A quasi-static polynomial nodal method for nuclear reactor by Jess C Gehin

By Jess C Gehin

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24a) gives requires us to know the perturbation From a perturbation the in the shape function, theory point of view we would like to compute the reac- tivity using only the steady-state solution. Thus, we must choose a non-trivial weight function such that 0. 31) 5sW(t) [M0 - Lo]ww = 0. 32) WT Transposing this equation [Mo - Lo] 5S(t)= gives Therefore, if we are to avoid first order errors in reactivity, we must choose the weight function such that [M0 - Lo]T w = O. 33) Thus the desired weight function is simply the adjoint of the static nodal equations.

Dependent of the neutron diffusion equation, Polynomial Nodal Equations When the polynomial nodal method is applied 1o tile transient the expansion coettlcients determine the expansion become time dependent. diffusion equations, The same procedure is used to coefficients as in the static case. First, the transverse inte- gration procedure is used to obtain one-dimensional equations. ,. , t) : - "-'0. ,,y , -'"" (u . n, + v,,rn,l "tltl' (t) ] v'g,u,tt, (t) "t') ( 3. ,D. integration for the precursor densities which vary spatially procedure has lead in the u-direction.

_,,,,. ,. "/coupled system of equatl _O nI which wouhl be to solve, _speci_|ly for a large uumher of et_ergy groups. With however, we can sitnplify the solution procedure. the nodal balance equation only the even expansion and the second tuou_ent equation for each node involve, coetticients and are not coupled to the other node. by solving the nodal balance _,quation, Eq. t_. and substituting Thus, into the Eq, (2,46), we can obtain _'_u:'_"" and %_,_"_'"" with one (; ,. ¢; 36 _i)lutii,n, Next.

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