K. Kobayashi and S. Tsumura

More documents

Recommendations

Info

Table I. One Group Constants 6) Moderator Core D (cm) 13.1 4.71 Σa(cm −1 ) 0.0177 0.0829 Σf(cm −1 ) 0.0594 ν 2.44 Xenon Iodine γ 0.003 0.061 λ(s −1 ) 0.209 ×10 −4 0.287 ×10 −4 σa(cm 2 ) 0.272 ×10 −17 by the finite difference method, and the flux and xenon densities thus obtained are shown in Fig.2 for the same case of Fig.1, where the average flux φ 0 1 = 5 × 1013cm−2sec−1 is used. From this figure, it is known that the assumption of sine shape and constant for the flux and xenon respectively, is reasonable. The critical thickness, coupling coefficients, damping time constant p and period are shown in Table II. In the coupled reactor theory, B =6.92 × 10−2cm−1 and δ=3.68cm are used in Eq.(113) for all cases, which are obtained by fitting the sine function of Eq.(113) to the numerical values of the flux obtained by the finite difference method. Table II. Critical Thickness, Coupling Coefficients, Damping Constant and Period 2a a) 1 Critical Thickness (cm) k11 k12 1/p Period (cm) FD Method b) CR Theory c) (×10 −2 ) (h) (h) 10 33.99 33.87 0.37% d) 0.9829 3.94 3.73 — e) 15 35.87 35.80 0.22% 1.0016 2.11 4.78 46.1 20 36.79 36.75 0.12% 1.0109 1.21 8.73 27.4 22.5 37.08 37.04 0.12% 1.0137 0.931 21.1 24.5 25 37.29 37.25 0.09% 1.0159 0.720 −26.5 23.9 a) Distance between cores b) Finite difference method c) Coupled reactor theory d) Difference from the finite difference method e) No oscillation As seen in Table II, the critical thickness by the coupled reactor theory approaches those by the finite difference method, as the distance between cores becomes larger. This may be due to the fact that one core becomes more independent of the other one as the distance between cores becomes larger, and the flux shape approaches to a pure sine shape. As shown in Table II, the coupling coefficient k12 becomes smaller, as the distance between cores, 2a1, becomes larger, then the xenon instability becomes larger. In the present approximations, ∆1 + ∆2 =2k 0 12. The conditions of Eqs.(89) and (91) for the 16
Importance Function G1(x) G1(x) 1 0.5 0 –a3 Reflector Core 1 Moderator Core 2 Reflector –a2 oscillation and divergence become –a1 a1 a2 a3 –50 0 50 Distance from the center of the syatem (cm) Figure 1. Importance function G1(x) 0.0043 = ∆− 2
Page 1 and 2: AN ANALYSIS OF XENON OSCILLATIONS U
Page 3 and 4: We use the boundary condition that
Page 5 and 6: Using the assumption that the fissi
Page 7 and 8: 2..3 KINETICS EQUATIONS FOR IODINE
Page 9 and 10: Solving the multi-group diffusion e
Page 11 and 12: which can be written in a form wher
Page 13 and 14: 2..6 CONTROL OF XENON OSCILLATIONS
Page 15: where κi = Σai/Di, i = c, r and
Page 19 and 20: AOI-AOX 0.002 0 -0.002 B C A D E -0
Page 21: CONCLUSIONS It has been shown that

K. Kobayashi and S. Tsumura

Create successful ePaper yourself

Delete template?

Save as template?