S4 Solution of the Transport Equation for Eigenvalues: Isotropic, Forward and Backward Scattering in a Slab

Year 2017, Volume: 12 Issue: 2, 1 - 5, 30.11.2017

Hakan Öztürk

Abstract

Abstract: The neutron transport equation is solved
numerically for monoenergetic neutrons in a finite homogeneous slab with
backward and forward scattering for the eigenvalue spectrum. The
forward-backward-isotropic (FBI) scattering kernel is chosen for representing
the neutron scattering in transport equation. Then, the transport equation is
converted into a discrete ordinates form by using the integral transform
technique with the even-order Gauss-Legendre quadrature set. Finally, the
eigenvalues are calculated for a medium from weakly absorbing to highly
scattering condition using various values of the scattering, backward and
forward scattering parameters. Gauss-Legendre quadrature sets are used for all
calculations and the calculated eigenvalues are given in the tables.

Keywords

Transport Equation , Forward and Backward Scattering , Discrete Ordinates , Eigenvalues

Transport Denkleminin Özdeğerler için S4 Çözümü: Dilimde İzotropik, İleri ve Geri Saçılma

Abstract

Özet: İleri ve geri saçılmalı sonlu homojen bir dilimde tek enerjili nötronların özdeğer spektrumu için nötron transport denklemi nümerik olarak çözülmüştür. Transport denklemindeki nötron saçılmasını temsilen, ileri-geri-izotropic (FBI) saçılma fonksiyonu tercih edilmiştir. Daha sonra, çift-mertebeli Gauss-Legendre kuadratür seti ile integral dönüşüm tekniği kullanılarak transport denklemi diskret-ordinatlar haline dönüştürülmüştür. Son olarak, faklı saçılma, ileri ve geri saçılma parametreleri kullanılarak zayıf yutulmalı bir ortamdan kuvvetli saçılmalı bir ortama kadar özdeğerler hesaplanmıştır. Bütün hesaplamalarda Gauss-Legendre kuadratür setleri kullanılmış ve hesaplanan özdeğerler çizelgelerde verilmiştir.

Keywords

Transport Denklemi , İleri ve Geri Saçılma , Diskret Ordinatlar , Özdeğerler

References

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