Research Article
A New Precursor Integral Method for Solving Space-Dependent Kinetic Equations in Neutronic and Thermal-Hydraulic Coupling System
Table 8
Comparison among flux approximations in the precursor integral method for HTR-PM reactivity insertion in Δt = 100 ms.
| | | Independent variables = 0.1 ms | Zero-order Taylor expansion | First-order Taylor expansion | Exponential expansion |
| | 0.0 | — | 1.00000 | 1.00000 | 1.00000 | 1.00000 | | 0.1 | 100.0 | 1.26681 | 1.21258 (−4.28e0) | 1.21549 (−4.05e0) | 1.21559 (−4.04e0) | | — | 10.0 | — | 1.25987 (−5.47e − 1) | 1.26017 (−5.24e − 1) | 1.26134 (−4.32e − 1) | | 0.2 | 100.0 | 1.38952 | 1.33279 (−4.08e0) | 1.33866 (−3.66e0) | 1.33883 (−3.64e0) | | — | 10.0 | — | 1.38296 (−4.72e − 1) | 1.38363 (−4.23e−1) | 1.38424 (−3.79e − 1) | | 0.3 | 100.0 | 1.45391 | 1.40613 (−3.28e0) | 1.41429 (−2.72e0) | 1.41449 (−2.71e0) | | — | 10.0 | — | 1.44884 (−3.48e − 1) | 1.44977 (−2.85e − 1) | 1.44978 (−2.84e − 1) | | 0.4 | 100.0 | 1.49410 | 1.45511 (−2.60e0) | 1.46484 (−1.95e0) | 1.46507 (−1.94e0) | | — | 10.0 | — | 1.49020 (−2.61e − 1) | 1.49129 (−1.88e − 1) | 1.49129 (−1.88e − 1) | | 0.5 | 100.0 | 1.52388 | 1.49118 (−2.14e0) | 1.50196 (−1.43e0) | 1.50220 (−1.42e0) | | - | 10.0 | — | 1.52071 (−2.08e−1) | 1.52188 (−1.31e − 1) | 1.52189 (1.30e − 1) | | 0.6 | 100.0 | 1.54891 | 1.52024 (−1.85e0) | 1.53172 (−1.10e0) | 1.53195 (−1.08e0) | | — | 10.0 | — | 1.54615 (−1.78e − 1) | 1.54738 (−9.87e − 2) | 1.54738 (−9.87e − 2) | | 0.7 | 100.0 | 1.57157 | 1.54533 (−1.66e0) | 1.55731 (−9.07e − 1) | 1.55754 (−8.92e − 1) | | — | 10.0 | — | 1.56903 (−1.61e − 1) | 1.57029 (−8.14e − 2) | 1.57029 (−8.14e − 2) | | 0.8 | 100.0 | 1.59289 | 1.56809 (−1.55e0) | 1.57029 (−8.14e − 2) | 1.58066 (−7.67e − 1) | | — | 10.0 | — | 1.59046 (−1.52e − 1) | 1.59175 (−7.15e − 2) | 1.59175 (−7.15e − 2) |
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