pp. 299–300.

    Google Scholar 

  10. H.H. Safwat:ASME J. Heat Transfer, 1970, vol. 92, pp. 198–201.

    Google Scholar 

  11. J.R. Howell and R.E. Durkee:ASME J. Heat Transfer, 1971, vol. 93, pp. 129–35.

    Google Scholar 

  12. J.R. Howell:Advances in Heat Transfer, T.F. Irvine, Jr. and J.P. Hartnett, eds., Academic Press, New York, NY, 1968, vol. 5, pp. 1–54.

    Google Scholar 

  13. J.S. Toor and R. Viskanta:Int. J. Heat Mass Transfer, 1968, vol. 11, pp. 883–97.

    Article  Google Scholar 

  14. G.K. Hicken, W.H. Giedt, and A.E. Bentley:Weld. J., 1991, vol. 70, pp. 69-s–75-s.

    Google Scholar 

  15. D.A. Schauer, W.H. Giedt, and S.M. Shintaku:Weld. J., 1978, vol. 57, pp. 127-s–133-s.

    Google Scholar 

  16. P.S. Wei and J.Y. Ho:Int. J. Heat Mass Transfer, 1990, vol. 33, pp. 2207–17.

    Article  Google Scholar 

  17. Metals Handbook, 9th ed., E.F. Nippes, coordinator, ASM, Metals Park, OH, 1983, vol. 6, pp. 649–51.

  18. E.M. Sparrow and R.D. Cess:Radiation Heat Transfer, Brooks/ Cole, Belmont, CA, 1966, chs. 1 and 7.

    Google Scholar 

  19. M.M. Collur and T. Debroy:Metall. Trans. B, 1989, vol. 20B, pp. 277–86.

    CAS  Google Scholar 

  20. D.G. Burkhard, D.L. Sheal, and R. Sexl:Int. J. Heat Mass Transfer, 1973, vol. 16, pp. 271–80.

    Article  Google Scholar 

  21. M.H.N. Naraghi: Ph.D. Thesis, University of Akron, Akron, OH, 1984.

    Google Scholar 

  22. R.C. Corlett:ASME J. Heat Transfer, 1966, vol. 88, pp. 376–82.

    CAS  Google Scholar 

  23. J.F. Ready:J. Appl. Phys., 1965, vol. 36, pp. 462–68.

    Article  Google Scholar 

  24. J.G. Andrews and D.R. Atthey:J. Inst. Math. Appl., 1975, vol. 15, pp. 59–72.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan China

    S. C. Wang (Graduate Student) & P. S. Wei (Professor)

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  1. S. C. Wang
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  2. P. S. Wei
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Wang, S.C., Wei, P.S. Energy-Beam redistribution and absorption in a drilling or welding cavity. Metall Trans B 23, 505–511 (1992). https://doi.org/10.1007/BF02649669

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