CN111063467A - Control method for temperature field of rod-shaped fuel element - Google Patents
Control method for temperature field of rod-shaped fuel element Download PDFInfo
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- CN111063467A CN111063467A CN201911318177.5A CN201911318177A CN111063467A CN 111063467 A CN111063467 A CN 111063467A CN 201911318177 A CN201911318177 A CN 201911318177A CN 111063467 A CN111063467 A CN 111063467A
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- G—PHYSICS
- G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
- G21D—NUCLEAR POWER PLANT
- G21D3/00—Control of nuclear power plant
- G21D3/08—Regulation of any parameters in the plant
- G21D3/10—Regulation of any parameters in the plant by a combination of a variable derived from neutron flux with other controlling variables, e.g. derived from temperature, cooling flow, pressure
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- G—PHYSICS
- G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
- G21C—NUCLEAR REACTORS
- G21C17/00—Monitoring; Testing ; Maintaining
- G21C17/10—Structural combination of fuel element, control rod, reactor core, or moderator structure with sensitive instruments, e.g. for measuring radioactivity, strain
- G21C17/112—Measuring temperature
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- G—PHYSICS
- G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
- G21D—NUCLEAR POWER PLANT
- G21D3/00—Control of nuclear power plant
- G21D3/001—Computer implemented control
- G21D3/004—Fuel shuffle simulation; fuel shuffle optimisation
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- G—PHYSICS
- G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
- G21D—NUCLEAR POWER PLANT
- G21D3/00—Control of nuclear power plant
- G21D3/04—Safety arrangements
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- 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
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- 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
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Abstract
The invention relates to the technical field of reactor thermal calculation, and particularly discloses a control method of a temperature field of a rod-shaped fuel element, which comprises the following steps: obtaining the temperature T (r) at the fuel boundary0) Volume heat release rate q of fuel and fuel pellet thermal conductivity k (T); according to T (r)0) Q and k (T), by the formulaCalculating the temperature T of the center of the fuel elementfWhere ρ is the density of the fuel pellets, cpIs the specific heat of the fuel, T (r, T) is the fuel pellet temperature, as a function of time T and the distance r from a point in the fuel pellets to the center of the pellets; judgment of TfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elementsIf so, stopping increasing the reactor power and properly reducing the reactor power; if not, the current reactor power may be maintained or the reactor power may be increased appropriately. The problem that whether the highest temperature of the fuel reaches or is close to the melting point of the fuel or not can not be judged in the prior art, and therefore whether the center of the fuel is molten or not can not be judged.
Description
Technical Field
The invention relates to the technical field of reactor thermal calculation, in particular to a control method of a temperature field of a rod-shaped fuel element.
Background
The fuel elements have a high activity and the fuel envelope is the first barrier to prevent radioactive material from leaking. To ensure that no melting of the fuel element occurs under any circumstances, the highest temperature within the fuel element must be known.
Because the temperature gradient can cause thermal stress, the spatial distribution of temperature is considered when designing the fuel pellet and the structural material, and the phenomena of creep, brittle fracture and the like of the material at high temperature have close relation with the temperature. The chemical reaction of the cladding surface and the coolant is also closely related to temperature. From a reactor physics standpoint, temperature changes in the fuel and moderator can cause reactivity feedback, affecting the reactor power, resulting in changes in the fuel heat release rate.
The prior art can only obtain the temperature of the reactor core coolant, but cannot obtain the temperature of the center of the fuel rod, namely the highest temperature, so that whether the highest temperature of the fuel reaches or is close to the melting point of the fuel or not and whether the center of the fuel is molten or not cannot be judged.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a control method of a temperature field of a rod-shaped fuel element, which can solve the problem that whether the highest temperature of fuel reaches or is close to the melting point of the fuel and whether the center of the fuel is molten cannot be judged in the prior art.
In order to achieve the above purposes, the technical scheme adopted by the invention is as follows:
the invention provides a control method of a temperature field of a rod-shaped fuel element, which comprises the following steps:
obtaining the temperature T (r) at the fuel boundary0) Volume heat release rate q of fuel and fuel pellet thermal conductivity k (T);
according to T (r)0) Q and k (T), by the formulaCalculating the temperature T of the center of the fuel elementfWhere ρ is the density of the fuel pellets, cpIs the specific heat of the fuel, T (r, T) is the fuel pellet temperature, as a function of time T and the distance r from a point in the fuel pellets to the center of the pellets;
judgment of TfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elementsIf so, stopping increasing and reducing the reactor power, and if not, slowly increasing or keeping the reactor power.
On the basis of the technical scheme, the method adopts a formulaCalculating the temperature T of the center of the fuel elementfThe method specifically comprises the following steps:
the simplified equation:
comprises the following steps:
WhereinriIs the length of the radius at the ith point, i is the radius r0The number of divided grids, Δ r is the length of each portion, Δ r ═ h, TiFor the temperature at the ith point, equation (2) is converted to:
after finishing, obtaining:
approximate valueSubstituting the right end of the formula (4) with a known value, the boundary value T (r)0) Is composed ofThe rest(s)Set as linear interpolation from boundary values, each grid is increased by x deg.C to obtainThen calculateThe equation of (a) is:
knowing the temperature of a point of fuelPushing the next grid point temperature into the fuel centerThe expression of (c) is assumed to be:
ui、via series of numbers to be recurred, wherein: u. of1=1,v1=x;
Increasing i in formula (5) to i +1, then
Substituting the formula (6) into the formula (7) to obtain
After finishing, obtaining:
obtain the number series { ui}、{viThe recursion of:
equations (6) and (8) constitute an iterative numerical program calculation that, instead of converging, yields the temperature T at the center of the rod fuelf。
On the basis of the technical scheme, the iterative convergence condition is thatWhen so, the iteration ends.
On the basis of the technical scheme, the epsilon is designated as 3 or 5.
On the basis of the technical scheme, x is 5.
Based on the technical scheme, the k (T) is determined according to the material of the fuel, and when the fuel is uranium dioxide, the thermal conductivity k (T) of the fuel pellets isT is the temperature of uranium dioxide.
On the basis of the technical scheme, the boundary temperature of the cladding is obtained through measurement, and the air gap thermal conductivity k is combinedqCladding thermal conductivity kgThe temperature T (r) at the fuel boundary is estimated0);
Wherein: air gap thermal conductivity kq=A·TBkW/(m.K), helium (He) filling, parameter values A ═ 1.58X 10-5B ═ 0.79, cladding thermal conductivity k of zirconium alloy materialgIs kg=k0+k1T+k2T2+k3T3(J/m.s.cndot.) C, wherein k is0=7.51J/m·s·℃,k1=2.09×10-2J/(m·s·℃2),k2=-1.45×10-5J/(m·s·℃3),k3=7.67×10-9J/(m·s·℃4)。
On the basis of the technical scheme, the T is judgedfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elementsIf so, stopping increasing and reducing the reactor power, otherwise, keeping or slowly increasing the reactor power, specifically comprising:
judgment of TfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elements;
If yes, the judgment signal triggers the relay to act, a fuel element temperature is high on a nuclear power device control console, an alarm red light flashes, a buzzer makes a noise, a nuclear power device operator immediately stops increasing the reactor power, and a control rod is inserted to reduce the reactor power;
if not, the signal is judged not to trigger the relay to act, the red alarm lamp does not flicker when the temperature of the fuel element is high on the control console of the nuclear power device, the buzzer does not make noise, and the power of the reactor is kept or slowly increased.
Compared with the prior art, the invention has the advantages that: when using the control method of the rod-like fuel element temperature field, the temperature T (r) at the fuel boundary is first acquired0) Volume heat release rate q of fuel and fuel pellet thermal conductivity k (T); then according to T (r)0) Q and k (T), by the formulaCalculating the temperature T of the center of the fuel elementfWhere ρ is the density of the fuel pellets, cpIs the specific heat of the fuel, T (r, T) is the fuel pellet temperature, as a function of time T and the distance r from a point in the fuel pellets to the center of the pellets; then, T is judgedfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elementsIf so, stopping increasing and reducing the reactor power, and if not, slowly increasing or keeping the reactor power. Therefore, whether the highest temperature reaches or is close to the melting point of the fuel can be judged, so that the control temperature of the rod-shaped fuel is controlled, and the central melting failure of the fuel is avoided.
Drawings
FIG. 1 is a flow chart of a method for controlling the temperature field of a rod fuel element in an embodiment of the present invention.
Fig. 2 is a fuel element temperature field profile obtained by the control method according to the embodiment of the present invention.
Detailed Description
Embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.
FIG. 1 is a flow chart of a method for controlling the temperature field of a rod fuel element in an embodiment of the present invention. As shown in fig. 1:
the invention provides a control method of a temperature field of a rod-shaped fuel element, which comprises the following steps:
s1: obtaining the temperature T (r) at the fuel boundary0) The volumetric heat release rate q of the fuel and the thermal conductivity k (T) of the fuel pellets.
In the present embodiment, the temperature at the boundary of the cladding is obtained by measurement, and the temperature T (r) at the boundary of the fuel is obtained by estimation0) The estimation method may be the following method, or may be estimated by estimation. And (3) calculating and determining the volume heat release rate q of the fuel through a reactor physical and thermal large-scale calculation software package program. The fuel pellet thermal conductivity k (t) is estimated from the material properties of the fuel.
Preferably, k (T) is dependent on the material of the fuel, and when the fuel is uranium dioxide, the thermal conductivity k (T) of the fuel pellets isT is the temperature of uranium dioxide.
Preferably, the boundary temperature of the cladding is obtained by measurement, in combination with the air gap thermal conductivity kqCladding thermal conductivity kgThe temperature T (r) at the fuel boundary is estimated0)。
Wherein: air gap thermal conductivity kq=A·TBkW/(m.K), helium (He) filling, parameter values A ═ 1.58X 10-5B ═ 0.79, cladding thermal conductivity k of zirconium alloy materialgIs kg=k0+k1T+k2T2+k3T3(J/m.s.cndot.) C, wherein k is0=7.51J/m·s·℃,k1=2.09×10-2J/(m·s·℃2),k2=-1.45×10-5J/(m·s·℃3),k3=7.67×10-9J/(m·s·℃4)。
S2: according to T (r)0) Q and k (T), by the formulaCalculating the temperature T of the center of the fuel elementfWhere ρ is the density of the fuel pellets, cpFor specific heat of the fuel, T (r, T) is the fuel pellet temperature, as a function of time T and the distance r from a point in the fuel pellets to the center of the pellets.
wherein Q is the heat flux density; k is the thermal conductivity of the material,is the gradient of temperature.
Since the compressibility of the solid is small, the shape of the solid does not change during heat conduction, and the fuel rod is thin and long, heat conduction in the axial direction can be ignored, and only heat conduction in the radial direction is considered. Then the laplace operator
Can be simplified as follows:
according to the fourier law of thermal conductivity, for a cylindrical fuel element, the heat transfer equation can be described as:
by the formulaCalculating the temperature T of the center of the fuel elementfThe method specifically comprises the following steps:
the simplified equation:
comprises the following steps:
WhereinriIs the length of the radius at the ith point, i is the radius r0The number of divided grids, Δ r is the length of each portion, Δ r ═ h, TiFor the temperature at the ith point, equation (2) is converted to:
after finishing, obtaining:
approximate valueSubstituting the right end of the formula (4) with a known value, the boundary value T (r)0) Is composed ofThe rest(s)Set as linear interpolation from boundary values, each grid is increased by x deg.C to obtainThen calculateThe equation of (a) is:
Preferably, x is 5.
Knowing the temperature of a point of fuelPushing the next grid point temperature into the fuel centerThe expression of (c) is assumed to be:
ui、vifor pending recursion series explicit u1=1,v1=x;
Increasing i in formula (5) to i +1, then
Substituting the formula (6) into the formula (7) to obtain
After finishing, obtaining:
obtain the number series { ui}、{viThe recursion of:
equations (6) and (8) constitute an iterative numerical program calculation that, instead of converging, yields the temperature T at the center of the rod fuelf。
Preferably, ε is designated as 3 or 5. In the present embodiment, ε is designated as 3 or 5, then if the fuel elements are divided into 100 compartments in the radial direction, then the temperature error per compartment is only 0.03 ℃ or 0.05 ℃, and the temperature at the center of the fuel element can be obtained very accurately.
S3: judgment of TfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elementsIf so, stopping increasing and reducing the reactor power, and if not, slowly increasing or keeping the reactor power.
Preferably, T is judgedfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elementsIf so, stopping increasing and reducing the reactor power, otherwise, keeping or slowly increasing the reactor power, specifically comprising:
judgment of TfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elements。
If yes, the signal triggers a relay to act, a red alarm lamp flashes when the temperature of a fuel element on a control console of the nuclear power device is high, a buzzer sounds noise, an operator of the nuclear power device immediately stops increasing the power of the reactor, and a control rod is inserted downwards to reduce the power of the reactor.
If not, the signal does not trigger the relay to act, the red alarm lamp does not flicker when the temperature of the fuel element is high on the control console of the nuclear power device, the buzzer does not make noise, and the power of the reactor is kept or slowly increased.
Fig. 2 is a fuel element temperature field profile obtained by the control method according to the embodiment of the present invention. As shown in fig. 2, the abscissa of the graph is the radius and the ordinate is the temperature. With this control method, rod-shaped fuel elements with radii of 8mm and 4mm were calculated. When the radius is 8mm, the surface temperature is 300 ℃, and the volume heat release rate is q1=300W/cm3When the temperature of the fuel center exceeds 3000 ℃; the volume heat release rate is q2=200W/cm3At times, the fuel core temperature exceeded 1500 ℃. If the fuel element radius is 4mm, the volumetric heat release rate is q1=300W/cm3At this time, the fuel core temperature does not exceed 700 ℃.
In summary, the following steps: when using the control method of the rod-like fuel element temperature field, the temperature T (r) at the fuel boundary is first acquired0) Volume heat release rate q of fuel and fuel pellet thermal conductivity k (T); then according to T (r)0) Q and k (T), by the formulaCalculating the temperature T of the center of the fuel elementfWhere ρ is the density of the fuel pellets, cpIs the specific heat of the fuel, T (r, T) is the fuel pellet temperature, as a function of time T and the distance r from a point in the fuel pellets to the center of the pellets; then, T is judgedfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elementsIf so, stopping increasing the reactor power, and if not, continuing to increase the reactor power. Thus, the judgment can be made mostWhether the high temperature reaches or approaches the melting point of the fuel or not, thereby controlling the control temperature of the rod-shaped fuel and avoiding the central melting failure of the fuel.
The present invention is not limited to the above-mentioned preferred embodiments, and any other products in various forms can be obtained by anyone with the teaching of the present invention, but any changes in the shape or structure thereof, which have the same or similar technical solutions as the present invention, are within the protection scope.
Claims (8)
1. A method of controlling a temperature field of a rod fuel element, comprising the steps of:
obtaining the temperature T (r) at the fuel boundary0) Volume heat release rate q of fuel and fuel pellet thermal conductivity k (T);
according to T (r)0) Q and k (T), by the formulaCalculating the temperature T of the center of the fuel elementfWhere ρ is the density of the fuel pellets, cpIs the specific heat of the fuel, T (r, T) is the fuel pellet temperature, as a function of time T and the distance r from a point in the fuel pellets to the center of the pellets;
judgment of TfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elementsIf so, stopping increasing and reducing the reactor power, and if not, slowly increasing or keeping the reactor power.
2. A method of controlling the temperature field of rod fuel elements according to claim 1, by the formulaCalculating the temperature T of the center of the fuel elementfThe method specifically comprises the following steps:
the simplified equation:
comprises the following steps:
WhereinriIs the length of the radius at the ith point, i is the radius r0The number of divided grids, Δ r is the length of each portion, Δ r ═ h, TiFor the temperature at the ith point, equation (2) is converted to:
after finishing, obtaining:
approximate value Ti (0)Where i is 0,1,2, …, n, and substituted into the right end of equation (4) to be a known value, the boundary value T (r)0) Is composed ofRest Ti (0)Where i is 0,1,2, …, n-1 is defined asLine linear interpolation, increasing x ℃ for each grid, to obtain Ti (j)Then, T is estimatedi (j+1)The equation of (a) is:
Ti (j+1)is the temperature at the ith point at the j +1 th iteration, j is a natural number,
knowing the temperature of a point of fuelPushing the next grid point temperature T into the fuel centeri (j+1)The expression of (c) is assumed to be:
ui、via series of numbers to be recurred, wherein: u. of1=1,v1=x;
Increasing i in formula (5) to i +1, then
Substituting the formula (6) into the formula (7) to obtain
After finishing, obtaining:
obtain the number series { ui}、{viThe recursion of:
equations (6) and (8) constitute an iterative numerical program calculation that, instead of converging, yields the temperature T at the center of the rod fuelf。
3. The method of controlling a rod fuel element temperature field according to claim 2, wherein the iterative convergence condition is when (T)i (j+1)-Ti (j)) If epsilon is less than epsilon, the iteration is ended.
4. A method of controlling a temperature field of rod shaped fuel elements according to claim 3, c h a r a c t e r i z e d in that epsilon is assigned 3 or 5.
5. A method of controlling a temperature field of rod shaped fuel elements according to claim 2, wherein x is 5.
7. A method for controlling the temperature field of rod shaped fuel elements according to claim 6, characterised in that the boundary temperature of the cladding is obtained by measurement, in combination with the air gap thermal conductivity kqCladding thermal conductivity kgThe temperature T (r) at the fuel boundary is estimated0);
Wherein: air gap thermal conductivity kq=A·TBkW/(m.K), helium (He) filling, parameter values A ═ 1.58X 10-5B ═ 0.79, cladding thermal conductivity k of zirconium alloy materialgIs kg=k0+k1T+k2T2+k3T3(J/m.s.cndot.) C, wherein k is0=7.51J/m·s·℃,k1=2.09×10-2J/(m·s·℃2),k2=-1.45×10-5J/(m·s·℃3),k3=7.67×10-9J/(m·s·℃4)。
8. A method of controlling a temperature field of a rod fuel element according to claim 1, wherein said determination T is madefWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elementsIf so, stopping increasing the reactor power, otherwise, maintaining or slowly increasing the reactor power, specifically comprising:
judgment of TfWhether or not less than a set threshold value T of a melting point temperature difference with the fuel elements;
If yes, the judgment signal triggers the relay to act, a fuel element temperature is high on a nuclear power device control console, an alarm red light flashes, a buzzer makes a noise, a nuclear power device operator immediately stops increasing the reactor power, and a control rod is inserted to reduce the reactor power;
if not, the signal is judged not to trigger the relay to act, the red alarm lamp does not flicker when the temperature of the fuel element is high on the control console of the nuclear power device, the buzzer does not make noise, and the power of the reactor is kept or slowly increased.
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JPS63758B2 (en) |
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Application publication date: 20200424 |