CN115828643B - Method for simultaneously moving multiple control rod groups to search critical by considering overlapping steps - Google Patents
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Abstract
The invention discloses a method for simultaneously moving a plurality of control rod groups to search for a critical point by considering overlapping steps, which comprises the steps of firstly, respectively inserting or extracting all the control rod groups participating in the critical search in a reactor core according to an initial reactor core effective increment factor of the critical search reactor core; then, calculating the whole reactor core to obtain a new reactor core effective increment factor; according to the total length of the movement of the control rod groups and the change of the effective increment factor of the reactor core, carrying out total height interpolation and rod position height calculation to obtain new rod positions of each control rod group when the reactor core is critical; adjusting the corresponding control rod group to a new rod position and carrying out whole reactor core transport calculation again; the above process is repeated until the core reaches a critical state. According to the invention, the multiple control rod groups can be used for carrying out critical searching calculation together, so that the number of times of whole reactor core transportation calculation in the traditional critical searching calculation process is reduced, and the situation of critical searching of the control rod groups by overlapping the walking rods can be considered. The method can be used for the critical searching calculation of the numerical reactor, and the calculation speed and efficiency are improved.
Description
Technical Field
The invention relates to the technical field of nuclear reactor core design and safety, in particular to a method for simultaneously moving a plurality of control rod groups to search for a critical point by considering overlapping steps.
Background
The reactor core critical searching process is an important working condition in the reactor operation process, and the reactor core is required to be in a critical state before the reactor core burnup point calculation and the reactor transient working condition calculation. Control of core reactivity by changing the position of the control rod sets is an important tool for core search criticality.
When large pressurized water reactors are operated, the requirements for the reactor core are in a critical state. However, as the operating time of the reactor increases, the burnup depth of burnup material increases, so that the core cannot remain critical, and thus at different burnup points, the core criticality needs to be achieved by moving the control rod groups inside the core. In the transient state of the nuclear reactor, the core is critical before the transient state occurs. For the physical procedure of the reactor, if the transient working condition is to be calculated, the position of the control rod is required to be changed continuously, the calculation is repeated until the reactor core reaches the critical value, and then the transient calculation can be performed, so that the process is extremely complicated.
The current critical search method mainly adopted in the numerical reactor procedure is a traditional linear interpolation method. And (3) carrying out critical search on the control rod groups one by one through the defined control rod group moving rod sequence until the reactor core reaches the critical state when one control rod group reaches a certain position. However, when the number of rod sets participating in the critical search in the reactor is excessive, the efficiency of the method is low, because at least one full core calculation is performed for each control rod set before the reactor reaches the critical, which consumes a lot of time, and the overlapping movement process of the control rod sets is difficult to consider by the critical search method.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention aims to provide a method for simultaneously moving a plurality of control rod groups to search for critical points by taking overlapping steps into consideration. Compared with the traditional method, the method greatly reduces the number of times of calculating the whole reactor core for searching the critical under a plurality of control rod groups, reduces the time required by calculating the searching critical, and can realize the process of overlapping step rod searching critical.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a method for simultaneously moving a plurality of control rod groups to search for critical points by considering overlapping steps comprises the following steps:
step 1: reading geometric information, material information, boundary conditions and control rod group information of a critical reactor core to be simulated;
step 2: obtaining information of each control rod group participating in the search critical according to the control rod group information obtained in the step 1, wherein the information comprises the sequence of each control rod group participating in the search critical, the minimum and maximum height of the control rod group and the initial position of each control rod group; then carrying out neutron transport calculation of the whole reactor core to obtain an effective proliferation coefficient of the reactor core in an initial state;
step 3: respectively processing according to the difference between the effective proliferation coefficient of the reactor core calculated in the step 2 and the absolute difference value of 1; if the absolute difference between the effective multiplication coefficient of the reactor core and 1 is larger than the convergence criterion and the effective multiplication coefficient of the reactor core is larger than 1, all control rod groups participating in the search of the reactor core are inserted into the reactor core through the movement of the control rods; if the absolute difference between the effective multiplication coefficient of the reactor core and 1 is larger than the convergence criterion and the effective multiplication coefficient of the reactor core is smaller than 1, all control rod groups which participate in the search critical of the reactor core are proposed to the reactor core through the movement of the control rods; if the absolute difference between the effective multiplication coefficient of the reactor core and 1 is smaller than the convergence criterion, the reactor core reaches a critical state at the moment, and the calculation is finished;
step 4: carrying out full-reactor core transport calculation again according to the new rod positions of the control rod groups to obtain reactor core effective increment factors under the new rod positions of the control rod groups; calculating to obtain the difference of the total heights of the control rod groups in two adjacent full core calculation by using a formula (4.1), calculating to obtain the average differential value of the control rod groups in two full core calculation by using a formula (4.2), and finally carrying out total height interpolation calculation by using a formula (4.3) and a formula (4.4) to obtain the total height of the new control rod group;
wherein,,
step 5: if the overlapping movement of the control rod groups is not considered, the N control rod groups are numbered to be 1-N according to the sequence of the searching critical of the control rod groups and the maximum height of each control rod group which can move, wherein the sequence of the searching critical of each control rod group is obtained through the step 2, and the total height of m control rod groups is assumed to be the maximum at the moment; calculating according to the formula (4.5) and the formula (4.6) to obtain the height of each control rod group in the next whole reactor core calculation;
wherein,,
h i+1,j+1 -the height of the (i+1) th control rod group at the (j+1) th full core calculation;
if the stacking movement of the control rod groups is considered, assuming that the stacking height among the control rod groups during the stacking movement is d, and the maximum heights of the control rod groups capable of moving are equal;
when the control bar set numbered 1 is stepped up to the maximum height, it is assumed that it is common at this time
The height of each control rod group is more than 0; the height and +.A.of each control bar group was determined by equation (4.7)>
Then the total height of the control rod group is calculated by a formula (4.8);
wherein,,
when (when)
When the height of the total n control rod groups is greater than 0, the control rod groups are supposed to be in total; the rod position height of the control rod group with the number from n to 1 is shown as a formula (4.9), and the size of n is calculated according to the formula (4.10);
when (when)
When n=n; />
In the rest of the cases, the formula (4.10) is satisfied
Calculated according to formula (4.10):
since n is a positive integer and the value range of n in the calculation result of the formula (4.10) is smaller than 1, only one integer n satisfies the condition; after n is calculated, the height of each control rod group is calculated by a formula (4.11) and a formula (4.9);
wherein,,
when H is j+1 >H critical And is also provided with
，/>
When the total m control rod groups reach the maximum height, the rootCalculating according to a formula (4.12) to obtain the size of m;
calculated according to formula (4.12):
since m is a positive integer and the value range of m in the calculation result of the formula (4.12) is smaller than 1, only one integer m satisfies the condition, and after m is calculated, the heights of the rest bar groups are calculated through the formulas (4.10), (4.11) and (4.9);
when H is j+1 >H critical ，
The number of the control rod groups with the rod position height smaller than the maximum value is assumed to be k, and the rod positions of the new control rod groups are calculated according to the following formula (4.13);
calculated according to formula (4.13):
wherein k is a positive integer, and the value range of k in the calculation result of the formula (4.13) is smaller than 1, so that only one integer k meets the condition; then calculating m=N-k to obtain m, and finally calculating through a formula (4.11) and a formula (4.9) to obtain the heights of the rest control rod groups;
wherein,,
step 6: repeating the processes in the step 4 and the step 5 until the absolute difference between the effective proliferation coefficient of the reactor core obtained by calculation of the whole reactor core and 1 is smaller than a convergence criterion under a certain control rod group height; and at the moment, the critical calculation of the reactor core is finished, and the height of each control rod group finally obtained is the critical rod position of the reactor core control rod group.
The convergence criterion in the step 3 and the step 6 considers the sharp tooth effect and the related test basis in the control rod moving process, and is set to be not more than
。
Compared with the prior art, the invention has the following outstanding advantages:
compared with the traditional method, the method disclosed by the invention has the advantages that the interpolation is carried out on the total height of all control rod groups participating in the search, and the heights of all rod groups are solved respectively, so that the number of times of calculation of the whole reactor core is reduced, the calculation time of the reactor core search is greatly reduced, and meanwhile, the function of overlapping step rod search is realized.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a 3×3 single component schematic.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
The present invention has been tested in the high fidelity physical computing program NECP-X. The specific implementation steps are shown in fig. 1. The simulated reactor core is modeled by a NECP-X program according to the geometric information, material information, boundary conditions and control rod group information of the reactor core in the input card. And (3) processing information in the input card in the NECP-X program to obtain information of each control rod group participating in the search threshold, wherein the information comprises the sequence of each control rod group participating in the search threshold, the minimum and maximum height of the movable control rod group and the initial position of each control rod group. A first full core transport calculation is then performed based on the initial positions of the control rods. And performing full-insert or full-lift treatment on the control rod groups participating in critical searching according to the calculated result, performing full-stack calculation again, obtaining new control rod group rod positions through total height interpolation and rod position calculation, and performing full-core transport calculation again according to the new control rod group rod positions. And repeating the above flow until the absolute difference between the effective increment coefficient of the reactor core obtained by the total reactor calculation under a certain rod position and 1 is smaller than the convergence criterion, and ending the critical calculation, wherein the rod position of the control rod group is the critical rod position. The following describes the specific calculation steps using a 3 x 3 single component problem:
step 1: a 3 x 3 single module is shown in fig. 2, which consists of 9 cells in total, with 9 rods in each cell. B, C, D and E are four different control rod groups, A is a guide pipe, the material of the fuel rods in the fourth cell adopts MOX fuel, and the material of the fuel rods in the other cells is UO 2 The fuel, the rest of the cell except the fuel rod is water.
Step 2: there are four control rod groups in total in the core: b C D E; wherein the control rod groups participating in the critical searching are B C D in sequence. Setting the minimum height of each bar set to be 0 (full insertion), the maximum height to be 60 steps (1 step=0.714 cm), setting the initial positions of the four bar sets to be full insertion, and setting the convergence criterion to be 30×10 -5 . Then, carrying out neutron transport calculation of the whole reactor core to obtain an initial effective proliferation coefficient of 0.896115 of the reactor core;
step 3: because the effective proliferation coefficient of the reactor core calculated in the step 2 is smaller than 1 and the absolute difference between the effective proliferation coefficient and 1 is larger than the convergence criterion, the NECP-X program moves all control rod groups BC D of the reactor core participating in critical searching to the maximum height of 60 steps through control rod movement;
step 4: and (4) carrying out full-core calculation again according to the new rod positions of the B C D control rod group. The effective increment factor of the obtained new reactor core is 1.026925. The total length of the movement of the control rod group is 180 steps in the calculation of two adjacent full cores through the formula (4.1), and then the average differential value of the control rod group in the calculation of two full cores is 72.67 multiplied by 10 through the calculation of the formula (4.2) -5 Step/step, finally, carrying out total height interpolation calculation through a formula (4.3) to obtain a new control rod group, wherein the total height of the new control rod group is 143 steps;
step 5: because there is no overlapping movement between the control rod groups. Calculating according to formulas (4.5) and (4.6) to obtain a new control rod group height, and B:60 steps, C:60 steps, D: step 23;
step 6: repeating the flow in the step 4 and the step 5 until when the rod position of the control rod group is B:60 steps, C:60 steps, D: at 26 steps, the effective multiplication coefficient of the reactor core obtained by calculation of the whole reactor core is 1.000212, and the absolute difference between the result and 1 is 21 multiplied by 10 -5 And is less than 30 x 10 of the convergence criterion -5 . And at the moment, the critical calculation of the reactor core is finished, and the rod positions of the control rod group finally obtained are the critical rod positions of the control rod group calculated by the reactor core.
Since the control rod has the sharp tooth effect in the moving process, the NECP-X program is used for carrying out explicit modeling on the rod positions of the control rod group obtained by calculation to verify the calculation result, and the calculation result is obtained by carrying out the calculation on the B:60 steps, C:60 steps, D: the rod position in 26 steps is highly explicitly modeled and calculated to obtain the final effective proliferation coefficient of 1.000430 with a critical gap of 43×10 -5 . To ensure that the bar position is indeed the optimal critical bar position, the control bar set bar position is B:60 steps, C:60 steps, D: the rod position of the 25 steps is also subjected to explicit modeling calculation to obtain an effective proliferation coefficient of 0.999297 and a critical gap of 70.3X10 -5 . The calculated rod position is thus determined to be the optimal critical rod position.
Table 1 is a comparison of the number of full core calculations for a conventional search run and the present method when the number of control rod sets involved in the search run is different. Compared with the traditional method, the method has obvious advantages in the critical searching calculation with a large number of control rod groups, greatly reduces the total core calculation times in the calculation process, and improves the calculation efficiency.
TABLE 1
In addition, the method can also consider the situation that the overlapped walking bars exist among the control bar groups. Taking the core as an example, the stacking height between B, C, D control rod groups is set to 15 steps.
Wherein step 1, step 2, step 3 and step 4 are the same as the above steps.
Step 5: at this time H critical The number of steps is =135,
= 3。H critical is smaller than the total height of the control rod group calculated in the step four and +.>
Equal to the total number of control bar sets. K=2 and m=1 are calculated according to formula (4.13), and then the height of each bar group is calculated by formulas (4.11) and (4.9) to be B:34 steps, C:49 steps, D:60 steps;
wherein,,
m-when obtaining the new rod position of the control rod group, the rod position height of the control rod group with the number of 1-m is the maximum;
step 6: repeating the flow in the step 4 and the step 5 until when the rod position of the control rod group is B:29, C:44 steps, D: at step 59, the effective multiplication coefficient of the core calculated from the whole core is 1.000172, and the absolute difference between the result and 1 is 17×10 -5 And is less than 30 x 10 of the convergence criterion -5 . And at the moment, the critical calculation of the reactor core is finished, and the rod positions of the control rod group finally obtained are the critical rod positions of the control rod group calculated by the reactor core.
Using NECP-X program to make explicit modeling on the above-mentioned calculated control rod group rod position to verify calculation result so as to obtain the final effective proliferation coefficient of 0.999222 and critical gap of 77.8X10 -5 . To ensure that the bar position is indeed the optimal bar position, the control bar set bar position is B:30, C:45 steps, D: the rod position of 60 steps is also subjected to explicit modeling calculation to obtain the effective proliferation coefficient of 1.001162 and the critical gap of 116.2 multiplied by 10 -5 . The calculated rod position is thus determined to be the optimal critical rod position. The method can be well applied to the calculation of the search critical of the control rod stacking step rod, and has higher precision.
Claims (2)
1. A method for simultaneously moving a plurality of control rod groups to search for critical points by considering overlapping steps is characterized by comprising the following steps: the method comprises the following steps:
step 1: reading geometric information, material information, boundary conditions and control rod group information of a critical reactor core to be simulated;
step 2: obtaining information of each control rod group participating in the search critical according to the control rod group information obtained in the step 1, wherein the information comprises the sequence of each control rod group participating in the search critical, the minimum and maximum height of the control rod group and the initial position of each control rod group; then carrying out neutron transport calculation of the whole reactor core to obtain an effective proliferation coefficient of the reactor core in an initial state;
step 3: respectively processing according to the difference between the effective proliferation coefficient of the reactor core calculated in the step 2 and the absolute difference value of 1; if the absolute difference between the effective multiplication coefficient of the reactor core and 1 is larger than the convergence criterion and the effective multiplication coefficient of the reactor core is larger than 1, all control rod groups participating in the search of the reactor core are inserted into the reactor core through the movement of the control rods; if the absolute difference between the effective multiplication coefficient of the reactor core and 1 is larger than the convergence criterion and the effective multiplication coefficient of the reactor core is smaller than 1, all control rod groups which participate in the search critical of the reactor core are proposed to the reactor core through the movement of the control rods; if the absolute difference between the effective multiplication coefficient of the reactor core and 1 is smaller than the convergence criterion, the reactor core reaches a critical state at the moment, and the calculation is finished;
step 4: carrying out full-reactor core transport calculation again according to the new rod positions of the control rod groups to obtain reactor core effective increment factors under the new rod positions of the control rod groups; calculating to obtain the difference of the total heights of the control rod groups in two adjacent full core calculation by using a formula (4.1), calculating to obtain the average differential value of the control rod groups in two full core calculation by using a formula (4.2), and finally carrying out total height interpolation calculation by using a formula (4.3) and a formula (4.4) to obtain the total height of the new control rod group;
wherein,,
ΔH j the difference j between the total height of each control rod group participating in the search and the total height of each control rod group participating in the search in the last calculation of the whole reactor core is more than or equal to 2;
n is the number of control rod groups participating in the search critical;
h i,j -the height of the ith control rod group at the jth full core calculation;
h i,j-1 -the height of the ith control rod group during the j-1 th full core calculation;
Δk j after the jth full core calculation, the last oneCompared with the calculation of the secondary total core, the average differential value of the control rod groups participating in the critical search is calculated;
k eff,j -the core effective increment coefficient obtained after the jth full core calculation;
k eff,j-1 -the effective increment coefficient of the reactor core obtained after the j-1 th calculation of the full reactor core;
H j+1 -the total height of the set of control rods involved in the search during the j+1th full core calculation;
H j -the j-th calculation of the total height of the set of control rods involved in the search;
H 1 -the total height of the set of control rods involved in the search upon the 1 st full core calculation;
h i,1 -the height of the ith control rod group at the 1 st full core calculation;
step 5: if the overlapping movement of the control rod groups is not considered, the N control rod groups are numbered to be 1-N according to the sequence of the searching critical of the control rod groups and the maximum height of each control rod group which can move, wherein the sequence of the searching critical of each control rod group is obtained through the step 2, and the total height of m control rod groups is assumed to be the maximum at the moment; when j+1st full core calculation is obtained according to the formula (4.5) and the formula (4.6), the total height of the control rod group participating in critical searching is calculated;
wherein,,
h i+1,j+1 -the height of the (i+1) th control rod group at the (j+1) th full core calculation;
h i_max -maximum height that the ith control bar set can move;
if the stacking movement of the control rod groups is considered, assuming that the stacking height among the control rod groups during the stacking movement is d, and the maximum heights of the control rod groups capable of moving are equal;
when the control rod group with the number of 1 moves to the maximum height in a stacking way, assuming that m control rod groups are in total higher than 0 at the moment; the height and m of each control rod group are calculated through a formula (4.7), and then the total height of the control rod group is calculated through a formula (4.8);
wherein,,
h i,critical -the height of the ith control bar set when the numbered 1 control bar set is stepped up to the maximum height; h is a 1_max -maximum height that the 1 st control bar set can move;
d, controlling the stacking height between rod groups;
n is the number of control rod groups participating in the search critical;
H critical -the total height of the control bar set participating in the search when the control bar set numbered 1 is stepped up to the maximum height;
m-number 1 of control bar sets when the control bar sets move to the maximum height in a stacking way, wherein the height of the control bar sets is greater than 0;
when H is j+1 <H critical When the height of the total n control rod groups is greater than 0, the control rod groups are supposed to be in total; the rod position height of the control rod group with the number from n to 1 is shown as a formula (4.9), and the size of n is calculated according to the formula (4.10);
when h m*,critical Not less than d and H critical -N·h m*,critical ≤H j+1 ＜H critical When n=n;
in the rest of the cases, the formula (4.10) is satisfied
Calculated according to formula (4.10):
since n is a positive integer and the value range of n in the calculation result of the formula (4.10) is smaller than 1, only one integer n satisfies the condition; after n is calculated, the height of each control rod group is calculated by a formula (4.11) and a formula (4.9);
wherein,,
H j+1 -the total height of the set of control rods involved in the search during the j+1th full core calculation;
h n,j -the height of the nth control rod group at the jth full core calculation;
d, controlling the stacking height between rod groups;
n-the number of control bar sets greater than 0;
n is the number of control rod groups participating in the search critical;
m-number 1 of control bar sets when the control bar sets move to the maximum height in a stacking way, wherein the height of the control bar sets is greater than 0;
H critical -the total height of the control bar set participating in the search when the control bar set numbered 1 is stepped up to the maximum height;
h i,critical -the height of the ith control bar set when the numbered 1 control bar set is stepped up to the maximum height;
when H is j+1 >H critical And m is<N，H j+1 ＜H critical +(N-m*)·h i_max When the control rod group is in total, assuming that m control rod groups reach the maximum height, calculating to obtain m according to a formula (4.12);
H critical -h 1_max +m*h 1_max ≤H j+1 ＜H critical -h 1_max +(m+1)*h 1_max (4.12)
calculated according to formula (4.12):
since m is a positive integer and the value range of m in the calculation result of the formula (4.12) is smaller than 1, only one integer m satisfies the condition, and after m is calculated, the heights of the rest bar groups are calculated through the formulas (4.10), (4.11) and (4.9);
when H is j+1 >H critical M=n or H j+1 ≥H critical +(N-m*)·h i_max The number of the control rod groups with the rod position height smaller than the maximum value is assumed to be k, and the rod positions of the new control rod groups are calculated according to the following formula (4.13);
calculated according to formula (4.13):
wherein k is a positive integer, and the value range of k in the calculation result of the formula (4.13) is smaller than 1, so that only one integer k meets the condition; then calculating m=N-k to obtain m, and finally calculating the heights of the rest control rod groups through a formula (4.11) and a formula (4.9);
wherein,,
H j+1 -the total height of the set of control rods involved in the search during the j+1th full core calculation;
h i,j -the height of the ith control rod group at the jth full core calculation;
h i_max -maximum height that the ith control bar set can move;
d, controlling the stacking height between rod groups;
n-the number of control bar sets greater than 0;
n is the number of control rod groups participating in the search critical;
m-number 1 of control bar sets when the control bar sets move to the maximum height in a stacking way, wherein the height of the control bar sets is greater than 0;
H critical -the total height of the control bar set participating in the search when the control bar set numbered 1 is stepped up to the maximum height;
h i,critical -the height of the ith control bar set when the numbered 1 control bar set is stepped up to the maximum height;
k is the number of control rod groups with the rod position height smaller than the maximum value;
step 6: repeating the processes in the step 4 and the step 5 until the absolute difference between the effective proliferation coefficient of the reactor core obtained by calculation of the whole reactor core and 1 is smaller than a convergence criterion under a certain control rod group height; and at the moment, the critical calculation of the reactor core is finished, and the height of each control rod group finally obtained is the critical rod position of the reactor core control rod group.
2. A method for simultaneous dynamic bar search critical for multiple control bar sets considering step-by-step as in claim 1, wherein: the convergence criteria described in step 3 and step 6 take into account the tine effect and related test criteria during movement of the control rod, the convergence criteria being set to no more than 50 x 10 -5 。
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| CN115331844B (en) * | 2022-09-08 | 2024-04-23 | 中国核动力研究设计院 | Method and system for measuring value of control rod under subcritical nuclear reactor |
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| CN114974631A (en) * | 2022-04-15 | 2022-08-30 | 华能山东石岛湾核电有限公司 | First charging and critical method for high-temperature gas cooled reactor |
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