Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Archives of Thermodynamics

The Journal of Committee on Thermodynamics and Combustion of Polish Academy of Sciences

4 Issues per year


CiteScore 2016: 0.54

SCImago Journal Rank (SJR) 2016: 0.319
Source Normalized Impact per Paper (SNIP) 2016: 0.598

Open Access
Online
ISSN
2083-6023
See all formats and pricing
More options …

Radiation heat transfer model using Monte Carlo ray tracing method on hierarchical ortho-Cartesian meshes and non-uniform rational basis spline surfaces for description of boundaries

Paweł Kuczyński
  • Corresponding author
  • Institute of Power Engineering — Research Institute, Thermal Division, Augustowka 36, 02-981 Warszawa, Poland
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Ryszard Białecki
  • Silesian University of Technology, Institute of Heat Engineering, Konarskiego 22, 44-100 Gliwice, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-12-04 | DOI: https://doi.org/10.2478/aoter-2014-0014

Abstract

The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD). The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS) surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.

Keywords: Radiation heat transfer; Monte Carlo; Ray traing; NUBRS surfaces

References

  • [1] Mahan J.R.: Radiation Heat Transfer: A Statistical Approach. JohnWiley & Sons, New York 2002.Google Scholar

  • [2] Modest M.F.: Radiative Heat Transfer, 2nd Edn. Academic Press, 2003.Google Scholar

  • [3] Zeeb C.N., Burns P.J., Branner K., Dolaghan J.: User’s manual for MONT3D-Vers. 2.4. Department of Mechanical Engineering. Colorado State University, Fort Collins 1999.Google Scholar

  • [4] OpenFOAM. www.openfoam.com.Google Scholar

  • [5] Fujimoto A.: Accelerated Ray Tracing. In: Proc. Computer Graphics, Tokyo 1985, 41-65.Google Scholar

  • [6] Fujimoto A., Tanaka T., Iwata K.: ARTS: Accelerated Ray-Tracing System. IEEE Comput. Graph. 6(1986), 4, 16-26.CrossrefGoogle Scholar

  • [7] Amanatides J., Woo A.: A Fast Voxel Traversal Algorithm for Ray Tracing. In: Proc. Eurographics Conf., 1987.Google Scholar

  • [8] Węcel G.: Mathematical Modelling of Coupled Radiative and Convective Heat Transfer. PhD. thesis. Silesian UT, Institute of Thermal Technology, Gliwice 2003.Google Scholar

  • [9] Białecki R.A., Węcel G.: Solution of conjugate radiation convection problems by a BEM FVM technique. J. Quant. Spectrosc. Radiat. Transf. 84(2004), 539-550.Google Scholar

  • [10] Zeeb C.N., Dolaghan J.S., Burns P.J.: An efficient Monte Carlo particle tracing algorithm for large, arbitrary geometries. Numer. Heat Tr. B-FUND 39(2001), 4, 325-344.Google Scholar

  • [11] Mazumder S.: Methods to accelerate ray tracing in the Monte Carlo Method for surface-to-surface radiation transport. J. Heat Transf. 128(2006), 9, 945-952.CrossrefGoogle Scholar

  • [12] Glassner A.S.: Space subdivision for fast ray tracing. IEEE Comput. Graph. 4(1984), 10, 15-22.CrossrefGoogle Scholar

  • [13] Jansen F. W.: Data structures for ray tracing. In: (L.R.A. Kessener et al., Eds.) Data structures for raster graphics. Springer-Verlag, Berlin 1986, 57-73.Google Scholar

  • [14] Piegl L., Tiller W.: The NURBS Book, Monographs in Visual Communication, 2nd Edn. Springer-Verlag, Berlin Heidelberg 1997.Google Scholar

  • [15] Farin G.: Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. Academic Press Inc., New York 1990.Google Scholar

  • [16] Pabst H.F., Springer J.P., Schollmeyer A., Lenhart R., Lessig C., Froehlich B.: Ray casting of trimmed NURBS surfaces on the GPU. In: Proc. Interactive Ray Tracing 2006, IEEE Symposium, 2006, 151-160.Google Scholar

  • [17] Whitted T.: An improved illumination model for shaded display. Commun. ACM. 23(1980), 6, 343-349.CrossrefGoogle Scholar

  • [18] Rubin S.M., Whitted T.: A 3-dimensional representation for fast rendering of complex scenes. Comput. Graphics 14(1980), 3, 110-116.Google Scholar

  • [19] Toth D.L.: On ray tracing parametric surfaces. Comput. Graphics 19(1985), 3, 171-179 (SIGGRAPH ’85 Proc.).Google Scholar

  • [20] Martin W., Cohen E., Fish R., Shirley P.: Practical ray tracing of trimmed NURBS surfaces. J. Graph. Tools 5(2000), 1, 27-52.Google Scholar

  • [21] Geimer M., Abert O.P.: Interactive ray tracing of trimmed bicubic Bezier surfaces without triangulation. In: Proc. 13th Int. Conf. in Central Europe on Computer Graphics, Visualizaction and Computer Vision WSCG 2005, 71-78.Google Scholar

  • [22] Abert O.P., Geimer M., Muller S.: Direct and fast ray tracing of NURBS surfaces. In: Proc. Interactive Ray Tracing 2006, IEEE Symposium, 2006, 161-168.Google Scholar

  • [23] Kajiya J.T.: Ray tracing parametric patches. Comput. Graphics 16(1982), 3, 245-254 (SIGGRAPH ’82 Proc.).Google Scholar

  • [24] Nishita T., Sederberg T.W., Kakimoto M.: Ray tracing trimmed rational surface patches. Comput. Graphics 24(1990), 4, 337-345.Google Scholar

  • [25] Efremov A., Havran V., Seidel H. P.: Robust and numerically stable Bezier clipping method for ray tracing NURBS surfaces. In: Proc. 21st Spring Conf. on Computer Graphics SCCG’05, 2005, 127-135.Google Scholar

  • [26] Wang S. W., Shih Z. C., Chang R. C.: An efficient and stable ray tracing algorithm for parametric surfaces. J. Inf. Sci. Eng. 18(2001), 541-561.Google Scholar

  • [27] Point Cloud Library. http://pointclouds.org/ Google Scholar

  • [28] Abert O. P.: Interactive ray tracing of NURBS surfaces by using SIMD instructions and the GPU in parallel. MSc. thesis. Univ. of Koblenz-Landau 2005.Google Scholar

  • [29] Kay T. L., Kajiya J. T.: Ray tracing complex scenes. Comput. Graphics 20(1986)(SIGGRAPH ’86 Proc.), (D.C. Evans, R.J. Athay, Eds.), 269-278 .Google Scholar

  • [30] Smits B.: Efficiency issues for ray-tracing. J. Graph. Tools 3(1998), 2, 1-14.Google Scholar

  • [31] Goldsmith J., Salmon J.: Automatic creation of object hierarchies for ray tracing. IEEE Comput. Graph. 7(1987), 5, 14-20.CrossrefGoogle Scholar

  • [32] Kopytov N.P., Mityushov E.A.: Mathematical model of reinforcement of shells made of composite materials and problem of uniform distribution of points on surfaces. Vestnik PGTU. Mechanika 4(2010), 55-66 (in Rusian).Google Scholar

  • [33] Kopytov N.P., Mityushov E.A.: The universal algorithm of uniform distribution of points on arbitrary analytic surfaces in three-dimensional space. Fund. Res. 4(2013), 618-622.Google Scholar

  • [34] Cengel Y.A.: Heat Transfer: A Practical Approach, International Edition, 2nd Edition. McGraw-Hill, 2003.Google Scholar

  • [35] ANSYS Inc. www.ansys.com.Google Scholar

  • [36] Seco Warwick Poland: www.secowarwick.com/pl Google Scholar

About the article

Received: 2014-02-15

Published Online: 2014-12-04

Published in Print: 2014-06-01


Citation Information: Archives of Thermodynamics, ISSN (Online) 2083-6023, DOI: https://doi.org/10.2478/aoter-2014-0014.

Export Citation

© Polish Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in