CN115828643A - Method for simultaneously moving rod search thresholds of multiple control rod groups in consideration of overlapping steps - Google Patents
Method for simultaneously moving rod search thresholds of multiple control rod groups in consideration of overlapping steps Download PDFInfo
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Abstract
The invention discloses a method for simultaneously operating search criticality by considering a plurality of control rod groups in a cascade manner, which comprises the following steps of firstly, respectively inserting or extracting all the control rod groups participating in the search criticality in a reactor core according to the initial effective value-added factors of the reactor core of the search criticality; then, calculating the whole reactor core to obtain a new effective value-added factor of the reactor core; according to the total moving length of the control rod groups and the change of the effective value-added factors of the reactor core, total height interpolation and rod position height calculation are carried out to obtain the new rod position 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 the transport calculation of the whole reactor core again; the above process is repeated until the core reaches the critical state. The method can not only carry out the search-critical calculation on a plurality of control rod groups together, reduce the total reactor core transport calculation times in the traditional search-critical calculation process, but also consider the condition that the control rod groups are stacked to carry out the search-critical calculation. The method can be used for the search-critical calculation of the numerical reactor, and improves the calculation speed and efficiency.
Description
Technical Field
The invention relates to the technical field of nuclear reactor core design and safety, in particular to a method for simultaneously performing rod search on a plurality of control rod groups in consideration of overlapping steps.
Background
The critical process of reactor core search is an important working condition in the reactor operation process, and the reactor core is required to be in a critical state before the calculation of the reactor core burnup point and the calculation of the reactor transient working condition. Controlling core reactivity by varying the position of the control rod sets is an important means of core criticality.
When a large pressurized water reactor is operated, the requirements on the reactor core are in a critical state. However, as the reactor operating time increases, the burn-up depth of the burnable material increases, so that the core cannot be maintained critical, and therefore, the core criticality is achieved by moving the control rod groups inside the core at different burn-up points. In the transient condition of the nuclear reactor, the reactor core must be in a critical state before the transient condition occurs. For the reactor physical procedure, if the transient operating condition needs to be calculated, the position of the control rod needs to be continuously changed, the calculation is repeatedly carried out, the transient calculation can not be carried out until the reactor core reaches the critical state, and the process is extremely complicated and complex.
The current critical search method mainly used in the numerical reactor process is the conventional linear interpolation method. And critical search is carried out on the control rod groups one by one through the specified 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 groups participating in the search is too large, the method is inefficient because the reactor is moved at least once for all the cores before reaching the critical value, which consumes a lot of time, and the search is difficult to consider the cascade movement of the control rod groups.
Disclosure of Invention
In order to overcome the problems in the prior art, the present invention provides a method for simultaneously performing a search for a plurality of control rod groups in consideration of overlapping steps, which does not use the conventional method for searching for the control rod groups one by one, and solves the total height of the control rod groups by interpolation using all the control rod groups participating in the search as a whole, thereby obtaining the height of each rod group. Compared with the traditional method, the method greatly reduces the number of times of calculating the whole reactor core of the search criticality under a plurality of control rod groups, reduces the time required by the search criticality calculation, and can realize the process of moving the rod search criticality in a cascading manner.
In order to achieve the purpose, the invention adopts the following technical scheme to implement:
a method for simultaneously operating a plurality of control rod groups in consideration of overlapping steps, comprising the steps of:
step 1: reading geometric information, material information, boundary conditions and control rod group information of a critical core to be simulated;
step 2: obtaining information of each control stick group participating in the search threshold according to the control stick group information obtained in the step 1, wherein the information comprises the sequence of each control stick group participating in the search threshold, the minimum and maximum movable heights and the initial position of each control stick group; then, performing neutron transport calculation on the whole reactor core to obtain the effective reactor core multiplication coefficient in an initial state;
and step 3: respectively processing according to the difference between the effective reactor core multiplication coefficient calculated in the step 2 and the absolute difference value of 1; if the absolute difference value of the effective reactor core multiplication coefficient and 1 is greater than the convergence criterion and the effective reactor core multiplication coefficient is greater than 1, inserting all control rod groups of the reactor core participating in the critical search into the reactor core by moving the control rods; if the absolute difference value of the effective reactor core multiplication coefficient and 1 is greater than the convergence criterion and the effective reactor core multiplication coefficient is less than 1, all control rod groups of the reactor core participating in the critical search are lifted out of the reactor core by moving the control rods; if the absolute difference value 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;
and 4, step 4: carrying out the transport calculation of the whole reactor core again according to the new rod position of the control rod group to obtain the effective value-added factors of the reactor core under the new rod position of the control rod group; calculating to obtain the difference of the total heights of the control rod groups in two adjacent whole core calculations through a formula (4.1), then calculating to obtain the average differential value of the control rod groups in the two whole core calculations through a formula (4.2), and finally carrying out total height interpolation calculation through a formula (4.3) and a formula (4.4) to obtain the total height of a new control rod group;
wherein, the first and the second end of the pipe are connected with each other,
and 5: if the overlapping movement of the control rod groups is not considered, numbering the N control rod groups according to the searching critical sequence of the control rod groups and the maximum height capable of moving of the control rod groups obtained in the step 2 into 1-N, and supposing that the heights of m control rod groups are the maximum at the moment; calculating according to a formula (4.5) and a formula (4.6) to obtain the height of each control rod group in the next total reactor core calculation;
wherein, the first and the second end of the pipe are connected with each other,
h i+1,j+1 -the height of the (i + 1) th control rod group at the time of the (j + 1) th total core calculation;
if the stacking movement of the control rod groups is considered, assuming that the stacking height of each control rod group during the stacking movement is d, the maximum height of the control rod groups capable of moving is equal;
when the control bar group numbered 1 is moved in steps 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 sum of each control rod group is obtained through the formula (4.7)
Then the total height of the control rod group at the moment is calculated by the formula (4.8);
wherein the content of the first and second substances,
when in use
If so, assuming that the height of the n control rod groups is more than 0; the height of the control rod group with the number from n to 1 is shown in a formula (4.9), and the size of n is calculated according to the formula (4.10);
when the temperature is higher than the set temperature
When N = N;
otherwise, the formula (4.10) is satisfied
Calculated according to equation (4.10):
since n is a positive integer and the value range of n in the calculation result of the formula (4.10) is less than 1, only one integer n meets the condition; after n is obtained through calculation, the height of each control rod group is obtained through calculation according to a formula (4.11) and a formula (4.9);
wherein the content of the first and second substances,
when H is present j+1 >H critical And is
，
When the height of the control rod group reaches the maximum height, the size of m is calculated according to a formula (4.12);
calculated according to equation (4.12):
since m is a positive integer and the value range of m in the calculation result of the formula (4.12) is less than 1, only one integer m meets the condition, and after m is obtained through calculation, the heights of the rest bar groups are obtained through calculation of the formula (4.10), the formula (4.11) and the formula (4.9);
when H is present j+1 >H critical ，
If the number of the control rod groups with the rod position height smaller than the maximum value is k, calculating to obtain the new rod position of each control rod group according to the following formula (4.13);
calculated according to equation (4.13):
k is a positive integer, and the value range of k in the calculation result of the formula (4.13) is less than 1, so that only one integer k meets the condition; then calculating the size of m by m = N-k, and finally calculating the height of the rest control rod groups by (4.11) and a formula (4.9);
wherein the content of the first and second substances,
step 6: repeating the processes in the step 4 and the step 5 until the absolute difference value between the effective reactor core multiplication coefficient obtained by the calculation of the whole reactor core and 1 is less than the convergence criterion under a certain control rod group height; at the moment, the critical calculation of the reactor core is finished, and the finally obtained height of each control rod group is the critical rod position of the reactor core control rod group.
The convergence criterion of the step 3 and the step 6 considers the tine effect and the related test basis in the control rod moving process, and the convergence criterion is set not to exceed
。
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 problem of the core search criticality of a plurality of control rod groups is avoided being calculated by adopting a traditional single rod group linear interpolation mode, the total heights of all the control rod groups participating in the search criticality are interpolated, the heights of all the control rod groups are respectively solved, the calculation times of the whole core are reduced, the calculation time of the core search criticality is greatly reduced, and the function of moving the core search criticality in a stacked step is realized.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic view of a 3 × 3 single component.
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 first modeled using the NECP-X program based on the geometric information, material information, boundary conditions and control rod set information for the core in the input card. By processing the information in the input card in the NECP-X program, information of each control stick group participating in the search threshold is obtained, including the sequence of participation of each control stick group in the search threshold, the minimum and maximum heights of the movement possible, and the initial position of each control stick group. A first full core transport calculation is then made based on the initial position of the control rods. And carrying out full interpolation or full extraction treatment on the control rod groups participating in the search criticality according to the calculated result, then carrying out full stack calculation again, obtaining the rod position of a new control rod group through total height interpolation and rod position calculation, and carrying out full core transport calculation again according to the rod position of the new control rod group. And repeating the process until the absolute difference value between the effective value-added coefficient of the reactor core obtained by the whole-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 at the moment is the critical rod position. The following describes the specific computation steps using a 3 × 3 single component problem:
step 1: a 3 x 3 single component as shown in fig. 2, the component consists of 9 cells, with 9 rods in each cell. B, C, D and E are four different control rod groups, A is a guide tube, MOX fuel is adopted as the material of the fuel rods in the fourth grid cell, and UO is adopted as the material of the fuel rods in the other grid cells 2 The fuel and the rest materials except the fuel rods in the grid cells are all water.
Step 2: there are a total of four control rod groups in the core: b, C, D, E; wherein the control rod groups participating in the search are sequentially B, C and D. Setting the minimum height moved by each bar group to be 0 (full interpolation), the maximum height to be 60 steps (1 step =0.714 cm), the initial positions of the four bar groups to be full interpolation, and the convergence criterion to be 30 × 10 -5 . Then, the neutron transport calculation of the whole reactor core is carried out to obtainUntil the initial effective multiplication coefficient of the reactor core is 0.896115;
and step 3: since the effective core multiplication coefficient calculated in step 2 is less than 1 and the absolute difference between the effective core multiplication coefficient and 1 is greater than the convergence criterion, the NECP-X program moves all the control rod groups bc D of which the core participates in the search criticality to the maximum height by the control rod movement by 60 steps;
and 4, step 4: and performing the whole core calculation again according to the new rod position of the B C D control rod group. The new effective value-added factor of the reactor core is 1.026925. Calculating by the formula (4.1) to obtain that the total length of the control rod group in the two adjacent whole core calculations is 180 steps, and then calculating by the formula (4.2) to obtain that the average differential value of the control rod group in the two whole core calculations is 72.67 × 10 -5 Step one, finally, carrying out total height interpolation calculation through a formula (4.3) to obtain the total height of the new control rod group in step 143;
and 5: because there is no overlapping motion between control rod groups. Calculating according to the formulas (4.5) and (4.6) to obtain a new control rod group height, B: step 60, C: step 60, D:23, step (2);
step 6: repeating the processes in the step 4 and the step 5 until the rod position of the control rod group is B: step 60, C: step 60, D: in 26 steps, the effective reactor core multiplication coefficient obtained by the calculation of the whole reactor core is 1.000212, and the absolute difference value of the result and 1 is 21 multiplied by 10 -5 And less than 30 x 10 of the convergence criterion -5 . At this time, the critical calculation of the reactor core is finished, and the rod position of the control rod group obtained finally is the critical rod position of the control rod group obtained by the calculation of the reactor core.
Since the tine effect exists during the control rod movement, the calculation results were verified by explicitly modeling the control rod set rod positions calculated above using the NECP-X program, by comparing B: step 60, C: step 60, D: the height of the rod position in the 26 steps is explicitly modeled and calculated, and the obtained final effective multiplication coefficient is 1.000430, and the difference from the critical value is 43 multiplied by 10 -5 . To ensure that the rod position is indeed the optimal critical rod position, the rod positions for the control rod group are B: step 60, C: step 60, D: the 25-step rod position is also subjected to explicit modeling calculation to obtain the effective multiplication coefficient of 0.999297 and the critical difference of 70.3 multiplied by 10 -5 . Thus, the deviceThe calculated rod position is determined as the optimal critical rod position.
Table 1 is a comparison of the total core count times for the conventional search and criticality approach when the number of control rod sets participating in the search is different. Compared with the traditional method, the method has obvious advantages in processing the search-critical calculation with more control rod groups, greatly reduces the total reactor core calculation times in the calculation process and improves the calculation efficiency.
TABLE 1
In addition, the method can also consider the condition that the overlapped walking rods exist among the control rod 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 above.
And 5: at this time H critical In the case of the number of steps of = 135,
= 3。H critical less than the total height of the control rod set calculated in step four
Equal to the total number of control rod groups. K =2,m =1 is calculated according to the formula (4.13), and then the height size of each bar group is calculated by the formulas (4.11) and (4.9) as B: step 34, C: step 49, D:60 steps;
wherein the content of the first and second substances,
m-when obtaining the new control rod group rod position, the rod position height of the control rod group with the number of 1-m is the maximum;
step 6: repeating the processes in the step 4 and the step 5 until the rod position of the control rod group is B: step 29, C: step 44, D: in step 59, the effective multiplication coefficient of the reactor core obtained by the calculation of the whole reactor core is 1.000172, and the absolute difference value of the result and 1 is 17 multiplied by 10 -5 And less than 30 x 10 of the convergence criterion -5 . At this time, the critical calculation of the reactor core is finished, and the rod position of the control rod group obtained finally is the critical rod position of the control rod group obtained by the calculation of the reactor core.
The control rod group position obtained by the calculation is subjected to explicit modeling by using a NECP-X program to verify the calculation result, and the final effective multiplication coefficient is 0.999222, and the critical difference is 77.8 multiplied by 10 -5 . To ensure that the rod position is indeed the optimal rod position, the rod positions for the control rod group are B: step 30, C: step 45, D: the bar position of 60 steps is also subjected to explicit modeling calculation to obtain the effective multiplication coefficient of 1.001162 and the critical difference of 116.2 multiplied by 10 -5 . Therefore, the calculated rod position is determined as the optimal critical rod position. The method can be well applied to the calculation of the search critical of the control rod stacking step motion rod, and has higher precision.
Claims (2)
1. A method for simultaneously performing a search by multiple control rod groups in consideration of overlapping steps, comprising: the method comprises the following steps:
step 1: reading geometric information, material information, boundary conditions and control rod group information of a critical core to be simulated;
and 2, step: obtaining information of each control stick group participating in the search threshold according to the control stick group information obtained in the step 1, wherein the information comprises the sequence of each control stick group participating in the search threshold, the minimum and maximum movable heights and the initial position of each control stick group; then, performing neutron transport calculation on the whole reactor core to obtain the effective reactor core multiplication coefficient in an initial state;
and 3, step 3: respectively processing according to the difference between the effective reactor core multiplication coefficient calculated in the step 2 and the absolute difference value of 1; if the absolute difference value of the effective reactor core multiplication coefficient and 1 is greater than the convergence criterion and the effective reactor core multiplication coefficient is greater than 1, inserting all control rod groups of the reactor core participating in the critical search into the reactor core by moving the control rods; if the absolute difference value of the effective reactor core multiplication coefficient and 1 is greater than the convergence criterion and the effective reactor core multiplication coefficient is less than 1, all control rod groups of the reactor core participating in the critical search are lifted out of the reactor core by moving the control rods; if the absolute difference value 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;
and 4, step 4: carrying out the transport calculation of the whole reactor core again according to the new rod position of the control rod group to obtain the effective value-added factors of the reactor core under the new rod position of the control rod group; calculating to obtain the difference of the total heights of the control rod groups in two adjacent whole core calculations through a formula (4.1), then calculating to obtain the average differential value of the control rod groups in the two whole core calculations through a formula (4.2), and finally carrying out total height interpolation calculation through a formula (4.3) and a formula (4.4) to obtain the total height of a new control rod group;
wherein the content of the first and second substances,
and 5: if the overlapping movement of the control rod groups is not considered, numbering N control rod groups according to the sequence of the search critical participation of each control rod group obtained in the step 2 and the maximum height capable of moving of each control rod group as 1-N, and assuming that the heights of m control rod groups reach the maximum at the moment; calculating according to a formula (4.5) and a formula (4.6) to obtain the height of each control rod group in the next total reactor core calculation;
wherein the content of the first and second substances,
h i+1,j+1 -the height of the (i + 1) th control rod group at the time of the (j + 1) th total core calculation;
if the step-stacking movement of the control rod groups is considered, assuming that the step-stacking height of each control rod group during the step-stacking movement is d, the maximum height of the control rod groups capable of moving is equal;
when the control bar group numbered 1 is moved in steps 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 sum of each control rod group is obtained through the formula (4.7)
Then the total height of the control rod group at the moment is calculated by the formula (4.8);
wherein the content of the first and second substances,
when in use
If so, assuming that the height of the n control rod groups is more than 0; the height of the control rod group with the number from n to 1 is shown in a formula (4.9), and the size of n is calculated according to the formula (4.10);
when in use
When N = N;
otherwise, the formula (4.10) is satisfied
Calculated according to equation (4.10):
since n is a positive integer and the value range of n in the calculation result of the formula (4.10) is less than 1, only one integer n meets the condition; computingAfter n is obtained, calculating the height of each control rod group through a formula (4.11) and a formula (4.9);
wherein the content of the first and second substances,
when H is present j+1 >H critical And is
，
When the height of the control rod group reaches the maximum height, the size of m is calculated according to a formula (4.12);
calculated according to equation (4.12):
when H is present j+1 >H critical ， 
If the number of the control rod groups with the rod position height smaller than the maximum value is k, calculating to obtain the new rod position of each control rod group according to the following formula (4.13);
calculated according to equation (4.13):
wherein the content of the first and second substances,
step 6: repeating the processes in the step 4 and the step 5 until the absolute difference value between the effective reactor core multiplication coefficient obtained by the calculation of the whole reactor core and 1 is less than the convergence criterion under a certain control rod group height; at the moment, the critical calculation of the reactor core is finished, and the finally obtained height of each control rod group is the critical rod position of the reactor core control rod group.
2. The method of claim 1, wherein the step-by-step simultaneous motion of the plurality of control rod groups is considered as follows: the convergence criterion of the steps 3 and 6 considers the tine effect and the relevant test basis in the control rod moving process, and the convergence criterion is set not to exceed
。
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