Analysis of Detailed Neutron Fluxes in a PWR Pressure Vessel by Two- and Three-Dimensional Pallas Transport Codes

To examine the effect of modeling of a pres-surized water reactor (PWR) on predicting neutron field at the beltline of its pressure vessel (PV), neutron transport calculations were performed for various models of a 1000-MW( electric) class PWR in three different geometries-(R,θ), (R,Z), and a combination of (X,Y,Z) and (R,θ). A three-dimen-sional calculation with PALLAS-XYZ is used as a standard for the other two-dimensional (R,θ) and (R,Z) calculations made with PALLAS-2DRT and -2DCY. The source normalization essential for the (R,θ) calculation is reasonably made by dividing the total source neutrons by an effective core length, which provides calculated results in fair agreement with those calculated with a standard model for both radial attenuation and azimuthal variation of the integral fluxes above 1.0 and 0.1 MeV and also of displacements per atom (dpa). The (R,Z) calculations made in two different models were reviewed to find which model is more reasonable in evaluating neutron integral fluxes and dpa in a pressure vessel without underestimation. The effect of neglect of the axial leakage in (R,θ) transport calculations on neutron fluxes in a PV at the beltline region indicates little effect up to the distance before the vessel outer surface in contrast with an appreciable effect outside it. The azimuthal peaking is conspicuous and a factor of ∼2.7 at 40 deg compared with the results at 0 deg in both integral fluxes above 1.0 and 0.1 MeV and dpa for the PWR. The peaking values at the PV inner surface are 3.8 X 10¹⁰ and 7.4 X 10¹⁰ n/cm^2.S for integral fluxes above 1.0 and 0.1 MeV, respectively, and 5.4 X 10⁻¹¹ dpa/s. The analysis of a PC A 8/7 configuration indicates accuracy of within 30% and the analysis of Arkansas Nuclear One PWR plant indicates accuracy of the order of 20% for integral fluxes above 1.0 and 0.5 MeV at one measuring position in the cavity behind its PV, although marked discrepancies within a factor of 2 are observed at several energies in a neutron energy spectrum at the same position. The integral flux above 1 MeV is 1.01 X 10¹⁰ n/cm^2. s at 12.5 deg, a peak azimuthal position of the inner surface of the PV; however, the azimuthal peaking is rather small (within 10%) compared with 9.29 X 10⁹ n/cm² .s at 0 deg.