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temp-gen and sigmas

master
gtheler 5 роки тому
джерело
коміт
6ffac2ad86
12 змінених файлів з 5918 додано та 1800 видалено
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      nafems4.md
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      sigmas-scl1.pdf
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      sigmas-scl1.svg
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      sigmas-scl2.pdf
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      sigmas-scl2.svg
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      sigmas-scl3.pdf
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      sigmas-scl4.pdf
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      sigmas-scl4.svg
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      temp-valve-commented.svg
  11. BIN
      temperature-generalization.png
  12. BIN
      thermal-dist.png

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nafems4.md Переглянути файл

@@ -477,7 +477,7 @@ We can then merge this idea by Asimov with an adapted version of the [Saint-Vena
2. assume the part of the full system which is not contained in this reduced mesh has an uniform (though not constant in time) temperature as if the reduced model was extended in each direction.


Instead of solving the transient heat-conduction problem on the full 200k-nodes mesh of [@fig:cad-figure], we solve in on a reduced model consisting of half the valve body a small length of the pipes at both the valve inlet and outlet as shown in [@fig:valve-mesh], which has 30k nodes. Once the temperature distribution\ $\hat{T}(\mathbf{x},t)$ for each time is obtained in the reduced mesh ([@fig:valve-temp]), the actual temperature distribution\ $T(\mathbf{x},t)$ is computed by an algebraic generalisation of $\hat{T}(\mathbf{x},t)$ in the full mesh of [@fig:mech]. Those locations which are not covered by the reduced model are generalised with a time-dependent uniform temperature which is the mean value of the temperature at the inlet and outlet of the reduced mesh, marked as “end faces” in\ [@fig:valve-temp]. It can also be seen there that since the nozzle made of carbon steel has a larger thermal conductivity the temperature is almost uniform whilst there is a non-trivial temperature distribution within then adjacent stainless steel valve body. Indeed, [@fig:temp-zoom] shows how the temperature at SCLs\ #2 and\ #4 evolve as a function of time during the ramp of transient #1. It is this difference one of the main reasons for the need to perform fatigue analysis of critical piping systems in a nuclear power plant.
Instead of solving the transient heat-conduction problem on the full 200k-nodes mesh of [@fig:cad-figure], we solve in on a reduced model consisting of half the valve body a small length of the pipes at both the valve inlet and outlet as shown in [@fig:valve-mesh], which has 30k nodes. Once the temperature distribution\ $\hat{T}(\mathbf{x},t)$ for each time is obtained in the reduced mesh ([@fig:valve-temp]), the actual temperature distribution\ $T(\mathbf{x},t)$ is computed by an algebraic generalisation of $\hat{T}(\mathbf{x},t)$ in the full mesh of [@fig:mech], as shown in [@fig:temp-generalization]. Those locations which are not covered by the reduced model are generalised with a time-dependent uniform temperature which is the mean value of the temperature at the inlet and outlet of the reduced mesh, marked as “end faces” in\ [@fig:valve-temp]. It can also be seen there that since the nozzle made of carbon steel has a larger thermal conductivity the temperature is almost uniform whilst there is a non-trivial temperature distribution within then adjacent stainless steel valve body. Indeed, [@fig:temp-zoom] shows how the temperature at SCLs\ #2 and\ #4 evolve as a function of time during the ramp of transient #1. It is this difference one of the main reasons for the need to perform fatigue analysis of critical piping systems in a nuclear power plant.

::::: {#fig:valve}
![Mesh with 30k nodes and 120k first-order tetrahedra.](thermal-mesh.png){#fig:valve-mesh width=100%}
@@ -487,6 +487,8 @@ Instead of solving the transient heat-conduction problem on the full 200k-nodes
Reduced mesh around the valve including the carbon-steel nozzle.
:::::

![Generalization of the temperature distribution from [@fig:valve-temp] to [@fig:mech].](temperature-generalization.png){#fig:temp-generalization width=100%}

![Temperature evolution at the SCLs for transient #1.](temp-zoom.svg){#fig:temp-zoom width=100%}


@@ -1035,7 +1037,7 @@ Finally we attempt to “break” the pipes successively solving many steady-sta

![SCL #4](sigmas-scl4.svg){#fig:sigmas-scl4}

Primary stresses at the internal points of two SCLs for the “break” step.
Juxtaposition of the principal stresses at the inner points of two SCLs.
::::

1. The material properties are temperature-dependent (we use data from [ASME\ II](https://en.wikipedia.org/wiki/ASME_Boiler_and_Pressure_Vessel_Code#ASME_BPVC_Section_II_-_Materials) part\ D).

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sigmas-scl1.pdf Переглянути файл


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sigmas-scl1.svg
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sigmas-scl2.pdf Переглянути файл


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sigmas-scl2.svg
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sigmas-scl3.pdf Переглянути файл


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sigmas-scl3.svg Переглянути файл

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