軽水炉サブチャンネル解析法と限界熱流束予測手法の開発

概要

軽水炉サブチャンネル解析法と限界熱流束予測手法の開発

淀 忠勝

目

次

NOMENCLATURE
LIST OF TABLES
LIST OF FIGURES

1章

序論 ................................................................................................................................... 1

1.1.

背景................................................................................................................................ 1

1.2.

軽水炉プラントの熱水力設計 .................................................................................... 5

1.2.1.

サブチャンネル解析コード ................................................................................ 6

1.2.2.

CHF 相関式 ........................................................................................................... 8

1.3.

本研究の目的及び本論文の構成 ................................................................................ 8

1 章の参考文献 .......................................................................................................................... 19
2章

炉心解析用二流体サブチャンネル解析コードの開発.............................................. 22

2.1.

緒言.............................................................................................................................. 22

2.2.

理論モデル.................................................................................................................. 23

2.2.1.

理論概要 .............................................................................................................. 23

2.2.2.

熱水力モデルの基礎式 ...................................................................................... 23

2.2.3.

熱水力モデルの構成式 ...................................................................................... 26

2.2.4.

離散化及び数値解法 .......................................................................................... 51

2.2.5.

燃料棒モデル ...................................................................................................... 52

2.3.

妥当性確認.................................................................................................................. 54

2.3.1.

NUPEC/PSBT 試験解析 ..................................................................................... 54

2.3.2.

ORNL/THTF 試験解析 ....................................................................................... 55

2.4.

結論.............................................................................................................................. 56

2 章の参考文献 .......................................................................................................................... 90
3章

DNB 型機構論モデルベース相関式の開発 ................................................................ 93

3.1.

緒言.............................................................................................................................. 93

3.2.

CHF データベース範囲 ............................................................................................. 96

3.3.

LSD モデルに基づく定式化 ..................................................................................... 97

3.3.1.

LSD モデルの概要 ............................................................................................. 97

3.3.2.

LSD モデルの簡略式の開発 ............................................................................. 99

3.4.

機構論モデルに基づく相関式の評価 .................................................................... 106

3.4.1.

LUT との比較 ................................................................................................... 106

3.4.2.

既存 CHF 予測手法との比較 .......................................................................... 107

3.5.

結論............................................................................................................................ 110

3 章の参考文献 ........................................................................................................................ 151
4章

ドライアウト型機構論モデルベース相関式の開発................................................ 154

4.1.

緒言............................................................................................................................ 154

4.2.

AFD モデル............................................................................................................... 156

4.2.1.

環状流長さ ........................................................................................................ 156

4.2.2.

液滴付着率 ........................................................................................................ 157

4.2.3.

液滴発生率 ........................................................................................................ 158

4.2.4.

環状流開始点のエントレインメント率 ........................................................ 160

4.3.

機構論ベース相関式の開発 .................................................................................... 161

4.3.1.

AFD モデルによる相関式の導出 ................................................................... 161

4.3.2.

無次元相関式𝜓𝜓の開発 ..................................................................................... 163

4.3.3.

CHF 相関式 ....................................................................................................... 165

4.4.

機構論モデルベース相関式の検証 ........................................................................ 165

4.5.

結論............................................................................................................................ 167

4 章の参考文献 ........................................................................................................................ 190
5章

結論 ............................................................................................................................... 193

5.1.

本研究による成果の統括........................................................................................ 193

5.2.

今後の研究課題と展望............................................................................................ 195

出版物一覧
謝辞

NOMENCLATURE

𝐴𝐴

Area [m2]

𝐶𝐶

Droplet concentration in the gas core [kg/m3]

𝐷𝐷

Tube diameter [m]

𝑎𝑎𝑖𝑖

𝐵𝐵𝐵𝐵
𝐶𝐶𝑏𝑏

𝐶𝐶𝑝𝑝𝑝𝑝
𝐷𝐷𝑒𝑒

Interfacial area concentration [1/m]
Boiling number, 𝑞𝑞𝐶𝐶𝐶𝐶𝐶𝐶 /𝐺𝐺ℎ𝑓𝑓𝑓𝑓 [-]
Boron concentration [-]

Liquid-phase heat capacity [kJ/K]
Hydraulic equivalent diameter [m]

𝐷𝐷𝑟𝑟𝑟𝑟𝑟𝑟

Fuel rod diameter [m]

𝐸𝐸

Entrainment [-]

𝐷𝐷𝐷𝐷𝐷𝐷𝑅𝑅𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

𝐹𝐹𝐾𝐾
𝑓𝑓

DNB limits based on 95% confidence level and 95% probability,
1/(𝜇𝜇(𝑅𝑅/𝑃𝑃) − 𝐹𝐹𝐾𝐾 𝜎𝜎(𝑅𝑅/𝑃𝑃)) [-]

Owen’s K factor [-]
Friction factor [-]

2

𝐺𝐺
g

Mass velocity [kg/m s]
Gravitational acceleration [m/s2]

ℎ

Enthalpy [kJ/kg]

ℎ𝑖𝑖𝑖𝑖

Inlet enthalpy [kJ/kg]

𝐻𝐻𝑖𝑖

ℎ𝐹𝐹𝐹𝐹
ℎ𝑓𝑓𝑓𝑓

𝑗𝑗

Interfacial heat transfer coefficient [kW/m3K]
Forced convection heat transfer coefficient [kW/m2K]
Latent heat of vaporization [kJ/kg]
Superficial velocity [m/s]

𝐾𝐾

Coefficient between vapor blanket velocity and local mixture velocity

𝑘𝑘𝑙𝑙

Liquid-phase thermal conductivity [kW/mK]

assuming turbulent boundary layer [-]

𝑘𝑘

Droplet mass transfer coefficient [m/s]

𝐿𝐿𝐿𝐿

Laplace number, 𝜌𝜌𝑙𝑙 𝐷𝐷𝐷𝐷/𝜇𝜇𝑙𝑙2 [-]

𝐿𝐿𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝ℎ

Length between fuel rods [m]

𝐿𝐿

𝐿𝐿𝑎𝑎𝑎𝑎𝑎𝑎

𝐿𝐿𝑏𝑏
𝑚𝑚

𝑁𝑁𝑟𝑟𝑟𝑟𝑟𝑟

Heated length [m]
Length of the annular flow region [m]
Vapor blanket length [m]

Droplet mass transfer rate [kg/m2s]
Rod number between flow areas [-]

𝑃𝑃

Pressure [MPa]

𝑞𝑞𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾

Referenced CHF of Katto mechanistic model [kW/m ]

2

𝑞𝑞𝐵𝐵

Fraction of heat flux for boiling [kW/m ]

𝑞𝑞𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽

Referenced CHF of Jiao mechanistic model [kW/m ]

𝑞𝑞𝐶𝐶𝐶𝐶𝐶𝐶
𝑞𝑞𝑝𝑝𝑝𝑝𝑝𝑝

𝑞𝑞𝐿𝐿𝐿𝐿𝐿𝐿
𝑅𝑅/𝑃𝑃

2

Critical heat flux (CHF) [kW/m ]

2

2

2

Predicted CHF [kW/m ]
2

CHF of Groeneveld's CHF look-up tables [kW/m ]
Ratio of predicted CHF to referenced CHF [-]

𝑅𝑅𝑅𝑅

Reynolds number, 𝐺𝐺𝐷𝐷/𝜇𝜇𝑙𝑙 [-]

𝑅𝑅𝑒𝑒𝑚𝑚

Reynolds number of homogeneous flow in subcooled flow,

𝑅𝑅𝑒𝑒𝑗𝑗𝑗𝑗

𝑅𝑅𝑒𝑒𝑙𝑙

Liquid-Phase Reynolds number in annular flow, 𝜌𝜌𝑙𝑙 𝑗𝑗𝑙𝑙 𝐷𝐷/𝜇𝜇𝑙𝑙 [-]

Liquid-Phase Reynolds number in subcooled flow, 𝐺𝐺𝐺𝐺/𝜇𝜇𝑙𝑙 [-]
𝐺𝐺𝐺𝐺/(𝜇𝜇𝑔𝑔 𝛼𝛼 + 𝜇𝜇𝑙𝑙 (1 − 𝛼𝛼(1 + 2.5𝛼𝛼))) [-]

𝑆𝑆𝐷𝐷′′′

Mass exchange rate [kg/m3s]

′′′
𝑆𝑆𝑀𝑀

Momentum exchange rate [kg/m2s]

𝑢𝑢𝑏𝑏∗

Dimensionless vapor blanket velocity, 𝜇𝜇𝑙𝑙 𝑢𝑢𝑏𝑏 /𝜎𝜎 [-]

𝑆𝑆𝐵𝐵′′′

Boron exchange rate [kg/m3s]

𝑢𝑢

Fluid velocity for x direction [m/s] (Chapter 2)

𝑆𝑆𝐻𝐻′′′

Energy exchange rate [kW/m3]

𝑢𝑢

Velocity for z direction [m/s] (Chapter 3 and 4)

𝑣𝑣

𝑤𝑤

Fluid velocity for y direction [m/s] (Chapter 2)
Fluid velocity for z direction [m/s] (Chapter 2)

𝑊𝑊𝑊𝑊

Weber number, 𝐺𝐺 2 𝐷𝐷/𝜌𝜌𝑙𝑙 𝜎𝜎 [-]

𝑥𝑥

Quality [-]

𝑥𝑥𝑠𝑠

Static quality [-]

𝑊𝑊𝑒𝑒𝑔𝑔𝑔𝑔

Thermal equilibrium quality [-]

𝑥𝑥𝑒𝑒

Flow quality [-]

𝑥𝑥𝑓𝑓

𝑧𝑧

Axial coordinate
Greek symbols

𝛼𝛼

Void fraction [-]

𝛿𝛿𝑙𝑙𝑙𝑙

Liquid film thickness in annular flow [m]

𝛤𝛤 ′′′

𝛿𝛿𝑠𝑠𝑠𝑠𝑠𝑠

1/3

Gas core Weber number, 𝜌𝜌𝑔𝑔 𝑗𝑗𝑔𝑔2 𝐷𝐷/𝜎𝜎�(𝜌𝜌𝑙𝑙 − 𝜌𝜌𝑔𝑔 )/𝜌𝜌𝑔𝑔 �

Vapor generation rate [kg/m3s]
Sublayer thickness in subcooled flow [m]

[-]

𝜇𝜇

Viscosity [Pa・s]

𝜏𝜏𝑖𝑖′′′

Interfacial friction [kg/m2s2]

Φ𝐿𝐿2

Two phase friction factor [-]

𝜌𝜌

Density [kg/m3]

𝜏𝜏𝑤𝑤

Wall shear stress [Pa]

Surface tension [N/m]

𝜎𝜎

′′′
𝜏𝜏𝑤𝑤

𝜓𝜓

Wall friction [kg/m2s2]
Dimensionless number for the integrated value of liquid film thickness [-]

Subscripts

𝑏𝑏

Vapor blanket

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

Critical

𝑒𝑒𝑒𝑒

Entrainment due to interfacial shear force

𝑑𝑑
𝑒𝑒

𝑒𝑒𝑒𝑒

𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

𝑔𝑔

𝑔𝑔𝑔𝑔

𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓

𝑖𝑖

𝑖𝑖𝑖𝑖

𝑙𝑙

𝑙𝑙𝑙𝑙

𝑙𝑙𝑙𝑙𝑙𝑙

𝑚𝑚

𝑀𝑀𝑀𝑀𝑀𝑀

𝑜𝑜

𝑜𝑜𝑜𝑜𝑜𝑜
𝑠𝑠𝑠𝑠𝑠𝑠

Deposition
Entrainment
Entrainment due to boiling
Outlet
Vapor
Gas core
Friction
Interfacial
Inlet
Liquid
Liquid film
Limit
Homogeneous flow
Turbulent mixing
Onset of the annular region
Outlet of the tube
Saturated

𝑆𝑆𝑆𝑆𝑆𝑆

Subcooled liquid

𝑆𝑆𝑆𝑆𝑆𝑆

Superheated vapor

𝑆𝑆𝑆𝑆𝑆𝑆

𝑆𝑆𝑆𝑆𝑆𝑆
𝑠𝑠𝑠𝑠𝑠𝑠

𝑇𝑇𝑇𝑇

Subcooled vapor
Superheated liquid
Subcooled
Two phases

𝑣𝑣

𝑉𝑉𝑉𝑉

𝑤𝑤

+

Vaporization
Void drift
Wall
Dimensionless

LIST OF TABLES

Table 1-1. Representative sub-channel analysis codes ................................................................ 12
Table 2-1. Applicable range of MG-S correlation ....................................................................... 58
Table 2-2. Constitutive models for fluid thermal-hydraulic analysis .......................................... 59
Table 2-3. ...

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