CN116401500A - Calculation method for nuclide concentration of long-distance concealed pipe inside and outside water body in periodic discharge mode - Google Patents
Calculation method for nuclide concentration of long-distance concealed pipe inside and outside water body in periodic discharge mode Download PDFInfo
- Publication number
- CN116401500A CN116401500A CN202310359013.7A CN202310359013A CN116401500A CN 116401500 A CN116401500 A CN 116401500A CN 202310359013 A CN202310359013 A CN 202310359013A CN 116401500 A CN116401500 A CN 116401500A
- Authority
- CN
- China
- Prior art keywords
- nuclide
- concentration
- flux
- concealed pipe
- long
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 title claims abstract description 43
- 238000004364 calculation method Methods 0.000 title claims abstract description 33
- 230000000737 periodic effect Effects 0.000 title claims abstract description 33
- 230000004907 flux Effects 0.000 claims abstract description 61
- 238000000034 method Methods 0.000 claims abstract description 27
- 230000008569 process Effects 0.000 claims abstract description 22
- 239000006185 dispersion Substances 0.000 claims abstract description 9
- 230000008859 change Effects 0.000 claims abstract description 7
- 238000009792 diffusion process Methods 0.000 claims description 6
- 239000003344 environmental pollutant Substances 0.000 claims description 3
- 231100000719 pollutant Toxicity 0.000 claims description 3
- 239000002915 spent fuel radioactive waste Substances 0.000 abstract description 8
- 238000011156 evaluation Methods 0.000 abstract description 2
- 230000032258 transport Effects 0.000 description 10
- 238000004458 analytical method Methods 0.000 description 6
- 239000000243 solution Substances 0.000 description 6
- 230000007613 environmental effect Effects 0.000 description 3
- 238000012795 verification Methods 0.000 description 3
- 230000009471 action Effects 0.000 description 2
- 230000003111 delayed effect Effects 0.000 description 2
- 239000012895 dilution Substances 0.000 description 2
- 238000010790 dilution Methods 0.000 description 2
- 230000025308 nuclear transport Effects 0.000 description 2
- 230000004044 response Effects 0.000 description 2
- 239000002699 waste material Substances 0.000 description 2
- YZCKVEUIGOORGS-NJFSPNSNSA-N Tritium Chemical compound [3H] YZCKVEUIGOORGS-NJFSPNSNSA-N 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000007865 diluting Methods 0.000 description 1
- 238000007599 discharging Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000002093 peripheral effect Effects 0.000 description 1
- 230000002285 radioactive effect Effects 0.000 description 1
- 229910052722 tritium Inorganic materials 0.000 description 1
- 238000010200 validation analysis Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E30/00—Energy generation of nuclear origin
- Y02E30/30—Nuclear fission reactors
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- General Physics & Mathematics (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Theoretical Computer Science (AREA)
- Algebra (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Monitoring And Testing Of Nuclear Reactors (AREA)
Abstract
The invention relates to a calculation method of the nuclide concentration of a long-distance concealed pipe inner and outer water body in a periodic discharge mode, which comprises the following steps: judging whether the hydraulic dispersion type process belongs to a long-time hydraulic dispersion type process; solving flux of the nuclide discharged at the inlet of the concealed pipe; expanding the periodic nuclide flux into a fourier series form; calculating the distribution of the nuclide concentration caused by constant component items of the nuclide flux; calculating the distribution of the nuclide concentration caused by the cosine component of the nuclide flux; calculating the distribution of the nuclide concentration caused by the sine series component of the nuclide flux; obtaining the concentration distribution of nuclides in the long-distance concealed pipe by linear superposition; obtaining the dynamic change of the nuclide concentration and flux of the outlet of the long-distance concealed pipe; and the concentration distribution of the nuclide in the sea area around the outlet of the long-distance concealed pipe. The invention provides a quantitative calculation method for the nuclide concentration of the water body inside and outside the long-distance concealed pipe in an accurate forecast period emission mode, and provides scientific basis for planning, demonstration and design of a spent fuel post-treatment plant and water environment safety evaluation.
Description
Technical Field
The invention relates to a calculation method of the nuclide concentration of a long-distance buried pipe in and out of water body in a periodic discharge mode, which is a hydraulic engineering design calculation method and is a calculation method applied to the drainage engineering of a nuclear power spent fuel post-treatment plant.
Background
In order to ensure the safety of nuclear power, radioactive nuclear waste is generated in the operation process of the nuclear power plant, and the nuclear waste is properly treated by a spent fuel post-treatment plant. In the normal operation process of the coastal spent fuel post-treatment plant, nuclides such as tritium and the like can be discharged to the environmental water body. In order to reduce the influence of the nuclides discharged by the coastal post-treatment plant on the environmental water body, the nuclides are required to be conveyed to a proper water area of the open sea for discharging through long-distance concealed pipes. In order to fully utilize the diluting and mixing characteristics of the sea tides, the nuclide discharge mode can adopt periodic discharge, namely multiple rows under the condition of better hydrodynamic conditions and fewer rows under the condition of poorer hydrodynamic conditions. In order to accurately grasp the ecological environmental influence of the sea area of the nuclides discharged by the spent fuel post-treatment plant, the nuclide concentration of the water body inside and outside the long-distance concealed pipe needs to be simulated and forecasted, and the calculation method of the nuclide concentration of the water body inside and outside the long-distance concealed pipe in a periodic discharge mode is an important technical support for developing the works by related departments, and has important significance for planning, designing and running of the spent fuel post-treatment plant.
The nuclide concentration transport of the water body inside and outside the long-distance concealed pipe involves two processes: the nuclear transport inside the concealed pipe and the nuclear transport in the sea area around the outlet of the concealed pipe. The hydrodynamic conditions inside and outside the concealed pipe have obvious difference: the flow state in the concealed pipe is pressurized flow, the flow state in the sea area around the concealed pipe is pressureless flow, and the concentration distribution of nuclides in the water body inside and outside the concealed pipe is difficult to calculate simultaneously based on a single pressurized flow model and a pressureless flow model. The existing calculation method is mainly aimed at continuous constant source discharge or short-distance hidden pipe periodic discharge, and does not consider the change of nuclide concentration along the flowing direction (longitudinal direction) of the hidden pipe, namely, the hidden pipe outlet concentration is assumed to be equal to the hidden pipe inlet concentration. For the periodic discharge of long-distance concealed pipes, the nuclide concentration is transported in the concealed pipes for a long time, and the outlet concentration and the inlet concentration of the concealed pipes are obviously different from each other: (1) The concentration of the outlet of the concealed pipe has a delayed response relative to the concentration of the inlet, i.e. the nuclide of the inlet of the concealed pipe needs to take several hours or even more to reach the outlet of the concealed pipe; (2) The concentration of nuclides in the concealed pipe is unevenly distributed in the water flow direction under the influence of water entrainment and dilution diffusion and in a periodical discharge mode, and the concentration of nuclides at the outlet of the concealed pipe is obviously different from the concentration at the inlet of the concealed pipe. Therefore, the existing method can not accurately reflect the delayed response of the nuclide concentration of the long-distance concealed pipe outlet and the entrainment and dilution diffusion effects of the concealed pipe water flow under the periodic discharge mode, thereby affecting the accuracy of simulating and forecasting the surrounding sea area nuclide concentration field by taking the nuclide flux of the concealed pipe outlet as a source item. Therefore, the exploration of the calculation method capable of accurately forecasting the nuclide concentration of the water body inside and outside the long-distance concealed pipe in the periodic emission mode has very important significance for planning, demonstration and design of the spent fuel post-treatment plant and water environment safety assessment.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a calculation method for the nuclide concentration of a long-distance concealed pipe inner and outer water body in a periodic discharge mode. The method utilizes an analytic method to calculate the nuclide concentration distribution in the pressured concealed pipe, obtains the variation process of the nuclide concentration and flux of the outlet of the concealed pipe, and simulates and calculates the sea area nuclide concentration field, thereby obtaining the nuclide concentration distribution of the water body inside and outside the concealed pipe.
The purpose of the invention is realized in the following way: a calculation method of the nuclide concentration of a long-distance concealed pipe inner and outer water body in a periodic discharge mode comprises the following steps:
step 1, judging whether the process belongs to a long-time hydraulic dispersion type process: whether the nuclide transport process in the concealed pipe belongs to a long-time hydraulic dispersion type process, namely: whether the ratio of the length L of the concealed pipe to the average flow velocity U of the section of the concealed pipe is far greater than the square of the hydraulic diameter W of the concealed pipe and the longitudinal diffusion coefficient D of nuclide in the flow of the concealed pipe ξ Ratio of; if yes, entering the next step, and if not, ending the calculation;
wherein a is 0 、a m 、b m Is the Fourier expansion coefficient; t is time; t is the nuclide emission period; m is the number of items of the Fourier series expansion of the nuclide flux, is a positive integer, and M is the maximum number of items of the Fourier series approximate expansion;
wherein:
λ n to satisfy the positive root of the following transcendental equation:
in the above formula: ζ is the pipe coordinate, ζ=0 represents the pipe inlet position; n is a positive integer;
lambda was calculated using the following algorithm n ：
i) Calculation of
Break point coordinates ζ of right item r ：
ii) calculation of
Break point coordinates u of left term r ：
iii) Calculating the initial coordinate xi of the interval where the 1 st positive root is s ：
Wherein: floor () is a rounding function;
iv) calculating
The interval in which the positive root is located:
[ξ s +iu r ,ξ s +(i+1)u r ],i＝0,2,4,…I
wherein: zeta type toy r The break point coordinates for the right item calculated in step i); u (u) r The first break point coordinates of the left term calculated for step ii); zeta type toy s The starting coordinates of the interval in which the 1 st positive root calculated in step iii) is located; n is n r Numbering the intervals in which the first positive root calculated for step iii) is located; i is an even number; i is the maximum value taken by I, and the larger I represents the higher number of the taken series items;
v) applying conventional numerical algorithm to the pairs
Solving each positive root interval to obtain lambda n ；
Step 5, calculating the distribution of the nuclide concentration caused by the cosine component of the nuclide flux: computing cosine series expansion term components
The resulting dark tube emission concentration profile:
step 7, obtaining the concentration distribution of the nuclide in the long-distance concealed pipe by linear superposition: by superimposing C 0 (ξ,t)、
Calculating the concentration profile in the dark tube caused by the nuclide flux q:
q out (t)＝QC(L,t)；
step 9, the concentration distribution of the nuclides in the sea area around the long-distance concealed pipe outlet: adding long-distance dark tube outlet flow and nuclide concentration as input parameters into a source item of a general pollutant transport model, establishing a nuclide concentration field model of a water area around the dark tube outlet, and calculating a nuclide concentration field of a sea area around the outlet;
the nuclide transport model boundary conditions are set as follows:
water level-flow rate boundary conditions: a free sliding boundary condition is adopted at the bank boundary, and a tide level boundary condition is adopted at the open sea boundary;
nuclide concentration boundary conditions: a zero flux boundary condition is adopted at the bank boundary, and a zero gradient boundary condition is adopted at the open sea boundary;
water level-flow rate initial conditions: the initial water level is set to be the average sea level height, and the initial flow rate is set to be 0;
nuclide concentration initial conditions: zero concentration initial conditions were set.
The invention has the advantages and beneficial effects that: according to the invention, complex periodic nuclide discharge flux at an inlet of the concealed pipe is expanded into flux in a Fourier series form, the nuclide concentration distribution in long-distance pressurized concealed pipe flowing under the action of single Fourier series flux is calculated by an analytic method, and then the nuclide concentration distribution in the concealed pipe is obtained based on a linear superposition principle, so that the change process of the nuclide concentration and flux at an outlet of the concealed pipe is obtained; and taking the outlet periodic nuclide concentration and the flow of the concealed pipe obtained by the analysis method as source items of a conventional sea area nuclide concentration transport model, and simulating and calculating a sea area nuclide concentration field so as to obtain the nuclide concentration distribution of the water body inside and outside the long-distance concealed pipe. The invention provides a quantitative calculation method for the nuclide concentration of the water body inside and outside the long-distance concealed pipe in an accurate forecast period emission mode, and provides scientific basis for planning, demonstration and design of a spent fuel post-treatment plant and water environment safety evaluation.
Drawings
The invention is further described below with reference to the drawings and examples.
FIG. 1 is a flow chart of a method according to an embodiment of the invention;
FIG. 2 shows the calculation results of the concentration distribution of the core element in the concealed pipe at different moments in the application example of the embodiment of the invention;
FIG. 3 is a graph showing the calculation of the concentration of the nuclide at the outlet of the concealed conduit with time in the application example of the embodiment of the present invention;
FIG. 4 is a graph showing the calculation of the flux of the nuclear species at the outlet of the blind pipe over time in an example of application of the embodiment of the present invention;
FIG. 5 is a contour of the instantaneous distribution of the concentration of a nuclear species around the outlet of a dark tube in an example application of an embodiment of the present invention;
FIG. 6 is a tidal level verification of a model in an example application of an embodiment of the present invention;
FIG. 7 is a graph showing the fixed point flow rate verification of a model in an example of application of an embodiment of the present invention;
FIG. 8 is a graph showing the verification of the direction of the fixed-point flow velocity of the model in the application example of the embodiment of the present invention.
Detailed Description
Embodiment one:
the embodiment is a calculation method of the nuclide concentration of the inner and outer water bodies of a long-distance concealed pipe in a periodic discharge mode, and the flow of the calculation method is shown in a figure 1.
According to the integral thought of the calculation method, the thought of combining an analysis algorithm with a numerical algorithm is adopted, complex periodic nuclide discharge flux at an inlet of the concealed pipe is unfolded to flux in a Fourier series form, the analysis method is used for calculating nuclide concentration distribution in long-distance pressurized concealed pipe flowing under the action of single Fourier series flux, then the nuclide concentration distribution in the concealed pipe is obtained based on a linear superposition principle, and further the change process of nuclide concentration and flux at an outlet of the concealed pipe is obtained; and taking the outlet periodic nuclide concentration and the flow of the concealed pipe obtained by the analysis method as source items of a conventional sea area nuclide concentration transport model, and simulating and calculating a sea area nuclide concentration field so as to obtain the nuclide concentration distribution of the water body inside and outside the long-distance concealed pipe.
The specific steps of the method in this embodiment are as follows:
step 1, judging whether the process belongs to a long-time hydraulic dispersion type process: whether the nuclide transport process in the concealed pipe belongs to a long-time hydraulic dispersion type process, namely: whether the ratio of the length L of the concealed pipe to the average flow velocity U of the section of the concealed pipe is far greater than the square of the hydraulic diameter W of the concealed pipe and the longitudinal diffusion coefficient D of nuclide in the flow of the concealed pipe ξ Ratio of; if yes, go to the next step, if not, end the calculation.
The step is to judge first
If so, the nuclide concentration in the concealed pipe is mainly distributed unevenly along the longitudinal direction in a long-time hydraulic dispersion process, and the nuclide concentration distribution of the water body inside and outside the long-distance concealed pipe can be calculated by adopting the calculation method.
Wherein the length L of the concealed pipe, the average flow velocity U of the section of the concealed pipe and the hydraulic diameter W of the concealed pipe are approximately determined in the initial stage of the design of the concealed pipe and are known values, and the longitudinal diffusion coefficient D of nuclide in the flow of the concealed pipe ξ Also in the case of a determination of the cross-sectional dimensions of the concealed conduit, the average flow velocity of the concealed conduit.
The following describes the calculation method of each step described in this embodiment with a certain project as an application example:
the engineering parameters are as follows: l=1000 m, u=0.05 m/s, D ξ ＝50m 2 /s，W＝2m
2×10 4 ＞＞0.08
The two differ by 6 orders of magnitude and can therefore be calculated using the method described in this example. Typically the two are several orders of magnitude different, i.e. considered to be much larger.
The application examples are as follows: periodic discharge flow parameters: q (Q) in ＝0.2m 3 /s，
T=12 hours=4.32×10 4 s. The nuclide concentration unit is set to be 1 per cubic meter, i.e. 1/m 3 . Thus (S)>
wherein a is 0 、a m 、b m Is the Fourier expansion coefficient; t is time; t is the nuclide emission period; m is the number of terms of the Fourier series expansion of the nuclide flux, is a positive integer, and M is the maximum number of terms of the Fourier series approximate expansion. In practical application, finite term (M term) series summation is selected according to the precision required by the user.
The application examples are as follows:
a 0 ＝2(1/s)
a m ＝0(1/s)
wherein:
λ n to satisfy the positive root of the following transcendental equation:
in the above formula: ζ is the pipe coordinate, ζ=0 represents the pipe inlet position; n is a positive integer and is selected according to the required precision.
Lambda was calculated using the following algorithm n ：
i) Calculating the coordinate xi of the break point of the right item of the formula (4) r ：
ii) calculating the break point coordinates u of the left term of (4) r ：
iii) Calculating the initial coordinate xi of the interval where the 1 st positive root is s ：
Wherein: floor () is a rounding function.
iv) calculating the interval of the positive root of (4)
[ξ s +iu r ,ξ s +(i+1)u r ],i＝0,2,4,…I (9)
Wherein: zeta type toy r The break point coordinates for the right item calculated in step i); u (u) r The first break point coordinates of the left term calculated for step ii); zeta type toy s The starting coordinates of the interval in which the 1 st positive root calculated in step iii) is located; n is n r Numbering the intervals in which the first positive root calculated for step iii) is located; i is an even number; i is the maximum value taken by I, and the larger I represents the higher number of the taken series items;
v) solving each positive root interval of (4) by adopting a conventional numerical algorithm to obtain lambda n 。
The application examples are as follows:
calculating an entry flux constant term component
The resulting dark tube emission concentration profile:
wherein:
λ n for positive root, the following transcendental equation is satisfied:
the application example here selects a 5-term series for summation.
Calculating lambda n
i) Calculating the coordinate xi of the break point of the right item of the formula (4) r ：
ii) calculating the break point coordinates u of the left term of (4) r ：
iii) Calculating the initial coordinate xi of the interval where the 1 st positive feature root is located s ：
ξ s ＝0
iv) calculating the interval of the characteristic root of (4):
[iu r ,(i+1)u r ],i＝0,2,4,…8
wherein: i is an even number;
v) solving the characteristic root interval of the formula (4) in the formula (9) by adopting a conventional numerical algorithm to obtain:
λ 1 ＝0.001570794109、λ 2 ＝0.004712367024、λ 3 ＝0.007853920200、λ 4 ＝0.01099545364、λ 5 ＝0.01413696734。
step 5, calculating the distribution of the nuclide concentration caused by the cosine component of the nuclide flux: computing cosine series expansion term components
The resulting dark tube emission concentration profile:
in practical application, finite term (N term) series summation is selected according to the precision required by the user.
The application examples are as follows: computing cosine series expansion term components
The resulting dark tube emission concentration profile:
in practical application, finite term (N term) series summation is selected according to the precision required by the user.
The application examples are as follows: calculating sinusoidal series expansion term components
The resulting dark tube emission concentration profile:
step 7, obtaining the concentration distribution of the nuclide in the long-distance concealed pipe in a periodic discharge mode by linear superposition: by superimposing C 0 (ξ,t)、
Calculating the concentration profile in the dark tube caused by the nuclide flux q:
the nuclide concentration C (xi, t) in the long-distance concealed pipe can be calculated by C 0 (ξ,t)、
The superposition was demonstrated as follows:
the nuclide concentration transport control equation, boundary conditions and initial conditions in the long-distance blind duct channel are as follows:
control equation:
boundary conditions:
initial conditions:
C(ξ,0)＝0 (15)
wherein: c is the concentration of the species in the flow of the concealed conduit, ζ is the concealed conduit position coordinate, ζ=0 is the concealed conduit inlet position coordinate, and ζ=l is the concealed conduit outlet position coordinate.
Due to C 0 (ξ,t)、
The solution problem is respectively satisfied:
C 0 (ξ,0)＝0 (18)
from the superposition of the linear equations, it is known that:
therefore, the solution of the formula (12) satisfies the control equation (13), the boundary condition (14) and the initial condition (15), namely the solution of the nuclide concentration in the long-distance blind duct channel.
The application examples are as follows: linear superposition calculation:
fig. 2 shows the concentration profiles of the nuclides in the dark tubes at different moments (6 hours, 12 hours, 18 hours, 24 hours) of the application example.
q out (t)＝QC(L,t)。 (28)
the application examples are as follows: calculating the nuclide concentration and flux q at the outlet of the concealed pipe out Is a periodic variation of (a):
C e (t)＝C(L,t)
q out (t)＝QC(L,t)＝0.2C(L,t)。
figure 3 shows the calculated results of the concentration of the outlet nuclide of the blind pipe over time. Figure 4 shows the calculation of the flux of the nuclear species at the outlet of the blind pipe over time. Table 1 shows the flow and concentration of the dark tube outlet nuclide over time for 1 discharge cycle. Table 2 gives the variation of the outlet nuclide flux of the blind pipe over time for 1 discharge cycle.
TABLE 1 variation of outlet nuclide flow and concentration of the blind tube (1 discharge cycle)
| Time(s) | Flow (m) 3 /s) | Concentration (1/m) 3 ) | Time(s) | Flow (m) 3 /s) | Concentration (1/m) 3 ) |
| 0 | 0.2 | 0 | 18000 | 0.2 | 12.85697 |
| 600 | 0.2 | 0.195966 | 18600 | 0.2 | 12.87678 |
| 1200 | 0.2 | 0.641684 | 19200 | 0.2 | 12.8661 |
| 1800 | 0.2 | 1.272187 | 19800 | 0.2 | 12.8258 |
| 2400 | 0.2 | 1.964003 | 20400 | 0.2 | 12.7569 |
| 3000 | 0.2 | 2.671111 | 21000 | 0.2 | 12.66059 |
| 3600 | 0.2 | 3.373521 | 21600 | 0.2 | 12.53823 |
| 4200 | 0.2 | 4.061833 | 22200 | 0.2 | 12.39129 |
| 4800 | 0.2 | 4.731502 | 22800 | 0.2 | 12.22144 |
| 5400 | 0.2 | 5.380271 | 23400 | 0.2 | 12.03043 |
| 6000 | 0.2 | 6.006934 | 24000 | 0.2 | 11.82016 |
| 6600 | 0.2 | 6.610725 | 24600 | 0.2 | 11.59264 |
| 7200 | 0.2 | 7.19103 | 25200 | 0.2 | 11.34998 |
| 7800 | 0.2 | 7.747247 | 25800 | 0.2 | 11.09438 |
| 8400 | 0.2 | 8.278734 | 26400 | 0.2 | 10.82809 |
| 9000 | 0.2 | 8.784796 | 27000 | 0.2 | 10.55344 |
| 9600 | 0.2 | 9.264686 | 27600 | 0.2 | 10.27278 |
| 10200 | 0.2 | 9.717624 | 28200 | 0.2 | 9.988517 |
| 10800 | 0.2 | 10.14282 | 28800 | 0.2 | 9.703027 |
| 11400 | 0.2 | 10.53948 | 29400 | 0.2 | 9.418702 |
| 12000 | 0.2 | 10.90684 | 30000 | 0.2 | 9.1379 |
| 12600 | 0.2 | 11.24419 | 30600 | 0.2 | 8.86294 |
| 13200 | 0.2 | 11.55089 | 31200 | 0.2 | 8.596079 |
| 13800 | 0.2 | 11.82636 | 31800 | 0.2 | 8.339503 |
| 14400 | 0.2 | 12.07014 | 32400 | 0.2 | 8.095305 |
| 15000 | 0.2 | 12.28187 | 33000 | 0.2 | 7.865474 |
| 15600 | 0.2 | 12.46134 | 33600 | 0.2 | 7.65188 |
| 16200 | 0.2 | 12.60845 | 34200 | 0.2 | 7.456258 |
| 16800 | 0.2 | 12.72326 | 34800 | 0.2 | 7.280199 |
| 17400 | 0.2 | 12.80598 | 35400 | 0.2 | 7.125138 |
TABLE 2 variation of the outlet nuclide flux of the concealed conduit over time (1 discharge cycle)
| Time(s) | Flux (1/s) | Time(s) | Flux (1/s) |
| 0 | 0 | 18000 | 2.571395 |
| 600 | 0.039193 | 18600 | 2.575356 |
| 1200 | 0.128337 | 19200 | 2.573221 |
| 1800 | 0.254437 | 19800 | 2.56516 |
| 2400 | 0.392801 | 20400 | 2.55138 |
| 3000 | 0.534222 | 21000 | 2.532119 |
| 3600 | 0.674704 | 21600 | 2.507645 |
| 4200 | 0.812367 | 22200 | 2.478259 |
| 4800 | 0.9463 | 22800 | 2.444287 |
| 5400 | 1.076054 | 23400 | 2.406085 |
| 6000 | 1.201387 | 24000 | 2.364032 |
| 6600 | 1.322145 | 24600 | 2.318528 |
| 7200 | 1.438206 | 25200 | 2.269997 |
| 7800 | 1.549449 | 25800 | 2.218876 |
| 8400 | 1.655747 | 26400 | 2.165618 |
| 9000 | 1.756959 | 27000 | 2.110688 |
| 9600 | 1.852937 | 27600 | 2.054557 |
| 10200 | 1.943525 | 28200 | 1.997703 |
| 10800 | 2.028563 | 28800 | 1.940605 |
| 11400 | 2.107895 | 29400 | 1.88374 |
| 12000 | 2.181368 | 30000 | 1.82758 |
| 12600 | 2.248839 | 30600 | 1.772588 |
| 13200 | 2.310177 | 31200 | 1.719216 |
| 13800 | 2.365272 | 31800 | 1.667901 |
| 14400 | 2.414028 | 32400 | 1.619061 |
| 15000 | 2.456375 | 33000 | 1.573095 |
| 15600 | 2.492268 | 33600 | 1.530376 |
| 16200 | 2.52169 | 34200 | 1.491252 |
| 16800 | 2.544652 | 34800 | 1.45604 |
| 17400 | 2.561195 | 35400 | 1.425028 |
Step 9, the concentration distribution of the nuclides in the sea area around the long-distance concealed pipe outlet: and adding the long-distance hidden pipe outlet flow and the nuclide concentration as input parameters into a source item of a general pollutant transportation model, establishing a nuclide concentration field model of a water area around the hidden pipe outlet, and calculating a nuclide concentration field of a sea area around the outlet.
The nuclide transport model boundary conditions are set as follows:
water level-flow rate boundary conditions: the bank boundary adopts a free sliding boundary condition, and the open sea boundary adopts a tide level boundary condition.
Nuclide concentration boundary conditions: a zero flux boundary condition is adopted at the bank boundary, and a zero gradient boundary condition is adopted at the open sea boundary.
Water level-flow rate initial conditions: the initial water level was set to mean sea level height and the initial flow rate was set to 0.
Nuclide concentration initial conditions: zero concentration initial conditions were set.
The application examples are as follows: and selecting the MIKE21 model as a peripheral nuclide transport model of the outlet, inputting the long-distance concealed pipe outlet position (506274,3808682), the outlet nuclide flow and concentration (13 calculation results) as source items into the MIKE21 model, and establishing a nuclide concentration field model of a water area around the concealed pipe outlet. The calculation is performed by taking a certain coastal area of southeast China as an example. In the MIKE21 model, the boundary conditions, initial conditions are set as follows:
boundary condition setting:
water level-flow rate boundary conditions: the bank boundary adopts a free sliding boundary condition, and the open sea boundary is given a periodic tide level process.
Nuclide concentration boundary conditions: the shore boundary adopts a zero flux boundary condition, and the open sea boundary adopts a zero gradient boundary condition.
Initial condition setting:
water level: giving an average sea level height;
flow rate: 0m/s;
nuclide concentration: zero initial concentration is used;
FIG. 5 shows the contour of the concentration distribution of the nuclear species around the outlet of the dark tube in the periodic discharge mode. Model tidal level, flow rate, flow direction validation results are shown in fig. 6-8.
Finally, it should be noted that the above only illustrates the technical solution of the present invention, and not limiting, and although the present invention has been described in detail with reference to the preferred arrangement, it will be understood by those skilled in the art that the technical solution of the present invention (such as the form of the concealed conduit, the application of various formulas or models, the sequence of steps, etc.) may be modified or replaced equivalently, without departing from the spirit and scope of the technical solution of the present invention.
Claims (1)
1. A calculation method of the nuclide concentration of a long-distance concealed pipe inner and outer water body in a periodic discharge mode is characterized by comprising the following steps:
step 1, judging whether the process belongs to a long-time hydraulic dispersion type process: whether the nuclide transport process in the concealed pipe belongs to a long-time hydraulic dispersion type process, namely: whether the ratio of the length L of the concealed pipe to the average flow velocity U of the section of the concealed pipe is far greater than the square of the hydraulic diameter W of the concealed pipe and the longitudinal diffusion coefficient D of nuclide in the flow of the concealed pipe ξ Ratio of; if yes, entering the next step, and if not, ending the calculation;
step 2, calculating flux q (t) of the nuclide discharged at the inlet of the concealed pipe: acquisition weekPhase discharge flow parameters: discharge flow rate Q in And a time-varying emission profile C in (t)：q(t)＝Q in C in (t)；
Step 3, expanding the periodical nuclide flux into a Fourier series form: expanding the periodic nuclear flux q (t) discharged at the inlet of the concealed pipe into a fourier series:
wherein a is 0 、a m 、b m Is the Fourier expansion coefficient; t is time; t is the nuclide emission period; m is the number of items of the Fourier series expansion of the nuclide flux, is a positive integer, and M is the maximum number of items of the Fourier series approximate expansion;
step 4, calculating the distribution of the nuclide concentration caused by constant component items of the nuclide flux: calculating constant term components of the flux of the inlet of the concealed conduit nuclide
The resulting emission concentration profile:
wherein:
λ n to satisfy the positive root of the following transcendental equation:
in the above formula: ζ is the pipe coordinate, ζ=0 represents the pipe inlet position; n is a positive integer, and is selected according to the required precision;
lambda was calculated using the following algorithm n ：
i) Calculation of
Break point coordinates ζ of right item r ：
ii) calculation of
Break point coordinates u of left term r ：
iii) Calculating the initial coordinate xi of the interval where the 1 st positive root is s ：
Wherein: floor () is a rounding function;
iv) calculating
The interval in which the positive root is located:
[ξ s +iu r ,ξ s +(i+1)u r ],i＝0,2,4,…I
wherein: zeta type toy r The break point coordinates for the right item calculated in step i); u (u) r The first break point coordinates of the left term calculated for step ii); zeta type toy s The starting coordinates of the interval in which the 1 st positive root calculated in step iii) is located; n is n r Numbering the intervals in which the first positive root calculated for step iii) is located; i is an even number; i is the maximum value taken by I, and the larger I represents the higher number of the taken series items;
v) applying conventional numerical algorithm to the pairs
Solving each positive root interval to obtain lambda n ；
Step 5, calculating the distribution of the nuclide concentration caused by the cosine component of the nuclide flux: computing cosine series expansion term components
The resulting dark tube emission concentration profile:
step 6, calculating the distribution of the nuclide concentration caused by the sine series component of the nuclide flux: calculating sinusoidal series expansion term components
The resulting dark tube emission concentration profile:
step 7, obtaining the concentration distribution of the nuclide in the long-distance concealed pipe by linear superposition: by superimposing C 0 (ξ,t)、
Calculating the concentration profile in the dark tube caused by the nuclide flux q:
step 8, obtaining the dynamic change of the nuclide concentration and flux of the long-distance concealed pipe outlet: calculating nuclide flux q at outlet of concealed pipe out Is a periodic variation of (a):
q out (t)＝QC(L,t)；
step 9, the concentration distribution of the nuclides in the sea area around the long-distance concealed pipe outlet: adding long-distance dark tube outlet flow and nuclide concentration as input parameters into a source item of a general pollutant transport model, establishing a nuclide concentration field model of a water area around the dark tube outlet, and calculating a nuclide concentration field of a sea area around the outlet;
the nuclide transport model boundary conditions are set as follows:
water level-flow rate boundary conditions: a free sliding boundary condition is adopted at the bank boundary, and a tide level boundary condition is adopted at the open sea boundary;
nuclide concentration boundary conditions: a zero flux boundary condition is adopted at the bank boundary, and a zero gradient boundary condition is adopted at the open sea boundary;
water level-flow rate initial conditions: the initial water level is set to be the average sea level height, and the initial flow rate is set to be 0;
nuclide concentration initial conditions: zero concentration initial conditions were set.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310359013.7A CN116401500B (en) | 2023-04-06 | 2023-04-06 | Calculation method for nuclide concentration of long-distance concealed pipe inside and outside water body in periodic discharge mode |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310359013.7A CN116401500B (en) | 2023-04-06 | 2023-04-06 | Calculation method for nuclide concentration of long-distance concealed pipe inside and outside water body in periodic discharge mode |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN116401500A true CN116401500A (en) | 2023-07-07 |
| CN116401500B CN116401500B (en) | 2023-09-29 |
Family
ID=87011831
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310359013.7A Active CN116401500B (en) | 2023-04-06 | 2023-04-06 | Calculation method for nuclide concentration of long-distance concealed pipe inside and outside water body in periodic discharge mode |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116401500B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040009455A1 (en) * | 2002-07-09 | 2004-01-15 | Ren-Tai Chiang | Monte carlo criticality-mode systems and methods for computing neutron and gamma fluence in a nuclear reactor |
| CN102867121A (en) * | 2012-09-06 | 2013-01-09 | 中国能源建设集团广东省电力设计研究院 | Method for analyzing influence of plume of cooling tower on nuclear waste gas concentration distribution on nuclear island |
| CN107133412A (en) * | 2017-05-15 | 2017-09-05 | 中国水利水电科学研究院 | The quick calculation method that multicomponent radionuclide concentration is forecast in a kind of river course |
| CN113282867A (en) * | 2020-02-19 | 2021-08-20 | 清华大学 | Method, apparatus, device and medium for predicting radiation dose rate of radionuclide |
| CN114386229A (en) * | 2021-11-30 | 2022-04-22 | 中国辐射防护研究院 | Radionuclide coastal real-time migration diffusion calculation method and system |
-
2023
- 2023-04-06 CN CN202310359013.7A patent/CN116401500B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040009455A1 (en) * | 2002-07-09 | 2004-01-15 | Ren-Tai Chiang | Monte carlo criticality-mode systems and methods for computing neutron and gamma fluence in a nuclear reactor |
| CN102867121A (en) * | 2012-09-06 | 2013-01-09 | 中国能源建设集团广东省电力设计研究院 | Method for analyzing influence of plume of cooling tower on nuclear waste gas concentration distribution on nuclear island |
| CN107133412A (en) * | 2017-05-15 | 2017-09-05 | 中国水利水电科学研究院 | The quick calculation method that multicomponent radionuclide concentration is forecast in a kind of river course |
| CN113282867A (en) * | 2020-02-19 | 2021-08-20 | 清华大学 | Method, apparatus, device and medium for predicting radiation dose rate of radionuclide |
| CN114386229A (en) * | 2021-11-30 | 2022-04-22 | 中国辐射防护研究院 | Radionuclide coastal real-time migration diffusion calculation method and system |
Non-Patent Citations (2)
| Title |
|---|
| PENGHUI YAO 等: "A Method of Monitoring Partial Discharge in Switchgear Based on Ozone Concentration", IEEE TRANSACTIONS ON PLASMA SCIENCE, vol. 47, no. 1, pages 654 - 660, XP011695633, DOI: 10.1109/TPS.2018.2876412 * |
| 王平 等: "湿地流动中污染物弥散过程的解析研究", 第二十九届全国水动力学研讨会, pages 1434 - 1441 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN116401500B (en) | 2023-09-29 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106815448B (en) | River attenuation type pollutant simulation method | |
| CN109101781B (en) | The calculation method of pollution sources contribution proportion in a kind of Complex River | |
| CN110197049B (en) | Non-metal pipeline leakage positioning method based on transient inverse problem | |
| Wan et al. | Water hammer simulation of a series pipe system using the MacCormack time marching scheme | |
| Nikpour et al. | Experimental and numerical simulation of water hammer | |
| CN109711107B (en) | Water resource burst water pollutant diffusion simulation system | |
| CN108760592B (en) | Fly ash carbon content online measurement method based on BP neural network | |
| CN105825047A (en) | Pipe network tip water quality simulation method based on GIS | |
| CN102968529A (en) | Method for quantifying computed result non-determinacy interval of water supply pipe network model | |
| Dayev et al. | Approximation of the discharge coefficient of differential pressure flowmeters using different soft computing strategies | |
| CN107977513A (en) | A kind of temperature predicting method when natural gas dynamic flows in gas distributing system based on route searching | |
| CN116245042A (en) | Ecological water demand calculating method based on hydrodynamic force-water environment-aquatic organisms | |
| CN102630426B (en) | Structure optimization method for Venturi fertilizer injector | |
| CN109460605A (en) | A method of predicting large-scale low-lift pump flow | |
| CN116401500B (en) | Calculation method for nuclide concentration of long-distance concealed pipe inside and outside water body in periodic discharge mode | |
| CN115422850A (en) | Method for judging pollution contribution rate of river inflow river drain outlet based on EFDC and edge calculation | |
| Horritt | Development of physically based meshes for two‐dimensional models of meandering channel flow | |
| CN106320257A (en) | Lake and reservoir channel storage curve determining method based on hydrometry | |
| CN104063609A (en) | Method of assisting in judging pollution source monitoring data validity by utilizing neural network | |
| CN111709198B (en) | Method for determining pipeline convergence energy loss coefficient by utilizing flow distribution | |
| CN116432551B (en) | River junction water quality distribution simulation method based on satellite image and CFD | |
| CN108280300B (en) | Big data flowmeter development method based on computational fluid dynamics | |
| Luo et al. | Output-based space-time mesh adaptation for unsteady aerodynamics | |
| Sutton et al. | Atmospheric dispersion of a heavier-than-air gas near a two-dimensional obstacle | |
| Chandraker et al. | Experimental and analytical investigations on core flow distribution and pressure distribution in the outlet header of a PHWR |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |