CN113504993B - Control rod sharp tooth effect processing method and system based on effective resonance section - Google Patents
Control rod sharp tooth effect processing method and system based on effective resonance section Download PDFInfo
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Abstract
The invention discloses a control rod sharp tooth effect treatment method based on an effective resonance sectionA method and system, the method comprising: modeling is conducted for a two-dimensional/one-dimensional method; determining rod positions, and carrying out two-dimensional non-uniform reactor core resonance calculation on a layer without control rod insertion or with control rod fully inserted to obtain a macroscopic section; for layer Z where there is a control rod portion inserted i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section; according to macroscopic cross section, pair Z i Carrying out transportation calculation by a two-dimensional reactor core characteristic line method by layers; based on two-dimensional transport calculation, after completing the numerical solution of the whole reactor core according to a two-dimensional/one-dimensional frame, carrying out microcosmic burnup calculation on each layer according to the axial average flux of each layer to obtain the axial average nuclear density of each burnup zone of each layer; based on the obtained axial average nuclear density of each layer, updating the initial model, and carrying out the next burnup step treatment until all burnup points to be unburnt are completed.
Description
Technical Field
The invention relates to the field of nuclear reactor physical numerical computation, in particular to a control rod sharp-tooth effect processing method and system based on an effective resonance section.
Background
For decades, the "two-step" method has been the classical method of reactor core physical analysis. The basic strategy is that firstly, energy spectrum calculation under various characteristic working conditions is carried out on a typical component, and a few-group homogenization section table or a fitting relation of the component is generated according to an equivalent homogenization theory; and secondly, carrying out neutron diffusion calculation on coarse net section blocks of the reactor core layer based on few uniform sections, and finally obtaining neutron characteristic parameters of interest such as the reactivity, the power distribution and the like of the reactor core. However, there are numerous approximations to the "two-step" system, which are increasingly faced with the increasing requirements of reactor economy, safety and functionality, the inherent drawbacks of which are increasingly manifest. In recent years, with the help of the rapid development of the large-scale computing capability of a computer, a high-fidelity one-step method system based on the neutron transport calculation of a whole reactor core becomes a research hot spot at home and abroad.
In the whole core neutron transport computing system, a two-dimensional/one-dimensional method is considered to be one of the most effective methods for considering precision, efficiency and resolution. The two-dimensional/one-dimensional method divides the three-dimensional non-uniform reactor core into a plurality of layers along the axial direction, each layer adopts a two-dimensional characteristic line method to carry out multi-group neutron transport calculation under the arrangement of fine geometric materials, and the layers are coupled by adopting one-dimensional transport or diffusion calculation; in addition, global computing synchronization convergence can be accelerated by coarse-mesh finite-difference techniques.
However, the two-dimensional/one-dimensional method also has some problems. Similar to the traditional nub method, the two-dimensional/one-dimensional method also suffers from the "tine effect" of the control rod, since each layer is assumed to be axially uniform. The sharp tooth effect refers to the phenomenon that when the tail end of a control rod is partially inserted into a certain uniform layer along the axial direction, the axial equivalent homogenization error is increased due to the strong absorption effect of the control rod on the center, and finally, the differential value curve of the control rod is caused to show non-physical sharp teeth.
In order to solve the problem, a sub-plane method, a sub-plane collision probability method, a sub-feature line method and the like are proposed in international order. Wherein the sub-plane approach still assumes that each sub-plane in the same layer has the same cross section and does not take into account the effect of control rod insertion on radial direction. The sub-plane collision probability method is improved by the two points, but the method has defects in the treatment of anisotropic scattering and complex geometric problems, and the characteristic line calculation is still based on the axial homogenization section. Meanwhile, these methods are only directed to the transport solver itself and do not give specific viable embodiments within a two-dimensional/one-dimensional system framework; this solution also has a critical impact on the effectiveness and cost of the control rod tine effect process.
Disclosure of Invention
The technical problem to be solved by the invention is that the existing control rod tine effect processing method still assumes that all sub-planes in the same layer have the same cross section, and the influence of control rod insertion on the radial direction is not considered; the sub-plane collision probability method has defects in the treatment of anisotropic scattering and complex geometric problems, and the characteristic line calculation is still based on the problem of axial homogenization of the cross section. The invention aims to provide a control rod sharp-tooth effect processing method and a control rod sharp-tooth effect processing system based on an effective resonance section.
The invention is realized by the following technical scheme:
in a first aspect, the present invention provides a control rod tine effect processing method based on a high-precision effective resonance section, the method comprising:
s1: acquiring geometric and material related parameters of a target reactor core, and modeling according to the definition of the geometric and material related parameters of the acquired target reactor core and a two-dimensional/one-dimensional method to obtain a problem model; wherein the problem model comprises a plurality of axially uniform layers having a fine geometry distribution in a radial direction;
s2: carrying out numerical solution on the problem model obtained in the step S1 by adopting a two-dimensional/one-dimensional method, and directly carrying out two-dimensional non-uniform reactor core resonance calculation (namely carrying out solution by adopting a conventional resonance calculation strategy) on a layer without control rod insertion or with control rod complete insertion according to a predefined rod position or a search rod position to obtain a macroscopic section; for layer Z where there is a control rod portion inserted i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section;
s3: according to the macroscopic cross section obtained in the step S2, the method comprises the following steps of i Carrying out transportation calculation by using a two-dimensional reactor core characteristic line method in a layer manner, wherein the transportation calculation is carried out by using the two-dimensional reactor core characteristic line methodSolving by using a volume-reconstruction flux weighting method or a sub-feature line method and the like;
s4: based on two-dimensional transport calculation, after completing the numerical solution of the whole reactor core according to a two-dimensional/one-dimensional frame, carrying out microcosmic burnup calculation on each layer according to the axial average flux of each layer to obtain the axial average nuclear density of each burnup zone of each layer;
s5: and (3) updating the problem model of the step S1 based on the axial average nuclear density of each layer obtained in the step S4, and carrying out the next burnup step treatment until all burnup points to be unburnt are completed.
The sub-plane method based on the existing control rod tine effect processing method still assumes that each sub-plane in the same layer has the same cross section, and does not consider the influence of control rod insertion on the radial direction; the sub-plane collision probability method has defects in the treatment of anisotropic scattering and complex geometric problems, and the characteristic line calculation is still based on the problem of axial homogenization of the cross section. The invention designs a control rod sharp-tooth effect processing method which fully considers comprehensive neutron factors such as resonance, transportation, burnup and the like in a two-dimensional/one-dimensional system frame.
The invention can fully consider the comprehensive neutron factors such as resonance, transportation, burnup and the like in a two-dimensional/one-dimensional system frame, fully consider the non-uniform effect of the axial direction and the radial direction in the problem of the insertion of the control rod part, and simultaneously, the number of the layer grids calculated in the axial direction by the transportation of the characteristic line method is not additionally increased, so that the calculation efficiency can be improved and the memory consumption can be reduced on the basis of good calculation accuracy in theory.
Further, layer Z for the case where the control rod portion is inserted as described in step S2 i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section; the method specifically comprises the following steps:
step 21: according to the tail end of each control rod group at Z i Layer axial directionN different positions within the height, Z in the axial direction i The layers are subdivided into n+1 sub-layers, and the different sub-layers differ only in having different control rod insertion states; wherein n is a positive integer;
step 22: respectively carrying out two-dimensional reactor core resonance calculation on n+1 sublayers generated in the step 21 to obtain radial high-precision effective resonance sections, namely microcosmic sections, of each sublayer;
step 23: according to the microcosmic section after the resonance treatment in the step 22, respectively calculating radial macroscopic section distribution of n+1 sub-layers; wherein for non-control rod portions inserted into the cells, the macroscopic cross-section is according to Z i Calculating the average nuclear density in the layer axial direction; for the cell in which the control rod part is inserted, the inserted part and the non-inserted part are respectively calculated according to the respective actual material nucleus densities;
step 24: determining a 'shadow area' of which part is inserted outside the control rod cells according to the radial macroscopic cross-section distribution of each sublayer obtained in the step 23; judgment of Z i And if the macroscopic cross section deviation of the control rod between the uppermost sub-layer and the lowermost sub-layer in the layer is larger than a set threshold value, the fuel cell is considered to be positioned in a 'shadow area' of the control rod. In particular, when the threshold is sufficiently large, the "shaded area" is only the control rod cell itself.
Step 25: the "shadow region" determined according to step 24, cross-section at Z for each sub-layer i Carrying out equivalent homogenization in the axial range of the layer; for the cells outside the 'shadow area', the axial all sub-layers adopt a simple volume weight generation layer to homogenize the macroscopic cross section; for the cells within the 'shadow area', continuously reserving different macroscopic cross sections of each sub-layer in the axial direction; thus finally for Z i The layers have different axial sub-layer cross sections only within the "shadow zone" and uniform axial cross sections outside the "shadow zone".
Further, the two-dimensional core resonance calculation in step 22 employs various non-uniform resonance algorithms that can meet the requirements, including typically a subgroup method, an embedded resonance self-screening method, and the like.
Further, the high precision obtained in step 22Effective resonance cross section sigma x,g The expression is as follows:
wherein: sigma (sigma) x Microcosmic cross-sections of the x type (x denotes total cross-section, absorption cross-section, fissile cross-section, etc.); phi (u) is neutron spectrum. Further, the macroscopic cross-section distribution expression obtained in step 23 is:
Σ x,g ＝∑ i N i σ x,g,i (2)
wherein: sigma and method for producing the same x,g Macroscopic cross section of the type x of the g energy group; n (N) i Is the i-th nuclide nuclear density; sigma (sigma) x,g,i An effective microscopic cross section of the type x of the g energy group of the ith nuclide.
Further, in the step S3, when a volume-reconstruction flux weighting method is adopted, a reconstruction flux is obtained by combining a three-dimensional coarse mesh finite difference or a one-dimensional axial calculation result, and the 'shadow area' is axially homogenized according to the reconstruction flux; when the sub-feature line method is employed, the "shadow region" is the region where the sub-feature line technique is used.
Further, in step S3, when the volume-reconstructed flux weighting method is adopted, the reconstructed flux is obtained by combining the finite difference of the three-dimensional coarse mesh or the one-dimensional axial calculation result, and the "shadow area" is axially homogenized by adopting the formula (4):
wherein: phi (phi) g (z) is the axial flux distribution in the portion of the insert layer;
the axial macroscopic section of the layer after re-homogenization;
when the sub-feature line method is adopted, the 'shadow area' is the area using the sub-feature line technology; the axial average flux is as in equation (5):
φ g,m ＝∑ z V z φ g,m,z (5)
wherein: phi (phi) g,m Neutron flux for the g-th energy group region m; phi (phi) g,m,z Calculating neutron mark flux for the m-th energy group region m sub-characteristic line layer z; v (V) z Is the sub-feature line layer z volume fraction.
In a second aspect, the present invention also provides a control rod tine effect processing system based on a high-precision effective resonance section, the system supporting the control rod tine effect processing method based on the high-precision effective resonance section, the system comprising:
the acquisition unit is used for acquiring the geometric and material related parameters of the target reactor core;
the problem model construction unit is used for modeling according to the obtained geometric and material related parameter definition of the target reactor core and facing a two-dimensional/one-dimensional method to obtain a problem model; wherein the problem model comprises a plurality of axially uniform layers having a fine geometry distribution in a radial direction;
the macroscopic section solving unit is used for carrying out numerical solution on the obtained problem model by adopting a two-dimensional/one-dimensional method, and directly carrying out two-dimensional non-uniform reactor core resonance calculation (namely solving by adopting a conventional resonance calculation strategy) on a layer without control rod insertion or with control rod complete insertion according to a predefined rod position or a search rod position to obtain a macroscopic section; for layer Z where there is a control rod portion inserted i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section;
two-dimensional/one-dimensional transport calculation unit for Z according to the obtained macroscopic cross section i Carrying out two-dimensional reactor core characteristic line method transportation calculation in a layer, wherein the two-dimensional reactor core characteristic line method transportation calculation adopts a volume-reconstruction flux weight method or a sub-characteristic line method and the like to carry out solving;
the microcosmic burnup calculation unit is used for carrying out microcosmic burnup calculation on each layer according to the axial average flux of each layer after completing the numerical solution of the whole reactor core according to a two-dimensional/one-dimensional frame based on two-dimensional transport calculation, so as to obtain the axial average nuclear density of each burnup area of the layer;
and the updating unit is used for updating the problem model of the problem model construction unit based on the obtained axial average nuclear density of each layer, and carrying out the next burnup step treatment until all the burnup points to be unburnt are completed.
Further, layer Z for the case where control rod portion insertion exists as described in the macroscopic section solving unit i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section; the specific implementation process is as follows:
according to the tail end of each control rod group at Z i N different positions within the axial height of the layer, Z i The layers are subdivided into n+1 sub-layers, and the different sub-layers differ only in having different control rod insertion states; wherein n is a positive integer;
respectively carrying out two-dimensional reactor core resonance calculation on the generated n+1 sub-layers to obtain radial high-precision effective resonance sections, namely microcosmic sections, of each sub-layer;
according to the microcosmic section after resonance treatment, respectively calculating radial macroscopic section distribution of n+1 sub-layers; wherein for non-control rod portions inserted into the cells, the macroscopic cross-section is according to Z i Calculating the average nuclear density in the layer axial direction; for the cell in which the control rod part is inserted, the inserted part and the non-inserted part are respectively calculated according to the respective actual material nucleus densities;
determining a 'shadow area' of which part is inserted outside the control rod cells according to the obtained radial macroscopic cross-section distribution of each sublayer; judgment of Z i And if the macroscopic cross section deviation of the control rod between the uppermost sub-layer and the lowermost sub-layer in the layer is larger than a set threshold value, the fuel cell is considered to be positioned in a 'shadow area' of the control rod. In particular, when the threshold is sufficiently large, the "shaded area" is only the control rod cell itself.
According to the determined 'shadow zone', the cross section of each sub-layer is Z i Carrying out equivalent homogenization in the axial range of the layer; for the cells outside the 'shadow area', the axial all sub-layers adopt a simple volume weight generation layer to homogenize the macroscopic cross section; for the inside of the "shadow areaThe grid element continuously keeps different macroscopic cross sections of each axial sub-layer; thus finally for Z i The layers have different axial sub-layer cross sections only within the "shadow areas" and are uniform in axial cross section outside the "shadow areas".
Further, when the two-dimensional/one-dimensional transportation calculation unit adopts a volume-reconstruction flux weight method, a three-dimensional coarse mesh finite difference or one-dimensional axial calculation result is combined to obtain a reconstruction flux, and the shadow area is axially homogenized according to the reconstruction flux; when the sub-feature line method is employed, the "shadow region" is the region where the sub-feature line technique is used.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention can fully consider the comprehensive neutron factors such as resonance, transportation, burnup and the like in a two-dimensional/one-dimensional system frame, fully consider the non-uniform effect of the axial direction and the radial direction in the problem of the insertion of the control rod part, and simultaneously, the number of the layer grids calculated in the axial direction by the transportation of the characteristic line method is not additionally increased, so that the calculation efficiency can be improved and the memory consumption can be reduced on the basis of good calculation accuracy in theory.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention. In the drawings:
FIG. 1 is a flow chart of a control rod tine effect processing method based on a high-precision effective resonance section.
Fig. 2 is a flow chart of a control rod tine effect processing method based on a high precision effective resonance section ("volume-flux weighting" technique) of the present invention.
Fig. 3 is a flow chart (sub-feature line technique) of a control rod tine effect processing method based on a high-precision effective resonance section.
FIG. 4 is an axial schematic view of an example of a control rod portion insertion problem of the present invention.
FIG. 5 is a radial schematic view of an example of a control rod portion insertion problem of the present invention.
FIG. 6 is a block diagram of a control rod tine effect processing system based on a high precision effective resonance cross section of the present invention.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present invention and the descriptions thereof are for illustrating the present invention only and are not to be construed as limiting the present invention.
Example 1
As shown in FIG. 1, the control rod tine effect processing method based on the high-precision effective resonance section comprises the following steps of:
s1: acquiring geometric and material related parameters of a target reactor core, and modeling according to the definition of the geometric and material related parameters of the acquired target reactor core and a two-dimensional/one-dimensional method to obtain a problem model; wherein the problem model comprises a plurality of axially uniform layers having a fine geometry distribution in a radial direction;
s2: carrying out numerical solution on the problem model obtained in the step S1 by adopting a two-dimensional/one-dimensional method, and directly carrying out two-dimensional non-uniform reactor core resonance calculation (namely carrying out solution by adopting a conventional resonance calculation strategy) on a layer without control rod insertion or with control rod complete insertion according to a predefined rod position or a search rod position to obtain a macroscopic section; for layer Z where there is a control rod portion inserted i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section;
s3: according to the macroscopic cross section obtained in the step S2, the method comprises the following steps of i Carrying out two-dimensional reactor core characteristic line method transportation calculation in a layer, wherein the two-dimensional reactor core characteristic line method transportation calculation adopts a volume-reconstruction flux weight method or a sub-characteristic line method and the like to carry out solving;
s4: based on two-dimensional transport calculation, after completing the numerical solution of the whole reactor core according to a two-dimensional/one-dimensional frame, carrying out microcosmic burnup calculation on each layer according to the axial average flux of each layer to obtain the axial average nuclear density of each burnup zone of each layer;
s5: and (3) updating the problem model of the step S1 based on the axial average nuclear density of each layer obtained in the step S4, and carrying out the next burnup step treatment until all burnup points to be unburnt are completed.
The specific implementation comprises the following steps:
step 1: acquiring geometric and material related parameters of a target reactor core, and modeling according to the definition of the geometric and material related parameters of the acquired target reactor core and a two-dimensional/one-dimensional method to obtain a problem model; wherein the problem model comprises a plurality of axially uniform layers radially having a fine geometry distribution, and a coarse-mesh finite-difference grid of the three-dimensional core.
Step 2: carrying out numerical solution on the problem model obtained in the step S1 by adopting a two-dimensional/one-dimensional method, directly carrying out two-dimensional non-uniform reactor core resonance calculation (namely carrying out solution by adopting a conventional resonance calculation strategy) on a layer without control rod insertion or with control rod complete insertion according to a predefined rod position or a search rod position, generating radial macroscopic section distribution of the layer, obtaining a macroscopic section, and transferring to the step 8 for carrying out transport calculation; for layer Z where there is a control rod portion inserted i Adopting the steps 3 to 7 to put in a method based on a high-precision effective resonance section for calculation and solving to obtain a macroscopic section;
step 3: according to the tail end of each control rod group at Z i N different positions within the axial height of the layer, Z i The layers are subdivided into n+1 sub-layers (as shown in FIG. 4), then the different sub-layers differ only by having different control rod insertion states (as shown in FIG. 5); wherein n is a positive integer;
step 4: respectively carrying out two-dimensional reactor core resonance calculation on n+1 sub-layers generated in the step 3 to obtain radial high-precision effective resonance sections, namely microcosmic sections, of each sub-layer; various non-uniform resonance algorithms capable of meeting the requirements, such as a subgroup method, an embedded resonance self-shielding method, and the like, can be adopted. The high-precision effective resonance section sigma is obtained by adopting a high-precision non-uniform resonance algorithm capable of meeting the requirements x,g The expression is as follows:
wherein: sigma (sigma) x Microcosmic cross-sections of the x type (x denotes total cross-section, absorption cross-section, fissile cross-section, etc.); phi (u) is neutron spectrum.
Step 5: according to the microcosmic section after the resonance treatment in the step 4, the radial macroscopic section distribution sigma of the n+1 sub-layers is calculated respectively x,g The method comprises the steps of carrying out a first treatment on the surface of the Wherein for non-control rod portions inserted into the cells, the macroscopic cross-section is according to Z i Calculating the average nuclear density in the layer axial direction; for the cell in which the control rod part is inserted, the inserted part and the non-inserted part are respectively calculated according to the respective actual material nucleus densities; specifically, macroscopic cross-sectional profile Σ x,g The expression is:
Σ x,g ＝∑ i N i σ x,g,i (2)
wherein: sigma and method for producing the same x,g Macroscopic cross section of the type x of the g energy group; n (N) i Is the i-th nuclide nuclear density; sigma (sigma) x,g,i An effective microscopic cross section of the type x of the g energy group of the ith nuclide.
Step 6: determining a 'shadow area' of which part is inserted outside the control rod cells according to the radial macroscopic cross-section distribution of each sublayer obtained in the step 5; judgment of Z i And if the macroscopic cross section deviation of the control rod between the uppermost sub-layer and the lowermost sub-layer in the layer is larger than a set threshold value, the fuel cell is considered to be positioned in a 'shadow area' of the control rod. In particular, when the threshold is sufficiently large, the "shaded area" is only the control rod cell itself. Taking macroscopic absorption cross-sections as an example, this criterion can be expressed as formula (3):
wherein:
macroscopic absorption cross sections of the corresponding areas of the two sublayers; epsilon is the "shadow region" decision threshold.
Step 7: determining according to step 6Is "shadow zone" of each sub-layer cross-section at Z i Carrying out equivalent homogenization in the axial range of the layer; for the cells outside the 'shadow area', the axial all sub-layers adopt a simple volume weight generation layer to homogenize the macroscopic cross section; for the cells within the 'shadow area', continuously reserving different macroscopic cross sections of each sub-layer in the axial direction; thus finally for Z i The layers have different axial sub-layer cross sections only within the "shadow zone" and uniform axial cross sections outside the "shadow zone".
Step 8: according to the determined macroscopic cross section, pair Z i Carrying out two-dimensional reactor core characteristic line method transportation calculation in a layer, wherein the two-dimensional reactor core characteristic line method transportation calculation adopts a volume-reconstruction flux weight method or a sub-characteristic line method and the like to carry out solving; when the volume-reconstruction flux weight method is adopted, adopting the overall flow as shown in fig. 2, acquiring the reconstruction flux by combining the finite difference of the three-dimensional coarse mesh or the one-dimensional axial calculation result, and carrying out axial homogenization as shown in a formula (4) according to the reconstruction flux; when the sub-feature line method is adopted, the overall flow shown in fig. 3 is adopted, the axial average flux is shown in formula (5), and the "shadow area" is the area using the sub-feature line technology.
Wherein: phi (phi) g (z) is the axial flux distribution in the portion of the insert layer;
the axial macroscopic section of the layer after re-homogenization;
φ g,m ＝∑ z V z φ g,m,z (5)
wherein: phi (phi) g,m Neutron flux for the g-th energy group region m; phi (phi) g,m,z Calculating neutron mark flux for the m-th energy group region m sub-characteristic line layer z; v (V) z Is the sub-feature line layer z volume fraction.
Step 9: based on two-dimensional transport calculation, after completing the numerical solution of the whole reactor core according to a two-dimensional/one-dimensional frame, for each layer, respectively carrying out microscopic burnup calculation of the layer according to the axial average flux of each layer, and solving a burnup equation which is shown as a formula (6) to obtain the axial average nuclear density of each burnup zone of the layer;
wherein: n (N) i (t) is the nuclear density of the nuclide i at time t; lambda (lambda) ji Generating rate coefficients for nuclide j through nuclide i; sigma (sigma) i Is the vanishing rate coefficient of nuclide i.
Step 10: and (3) updating the problem model of the step (1) based on the axial average nuclear density of each layer obtained in the step (9), and carrying out the next burnup step treatment until all burnup points to be unburnt are completed.
The invention designs a control rod sharp-tooth effect processing method which fully considers comprehensive neutron factors such as resonance, transportation, burnup and the like in a two-dimensional/one-dimensional system frame. Specifically, 1, modeling is conducted on a two-dimensional/one-dimensional method; 2. determining rod positions, directly carrying out two-dimensional non-uniform reactor core resonance calculation on a layer without control rod insertion or with control rod fully inserted, calculating a macroscopic section, and proceeding to the step 8; for the layers with the control rod part inserted condition, calculating a macroscopic section by adopting the steps 3 to 7; 3. subdividing the sub-layers according to different positions of the tail ends of each rod group in the inner layer along the axial direction; 4. respectively carrying out two-dimensional heterogeneous reactor core resonance calculation on each sub-layer to obtain effective resonance section distribution; 5. calculating radial macroscopic cross section distribution of each sub-layer; 6. determining a 'shadow area' of which part is inserted outside the control rod cells; 7. homogenizing macroscopic cross sections of cells except for a shadow area by adopting a volume weight generating layer; 8. according to the macroscopic section, carrying out two-dimensional/one-dimensional transportation calculation by adopting a volume-reconstruction flux weighting method or a sub-characteristic line method; 9. performing microscopic burnup calculation according to the axial average flux; 10. and updating the axial average nuclear density of each layer, and carrying out the next burnup step calculation. The method not only fully considers the non-uniform effect of the axial direction and the radial direction in the problem of partial insertion of the control rod, but also does not additionally increase the number of the layer grids in the axial direction by the transmission calculation of the characteristic line method, and can theoretically process the sharp tooth effect of the control rod with good precision, improve the calculation efficiency and reduce the memory consumption.
Example 2
As shown in fig. 1 to 6, the difference between the present embodiment and embodiment 1 is that the present embodiment provides a control rod tine effect processing system based on a high-precision effective resonance section, which supports a control rod tine effect processing method based on a high-precision effective resonance section as shown in fig. 6, and the system includes:
the acquisition unit is used for acquiring the geometric and material related parameters of the target reactor core;
the problem model construction unit is used for modeling according to the obtained geometric and material related parameter definition of the target reactor core and facing a two-dimensional/one-dimensional method to obtain a problem model; wherein the problem model comprises a plurality of axially uniform layers having a fine geometry distribution in a radial direction;
the macroscopic section solving unit is used for carrying out numerical solution on the obtained problem model by adopting a two-dimensional/one-dimensional method, and directly carrying out two-dimensional non-uniform reactor core resonance calculation (namely solving by adopting a conventional resonance calculation strategy) on a layer without control rod insertion or with control rod complete insertion according to a predefined rod position or a search rod position to obtain a macroscopic section; for layer Z where there is a control rod portion inserted i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section;
two-dimensional/one-dimensional transport calculation unit for Z according to the obtained macroscopic cross section i Carrying out two-dimensional reactor core characteristic line method transportation calculation in a layer, wherein the two-dimensional reactor core characteristic line method transportation calculation adopts a volume-reconstruction flux weight method or a sub-characteristic line method and the like to carry out solving;
the microcosmic burnup calculation unit is used for carrying out microcosmic burnup calculation on each layer according to the axial average flux of each layer after completing the numerical solution of the whole reactor core according to a two-dimensional/one-dimensional frame based on two-dimensional transport calculation, so as to obtain the axial average nuclear density of each burnup area of the layer;
and the updating unit is used for updating the problem model of the problem model construction unit based on the obtained axial average nuclear density of each layer, and carrying out the next burnup step treatment until all the burnup points to be unburnt are completed.
In particular, layer Z for the case of control rod part insertion described in the macroscopic section solving unit i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section; the specific implementation process is as follows:
according to the tail end of each control rod group at Z i N different positions within the axial height of the layer, Z i The layers are subdivided into n+1 sub-layers, and the different sub-layers differ only in having different control rod insertion states; wherein n is a positive integer;
respectively carrying out two-dimensional reactor core resonance calculation on the generated n+1 sub-layers to obtain radial high-precision effective resonance sections, namely microcosmic sections, of each sub-layer;
according to the microcosmic section after resonance treatment, respectively calculating radial macroscopic section distribution of n+1 sub-layers; wherein for non-control rod portions inserted into the cells, the macroscopic cross-section is according to Z i Calculating the average nuclear density in the layer axial direction; for the cell in which the control rod part is inserted, the inserted part and the non-inserted part are respectively calculated according to the respective actual material nucleus densities;
determining a 'shadow area' of which part is inserted outside the control rod cells according to the obtained radial macroscopic cross-section distribution of each sublayer; judgment of Z i And if the macroscopic cross section deviation of the control rod between the uppermost sub-layer and the lowermost sub-layer in the layer is larger than a set threshold value, the fuel cell is considered to be positioned in a 'shadow area' of the control rod. In particular, when the threshold is sufficiently large, the "shaded area" is only the control rod cell itself.
For each sub-zone according to the determined "shadow zoneLayer cross section at Z i Carrying out equivalent homogenization in the axial range of the layer; for the cells outside the 'shadow area', the axial all sub-layers adopt a simple volume weight generation layer to homogenize the macroscopic cross section; for the cells within the 'shadow area', continuously reserving different macroscopic cross sections of each sub-layer in the axial direction; thus finally for Z i The layers have different axial sub-layer cross sections only within the "shadow areas" and are uniform in axial cross section outside the "shadow areas".
Specifically, when a volume-reconstruction flux weight method is adopted in the two-dimensional/one-dimensional transportation calculation unit, a three-dimensional coarse mesh finite difference or one-dimensional axial calculation result is combined to obtain a reconstruction flux, and the shadow area is axially homogenized according to the reconstruction flux; when the sub-feature line method is employed, the "shadow region" is the region where the sub-feature line technique is used.
The system can fully consider the comprehensive neutron factors such as resonance, transportation, burnup and the like in a two-dimensional/one-dimensional system frame, fully consider the non-uniform effect of the axial direction and the radial direction in the problem of the insertion of the control rod part, simultaneously, do not additionally increase the number of the layer grids calculated in the axial direction by the transportation of the characteristic line method, and can theoretically improve the calculation efficiency and reduce the memory consumption on the basis of good calculation accuracy level.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (5)
1. A control rod sharp tooth effect processing method based on a high-precision effective resonance section is characterized by comprising the following steps:
s1: acquiring geometric and material related parameters of a target reactor core, and modeling according to the acquired geometric and material related parameters of the target reactor core and a two-dimensional/one-dimensional method to obtain a problem model;
s2: carrying out numerical solution on the problem model obtained in the step S1 by adopting a two-dimensional/one-dimensional method, and directly carrying out two-dimensional non-uniform reactor core resonance calculation on a layer without control rod insertion or with control rod complete insertion according to a predefined rod position or a search rod position to obtain a macroscopic section; for layer Z where there is a control rod portion inserted i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section;
s3: according to the macroscopic cross section obtained in the step S2, the method comprises the following steps of i Carrying out two-dimensional reactor core characteristic line method transportation calculation in a layer, wherein the two-dimensional reactor core characteristic line method transportation calculation adopts a volume-reconstruction flux weight method or a sub-characteristic line method for solving;
s4: based on two-dimensional transport calculation, after completing the numerical solution of the whole reactor core according to a two-dimensional/one-dimensional frame, carrying out microcosmic burnup calculation on each layer according to the axial average flux of each layer to obtain the axial average nuclear density of each burnup zone of each layer;
s5: updating the problem model of the step S1 based on the axial average nuclear density of each layer obtained in the step S4, and developing the next burnup step treatment until all burnup points to be unburnt are completed;
layer Z for the case where control rod portion insertion exists as described in step S2 i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section; the method specifically comprises the following steps:
step 21: according to the tail end of each control rod group at Z i N different positions within the axial height of the layer, Z i The layers are divided into n+1 sub-layers, and the different sub-layers only differ in having different control rod insertion states; wherein n is a positive integer;
step 22: respectively carrying out two-dimensional reactor core resonance calculation on n+1 sublayers generated in the step 21 to obtain radial high-precision effective resonance sections, namely microcosmic sections, of each sublayer;
step 23: according to the microcosmic section after the resonance treatment in the step 22, respectively calculating radial macroscopic section distribution of n+1 sub-layers; wherein for non-control rod portions inserted into cells, macroscopic cross-sectionsAccording to Z i Calculating the average nuclear density in the layer axial direction; for the cell in which the control rod part is inserted, the inserted part and the non-inserted part are respectively calculated according to the respective actual material nucleus densities;
step 24: determining a shadow area of which part is inserted outside the control rod cells according to the radial macroscopic cross-section distribution of each sublayer obtained in the step 23; judgment of Z i Macroscopic cross-section deviation of a control rod between two sublayers at the uppermost end and the lowermost end in the layer, which is close to a corresponding region of a fuel cell, if the macroscopic cross-section deviation is larger than a set threshold value, the fuel cell is considered to be positioned in a shadow region of the control rod;
step 25: cross-section at Z for each sub-layer according to the shadow zone determined in step 24 i Carrying out equivalent homogenization in the axial range of the layer; for the cells outside the shadow area, homogenizing macroscopic cross sections of the volume weight generating layers in the axial direction of each sublayer; for the cells within the shadow area, continuously reserving different macroscopic cross sections of each sub-layer in the axial direction;
in the step S3, when a volume-reconstruction flux weighting method is adopted, a three-dimensional coarse mesh finite difference or a one-dimensional axial calculation result is combined to obtain a reconstruction flux, and the shadow area is axially homogenized according to the reconstruction flux; when the sub-feature line method is adopted, the shadow area is the area using the sub-feature line technology;
in the step S3, when a volume-reconstruction flux weighting method is adopted, a reconstruction flux is obtained by combining a three-dimensional coarse mesh finite difference or a one-dimensional axial calculation result, and an axial homogenization is carried out on a shadow area by adopting a formula (4):
wherein: phi (phi) g (z) is the axial flux distribution in the portion of the insert layer;
the axial macroscopic section of the layer after re-homogenization;
when the sub-feature line method is adopted, the shadow area is the area using the sub-feature line technology; the axial average flux is as in equation (5):
φ g,m ＝∑ z V z φ g,m,z (5)
wherein: phi (phi) g,m Neutron flux for the g-th energy group region m; phi (phi) g,m,z Calculating neutron mark flux for the m-th energy group region m sub-characteristic line layer z; v (V) z Is the sub-feature line layer z volume fraction.
2. The control rod tine effect processing method based on the high-precision effective resonance section according to claim 1, wherein the two-dimensional core resonance calculation in the step 22 adopts various non-uniform resonance algorithms capable of meeting requirements, including a typical subgroup method and an embedded resonance self-shielding method.
3. The control rod tine effect processing method based on the high-precision effective resonance cross section according to claim 2, wherein the high-precision effective resonance cross section σ obtained in step 22 x,g The expression is as follows:
wherein: sigma (sigma) x Is a microscopic cross section of the x type; phi (u) is neutron spectrum.
4. The control rod tine effect processing method based on the high-precision effective resonance section according to claim 1, wherein the macroscopic section distribution expression obtained in step 23 is:
Σ x,g ＝∑ i N i σ x,g,i (2)
wherein: sigma and method for producing the same x,g Macroscopic cross section of the type x of the g energy group; n (N) i Is the i-th nuclide nuclear density; sigma (sigma) x,g,i An effective microscopic cross section of the type x of the g energy group of the ith nuclide.
5. A control rod tine effect treatment system based on a high precision effective resonance cross section, characterized in that the system supports a control rod tine effect treatment method based on a high precision effective resonance cross section according to any one of claims 1 to 4, the system comprising:
the acquisition unit is used for acquiring the geometric and material related parameters of the target reactor core;
the problem model construction unit is used for modeling according to the acquired geometric and material related parameters of the target reactor core and facing a two-dimensional/one-dimensional method to obtain a problem model;
the macroscopic section solving unit is used for carrying out numerical solution on the obtained problem model by adopting a two-dimensional/one-dimensional method, and directly carrying out two-dimensional non-uniform reactor core resonance calculation on a layer without control rod insertion or with control rod full insertion according to the predefined rod position or the searching rod position to obtain a macroscopic section; for layer Z where there is a control rod portion inserted i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section;
two-dimensional/one-dimensional transport calculation unit for Z according to the obtained macroscopic cross section i Carrying out two-dimensional reactor core characteristic line method transportation calculation in a layer, wherein the two-dimensional reactor core characteristic line method transportation calculation adopts a volume-reconstruction flux weight method or a sub-characteristic line method for solving;
the microcosmic burnup calculation unit is used for carrying out microcosmic burnup calculation on each layer according to the axial average flux of each layer after completing the numerical solution of the whole reactor core according to a two-dimensional/one-dimensional frame based on two-dimensional transport calculation, so as to obtain the axial average nuclear density of each burnup area of the layer;
the updating unit is used for updating the problem model of the problem model construction unit based on the obtained axial average nuclear density of each layer, and developing the next burnup step treatment until all burnup points to be unburnt are completed;
layer Z for the presence of control rod portion insertion as described in the macroscopic section solving unit i Calculating and solving by adopting a method based on a high-precision effective resonance section to obtain a macroscopic section; the specific implementation process is as follows:
according to the tail end of each control rod group at Z i N different positions within the axial height of the layer, Z i The layers are divided into n+1 sub-layers, and the different sub-layers only differ in having different control rod insertion states; wherein n is a positive integer;
respectively carrying out two-dimensional reactor core resonance calculation on the generated n+1 sub-layers to obtain radial high-precision effective resonance sections, namely microcosmic sections, of each sub-layer;
according to the microcosmic section after resonance treatment, respectively calculating radial macroscopic section distribution of n+1 sub-layers; wherein for non-control rod portions inserted into the cells, the macroscopic cross-section is according to Z i Calculating the average nuclear density in the layer axial direction; for the cell in which the control rod part is inserted, the inserted part and the non-inserted part are respectively calculated according to the respective actual material nucleus densities;
determining a shadow area of which part is inserted outside the control rod cells according to the obtained radial macroscopic cross section distribution of each sublayer; judgment of Z i Macroscopic cross-section deviation of a control rod between two sublayers at the uppermost end and the lowermost end in the layer, which is close to a corresponding region of a fuel cell, if the macroscopic cross-section deviation is larger than a set threshold value, the fuel cell is considered to be positioned in a shadow region of the control rod;
cross-section at Z for each sub-layer according to the determined shadow zone i Carrying out equivalent homogenization in the axial range of the layer; for the cells outside the shadow area, homogenizing macroscopic cross sections of the volume weight generating layers in the axial direction of each sublayer; for the cells within the shadow area, continuously reserving different macroscopic cross sections of each sub-layer in the axial direction;
when a volume-reconstruction flux weight method is adopted in the two-dimensional/one-dimensional transport calculation unit, a three-dimensional coarse mesh finite difference or one-dimensional axial calculation result is combined to obtain a reconstruction flux, and the shadow area is axially homogenized according to the reconstruction flux; when the sub-feature line method is adopted, the shadow area is the area using the sub-feature line technology;
when a volume-reconstruction flux weight method is adopted, a three-dimensional coarse mesh finite difference or a one-dimensional axial calculation result is combined to obtain a reconstruction flux, and an equation (4) is adopted to axially homogenize a shadow area:
wherein: phi (phi) g (z) is the axial flux distribution in the portion of the insert layer;
the axial macroscopic section of the layer after re-homogenization;
when the sub-feature line method is adopted, the shadow area is the area using the sub-feature line technology; the axial average flux is as in equation (5):
φ g,m ＝∑ z V z φ g,m,z (5)
wherein: phi (phi) g,m Neutron flux for the g-th energy group region m; phi (phi) g,m,z Calculating neutron mark flux for the m-th energy group region m sub-characteristic line layer z; v (V) z Is the sub-feature line layer z volume fraction.
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| JP5773681B2 (en) * | 2011-02-18 | 2015-09-02 | 三菱重工業株式会社 | Resonance calculation program and analyzer |
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| CN105426657A (en) * | 2015-10-30 | 2016-03-23 | 西安交通大学 | Method for eliminating control rod tine effect in reactor core calculation |
| CN106126932A (en) * | 2016-06-24 | 2016-11-16 | 西安交通大学 | A kind of processing method of presurized water reactor locking nub method control rod pointed tooth effect |
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