CN103020468A - Nuclear thermal coupling computing method for nuclear reactor - Google Patents

Abstract

The invention discloses a nuclear thermal coupling computing method for a nuclear reactor. A mathematical model for nuclear thermal coupling computation is constructed, and a fixed point equation of power distribution is solved, so that nuclear thermal coupling power distribution is obtained. The computing method comprises the following specific ways: initial power distribution is set to be average distribution; an iterated function containing a relaxing factor lambda is constructed, the power distribution is iterated twice successively, the power change rate of the successively iterated function is computed, and if the power change rate of N grids is smaller than 1, the power distribution can be solved in a successive iteration method; and otherwise, the power distribution is solved with a partially iterated function. A computational formula of a maximum relaxing factor in a partial iteration method is given, and sinusoidal distribution is recommended to be used as the initial power distribution. The nuclear thermal coupling computing method provides convenience for the design and analysis of the reactor.

Description

Nuclear reactor nuclear heat coupling calculation

Technical field

The present invention relates to the nuclear engineering field, more specifically, relate to nuclear reactor nuclear heat coupling calculation; Specifically comprise mathematical model, convergence judgement and method for solving that the coupling of nuclear reactor nuclear heat is calculated.

Background technology

The mankind demand of the energy is increased day by day, and under the day by day rare situation of traditional fossil energy, nuclear energy power generation more and more comes into one's own in recent years.Yet present most popular reactor type is such as presurized water reactor, boiling-water reactor, owing to be limited by its lower thermal transition efficient and fuel availability, and the risk of nuclear accident and nuclear proliferation, must the more advanced and safe novel nuclear power system of research and design, i.e. the 4th generation of technology such as nuclear energy system.The 4th generation of technology such as nuclear energy system comprises: gas cooled fast reactor system, lead alloy liquid metal cooled fast shut-down system, molten salt react ion shut-down system, liquid metal sodium cooling fast reactor system, very high temperature gas cooled reactor system and overcritical water-cooled reactor system.In order to improve the thermal efficiency, the running temperature of these new heap types is all higher, and moderator/cooling medium operating condition changes greatly, and power density is large, has stronger nuclear heat coupling behavior.In the design of novel reaction heap and stability and safety analysis, the nuclear heat Coupling Research is very crucial.

Wherein, supercritical water reactor has simple compact, high, the thermal efficiency advantages of higher of power density of core structure as unique water cooled reator in the 4th generation reactor concept, be considered to be hopeful to realize most the 4th generation one of reactor.On the other hand, it is very violent that the physical property of supercritical water changes, and it is very inhomogeneous to cause moderator and coolant density to distribute, thereby cause the disturbance of core power, causes strong nuclear heat feedback so that the more conventional presurized water reactor complexity of the nuclear heat of supercritical water reactor coupling many.

Therefore, when the novel reaction heap that has strong nuclear heat coupling behavior such as supercritical water reactor etc. being carried out the nuclear heat coupling calculate, traditional process of iteration is no longer applicable.At present, main rule of thumb or by repeatedly attempting selecting suitable alternative manner when carrying out the nuclear heat coupling and calculate both at home and abroad, general method for solving when not yet proposing the decision method of mathematical model, iteration convergence for nuclear reactor nuclear heat coupling and different heap type and carrying out the nuclear heat coupling and calculate makes troubles for the design and analysis of reactor.

Summary of the invention

Have inapplicable deficiency in the novel reaction heap of strong nuclear heat coupling behavior in order to overcome existing traditional process of iteration at some, the present invention proposes a kind of nuclear reactor nuclear heat coupling calculation, for the design and analysis of reactor is provided convenience.

To achieve these goals, technical scheme of the present invention is:

A kind of nuclear reactor nuclear heat coupling calculation makes up the mathematical model that the coupling of nuclear reactor nuclear heat is calculated, and finds the solution the Fixed-point equation that distributes about power, distributes thereby obtain the nuclear heat coupled power; Its concrete mode is:

S1. establish initial axial line power density distribution q ₀(i) for being evenly distributed, namely

P is single excellent power, and H is the axial heated length of fuel rod;

S2. structure contains the iteration function of relaxation factor λ:

q _K+1(i)=g (q _k(i))=λ * f (q _k(i))+(1-λ) * q _k(i), wherein $q_{0^{k+1}}\left(i\right)=f\left(q_k\left(i\right)\right),$ To linear power density distribution q ₀(i), carry out double iteration, obtain

${\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HDA00002658307900021.png"\; state="\{\{state\}\}">q</figure-callout>}}_1=\mathrm{\&lambda;}\&times;q_{0^1}\left(i\right)+(1-\mathrm{\&lambda;})\&times;q_0\left(i\right)$ With $q_{0^2}\left(i\right)=f\left(q_1\right);$

S3. utilize q ₀(i),

With

Calculate the power variation rate f ' (q (i)) of successive iteration function f (q (i)), $f^{\&prime;}\left(q\left(i\right)\right)=\frac{(f\left(q_1\left(i\right)\right)-f\left(q_0\left(i\right)\right)}{(q_1\left(i\right)-q_0\left(i\right))}=\frac{(q_{0^2}\left(i\right)-q_{0^1}\left(i\right))}{(q_1\left(i\right)-q_0\left(i\right))};$

If S4. | f'(q (i)) |＜1, namely the power of N grid is all restrained, and then finds the solution the Fixed-point equation that distributes about power with successive iteration method, distributes thereby obtain the nuclear heat coupled power; If exist | f ' (q (i)) | 〉=1, then adopt part iteration function g (q (i)) to find the solution the Fixed-point equation that distributes about power, distribute thereby obtain the nuclear heat coupled power;

Above-mentioned steps S1 to step S4, i=1,2..., N, relaxation factor λ≤0.01.

For new heap types such as supercritical water reactors, because its nuclear heat coupling behavior is stronger, the subtle change that power distributes will cause the acute variation of moderator and coolant density, also produces violent variation thereby power is distributed.Therefore finding the solution the power distribution of the new heap type nuclear heat couplings such as supercritical water reactor with traditional successive iteration method, is infeasible, adopts this method can well overcome this problem.

Select very little relaxation factor λ can guarantee convergence in the reality, but also can spend more computing time.Therefore the relaxation factor λ that has a maximum _Max, can guarantee convergence, can make again computing time as far as possible few, and in actual computation, consider from conservative, can suitably select to compare λ when selecting relaxation factor λ _MaxSmaller value.Make new iteration function g (x) convergence, to N grid all must satisfy-1＜[g'(q (i))=λ * f'(q (i))+1-λ]＜1, i=1,2, ..., N considers f ' (q (i)), i=1,2, ..., N is negative value, following formula is equivalent to λ * (1-f'(q (i)) _Max)＜2, | f'(q (i)) _Max| be the maximal value of power variation rate absolute value, f'(q (i)) _MaxBe negative value.

The maximal value λ of relaxation factor _MaxDefinite mode be:

S21. establish initial axial line power density distribution q ₀(i) for being evenly distributed, namely

P is single excellent power, and H is the axial heated length of fuel rod;

S22. structure contains the iteration function of relaxation factor λ:

q _K+1(i)=g (q _k(i))=λ * f (q _k(i))+(1-λ) * q _k(i), wherein $q_{0^{k+1}}\left(i\right)=f\left(q_k\left(i\right)\right),$ To linear power density distribution q ₀(i), carry out double iteration, obtain ${\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HDA00002658307900021.png"\; state="\{\{state\}\}">q</figure-callout>}}_1=\mathrm{\&lambda;}\&times;q_{0^1}\left(i\right)+(1-\mathrm{\&lambda;})\&times;q_0\left(i\right)$ With $q_{0^2}\left(i\right)=f\left(q_1\right),$ λ≤0.01 wherein;

S23. according to q ₀(i),

With

Calculate $f^{\&prime;}\left(q\left(i\right)\right)=\frac{q_{0^2}\left(i\right)-q_{0^1}\left(i\right)}{q_1\left(i\right)-q_0\left(i\right)},$ Find out maximum power variation rate | f'(q _k(i)) _Max|, then ${\mathrm{\&lambda;}}_{\max }=\frac{2}{1-f^{\&prime;}{\left(q_k\left(i\right)\right)}_{\max }};$ F ' (q (i)) wherein _MaxBe negative value;

Above-mentioned steps S21 to step S23, i=1,2..., N.

Utilize following formula can choose rapidly the maximal value of relaxation factor, avoided repeatedly calculating attempting, thereby saved computing time, the nuclear heat coupling is calculated and has been brought facility when designing for reactor.

Further, described ${\mathrm{\&lambda;}}_{\max }=\frac{2}{1-f^{\&prime;}{\left(q_k\left(i\right)\right)}_{\max }}\&ap;0.1909.$

Further, adopting part iteration function g (q (i)) to find the solution the power distribution among the described step S4 specifically may further comprise the steps:

The axial line power density distribution of S41. establishing is q ₀(i), wherein initial power is distributed as the power distribution of satisfying single excellent power constraint;

S42. by iterative formula q _K+1(i)=g (q _k(i))=λ * f (q _k(i))+(1-λ) * q _k(i) constantly carry out iteration, until

Be q _k(i) be that required nuclear heat coupled power distributes; I=1 wherein, 2..., N, λ＜λ _MaxWherein ε is the maximal value of relative error, and ε=1% is that relative error can not greater than 1%, in actual computation, can change ε according to the precision needs of reality.

Further, the initial power distribution q among the described step S41 ₀(i) for being evenly distributed or Sine distribution.

Further, described initial power distribution q ₀(i) be Sine distribution.Result of calculation shows that in the identical situation of relaxation factor, initial power distributes and uses Sine distribution need to carry out iteration 46 times, and average power distribution then needs 71 times.Use Sine distribution can reach sooner convergence, can reduce by 35% computing time.Result of calculation shows that in the identical situation of relaxation factor, initial power distributes and uses Sine distribution need to carry out iteration 46 times, and average power distribution then needs 71 times.Use Sine distribution can reach sooner convergence, can reduce by 35% computing time.

Compared with prior art, beneficial effect of the present invention:

1) mathematical model of calculating by introducing the coupling of nuclear reactor nuclear heat restrains judgement to successive iteration method, and calculating for the nuclear heat coupling of various reactor types provides anticipation and guide;

2) by introducing relaxation factor λ, replaced traditional successive iteration method with the part process of iteration, avoided the new heap type such as supercritical water reactor because strong nuclear heat coupling the interacts oscillation of power that causes with disperse;

3) judge the power variation rate obtain according to convergence, determine to contain the maximal value of the relaxation factor λ in the part iteration function of relaxation factor λ, the effect that acquisition can restrain and can save computing time as far as possible;

4) proposed in iteration, initial power distributes and uses sinusoidal power distribution the most reasonable generally speaking.The present invention is that the design and analysis of various reactor types is provided convenience.

Description of drawings

Fig. 1 is convergence decision flowchart of the present invention.

Fig. 2 is that the present invention selects the relaxation factor process flow diagram.

Fig. 3 is nuclear heat coupling process flow diagram of the present invention.

Embodiment

The present invention will be further described below in conjunction with accompanying drawing, but embodiments of the present invention are not limited to this.

One, the mathematical model of nuclear reactor nuclear heat coupling calculating

The mathematical model that the nuclear heat coupling is calculated: find the solution the equation of an x=f (x), namely find the solution the Fixed-point equation of x.Unknown number x specifically refers to the axial line power density distribution in the nuclear heat coupling is calculated, suppose a known power distribution q _k(i), i=1,2...N(N are the grid number of axially dividing), calculate and neutronics calculating by thermal-hydraulic, can access new power distribution q _K+1(i), i=1,2...N, it is consistent with old power distribution that the purpose of nuclear heat coupling makes new power distribute just.

Successive iteration method is found the solution the mathematical model that the nuclear heat coupled power distributes: if f (x) is continuous, can construct iterative x _K+1=f (x _k), k=0,1 ... be called the fixed point process of iteration, f (x) is called iteration function.Given initial approximation x ₀, obtain sequence { x by successive iteration _k, if

Can prove x ^*=f (x ^*), i.e. x ^*Fixed point for f (x).

Two, the convergence of nuclear heat coupling successive iteration method is judged

Successive iteration method is the common method during the nuclear heat coupling is calculated, and namely supposes an initial power distribution q ₀(i), i=1,2...N(N are the grid number of axially dividing), by iterative formula q _K+1(i)=f (q _k(i)), i=1,2...N constantly carry out iteration, until

ε is the very little number that the condition of convergence is set, in the present embodiment ε=1%.

But for new heap types such as supercritical water reactors, because its nuclear heat coupling behavior is stronger than conventional presurized water reactor, the subtle change that power distributes will cause the acute variation of moderator and coolant density, also produces violent variation thereby power is distributed.Therefore finding the solution the power distribution of the new heap type nuclear heat couplings such as supercritical water reactor with traditional successive iteration method, is infeasible.

Theorem according to fixed point process of iteration local convergence: establish x ^*Be the fixed point of f (x), f'(x) at x ^*Neighborhood S continuous, and | f'(x ^*) |＜1, process of iteration local convergence then.For the very strong heap type of nuclear heat coupling behavior, the rate of change of power | f'(q ^*(i))〉1, if with traditional successive iteration, can cause the vibration of power and maximum deviation, cause and can't restrain.

Therefore, carry out must whether restraining successive iteration method and judging before the nuclear heat coupling calculating, decision method, as shown in Figure 1, for:

S11. suppose that initial axial line power density distribution is for being evenly distributed, namely

I=1,2...N, P are single excellent power, and H is the axial heated length of fuel rod;

S12. structure contains the new iteration function of relaxation factor λ, and λ should suitably get less value, such as λ=0.01 or 0.001.To initial line power density distribution q ₀(i), i=1,2...N carries out double iteration,

Arrive

q ₁(i) and

S13. utilize q ₀(i),

q ₁(i) and

Rate of change that can rated output $f^{\&prime;}\left(q\left(i\right)\right)=\frac{(f\left(q_1\left(i\right)\right)-f\left(q_0\left(i\right)\right)}{(q_1\left(i\right)-q_0\left(i\right))}=\frac{(q_{0^2}\left(i\right)-q_{0^1}\left(i\right))}{(q_1\left(i\right)-q_0\left(i\right))}.$ If | f'(q (i)) |＜1, i=1,2...N, namely the power of N grid is all restrained, and then can enough successive iteration methods carry out the power iteration; If exist | f'(q (i)) | 〉=1, then can not use successive iteration method.

Present embodiment is calculated as example with the nuclear heat coupling of supercritical water reactor, and when convergence was judged, power distribution iteration was got λ=new iteration function g (q of 0.001 structure _k(i))=0.001 * f (q _k(i))+0.999 * q _k(i).The linear power density of choosing continuous three iteration distributes as shown in table 1.In the table 1, front 20 data of each iteration are the front q of substitution f (x) _k(i), rear 20 data are to obtain behind the substitution f (x)

And $q_{k+1}\left(i\right)=0.001\&times;q_{0^{k+1}}\left(i\right)+0.999\&times;q_k\left(i\right).$

The linear power density distribution q (i) of continuous three iteration of table 1 (W/m)

Iteration for the first time

q ₀(i)

f(q ₀(i))

Iteration for the second time

q ₁(i)

f(q ₁(i))

Iteration for the third time

q ₂(i)

f(q ₂(i))

For the iteration function f (x) of direct successive iteration,

$f^{\&prime;}\left(q\left(i\right)\right)=\frac{(f\left(q_1\left(i\right)\right)-f\left(q_0\left(i\right)\right)}{(q_1\left(i\right)-q_0\left(i\right))}=\frac{(q_{0^2}\left(i\right)-q_{0^1}\left(i\right))}{(q_1\left(i\right)-q_0\left(i\right))}$

By following formula and table 1, can table 2:

The power variation rate f'(q (i) of table 2 successive iteration function)

As seen from the above table, 20 f'(q _k12 absolute values are arranged greater than 1 (i)), namely have 12 places not restrain.It is infeasible that the power of therefore, finding the solution supercritical water reactor nuclear heat coupling by the method for successive iteration distributes.In addition, 20 f'(q _k(i)) there are 19 all to be negative value in, illustrate that increased power causes that the density of water reduces, cause conversely power to descend.

Three, the general method for solving of nuclear heat coupling

(1) relaxation factor λ and new iteration function g (x)

When determining successive iteration method and can't restrain, must use new alternative manner.This patent has been introduced relaxation factor λ (λ〉0) in the renewal expression formula of power, this level result of calculation and last layer time result's difference is done suitably reduction, to avoid causing dispersing of nonlinear iteration process owing to difference is excessive.Constructed new iteration function g (x), made g (x) satisfy the condition of convergence of successive iteration.New iteration function g (x) is:

q _K+1(i)=g (q _k(i))=q _k(i)+λ * (f (q _k(i))-q _k(i))=λ * f (q _k(i))+(1-λ) * q _k(i), i=1,2... is if N

Then get the limit by the following formula two ends,

$q^{*}=\underset{k\&RightArrow;\&infin;}{\lim }{q}_{k+1}=\mathrm{\&lambda;}\&times;\underset{k\&RightArrow;\&infin;}{\lim }f\left(q_k\right)+(1-\mathrm{\&lambda;})\&times;\underset{k\&RightArrow;\&infin;}{\lim }{q}_k=\mathrm{\&lambda;}\&times;f\left(\underset{k\&RightArrow;\&infin;}{\lim }{q}_k\right)+(1-\mathrm{\&lambda;})\&times;q^{*}$

Be equivalent to q ^*=f (q ^*), the q that therefore obtains by new iteration function g (x) ^*Be the fixed point of f (q), namely required power distributes.To g (x) two ends differentiate, can get

g(q _k(i))＝λ×f(q _k(i))+1-λ，i＝1,2...,N

By this conversion, so that the variation of power is so inviolent during the power iteration, thus can enough process of iteration of asking fixed point.

Present embodiment is attempted by calculating, and gets λ=new iteration function of 0.18 structure

G (q _k(i))=0.18 * f (q _k(i))+0.82 * q _k(i), can get

g'(q(i))＝(g(q ₁(i))-g(q ₀(i)))/(q ₁(i)-q ₀(i))=(q ₂(i)-q ₁(i))/(q ₁(i)-q ₀(i))

Similar to the calculating of second portion " convergence of nuclear heat coupling successive iteration method is judged ", initial power distributes and still selects to be evenly distributed, and can obtain the power variation rate f'(q (i) of the successive iteration method of λ=0.18 correspondence), as shown in table 3.Can be obtained simultaneously the power variation rate g'(q (i) of part process of iteration by following formula), as shown in table 4.

The power variation rate f'(q (i) of table 3 successive iteration function)

As seen from the above table, 20 f'(q _k17 absolute values are arranged greater than 1 (i)).In addition, 20 f ' (q _k(i)) there are 19 all to be negative value in.

The power variation rate g'(q (i) of table 4 part iteration function)

Can be got 20 g'(q by table 4 _k(i)) only have 2 absolute values in all greater than 1, and its absolute value is very near 1, than the f'(q (i) of correspondence) little.In next iteration, if the power convergence of this grid can guarantee whole power convergence.Therefore, by the conversion of iteration function, can make and find the solution the iteration convergence that power distributes.Simultaneously, contrast can find that the result in table 4 and the table 3 satisfies g'(q _k(i))=0.18 * f'(q _k(i))+0.82, i=1,2..., the relation of N.

(2) computing formula of selection relaxation factor λ

Select very little relaxation factor λ no doubt can guarantee convergence, but also can spend more computing time.Therefore the relaxation factor λ that has a maximum _Max, can guarantee convergence, can make again computing time as far as possible few.According to the successive iteration convergence criterion that second portion proposes, make new iteration function g (x) convergence, to N grid all must be satisfied-1＜[g'(q (i))=λ * f'(q (i))+1-λ]＜1, i=1,2 ..., N, consider f'(q (i)), i=1,2 ..., N is negative value, and following formula is equivalent to λ * (1-f'(q (i)) _Max)＜2, | f'(q (i)) _Max| be the maximal value of power variation rate absolute value, f'(q (i)) _MaxBe negative value.Can get maximum relaxation factor λ _MaxComputing formula:

$\mathrm{\&lambda;}<{\mathrm{\&lambda;}}_{\max }=\frac{2}{1-f^{\&prime;}{\left(q_k\left(i\right)\right)}_{\max }}$

Utilize following formula to choose rapidly relaxation factor, avoided repeatedly calculating attempting, thereby saved computing time, the nuclear heat coupling is calculated and has been brought facility when designing for reactor.

When the general heap type of the below's detailed description carries out the nuclear heat coupling, the system of selection of relaxation factor, as shown in Figure 2:

S21. establish initial axial line power density distribution q ₀(i) for being evenly distributed, namely

P is single excellent power, and H is the axial heated length of fuel rod;

S22. structure contains the iteration function of relaxation factor λ:

q _K+1(i)=g (q _k(i))=λ * f (q _k(i))+(1-λ) * q _k(i), λ≤0.01 wherein,

To linear power density distribution q ₀(i), carry out double iteration, obtain $q_{0^1}\left(i\right)=f\left(q_0\right),$ ${\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HDA00002658307900021.png"\; state="\{\{state\}\}">q</figure-callout>}}_1=\mathrm{\&lambda;}\&times;q_{0^1}\left(i\right)+(1-\mathrm{\&lambda;})\&times;q_0\left(i\right)$ With $q_{0^2}\left(i\right)=f\left(q_1\right);$ As shown in table 1;

S23. according to q ₀(i),

With

Calculate $f^{\&prime;}\left(q\left(i\right)\right)=\frac{q_{0^2}\left(i\right)-q_{0^1}\left(i\right)}{q_1\left(i\right)-q_0\left(i\right)},$ As shown in table 2, find out maximum power variation rate | f'(q _k(i)) _Max|.

S24. with f'(q _k(i)) _MaxSubstitution λ _MaxComputing formula Try to achieve λ _MaxTheoretical value.

S25. in actual computation, consider from conservative, select relaxation factor λ can suitably select to compare λ _MaxSmaller value.

In the present embodiment, can access the maximal value f'(q of power variation rate from table 2 _k(i)) _Max=-9.47626, substitution relaxation factor λ _MaxComputing formula, can get:

${\mathrm{\&lambda;}}_{\max }=\frac{2}{1-f^{\&prime;}{\left(q_k\left(i\right)\right)}_{\max }}\&ap;0.1909,$ Conservative consideration, relaxation factor λ=0.18th selected in the front, and be proper, can either guarantee convergence, can save computing time again as far as possible.

(3) part solution by iterative method power distributes

After relaxation factor λ chooses out, can distribute by the part solution by iterative method power that contains relaxation factor, concrete steps are as follows, as shown in Figure 3:

S31. construct new iteration function g (x), obtain new iterative relation formula: q _K+1(i)=g (q _k(i))=λ * f (q _k(i))+(1-λ) * q _k(i), i=1,2..., N, the wherein relaxation factor of λ for being chosen by the method for Fig. 2;

S32. establish an initial power distribution q ₀(i), i=1,2...N, it is that any power that satisfies single excellent power constraint distributes that the initial power here distributes, such as Sine distribution or average power distribution etc., simultaneously, result of calculation shows, in the identical situation of relaxation factor, initial power distributes and uses Sine distribution need to carry out iteration 46 times, and average power distribution then needs 71 times.Use Sine distribution can reach sooner convergence, can reduce by 35% computing time.Therefore, the present invention proposes: in the ordinary course of things, it is the most rational that Sine distribution is used in the initial power distribution;

S33. by iterative formula q _K+1(i)=g (q _k(i)), i=1,2...N constantly carry out iteration, until

ε is the very little number that the condition of convergence is set, for example ε=1%.At this moment, f (q _kAnd q (i)) _k(i) very approaching, q _k(i) being required nuclear heat coupled power distributes.

Above-described embodiments of the present invention do not consist of the restriction to protection domain of the present invention.Any modification of within spiritual principles of the present invention, having done, be equal to and replace and improvement etc., all should be included within the claim protection domain of the present invention.

Claims (6)

1. a nuclear reactor nuclear heat coupling calculation is characterized in that, makes up the mathematical model that the coupling of nuclear reactor nuclear heat is calculated, and finds the solution the Fixed-point equation that distributes about power, distributes thereby obtain the nuclear heat coupled power; Its concrete mode is:

S1. establish initial axial line power density distribution q ₀(i) for being evenly distributed, namely

P is single excellent power, and H is the axial heated length of fuel rod;

S2. structure contains the iteration function of relaxation factor λ:

q _K+1(i)=g (q _k(i))=λ * f (q _k(i))+(1-λ) * q _k(i), wherein $q_{0^{k+1}}\left(i\right)=f\left(q_k\left(i\right)\right),$ To linear power density distribution q ₀(i), carry out double iteration, obtain

$q_1=\mathrm{\&lambda;}\&times;q_{0^1}\left(i\right)+(1-\mathrm{\&lambda;})\&times;q_0\left(i\right)$ With $q_{0^2}\left(i\right)=f\left(q_1\right);$

S3. utilize q ₀(i),

With

Calculate the power variation rate f ' (q (i)) of successive iteration function f (q (i)), $f^{\&prime;}\left(q\left(i\right)\right)=\frac{(f\left(q_1\left(i\right)\right)-f\left(q_0\left(i\right)\right)}{(q_1\left(i\right)-q_0\left(i\right))}=\frac{(q_{0^2}\left(i\right)-q_{0^1}\left(i\right))}{(q_1\left(i\right)-q_0\left(i\right))};$

If S4. | f'(q (i)) |＜1, namely the power of N grid is all restrained, and then finds the solution the Fixed-point equation that distributes about power with successive iteration method, distributes thereby obtain the nuclear heat coupled power; If exist | f ' (q (i)) | 〉=1, then adopt part iteration function g (q (i)) to find the solution the Fixed-point equation that distributes about power, distribute thereby obtain the nuclear heat coupled power;

Above-mentioned steps S1 to step S4, i=1,2..., N, relaxation factor λ≤0.01.

2. nuclear reactor nuclear heat coupling calculation according to claim 1 is characterized in that the maximal value λ of relaxation factor _MaxDefinite mode be:

S21. establish initial axial line power density distribution q ₀(i) for being evenly distributed, namely

P is single excellent power, and H is the axial heated length of fuel rod;

S22. structure contains the iteration function of relaxation factor λ:

q _K+1(i)=g (q _k(i))=λ * f (q _k(i))+(1-λ) * q _k(i), wherein $q_{0^{k+1}}\left(i\right)=f\left(q_k\left(i\right)\right),$ To linear power density distribution q ₀(i), carry out double iteration, obtain

$q_1=\mathrm{\&lambda;}\&times;q_{0^1}\left(i\right)+(1-\mathrm{\&lambda;})\&times;q_0\left(i\right)$ With $q_{0^2}\left(i\right)=f\left(q_1\right),$ λ≤0.01 wherein;

S23. according to q ₀(i),

With

Calculate $f^{\&prime;}\left(q\left(i\right)\right)=\frac{q_{0^2}\left(i\right)-q_{0^1}\left(i\right)}{q_1\left(i\right)-q_0\left(i\right)},$ Find out maximum power variation rate | f'(q _k(i)) _Max|, then ${\mathrm{\&lambda;}}_{\max }=\frac{2}{1-f^{\&prime;}{\left(q_k\left(i\right)\right)}_{\max }};$

Above-mentioned steps S21 to step S23, i=1,2..., N.

3. nuclear reactor nuclear heat coupling calculation according to claim 2 is characterized in that, and is described ${\mathrm{\&lambda;}}_{\max }=\frac{2}{1-f^{\&prime;}{\left(q_k\left(i\right)\right)}_{\max }}\&ap;0.1909.$

4. nuclear reactor nuclear heat coupling calculation according to claim 2 is characterized in that, adopts part iteration function g (q (i)) to find the solution the power distribution among the described step S4 and specifically may further comprise the steps:

The axial line power density distribution of S41. establishing is q ₀(i), wherein initial power is distributed as the power distribution of satisfying single excellent power constraint;

S42. by iterative formula q _K+1(i)=g (q _k(i))=λ * f (q _k(i))+(1-λ) * q _k(i) constantly carry out iteration, until

Be q _k(i) be that required nuclear heat coupled power distributes; I=1 wherein, 2..., N, λ＜λ _Max

5. nuclear reactor nuclear heat coupling calculation according to claim 4 is characterized in that, the initial power distribution q among the described step S41 ₀(i) for being evenly distributed or Sine distribution.

6. nuclear reactor nuclear heat coupling calculation according to claim 5 is characterized in that, described initial power distribution q ₀(i) be Sine distribution.

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