A kind of method and equipment for critical boron concentration search
A technology of boron concentration and equipment, applied in design optimization/simulation, complex mathematical operations, reduction of greenhouse gases, etc., can solve problems such as large impact, low search efficiency, and increased calculation amount, so as to avoid human subjective guessing and improve Search efficiency, the effect of reducing the number of searches
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Embodiment 1
[0061] This embodiment provides a method for searching for critical boron concentration by using an inverse perturbation algorithm. The derivation process is as follows:
[0062] Step 1, calculation of boron concentration value based on perturbation theory
[0063] The key step in the search for critical boron concentration is to obtain the boron concentration value, which can be calculated by perturbation theory. The neutron equilibrium equation can be expressed as equation (1):
[0064] Aψ-λBψ=0 (9);
[0065] Among them, B is the fission operator, A is the sum of other operators except the fission operator, λ is the reciprocal of the effective multiplication factor, and ψ is the neutron flux. The perturbed state of Equation (16) can be expressed as Equation (2):
[0066] A'ψ'-λ'B'ψ'=0(10); where δ represents partial differential; A'=A+δA, B'=B+δB, λ'=λ+δλ, ψ'=ψ+ δψ, substituted into equation (16), retaining the first-order differential term, ignoring higher-order small q...
Embodiment 2
[0087] Based on a method for realizing critical boron concentration search using an inverse perturbation algorithm provided in Embodiment 1, a specific calculation case is given as follows:
[0088] like figure 1 As shown, the specific process of the inverse perturbation algorithm (IPM) of the present invention and the existing Newton-Raphson method (NPM) are shown. Both of them complete the function of critical search through iteration, and the difference lies in the calculation of the boron concentration value. . The inverse perturbation algorithm uses the perturbation theory to calculate the boron concentration value by combining the neutron flux and the accompanying neutron flux, without the need for two critical calculations; while the Newton-Raphson method requires two calculations of the boron concentration value to obtain the effective proliferation factor k eff Only then can the boron concentration value be calculated. Apply the above two methods to a cell benchmark...
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