Half-space albedo problem for the Anlı-Güngör scattering function
-
Ali Zafer Bozkır
,
Recep Gökhan Türeci
Abstract
One speed, time-independent and homogeneous medium neutron transport equation is solved for second order scattering using the Anlı-Güngör scattering function which is a recently investigated scattering function. The scattering function depends on Legendre polynomials and the t parameter which is defined on the interval [−1, 1]. A half-space albedo problem is examined with the FN method and the recently developed SVD method. Albedo values are calculated with two methods and tabulated. Thus, the albedo values for the Anlı-Güngör scattering are compared with these methods. The behaviour of the scattering function is similar to İnönü’s scattering function according to calculated results.
-
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: None declared.
-
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Anli, F., Yasa, F., and Güngör, S. (2005). General eigenvalue spectrum in a one-dimensional slab geometry transport equation. Nucl. Sci. Eng. 150: 72–77, https://doi.org/10.13182/nse05-a2502.Search in Google Scholar
Case, K.M. and Zweifel, P.F. (1967). Linear transport theory. London: Addison-Wesley.Search in Google Scholar
Grandjean, P. and Siewert, C.E. (1979). The FN method in neutron-transport theory, Part II: applications and numerical results. Nucl. Sci. Eng. 69: 161–168, https://doi.org/10.13182/nse79-a20608.Search in Google Scholar
İnönü, E. (1973). A theorem on anisotropic scattering. Transport Theor. Stat. Phys. 3: 137–146.10.1080/00411457308205276Search in Google Scholar
İnönü, E. (1976). Scaling and time inversion for the linear mono-energetic Boltzmann equation. Phys. Fluid. 19: 1332–1335.10.1063/1.861659Search in Google Scholar
Kavenoky, A. (1978). The CN method of solving the transport equation: application to plane geometry. Nucl. Sci. Eng. 65: 209–225, https://doi.org/10.13182/nse78-a27152.Search in Google Scholar
Kawai, M., Hayashida, Y., and Uematsu, M. (1985a). Applicability of albedo-Sn transport method to analysis of radiation shielding problem. J. Nucl. Sci. Technol. 22: 959–971, https://doi.org/10.1080/18811248.1985.9735752.Search in Google Scholar
Kawai, M., Itoh, J., Hayashida, Y., and Uematsu, M. (1985b). Development of albedo-Sn transport method to analyze radiation shielding problem. J. Nucl. Sci. Technol. 22: 859–869, https://doi.org/10.1080/18811248.1985.9735738.Search in Google Scholar
Lamarsh, J.R. (1966). Introduction to nuclear reactor theory, 1st ed. New York: Addison-Wesley.Search in Google Scholar
Lamarsh, J.R. and Baratta, A.J. (2001). Introduction to nuclear engineering, 3rd ed. New Jersey: Prentice-Hall.Search in Google Scholar
Mika, J.R. (1961). Neutron transport with anisotropic scattering. Nucl. Sci. Eng. 11: 415–427, https://doi.org/10.13182/nse61-1.Search in Google Scholar
Nishimura, T., Tada, K., Yokobori, H., and Sugawara, A. (1980). Development of discrete ordinates SN code in three-dimensional (X, Y, Z) geometry for shielding design. J. Nucl. Sci. Technol. 17: 539–558, https://doi.org/10.1080/18811248.1980.9732620.Search in Google Scholar
Sahni, D.C. and Kumar, V. (1987). Numerical solution of singular integral equations of neutron transport problems. Transport Theor. Stat. Phys. 16: 959–978, https://doi.org/10.1080/00411458708204601.Search in Google Scholar
Sahni, D.C. and Tureci, R.G. (2018). Discrete eigenvalues of case spectrum with anisotropic scattering. Nucl. Sci. Eng. 191: 121–135, https://doi.org/10.1080/00295639.2018.1463748.Search in Google Scholar
Sahni, D.C., Tureci, R.G., and Bozkir, A.Z. (2019). Partial range completeness of case eigenfunctions and numerical solution of singular integral equations of particle transport problems. Paper presented at 26th International Conference on Transport Theory (ICTT-26), Paris, France, 23–27 September 2019.10.1080/23324309.2020.1819329Search in Google Scholar
Sahni, D.C., Tureci, R.G., and Bozkir, A.Z. (2020). Partial range completeness of case eigenfunctions and numerical solution of singular integral equations of particle transport problems. J. Comput. Theor. Transp. 49: 349–367, https://doi.org/10.1080/23324309.2020.1819329.Search in Google Scholar
Siewert, C.E. and Benoist, P. (1979). The FN method in neutron-transport theory, Part I: theory and applications. Nucl. Sci. Eng. 69: 156–160, https://doi.org/10.13182/nse79-1.Search in Google Scholar
Tureci, R.G. (2007). The albedo problem for pure-triplet scattering. Kerntechnik 72: 290–298, https://doi.org/10.3139/124.100358.Search in Google Scholar
Türeci, R.G. (2020). Half-space albedo problem for İnönü, linear and quadratic anisotropic scattering. Nucl. Eng. Technol. 52: 700–707.10.1016/j.net.2019.10.008Search in Google Scholar
Türeci, R.G. and Bülbül, A. (2021). Case’s method for Anlı-Güngör scattering formula. SDUFASJS, in press.10.29233/sdufeffd.925308Search in Google Scholar
Tureci, R.G. and Tureci, D. (2007). Time dependent albedo problem for quadratic anisotropic scattering. Kerntechnik 72: 59–65, https://doi.org/10.3139/124.100319.Search in Google Scholar
Türeci, R.G. and Türeci, D. (2017). Half-space albedo problem with modified FN method for linear and quadratic anisotropic scattering. Kerntechnik 82: 239–245.10.3139/124.110641Search in Google Scholar
Wolfram Research, Inc., Mathematica, Version 12.2.0, Champaign, IL (2019). Available at: https://reference.wolfram.com/legacy/language/v12/ (Accessed 23 December 2021).Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Study of a perforated hollow cylinder and twisted tape inserts as a compound device in a circular tube for heat transfer enhancement
- Pool boiling performance of oxide nanofluid on a downward-facing heating surface
- The CANDLE burnup strategy applied to small modular pressurized water reactor loading with fully ceramic microencapsulated fuel
- Automatic sentiment analysis of public opinion on nuclear energy
- One-dimensional and three-dimensional coupling simulation research of centrifugal cascade hydraulics
- Analysis of the anticipated transient without scram (ATWS) initiated by emergency power mode through the full scope simulator
- Application of radio analytical tracer technique to study the performance of industrial grade ion exchange resin exposed to UV radiations
- Radioactive waste treatment technology: a review
- Positron annihilation lifetime spectroscopy of annealed tungsten
- Simulation of cobalt-60 production in research reactors using OpenMC Monte Carlo code
- Half-space albedo problem for the Anlı-Güngör scattering function
- Calendar of events
Articles in the same Issue
- Frontmatter
- Study of a perforated hollow cylinder and twisted tape inserts as a compound device in a circular tube for heat transfer enhancement
- Pool boiling performance of oxide nanofluid on a downward-facing heating surface
- The CANDLE burnup strategy applied to small modular pressurized water reactor loading with fully ceramic microencapsulated fuel
- Automatic sentiment analysis of public opinion on nuclear energy
- One-dimensional and three-dimensional coupling simulation research of centrifugal cascade hydraulics
- Analysis of the anticipated transient without scram (ATWS) initiated by emergency power mode through the full scope simulator
- Application of radio analytical tracer technique to study the performance of industrial grade ion exchange resin exposed to UV radiations
- Radioactive waste treatment technology: a review
- Positron annihilation lifetime spectroscopy of annealed tungsten
- Simulation of cobalt-60 production in research reactors using OpenMC Monte Carlo code
- Half-space albedo problem for the Anlı-Güngör scattering function
- Calendar of events
