CN101162455B - Method for simulating nuclear reactors in threshold state - Google Patents

Abstract

The present invention belongs to the nuclear reactor field, and in particular relates to a critical state simulation method of nuclear reactor, comprising the following steps: (1) a model is bononized and diluted to obtain the variable quantity of boron concentration; (2) the variable quantity of overlapping step rod position is obtained through the conversion formula of the overlapping step rod position and a single rod of a rod position control model; (3) the variable quantity of boron concentration and the variable quantity of overlapping step rod position are substituted into a reactive model to obtain reactive variable quantity; (4) neutron number is obtained through the reactive model; (5) when the boron concentration and the rod position of a control rod are changed and the neutron number is changeless, a reactor achieves a critical state then. The use of the method of the present invention can dynamically and intuitively show the relation of the neutron number and reactivity in real time. As a numerical solution based on computers is adopted, the neutron number can be very accurately worked out to the change of reactivity in any form. The present invention is few in resources needed, which can be realized with only one computer needed. Parameter can be flexibly changed so as to adapt the present invention to critical state achieving characteristics of the reactors in different structures.

Description

Method for simulating nuclear reactors in threshold state

Technical field

The present invention relates to a kind of nuclear mockup method, particularly a kind of method for simulating nuclear reactors in threshold state.

Background technology

It is critical that nuclear reactor reaches, and the neutron number that is about to reactor is stabilized in some values and does not change, and can make nuclear process controlled, can utilize this stable energy that nuclear reaction discharged to generate electricity like this.

Make nuclear reactor reach critical conditions be any nuclear reactor operating personnel the essential technical ability of grasping, existing nuclear reactor reaches critical conditions to be realized by large-scale analog machine simulated operation.Use large-scale analog machine simulation nuclear reactor to reach critical conditions and have many shortcomings: manpower and materials are required height, need the special messenger to cooperate; Need daily servicing; Lack dirigibility, can not change parameter at any time and be used for theoretical research; Large-scale analog machine fixed-site, limited amount and simulation cycle are long.

Summary of the invention

The object of the present invention is to provide a kind of method for simulating nuclear reactors in threshold state.

A kind of method for simulating nuclear reactors in threshold state may further comprise the steps:

(1) reactor is carried out boronation or dilution operation, obtain the boron concentration c that boronation or dilution are introduced ₁, boronation or dilution volume v, reactor water capacity v ₀, with parameter c ₁, v, v ₀The substitution boronation is diluted equation, obtains the boron concentration c variable quantity dc of reactor;

Described boronation dilution equation is:

c ₁dv＝v ₀dc+cdv

In the formula:

The boron concentration of c---reactor

c ₁---by the boron concentration of boronation or dilution introducing, when being the boronation state, c ₁Value be 7 * 10 ^-3, be 0 when for diluted state

v ₀---the water capacity of reactor, this value is relevant with reactor structure, to same reactor, should value be similar to constant when reactor operation

V---boronation or dilution volume, this value depend on the poor of the existing boron concentration of reactor and itself and the boron concentration that will reach, and do not have concrete scope, and span can be very big, if do not consider the timeliness economy, theoretical value can be zero to infinity

(2) reactor is carried out the lifting or the step-down operation of control rod position, when carrying out rod withdrawal control, increased the value of excellent figure place l of folded step; During plunger control, reduced the value of excellent figure place l of folded step,, calculated the variable quantity dl of rod position l of folded step by the folded step rod position of rod position controlling models and the conversion relation formula of single rod;

Described folded step rod position with the conversion relation formula of single rod is:

When reactor has i group control rod, the highest rod position is a step, when minimum rod position go on foot for b, the excellent conversion relation formula of the folded step rod of described rod position controlling models and list as shown in the formula:

$\left\{\begin{array}{cc}{N}_1=l+b& (l=0~(a-b))\\ N_1=l+x-(a-2b)& (l=(a-b)-x~2(a-b)-x)\\ N_3=l+2x-(2a-3b)& (l=2(a-b)-2x~3(a-b)-2x)\\ .& .\\ .& .\\ .& .\\ N_i=l+(i-1)x-[(i-1)a-\mathrm{ib}]& (l=(i-1)(a-b)-(i-1)x~i(a-b)-(i-1)x)\end{array}\right.$

In the formula:

The folded excellent figure place of step of l-

N _iThe excellent figure place of-i

The overlapping step number of x-

The highest rod of a-position step number

The minimum rod of b-position step number.

(3) with the reactive computation model of rod position variable quantity dl substitution of folded step that obtains in the boron concentration change amount dc that obtains in the step (1) and the step (2), obtain reactive variable quantity d ρ;

Described reactive computation model is:

dρ＝k ₁dc+k ₂dl

In the formula:

D ρ-reactive variable quantity

k ₁-boron concentration change amount influences the scale-up factor of changes of reactivity amount

k ₂-rod position variable quantity influences the scale-up factor of changes of reactivity amount

The boron concentration change amount of dc-reactor

Dl-rod position of folded step variable quantity;

Described boron concentration change amount influences the scale-up factor k of changes of reactivity amount ₁Can be constant or nonlinear factor; k ₁Its scope is-70 * 10 during for constant ^-5～0; k ₁Value depend on the burnup of reactor boron concentration, reactor coolant temperature, reactor structure, nuclear fuel, the position of control rod; k ₁During for nonlinear factor, use conic fitting method or cubic curve fitting process to coefficient k ₁Carrying out non-linearization handles.

Described rod position variable quantity influences the scale-up factor k of changes of reactivity amount ₂All can be constant or nonlinear factor; k ₂Its scope is 0～10 * 10 during for constant ^-5, k ₂Value depend on the burnup of reactor boron concentration, reactor coolant temperature, reactor structure, nuclear fuel, the position of control rod; k ₂During for nonlinear factor, use conic fitting method or cubic curve fitting process to coefficient k ₂Carrying out non-linearization handles.

(4) set primary neutron count n, delayed neutron fraction β, disintegration constant λ, on average for time l, add neutron source strength q, reactive ρ, reactive ρ is the reactive ρ by reactor model initial setting ₀The changes of reactivity amount d ρ addition that obtains with reactive computation model constitutes, that is: ρ=ρ ₀+ d ρ;

Bring the parameter and the reactive ρ of above-mentioned all settings into variable quantity that the reactor model obtains neutron number in the unit interval Rate of change with pioneer's check figure

Described reactor model is set up according to point-reactor kinetic equation, and the reactor model is:

$\left\{\begin{array}{c}\frac{\mathrm{dn}}{\mathrm{dt}}=\frac{\mathrm{\ρ}-\mathrm{\β}}{l}n+\underset{i=1}{\overset{6}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{c}_i+q\\ \frac{{\mathrm{dc}}_i}{\mathrm{dt}}=\frac{{\mathrm{\β}}_i}{l}n-{\mathrm{\λ}}_i{c}_i\end{array}i=\mathrm{1,2},...6\right.$

N---neutron number

I---because the nuclear reaction meeting produces multiple pioneer and examines type, each pioneer examines the fall time difference of type, has pioneer's nuclear of 6 kinds of main types, thus i=1,2 ... 6

β _i---delayed neutron fraction β is the neutron number that is produced by pioneer's nuclear decay, owing to have pioneer's nuclear of 6 kinds of main types, so β is arranged _i

β---delayed neutron fraction, delayed neutron fraction are to account for the ratio that nuclear reaction produces all neutron numbers by the neutron number that pioneer's nuclear decay produces,

Be generally 0.0065, $\mathrm{\β}=\underset{i=1-6}{\mathrm{\Σ}}{\mathrm{\β}}_i$

λ---disintegration constant, its scope are 0.01～10 per second

L---on average for the time, its scope is 0.0849 second

Q---add the neutron source strength, depend on type of reactor, no determined value, the reactor that has does not have the neutron of adding source strength, promptly gets q=0

ρ---reactivity

c _i---pioneer's check figure, it depends on reactor capability, theoretical value can be zero to infinitely great, because of real reaction heap power limited, pioneer's check figure c _iCan not be infinitely great

---the variable quantity of neutron number in the unit interval

---the neutron number that all neutrons produce when being fast neutron

---because of deferred and deducted neutron inventory

---each pioneer examines the delayed neutron sum of generation

---the rate of change of pioneer's check figure

N---neutron number

When (5) the boron concentration c in the step (1) changed, boron concentration change amount dc changed thereupon, and the variable quantity d ρ of inducing reaction property changes, thereby had changed the value of reactive ρ in the reactor model, so neutron number n changes;

Rod position variable quantity dl changed thereupon when control rod rod position changed in the step (2), and the variable quantity d ρ of inducing reaction property changes, thereby has changed the value of reactive ρ in the reactor model, so neutron number n changes;

Neutron number n does not change when changing boron concentration and control rod rod position, i.e. the variable quantity of neutron number in the unit interval $\frac{\mathrm{dn}}{\mathrm{dt}}=0$ The time, nuclear reactors in threshold state;

Boronation dilution operation stops when reactor reaches critical conditions.

Use method of the present invention: can dynamically intuitively show neutron number and reactive relation in real time; Because adopt the computer based numerical solution, for any type of variation of reactivity, the neutron number average can be calculated by point-device; Resource requirement is few, only needs a computing machine to realize; Can change parameter neatly, with the critical characteristic that reaches of the reactor that adapts to different structure.

Embodiment

Embodiment 1

(1) reactor is carried out boronation dilution operation, obtain the boron concentration c that boronation or dilution are introduced ₁, boronation or dilution volume v, reactor water capacity v ₀, with parameter c ₁, v, v ₀Substitution boronation dilution equation, boronation dilution equation is as follows:

c ₁dv＝v ₀dc+cdv

In the formula:

The boron concentration of c---reactor

c ₁---by the boron concentration of boronation or dilution introducing, when being the boronation state, c ₁Value be 7 * 10 ^-3, be 0 when for diluted state

v ₀---the water capacity of reactor, this value is relevant with reactor structure, to same reactor, should value be similar to constant when reactor operation

V---boronation or dilution volume, this value depend on the poor of the existing boron concentration of reactor and itself and the boron concentration that will reach, and do not have concrete scope, and span can be very big, if do not consider the timeliness economy, theoretical value can be zero to infinity

Obtain the variable quantity dc of the boron concentration of the boron concentration c of reactor and reactor by following formula, boronation dilution operation stops when reactor reaches critical conditions.

(2) carry out the lifting or the decline of control rod position, when carrying out rod withdrawal control, increased the value of excellent figure place l of folded step; During plunger control, reduced the value of excellent figure place l of folded step; Reactor has 4 groups of control rods, and its highest rod position was 225 steps, and minimum rod position was 5 steps, and folded step rod position is as follows with the conversion relation formula of single rod:

$\left\{\begin{array}{cc}{N}_1=l+5& (l=0~220)\\ N_2=l+x-215& (l=220-x~440-x)\\ N_3=l+2x-435& (l=440-2x~660-2x)\\ N_4=l+3x-655& (l=660-3x~880-3x)\end{array}\right.$

In the formula:

The folded excellent figure place of step of l-

N ₁-1 rod rod figure place

N ₂-2 rods rod figure place

N ₃-3 rods rod figure place

N ₄-4 rods rod figure place

The overlapping step number of x-

Thereby calculate 1,2,3,4 rods, the folded numerical value that goes on foot rod position l by following formula, draw the variable quantity dl of a folded step rod l by the numerical value change of excellent position l of folded step.

(3) with the reactive computation model of rod position variable quantity dl substitution that obtains in the boron concentration change amount dc that obtains in the step (1) and the step (2); Owing to reach in the critical process, the coolant temperature variable quantity is small in the reactor, therefore when considering, ignored because of coolant temperature changes reactive influence to reactive influence factor, when having considered excellent position with the boron concentration change to reactive influence; Reactive computation model as shown in the formula:

dρ＝k ₁dc+k ₂dl

In the formula:

D ρ-reactive variable quantity

k ₁-boron concentration change amount influences the scale-up factor of changes of reactivity amount

k ₂-rod position variable quantity influences the scale-up factor of changes of reactivity amount

The boron concentration change amount of dc-reactor

Dl-rod position variable quantity

Draw reactive variable quantity d ρ by following formula.

With rod position and boron concentration to reactive linearization, i.e. k in the following formula of influencing ₁, k ₂Coefficient is a constant, k ₁Scope be-70 * 10 ^-5～0, k ₂Scope be 0～10 * 10 ^-5As the more accurate numerical value of needs, and for different type of reactors or same reactor different times k ₁, k ₂The value difference, k ₁, k ₂Value depend on the burnup of reactor boron concentration, reactor coolant temperature, reactor structure, nuclear fuel, the position of control rod.Use conic fitting method or cubic curve fitting process to coefficient k ₁, k ₂Carrying out non-linearization handles.

(4) set neutron number n, delayed neutron fraction β, disintegration constant λ, on average for time l, add neutron source strength q, reactive ρ, reactive ρ is the reactive ρ by reactor model initial setting ₀The changes of reactivity amount d ρ addition that obtains with reactive computation model constitutes, that is: ρ=ρ ₀+ d ρ, wherein ρ ₀In simulation process, be constant, for the simulation process ρ of homogeneous not as initial setting ₀Be different constants; Bring the parameter and the reactive ρ of above-mentioned all settings into the reactor model, the reactor model is set up according to point-reactor kinetic equation, the reactor model as shown in the formula:

$\left\{\begin{array}{c}\frac{\mathrm{dn}}{\mathrm{dt}}=\frac{\mathrm{\ρ}-\mathrm{\β}}{l}n+\underset{i=1}{\overset{6}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{c}_i+q\\ \frac{{\mathrm{dc}}_i}{\mathrm{dt}}=\frac{{\mathrm{\β}}_i}{l}n-{\mathrm{\λ}}_i{c}_i\end{array}i=\mathrm{1,2},...6\right.$

In the formula:

N---neutron number

I---because the nuclear reaction meeting produces multiple pioneer and examines type, each pioneer examines the fall time difference of type, has pioneer's nuclear of 6 kinds of main types, thus i=1,2 ... 6

β _i---delayed neutron fraction β is the neutron number that is produced by pioneer's nuclear decay, owing to have pioneer's nuclear of 6 kinds of main types, so β is arranged _i

β---delayed neutron fraction, delayed neutron fraction are to account for the ratio that nuclear reaction produces all neutron numbers by the neutron number that pioneer's nuclear decay produces, and are generally 0.0065, $\mathrm{\β}=\underset{i=1-6}{\mathrm{\Σ}}{\mathrm{\β}}_i$

λ---disintegration constant, its scope are 0.01～10 per second

L---on average for the time, its scope is 0.0849 second

Q---add the neutron source strength, depend on type of reactor, no determined value; The reactor that has does not have the neutron of adding source strength, promptly gets q=0

ρ---reactivity

c _i---pioneer's check figure, it depends on the power of reactor, theoretical value can be zero to infinitely great,, because of real reaction heap power limited, pioneer's check figure c _iCan not be infinitely great

---the variable quantity of neutron number in the unit interval

---the neutron number that all neutrons produce when being fast neutron

---because of deferred and deducted neutron inventory

---each pioneer examines the delayed neutron sum of generation

---the rate of change of pioneer's check figure

Draw the variable quantity of neutron number in the unit interval by following formula Rate of change with pioneer's check figure

(5) boron concentration change amount dc changes thereupon during the variation of the boron concentration in the step (1), and the variable quantity d ρ of inducing reaction property changes, thereby has changed the value of reactive ρ in the reactor model, so neutron number n changes; Rod position variable quantity dl changed thereupon when control rod rod position changed in the step (2), and the variable quantity d ρ of inducing reaction property changes, thereby has changed the value of reactive ρ in the reactor model, so neutron number n changes.

Suppose that neutron number is n when moment t, when moment t+dt, the neutron number that is gone out by the reactor Model Calculation is n ' so, nuclear reactors in threshold state during n '=n; Promptly when changing boron concentration and control rod rod position, the variable quantity of neutron number in the unit interval $\frac{\mathrm{dn}}{\mathrm{dt}}=0$ Nuclear reactors in threshold state then.

When reactor reaches critical conditions, because neutron number n is constant, promptly $\frac{\mathrm{dn}}{\mathrm{dt}}=0,$ And delayed neutron fraction β is a constant, so the delayed neutron number

Constant, because pioneer's nuclear decay constant λ is constant, pretend pioneer's check figure c again into delayed neutron _iConstant, therefore $\frac{{\mathrm{dc}}_i}{\mathrm{dt}}=0.$

Variable quantity with neutron number in the unit interval

Bring the formula of neutron period T into:

$T=\frac{n}{\mathrm{dn}/\mathrm{dt}}$

In the formula:

T---the pile neutron cycle

N---neutron number

The variable quantity of neutron number in unit interval Nuclear reactors in threshold state when being zero, as from the foregoing during nuclear reactors in threshold state in subcycle be infinity.

Embodiment 2

Be that with the different of embodiment 1 reactor in the step (2) has 3 groups of control rods, its highest rod position was 225 steps, and minimum rod position was 5 steps, and folded step rod position is as follows with the conversion relation formula of single rod:

$\left\{\begin{array}{cc}{N}_1=l+5& (l=0~220)\\ N_2=l+x-215& (l=220-x~440-x)\\ N_3=l+2x-435& (l=440-2x~660-2x)\end{array}\right.$

In the formula:

The folded excellent figure place of step of l-

N ₁-1 rod rod figure place

N ₂-2 rods rod figure place

N ₃-3 rods rod figure place

The overlapping step number of x-

Thereby calculate 1,2,3 rods, the folded numerical value that goes on foot rod position l by following formula, draw the variable quantity dl of a folded step rod l by the numerical value change of excellent position l of folded step.

Embodiment 3

Be that with the different of embodiment 1 reactor in the step (2) has A, B, four groups of control rods of C, D, its highest rod position was 220 steps, and minimum rod position was 0 step, and folded step rod position is as follows with the conversion relation formula of single rod:

$\left\{\begin{array}{cc}{N}_1=l& (l=0~220)\\ N_2=l+x-220& (l=220-x~440-x)\\ N_3=l+2x-440& (l=440-2x~660-2x)\\ N_4=l+3x-660& (l=660-3x~880-3x)\end{array}\right.$

In the formula:

The folded excellent figure place of step of l-

N ₁-1 rod rod figure place

N ₂-2 rods rod figure place

N ₃-3 rods rod figure place

N ₄-4 rods rod figure place

The overlapping step number of x-

Thereby calculate 1,2,3,4 rods, the folded numerical value that goes on foot rod position l by following formula, draw the variable quantity dl of a folded step rod l by the numerical value change of excellent position l of folded step.

Claims (1)

1. method for simulating nuclear reactors in threshold state may further comprise the steps:

(1) reactor is carried out boronation or dilution operation, obtain the boron concentration c that boronation or dilution are introduced ₁, boronation or dilution volume v, reactor water capacity v ₀, with parameter c ₁, v, v ₀The substitution boronation is diluted equation, obtains the boron concentration c variable quantity dc of reactor;

Described boronation dilution equation is:

c ₁dv＝v ₀dc+cdv

In the formula:

The boron concentration of c---reactor

c ₁---by the boron concentration of boronation or dilution introducing, when being the boronation state, c ₁Value be 7 * 10 ^-3, be 0 when for diluted state

v ₀---the water capacity of reactor, this value is relevant with reactor structure, to same reactor, should value be similar to constant when reactor operation

V---boronation or dilution volume, this value depend on the poor of the existing boron concentration of reactor and itself and the boron concentration that will reach, and do not have concrete scope, and span can be very big, if do not consider the timeliness economy, theoretical value can be zero to infinity

(2) reactor is carried out the lifting or the step-down operation of control rod position, when carrying out rod withdrawal control, increased the value of excellent figure place l of folded step; During plunger control, reduced the value of excellent figure place l of folded step,, calculated the variable quantity dl of rod position l of folded step by the folded step rod position of rod position controlling models and the conversion relation formula of single rod;

Described folded step rod position with the conversion relation formula of single rod is:

When reactor has i group control rod, the highest rod position is a step, when minimum rod position go on foot for b, the excellent conversion relation formula of the folded step rod of described rod position controlling models and list as shown in the formula:

In the formula:

The folded excellent figure place of step of l-

N _iThe excellent figure place of-i

The overlapping step number of x-

The highest rod of a-position step number

The minimum rod of b-position step number

(3) with the reactive computation model of rod position variable quantity dl substitution of folded step that obtains in the boron concentration change amount dc that obtains in the step (1) and the step (2), obtain reactive variable quantity d ρ;

Described reactive computation model is:

dρ＝k ₁dc+k ₂dl

In the formula:

D ρ-reactive variable quantity

k ₁-boron concentration change amount influences the scale-up factor of changes of reactivity amount

k ₂-rod position variable quantity influences the scale-up factor of changes of reactivity amount

The boron concentration change amount of dc-reactor

Dl-rod position of folded step variable quantity

Described boron concentration change amount influences the scale-up factor k of changes of reactivity amount ₁Can be constant or nonlinear factor; k ₁Its scope is-70 * 10 during for constant ^-5～0; k ₁Value depend on the burnup of reactor boron concentration, reactor coolant temperature, reactor structure, nuclear fuel, the position of control rod; k ₁During for nonlinear factor, use conic fitting method or cubic curve fitting process to coefficient k ₁Carrying out non-linearization handles;

Described rod position variable quantity influences the scale-up factor k of changes of reactivity amount ₂All can be constant or nonlinear factor; k ₂Its scope is 0～10 * 10 during for constant ^-5, k ₂Value depend on the burnup of reactor boron concentration, reactor coolant temperature, reactor structure, nuclear fuel, the position of control rod; k ₂During for nonlinear factor, use conic fitting method or cubic curve fitting process to coefficient k ₂Carrying out non-linearization handles;

(4) set primary neutron count n, delayed neutron fraction β, disintegration constant λ, on average for time l, add neutron source strength q, reactive ρ, reactive ρ is the reactive ρ by reactor model initial setting ₀The changes of reactivity amount d ρ addition that obtains with reactive computation model constitutes, that is: ρ=ρ ₀+ d ρ;

Bring the parameter and the reactive ρ of above-mentioned all settings into variable quantity that the reactor model obtains neutron number in the unit interval

Rate of change with pioneer's check figure

Described reactor model is set up according to point-reactor kinetic equation, and the reactor model is:

N---neutron number

I---because the nuclear reaction meeting produces multiple pioneer and examines type, each pioneer examines the fall time difference of type, has pioneer's nuclear of 6 kinds of main types, thus i=1,2 ... 6

β _i---delayed neutron fraction β is the neutron number that is produced by pioneer's nuclear decay, owing to have pioneer's nuclear of 6 kinds of main types, so β is arranged _i

β---delayed neutron fraction, delayed neutron fraction are to account for the ratio that nuclear reaction produces all neutron numbers by the neutron number that pioneer's nuclear decay produces, and are generally 0.0065,

λ---disintegration constant, its scope are 0.01～10 per second

L---on average for the time, its scope is 0.0849 second

Q---add the neutron source strength, depend on type of reactor, no determined value, the reactor that has does not have the neutron of adding source strength, promptly gets q=0

ρ---reactivity

c _i---pioneer's check figure, it depends on reactor capability, theoretical value can be zero to infinitely great, because of real reaction heap power limited, pioneer's check figure c _iCan not be infinitely great

---the variable quantity of neutron number in the unit interval

---the neutron number that all neutrons produce when being fast neutron

---because of deferred and deducted neutron inventory

---each pioneer examines the delayed neutron sum of generation

---the rate of change of pioneer's check figure

N---neutron number

When (5) the boron concentration c in the step (1) changed, boron concentration change amount dc changed thereupon, and the variable quantity d ρ of inducing reaction property changes, thereby had changed the value of reactive ρ in the reactor model, so neutron number n changes;

Rod position variable quantity dl changed thereupon when control rod rod position changed in the step (2), and the variable quantity d ρ of inducing reaction property changes, thereby has changed the value of reactive ρ in the reactor model, so neutron number n changes;

Neutron number n does not change when changing boron concentration and control rod rod position, i.e. the variable quantity of neutron number in the unit interval

The time, nuclear reactors in threshold state;

Boronation dilution operation stops when reactor reaches critical conditions.