CN115408758B - Distributed multi-layer material thermal component node division and heat conduction calculation method in containment - Google Patents
Distributed multi-layer material thermal component node division and heat conduction calculation method in containment Download PDFInfo
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- CN115408758B CN115408758B CN202211137740.0A CN202211137740A CN115408758B CN 115408758 B CN115408758 B CN 115408758B CN 202211137740 A CN202211137740 A CN 202211137740A CN 115408758 B CN115408758 B CN 115408758B
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Abstract
The invention discloses a distributed multi-layer material thermal component node dividing and heat conduction calculating method in a containment, which comprises the following steps: 1. specifying the total material layer number, critical thermal conductivity, material thickness of each layer, thermal conductivity, density and specific heat capacity of the multi-layer material thermal component; 2. judging whether the thermal conductivity of the material is greater than the critical thermal conductivity, if so, going to the step 3, otherwise, going to the step 4; 3. dividing the current material into uniform nodes; 4. dividing the current material into non-uniform nodes; 5. judging whether all material nodes are divided; 6. calculating the total number of nodes; 7. initializing the temperature of each node; 8. the temperature of each node of the multi-layer material thermal member is solved. The method can divide nodes of the distributed multi-layer material thermal components in the containment, realizes heat conduction calculation of the multi-layer material thermal components, accurately solves the temperature of each node of the multi-layer material thermal components, and has important significance for analyzing the thermal hydraulic state in the containment.
Description
Technical Field
The invention belongs to the field of thermal hydraulic calculation of a containment vessel of a nuclear reactor, and particularly relates to a distributed multi-layer material thermal component node division and heat conduction calculation method in the containment vessel.
Background
The containment is the last barrier in pressurized water reactor nuclear power plants to prevent release of radioactive materials into the environment. When a water loss accident occurs, a large amount of high-temperature and high-pressure gas enters the containment, and the physical phenomena and transient response processes in each compartment of the containment can be calculated by using a multi-node containment program.
In multi-node containment thermohydraulic analysis programs, distributed thermal components are used to simulate walls between compartments, and at present such programs can only perform thermal conductivity calculations on single material thermal components. However, the walls between some compartments within the containment are constructed of multiple layers of material, and existing procedures are not capable of conducting heat calculations to distributed multiple layer material thermal components.
Disclosure of Invention
In order to fill the blank of the research, the invention provides a distributed multi-layer material thermal component node division and heat conduction calculation method in a containment, which can accurately calculate the heat conduction condition of a multi-layer material wall in the containment and has important significance for analyzing physical phenomena and transient response in a pressurized water reactor containment compartment.
The wall body heat conduction condition formed by multiple layers of materials in the containment can be accurately calculated.
In order to achieve the above purpose, the invention adopts the following technical scheme: the distributed multi-layer material thermal component node division and heat conduction calculation method in the containment comprises the following steps:
step 1: specifying the total material layer number N and critical thermal conductivity k of the multi-layer material thermal component 0 Thickness x of each layer of material i Thermal conductivity k i Density ρ i Specific heat capacity c i ；
Step 2: node division is carried out on the material of the ith layer: when the thermal conductivity k of the material of the ith layer i ＞k 0 When the material layer is divided into uniform nodes in the step 3; when the thermal conductivity k of the material of the ith layer i ≤k 0 When the non-uniform nodes are divided for the layer of material in step 4;
step 3: the method for dividing the uniform nodes comprises the following steps:
calculating node thickness Δx ij ：
Δx i -node thickness;
x i -material thickness;
n i -customizing the number of nodes;
step 4: the non-uniform nodes are divided by the following specific method:
calculating the thickness of the fine node and the coarse node:
1) Fine node thickness:
Δx i,f -fine node thickness;
Δt-the time step;
a i -thermal diffusivity of the material;
ρ i -material density;
c i -specific heat capacity of the material;
2) Rough node thickness:
Δx i,c -rough node thickness;
n i,f -customizing the number of fine nodes;
n i,c -customizing the number of coarse nodes;
3) Comparing the fine node thickness Deltax i,c And a rough node thickness Deltax i,f ：
If Deltax i,f ＞Δx i,c Jumping to 4), and updating the thickness of the rough node; otherwise, jump to 5);
4) Reducing self-emissionDefining the number n of rough nodes i,c Up to Deltax i,f ≤Δx i,c ；
5) Calculating the number n of material nodes of the ith layer i ：
n i ＝n i,f +n i,c
Step 5: judging whether all materials finish node division; if yes, go to step 6, otherwise go to step 2;
step 6: calculating the total number n of the thermal member nodes of the multilayer material:
n-total number of multi-layer material thermal component nodes;
step 7: initializing the temperature of each node;
step 8: the temperature of each node of the multi-layer material thermal component is solved by utilizing a one-dimensional heat conduction equation without a heat source, and the specific method is as follows:
1) The internal nodes, namely No. 2 to No. n-1 nodes, the finite difference format of the one-dimensional heat conduction equation is as follows:
ρ j -node material density number j;
c j -the specific heat capacity of the j-th node material;
Δx j -node j thickness;
Δt-the time step;
T j -node temperature at j at the end of the time step;
T j 0 -the temperature of the j-th node at the beginning of the time step;
T j-1 -node temperature at the end of the time step j-1;
T j+1 -node temperature at j+1 at the end of the time step;
R j -j thThermal resistance between the number node and the j-1 node;
R j+1 -thermal resistance between the j-th node and the j+1-th node;
Δx j-1 -node thickness j-1;
k j-1 -thermal conductivity of the j-1 th node material;
Δx j -node j thickness;
k j -thermal conductivity of the j-th node material;
R gap,j-1,j -a gap thermal resistance between the j-1 node and the j node; if the materials of the j-th node and the j-1-th node are the same, the node is 0;
Δx j -node j thickness;
k j -thermal conductivity of the j-th node material;
Δx j+1 -node thickness j+1;
k j+1 -thermal conductivity of the j+1st node material;
R gap,j,j+1 -a gap thermal resistance between the j-th node and the j+1-th node; if the materials of the j-th node and the j-1-th node are the same, the node is 0;
2) Boundary nodes, namely node 1 and node n, have the finite difference format:
node 1:
ρ 1 -node material density No. 1;
c 1 -specific heat capacity of the No. 1 node material;
Δx 1 node number 1 thickness;
Δt-the time step;
T 1 -node temperature number 1 at the end of the time step;
T 1 0 -the time step initial node number 1 temperature;
T 2 -node number 2 temperature at the end of the time step;
h 1 -the convective heat transfer coefficient of the thermal member and the fluid;
T ∞,1 -fluid temperature at the thermal member;
R 1 -a thermal resistance between node 1 and node 2, 0 if the materials of node 1 and node 2 are the same;
Δx 1 node number 1 thickness;
Δx 2 node number 2 thickness;
k 1 -thermal conductivity of the No. 1 node material;
k 2 -thermal conductivity of the No. 2 node material;
similarly calculating an nth node;
and obtaining the temperature of each node of the multi-layer material thermal component by solving the one-dimensional heat conduction equation.
Compared with the prior art, the invention has the following advantages:
1) The nodes can be divided for distributed multi-layer material thermal components in the containment;
2) The heat conduction calculation of the multi-layer material thermal component is realized by adding gap thermal resistance between nodes of different materials, so that the temperature of each node is solved;
3) The node division scheme and the calculation model are independent, the method has strong universality, and can be suitable for multi-node containment thermodynamic and hydraulic analysis programs of different types;
4) The invention can accurately simulate the unsteady state heat conduction of the distributed multilayer material thermal component and provide more accurate calculation data for engineering design.
Drawings
FIG. 1 is a flow chart of a multi-layer material thermal component node division and thermal conduction calculation;
FIG. 2 is a schematic diagram of a multi-layer material thermal member;
FIG. 3 is a schematic illustration of a uniform division of nodes by thermal means;
FIG. 4 is a schematic diagram of a non-uniform division of nodes by thermal means.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
The invention relates to a distributed multi-layer material thermal component node dividing and heat conduction calculating method in a containment, and fig. 1 is a flow chart of the invention, comprising the following steps:
step 1: FIG. 2 is a schematic view of a thermal component of a multilayer material, with different textures representing different materials, and the number of layers N of the thermal component material being 4, the critical thermal conductivity k being specified 0 Thickness x of each layer of material i Thermal conductivity k i Density ρ i Specific heat capacity c i ；
Step 2: node division is carried out on the material of the ith layer: when the thermal conductivity k of the material of the ith layer i ＞k 0 When the material layer is divided into uniform nodes in the step 3; when the thermal conductivity k of the material of the ith layer i ≤k 0 When the non-uniform nodes are divided for the layer of material in step 4;
step 3: FIG. 3 is a schematic diagram of uniform node partitioning for a thermal component, with a custom node number n i 9, the specific dividing method is as follows:
calculating node thickness Δx ij ：
Δx i -node thickness;
x i -material thickness;
n i -customizing the number of nodes;
step 4: FIG. 4 is a schematic diagram of non-uniform node partitioning of a hot component, with custom fine nodes n i,f And custom rough node number n i,c 9, and the specific dividing method is as follows:
calculating the thickness of the fine node and the coarse node:
1) Fine node thickness:
Δx i,f -fine node thickness;
Δt-the time step;
a i -thermal diffusivity of the material;
ρ i -material density;
c i -specific heat capacity of the material;
2) Rough node thickness:
Δx i,c -rough node thickness;
n i,f -customizing the number of fine nodes;
n i,c -customizing the number of coarse nodes;
3) Comparing the fine node thickness Deltax i,c And a rough node thickness Deltax i,f ：
If Deltax i,f ＞Δx i,c Jumping to 4), and updating the thickness of the rough node; otherwise, jump to 5);
4) Reducing custom rough node number n i,c Up to Deltax i,f ≤Δx i,c ；
5) Calculating the number n of material nodes of the ith layer i ：
n i ＝n i,f +n i,c
Step 5: node division is carried out on the next layer of material, and the division sequence is divided from left to right in sequence; for the thermal component in fig. 2, the division sequence is material 1, material 2, material 3, and material 4; judging whether all materials finish node division; if yes, go to step 6, otherwise go to step 2;
step 6: calculating the total number n of the thermal member nodes of the multilayer material:
n-total number of multi-layer material thermal component nodes;
step 7: initializing the temperature of each node;
step 8: the heat component is simplified into a one-dimensional infinite plate, and the temperature of each node of the multi-layer material heat component can be rapidly solved by utilizing a one-dimensional heat conduction equation without a heat source, and the specific method is as follows:
1) The internal nodes, namely No. 2 to No. n-1 nodes, the one-dimensional heat conduction equation adopts a central differential format, and the method specifically comprises the following steps:
ρ j -node material density number j;
c j -the specific heat capacity of the j-th node material;
Δx j -node j thickness;
Δt-the time step;
T j -node temperature at j at the end of the time step;
T j 0 -the temperature of the j-th node at the beginning of the time step;
T j-1 ——the temperature of the j-1 node at the end of the time step;
T j+1 -node temperature at j+1 at the end of the time step;
R j -thermal resistance between the j-th node and the j-1-th node;
R j+1 -thermal resistance between the j-th node and the j+1-th node;
Δx j-1 -node thickness j-1;
k j-1 -thermal conductivity of the j-1 th node material;
Δx j -node j thickness;
k j -thermal conductivity of the j-th node material;
R gap,j-1,j -a gap thermal resistance between the j-1 node and the j node; if the materials of the j-th node and the j-1-th node are the same, the node is 0;
Δx j -node j thickness;
k j -thermal conductivity of the j-th node material;
Δx j+1 -node thickness j+1;
k j+1 -thermal conductivity of the j+1st node material;
R gap,j,j+1 -a gap thermal resistance between the j-th node and the j+1-th node; if the materials of the j-th node and the j-1-th node are the same, the node is 0;
2) Boundary nodes, namely node 1 and node n, have the finite difference format:
node 1:
ρ 1 -node material density No. 1;
c 1 -specific heat capacity of the No. 1 node material;
Δx 1 node number 1 thickness;
Δt-the time step;
T 1 -node temperature number 1 at the end of the time step;
T 1 0 -the time step initial node number 1 temperature;
T 2 -node number 2 temperature at the end of the time step;
h 1 -the convective heat transfer coefficient of the thermal member and the fluid;
T ∞,1 -fluid temperature at the thermal member;
R 1 -a thermal resistance between node 1 and node 2, 0 if the materials of node 1 and node 2 are the same;
Δx 1 node number 1 thickness;
Δx 2 node number 2 thickness;
k 1 -thermal conductivity of the No. 1 node material;
k 2 -thermal conductivity of the No. 2 node material;
similarly calculating an nth node;
and obtaining the temperature of each node of the multi-layer material thermal component by solving the one-dimensional heat conduction equation.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (1)
1. A distributed multi-layer material thermal component node dividing and heat conduction calculating method in a containment is characterized in that: the method comprises the following steps:
step 1: specifying the total material layer number N and critical thermal conductivity k of the multi-layer material thermal component 0 Thickness x of each layer of material i Thermal conductivity k i Density ρ i Specific heat capacity c i ；
Step 2: node division is carried out on the material of the ith layer: when the thermal conductivity k of the material of the ith layer i ＞k 0 When the material layer is divided into uniform nodes in the step 3; when the thermal conductivity k of the material of the ith layer i ≤k 0 When the non-uniform nodes are divided for the layer of material in step 4;
step 3: the method for dividing the uniform nodes comprises the following steps:
calculating node thickness Δx ij ：
Wherein:
Δx i -node thickness;
x i -material thickness;
n i -customizing the number of nodes;
step 4: the non-uniform nodes are divided by the following specific method:
calculating the thickness of the fine node and the coarse node:
1) Fine node thickness:
wherein:
Δx i,f -fine node thickness;
Δt-the time step;
a i -thermal diffusivity of the material;
ρ i -material density;
c i -specific heat capacity of the material;
2) Rough node thickness:
wherein:
Δx i,c -rough node thickness;
n i,f -customizing the number of fine nodes;
n i,c -customizing the number of coarse nodes;
3) Comparing the fine node thickness Deltax i,c And a rough node thickness Deltax i,f ：
If Deltax i,f ＞Δx i,c Jumping to 4), and updating the thickness of the rough node; otherwise, jump to 5);
4) Reducing custom rough node number n i,c Up to Deltax i,f ≤Δx i,c ；
5) Calculating the number n of material nodes of the ith layer i ：
n i ＝n i,f +n i,c
Step 5: judging whether all materials finish node division; if yes, go to step 6, otherwise go to step 2;
step 6: calculating the total number n of the thermal member nodes of the multilayer material:
wherein:
n-total number of multi-layer material thermal component nodes;
step 7: initializing the temperature of each node;
step 8: the temperature of each node of the multi-layer material thermal component is solved by utilizing a one-dimensional heat conduction equation without a heat source, and the specific method is as follows:
1) The internal nodes, namely No. 2 to No. n-1 nodes, the finite difference format of the one-dimensional heat conduction equation is as follows:
wherein:
ρ j -node material density number j;
c j -the specific heat capacity of the j-th node material;
Δx j -node j thickness;
Δt-the time step;
T j -node temperature at j at the end of the time step;
T j-1 -node temperature at the end of the time step j-1;
T j+1 -node temperature at j+1 at the end of the time step;
R j -thermal resistance between the j-th node and the j-1-th node;
R j+1 -thermal resistance between the j-th node and the j+1-th node;
wherein:
Δx j-1 -node thickness j-1;
k j-1 -thermal conductivity of the j-1 th node material;
Δx j -node j thickness;
k j -thermal conductivity of the j-th node material;
R gap,j-1,j -a gap thermal resistance between the j-1 node and the j node; if the materials of the j-th node and the j-1-th node are the same, the node is 0;
wherein:
Δx j -node j thickness;
k j -thermal conductivity of the j-th node material;
Δx j+1 -node thickness j+1;
k j+1 -thermal conductivity of the j+1st node material;
R gap,j,j+1 -a gap thermal resistance between the j-th node and the j+1-th node; if the materials of the j-th node and the j-1-th node are the same, the node is 0;
2) Boundary nodes, namely node 1 and node n, have the finite difference format:
node 1:
wherein:
ρ 1 -node material density No. 1;
c 1 -specific heat capacity of the No. 1 node material;
Δx 1 node number 1 thickness;
Δt-the time step;
T 1 -node temperature number 1 at the end of the time step;
T 1 0 -the time step initial node number 1 temperature;
T 2 -node number 2 temperature at the end of the time step;
h 1 -the convective heat transfer coefficient of the thermal member and the fluid;
T ∞,1 -fluid temperature at the thermal member;
R 1 -a thermal resistance between node 1 and node 2, 0 if the materials of node 1 and node 2 are the same;
wherein:
Δx 1 node number 1 thickness;
Δx 2 node number 2 thickness;
k 1 -thermal conductivity of the No. 1 node material;
k 2 -thermal conductivity of the No. 2 node material;
similarly calculating an nth node;
and obtaining the temperature of each node of the multi-layer material thermal component by solving the one-dimensional heat conduction equation.
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| WO2022147978A1 (en) * | 2021-01-08 | 2022-07-14 | 深圳中广核工程设计有限公司 | Straight pipeline inner wall surface temperature measurement and transient identification method and computer terminal |
| CN114547790A (en) * | 2022-01-17 | 2022-05-27 | 西北工业大学 | Calculation method for evaluating heat insulation performance of complex multi-layer thermal protection structure |
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