RU2528401C1 - Method of measuring neutron power of nuclear reactor in absolute units - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: in the method of measuring neutron power of a nuclear reactor in absolute units F=V·γ, where V is the reactor power value in arbitrary units, γ is a coefficient of proportionality, neutron power of the nuclear reactor in arbitrary units is measured as the average count rate of the neutron detector in a stationary critical state using measurement means. The coefficient of proportionality is calculated using an autocorrelation function value. The means of measuring the number of neutrons used is an ionisation chamber for determining fluctuation of the number of neutrons. The method includes separately measuring the average value of current of the ionisation chamber and the fluctuating component of the current of the ionisation chamber continuously over time with a discrete interval, calculating the autocorrelation function of the fluctuating current of the ionisation chamber and then calculating the coefficient of proportionality.

EFFECT: increasing the maximum values of F.

3 cl, 1 dwg, 1 tbl

Description

The invention relates to the physics of nuclear reactors and can be used to measure the F - neutron power of the reactor in absolute units. The measurement tasks of the reactor F must be solved when designing radiation protection, when determining the radiation resistance of VVER reactor vessels. This problem is solved during the launches of space nuclear power plants (CNES). The start of the nuclear power plant is carried out strictly in time taking into account the measurement results F. Slow or excessively fast output of the nuclear power plant at its rated power can be detrimental to it. The task in this case is complicated by the fact that the F of the reactor is to be measured in absolute units at all stages of the start-up of the reactor.

Symbols accepted in the text

F - neutron power of the reactor in absolute units [fission / second or watt]

V is the value of the reactor power in relative units [counts / second or amperes]

γ - number, proportionality coefficient [watt / ampere or division / (second - ampere)]

ε is the neutron detector efficiency [count / fission].

t - time [second]

τ - time [second]

C is the number of samples of the detector [count]

φ _хх (τ) - autocorrelation function of the number of samples of the detector [sample ² ]

f _xx (t) - autocorrelation function [ampere ² ]

I (t) - current [ampere]

- значение среднего значения тока ионизационной камеры [ампер] $$\overline{I}$$

- the value of the average current of the ionization chamber [ampere]

i (t) - fluctuating values of the ionization chamber current in time [ampere]

Y - parameter determined during the processing of experimental data [ampere / division or ampere / (watt · second)]

α - parameter, [1 / second]

D _ν = 0.795 - tabular dimensionless quantity

β _eff - dimensionless quantity

Δt - interval of measurement resolution [second]

The measurement problem F is solved in two stages. At the first, relatively simple stage, a method is chosen for measuring the reactor power in relative units (count rate of neutron detectors, current of the ionization chamber, etc.). It is important that the result of measurements of reactor power in relative units is proportional to the reactor power in absolute units. This proportionality coefficient should remain unchanged in a given range of changes of F, i.e. in this range the equality should be satisfied:

$$F=V\cdot \gamma ,gde\left(\mathrm{one}\right)$$

F is the value of the neutron power of the reactor in absolute units (in watts or in divisions per second)

V is the value of the reactor power in relative units (count rate of the neutron detector, current flowing through the ionization chamber)

γ is the coefficient of proportionality.

In the second stage, the reactor power is measured simultaneously in absolute and relative units. Based on the results of these measurements, the value of γ is calculated. Further, to determine F in the proportional band, it is enough to measure the power in relative units and multiply this measurement result by γ. The rated power of reactors is usually many orders of magnitude greater than the power level that can be measured experimentally. In practical work, the results of calculations of γ at the reactor power levels, comparable with the nominal level, are most valued.

It is proposed to measure F by statistical methods. Several varieties of statistical methods for measuring F in a critical state of a reactor are known. These methods differ in detail, all based on the study of fluctuations in the number of neutrons in a reactor. A characteristic property of fluctuations is a decrease in their amplitudes at the levels of the average values of the neutron numbers with increasing neutron power. Accordingly, the common drawback of all statistical methods without exception is the relatively small power levels at which they can be implemented. A known method of measuring F - the method of correlation analysis (MCA) is a prototype. The well-known American specialist R. Urig in his monograph “Statistical Methods in the Physics of Nuclear Reactors” (Atomizdat. 1974. Moscow) on the MCA on page 55 writes: “It should be noted that ... the background values depend on ... F ² , at that time as the amplitude ... depends only on F. Therefore, this method is limited to very low fission rates. "

MCA is based on measuring the probability of detecting a neutron at time t + τ, provided that the neutron was previously detected at time t. This probability is called the autocorrelation function φ _xx (τ) of measuring the number of samples of the detector. The values of the function φ _xx (τ) are calculated according to the results of measurements of the number of samples of the detector according to the formula:

$${\varphi }_{xx}\left(\tau \right)={\displaystyle \sum _{m=\mathrm{one}}^{N-n}\frac{C_m{C}_{m+n}}{N-n},\text{(2)}}$$

Where

C _m, C _{m + n} are the number of samples of the detector for the time interval Δt at time t and t + τ, respectively,

t = k · Δt, k = 1,2,3 ...

n = 0,1,2, ...

N is the number of samples of the detector (N >> n).

Based on the characteristics of the nuclear fission chain reaction and the properties of a stationary critical reactor without delayed neutrons, we can write the relation connecting the function φ _xx (τ) at τ> 0 with the parameters of such a reactor (R. Urig, “Statistical Methods in the Physics of Nuclear Reactors” (Atomizdat. 1974 Moscow):

$${\varphi }_{xx}\left(\tau \right)={\left(F\cdot \epsilon \cdot \Delta t\right)}^2+F\cdot \epsilon \cdot \Delta t\cdot [\frac{\epsilon \cdot D_{\nu }}{2\cdot {\beta }_{eff}^2}\cdot \alpha \cdot \Delta t\cdot e^{-\alpha \tau }],\text{Where}\text{(3)}$$

ε is the efficiency of the experimental detector

D _ν - Dyven parameter (constant, tabular value), D _ν = 0.795 for U ²³⁵ ,

β _eff is the effective fraction of delayed neutrons (a value known from the results of independent experiments or calculated from programs for calculating the kinetics of reactors),

α is the decay constant of instantaneous neutrons in a critical reactor.

The formula numerically describes fluctuations of the neutron flux in the time domain. The first term of this formula describes the probability of random pairs of neutron counts. The second term describes the probability of correlated pairs of neutron samples having a common origin. If you implement measurements directly using formula (3) when processing experimental data to determine power in absolute units, then there is a limit on power, calculated in fractions of a watt, above which measurements will become impossible. Indeed, in formula (3), the first term (background component) proportional to (F · ε) ² , starting from the indicated power limit, becomes many times larger than the second term proportional to F · ε.

). При низкой эффективности детектора (ε<<10^-4) вероятность коррелированных пар отсчетов становится много меньше случайных пар отсчетов. В этом случае не удается измерить какие-либо параметры реактора ни МКА, ни любым другим статистическим методом.A characteristic feature of statistical methods for measuring reactor parameters is the requirement for a sufficiently high efficiency of the experimental detector (ε ~ $${\beta }_{eff}^2\approx {10}^{-\mathrm{four}}$$

) With low detector efficiency (ε << 10 ^-4 ), the probability of correlated sample pairs becomes much less than random sample pairs. In this case, it is not possible to measure any reactor parameters either by the MCA or by any other statistical method.

функции I(t) и флуктуирующей составляющей $$i(t):I(t)=\overline{I}+i(t)$$

. В этих случаях корреляционная функция рассчитывается по формуле:A modernized method of correlation analysis (CIA) is proposed. This method provides measurements of reactor power to levels calculated in kilowatts. During IMCT implementation, fluctuations in the number of neutrons I (t) are presented as the sum of the average value $$\overline{I}$$

function I (t) and fluctuating component $$i(t):I(t)=\overline{I}+i(t)$$

. In these cases, the correlation function is calculated by the formula:

$$f_{xx}(t)={\displaystyle \sum _{m=\mathrm{one}}^{N-n}\frac{\left(i_m\cdot i_{m+n}\right)}{N-n},\text{Where}\text{(four)}}$$

i _m , i _{m + n} - alternating currents at time T and T + t, respectively.

t = k · Δt, k = 1,2,3 ...

n = 0,1,2, ...

N is the number of numbers of samples of the detector (N >> n)

The technical result, which the invention is directed to, is to increase the maximum values of F, measured in the following way,

The method of measuring the neutron power of a nuclear reactor in absolute units F = V · γ, where

V is the value of the reactor power in relative units,

γ = proportionality coefficient,

, измеряя отдельно среднее значение тока ионизационной камеры $$\overline{I}$$

и флуктуирующую составляющую тока ионизационной камеры i(t) непрерывно во времени с интервалом дискретности Δt, рассчитывают автокорреляционную функцию флуктуирующего тока ионизационной камеры по формулеin this case, the neutron power of a nuclear reactor in relative units is measured as the average count rate of a neutron detector in a stationary critical state by measuring means, and the proportionality coefficient is calculated using the value of the autocorrelation function, while an ionization chamber is used as a means of measuring the number of neutrons to determine the fluctuation of the number of neutrons $$I(t)=\overline{I}+i(t)$$

, measuring separately the average current value of the ionization chamber $$\overline{I}$$

and the fluctuating component of the current of the ionization chamber i (t) continuously in time with a discrete interval Δt, the autocorrelation function of the fluctuating current of the ionization chamber is calculated by the formula

, где $$f_{xx}(t)={\displaystyle \sum _{m=\mathrm{one}}^{N-n}\frac{\left(i_m\cdot i_{m+n}\right)}{N-n}}$$

where

i _m , i _{m + n} - alternating currents at time T and T + t, respectively.

t = k · Δt, k = 1,2,3 ...

n = 0,1,2, ...

N is the number of numbers of samples of the detector (N >> n),

after which the proportionality coefficient is calculated

γ = Y · exp (-α · t), where

, $$Y=\frac{\overline{I}}{fxx(t)}\cdot \frac{\alpha \cdot D_{\nu }}{2\cdot {\left({\beta }_{eff}\right)}^2}$$

,

D _ν - Dyven parameter (constant, tabular value), D _ν = 0.795 for U ²³⁵ ,

β _eff is the effective fraction of delayed neutrons

α is the decay constant of instantaneous neutrons in a critical reactor.

In this case, the discrete interval Δt≈0.1 / α is selected.

In addition, the number of measurements i (t) in time should be at least ten thousand.

Thus, an increase in the measured power is achieved due to:

1) use of an ionization chamber as a neutron detector in an experiment

2) clipping at the hardware level of the constant component from I (t) - the result of measurements of fluctuations in the number of neutrons

и отдельно i(t) - флуктуирующих значений тока ионизационной камеры во времени t с помощью усилителя У7-6 (или его аналога) с записью измеренных значений i(t) в оперативную память компьютера3) measurements of the average current value $$\left(\overline{I}\right)$$

and separately i (t) - fluctuating values of the ionization chamber current in time t with the help of the U7-6 amplifier (or its analogue) with recording the measured values of i (t) in the computer’s RAM

4) calculation of the correlation function f _xx (t) according to formula (4) using the measurement results i (t)

5) conversion of the formula (3) to the working form:

- среднее значение тока ионизационной камеры (результат измерений мощности реактора в относительных единицах) $$\overline{I}$$

- the average value of the current of the ionization chamber (the result of measurements of reactor power in relative units)

α - parameter

Dν, β _{eff -} parameters whose values are known from independent experiments

для определения параметров Y и α методом наименьших квадратов с учетом вида формулы (5)6) use of measured values $$f_{xx}(t)/\overline{I}$$

for determining the parameters Y and α by the least squares method taking into account the form of formula (5)

7) calculating the desired value of the proportionality coefficient γ according to the formula:

$$\text{γ}=\frac{\text{α}\cdot \text{Dν}}{\text{2}\cdot \text{Y}\cdot {\left({\text{β}}_{\text{eff}}\right)}^{\text{2}}}\text{(6)}$$

и i(t) во времени непрерывно с интервалом дискретности Δt от начала до конца эксперимента. Экспериментальная установка состоит из детектора нейтронов (ионизационной камеры), электрометра для измерений среднего значения тока ионизационной камеры, усилителя типа У7-6 (или его аналога) для измерений флуктуирующих значений тока ионизационной камеры на уровне среднего значения тока, преобразователя сигнала с выхода усилителя У7-6 в цифровой код, компьютера с программой, обеспечивающей запись цифрового кода в оперативную память PC и внешние носители информации. Выводят реактор в стационарное критическое состояние на заданный уровень нейтронной мощности реактора. Уровень мощности реактора ограничен максимальным значением тока ионизационной камеры, записанным в ее паспорте. Включают компьютер. Вводят в оперативную память компьютера, сопряженного с экспериментальной аппаратурой, программу записи результатов измерений значения $$\overline{I}$$

и i(t) во времени непрерывно с интервалом дискретности Δt. Указывают в программе значение Δt и число значений функции, которое планируется реализовать для достижения требуемой точности эксперимента. Обычно число значений функций i(t), записываемых в оперативную память компьютера, несколько десятков тысяч. Интервал Δt рекомендуется выбирать из расчета: Δt≈0.1/α. Примерное значение параметра α должно быть известно до опыта.The proposed method for measuring the value of γ is called the modernized method of correlation analysis, which consists in the fact that include an experimental setup for measuring values $$\overline{I}$$

and i (t) in time continuously with a discrete interval Δt from the beginning to the end of the experiment. The experimental setup consists of a neutron detector (ionization chamber), an electrometer for measuring the average current value of the ionization chamber, an U7-6 type amplifier (or its analogue) for measuring fluctuating current values of the ionization chamber at the level of the average current value, and a signal converter from the output of the U7- amplifier 6 into a digital code, a computer with a program that records the digital code into the RAM of the PC and external storage media. The reactor is brought into a stationary critical state at a predetermined neutron power level of the reactor. The power level of the reactor is limited by the maximum current value of the ionization chamber recorded in its passport. Turn on the computer. Enter into the random access memory of the computer interfaced with the experimental equipment, a program for recording the results of measurements of the value $$\overline{I}$$

and i (t) in time continuously with a discrete interval Δt. Indicate in the program the value Δt and the number of values of the function, which is planned to be implemented to achieve the required accuracy of the experiment. Typically, the number of values of the functions i (t) recorded in the computer's RAM is several tens of thousands. The interval Δt is recommended to be selected from the calculation: Δt≈0.1 / α. The approximate value of the parameter α should be known before the experiment.

In support of the possibility of realizing measurements of MMCA values of γ, a series of experiments was carried out at the reactor. The γ value was measured at three neutron power levels of ~ 50 watts, ~ 100 watts, and ~ 500 watts.

по данным измерений токов i(t) ионизационной камеры КНК-56 на трех уровнях мощности критсборки. Значения функций $$f_{xx}(t)/\overline{I}$$

помечены точками, совокупность этих данных обработана методом наименьших квадратов с учетом вида формулы (5). Пунктирной линией обозначена кривая, имеющая следующие параметры в результате обработки данных:The drawing on a semi-logarithmic scale shows the results of the calculation of the values of the functions $$f_{xx}(t)/\overline{I}$$

according to measurements of currents i (t) of the KNK-56 ionization chamber at three power levels of critical assembly. Function Values $$f_{xx}(t)/\overline{I}$$

are marked with dots, the totality of this data is processed by the least squares method taking into account the form of formula (5). The dashed line indicates a curve having the following parameters as a result of data processing:

приведены в таблице.α = - (654 ± 1) s ^-1 , Y = exp (-24.80 ± 0.01). Based on this Y value, the sought value γ = 0.772 · 10 ⁷ watts / amperes was calculated. The results of measurements of the average currents of the ionization chamber KNK-56 at three power levels of the critical assembly and the coefficient γ were used to calculate F. The results of calculating the values of F and the corresponding values $$\overline{I}$$

are given in the table.

n one 2 3

n (мкА) $$\overline{I}$$

n (μA) 6.76 ± 0.1 13.3 ± 0.1 66.9 ± 0.1 Fn (watt) 52.2 ± 1 102.7 ± 1 516.8 ± 1

и i(t), соответственно уменьшается влияние помех на результат эксперимента.The experimental results shown in the table confirm the possibility of measuring the power of the reactor F by the proposed method. Compared to the well-known MCA, MMCA has no limitations due to ever-increasing values of background values compared to informative values due to the absence of background values. Moreover, it is advisable to conduct measurements of MCMC as far as possible at the highest power levels of reactor F. When measuring currents in ionization chambers, interference is inevitably present, the level of which does not depend on the value of reactor power F. As the average reactor power F increases, the average currents increase $$\overline{I}$$

and i (t), respectively, the influence of interference on the result of the experiment decreases.

Claims (3)

1. The method of measuring the neutron power of a nuclear reactor in absolute units F = V · γ, where
V is the value of the reactor power in relative units,
γ = proportionality coefficient,
the neutron power of a nuclear reactor in relative units is measured as the average count rate of a neutron detector in a stationary critical state by measuring instruments, and the proportionality coefficient is calculated using the value of the autocorrelation function, characterized in that an ionization chamber is used as a means of measuring the number of neutrons to determine the fluctuation of the number neutrons $$\text{I (t)}=\overline{\text{I}}+\text{i (t)}$$

, measuring separately the average current value of the ionization chamber $$\overline{I}$$

and the fluctuating component of the current of the ionization chamber i (t) continuously in time with a discrete interval Δt, the autocorrelation function of the fluctuating current of the ionization chamber is calculated by the formula
$$f_{xx}(t)={\displaystyle \sum _{m=\mathrm{one}}^{N-n}\frac{\left(i_m\cdot i_{m+n}\right)}{N-n},\text{Where}}$$

i _m , i _{m + n} - alternating currents at time T and T + t, respectively
t = k · Δt, k = 1, 2, 3 ...
n = 0, 1, 2 ...
after which the proportionality coefficient is calculated
N is the number of numbers of samples of the detector (N >> n)
γ = Y · exp (-α · t), where
$$Y=\frac{\overline{I}}{f_{xx}(t)}\cdot \frac{\alpha \cdot D_v}{2\cdot {\left({\beta }_{eff}\right)}^2},$$

D _v - Diven’s parameter (constant, tabular value), D _v = 0.795 for U ²³⁵ ,
B _eff is the effective fraction of delayed neutrons,
α is the decay constant of instantaneous neutrons in a critical reactor. 2. The method according to claim 1, characterized in that the discrete interval Δt≈0.1 / α is selected. 3. The method according to claim 1, characterized in that the number of measurements i (t) in time should be at least ten thousand.