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

By Jess C Gehin

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Cut Cut 1'" gu ( ul _llu ,ran The remaining term in Eq. I (,,P, """,,,, L""'"' + " .. ,,r t,.. ,, , _s,_,,,,, _,,,,,,,++. integrated flux since the leakages are related to the net currents which are in turn related to the spatial derivative of the flux, Hence, t tte leakages for a third order polynomial approximation have a quadratic form, Since the leakages are typically smaller than the net currents, errors in the leakages should be smaller and less significant the errors in the net currents.

AC',dt), d = 1,'_,,, ,,, , D, An equation for the shape function results front substitution (3,25) of the factorization 13,17i into Eq. fia) V t ,I _lSttlT'lti):_ Mlt} ...... L(t) i3,26t function we obtain V,. t 7,(t---_)d_Tlt) ! ,t q(t) S(t)+ _== _,\d ca(t) 'r( t ) _ -----. plitude fuiiction is still present in this equation. z,) Thus, the calculation of the shape function at a given time requires that we know the amplitude function at that time. averaged we can solve the time dependent fluxes and apply the normalization, 53 nodal equations, Eq.

Cross Section Feedback For the purposes of this investigation, hydraulics behavior the cross section feedback from the thermal. o,.. 0and p:0 represent the reference conditions. pendence can, in general, accurately represent ranges of the temperatures and densities. The linear functional the actual cross sections over limited For the purposes of this investigation 58 de- this linear assumption will be sutt_cient. Actual design calculations, however, may require that Eq, t3,35) be replaced by table look-up or polynomial fitting procedures to obtain a tnore accurate cross section representation.

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