JP2005083842A - Void rate of boiling water reactor - Google Patents

Void rate of boiling water reactor Download PDF

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JP2005083842A
JP2005083842A JP2003314910A JP2003314910A JP2005083842A JP 2005083842 A JP2005083842 A JP 2005083842A JP 2003314910 A JP2003314910 A JP 2003314910A JP 2003314910 A JP2003314910 A JP 2003314910A JP 2005083842 A JP2005083842 A JP 2005083842A
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JP4323901B2 (en
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Toshihisa Shirakawa
白川利久
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Abstract

<P>PROBLEM TO BE SOLVED: To propose a new correlation expression of a void rate α on a steam content χ in a nuclear power plant with a boiling water reactor. <P>SOLUTION: A new correlation expression of the void rate α on the steam content χ is formulated. An expression to pronouncedly find the speeds of saturated steam and saturated water in the domain where χ is 0 to 1.0 is also formulated. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

本発明は特に沸騰水型原子炉のボイド率の相関式に関する。   The present invention particularly relates to a correlation formula of the void fraction of a boiling water reactor.

沸騰水型原子炉は、原子炉内の核燃料で発生した熱を冷却材である水に伝達し原子炉内で液体の水を沸騰させ蒸気を発生する。蒸気はタービンに導かれ電気を発生する。沸騰水型原子炉を中核とした沸騰水型原子力発電所は、火力発電所同様に多くの機器系統から構成されている。運転には多くの計測、制御装置が必要である。大量のデータを効率的に取り扱う計算機が広く利用されている。
図１は沸騰水型原子力発電所における従来の計算機の主要な性能計算項目である。計測値を元にして、プラント性能計算と炉心性能計算を実施し表示、記録する。
プラント性能計算は、火力発電所で計算されているものと類似している。給水加熱器性能等の原子力発電所を構成している諸機器の性能、熱収支等の計算を実施し表示、記録する。
炉心性能計算は、原子炉運転を安全に管理するために原子炉熱出力等を計算し表示、記録する。核燃料であるウランやプルトニウムの中性子との反応は中性子の速度によって変わり、中性子の速度は減速材である水の量により変わる。沸騰水型原子炉では図２に示すように核燃料を内包する核燃料棒（１）の下部から流入した液体の水（１１）は核燃料棒（１）の上部の冷却材出口に行くにつれ核燃料から熱を受けて液体の一部は蒸気（１２）になる。液体である水（１１）と気体である蒸気（１２）が共存して流れている二相流の流路断面における単位高さ当たりの（蒸気が占める面積）÷（蒸気と液体である水が占める流路断面積）をボイド率と呼びαと表されている。ボイド率αは核燃料棒（１）の下部ではゼロであり核燃料棒（１）の上部では７０％にもなり、高さｚが増加するにつれ大きくなるからボイド率分布α(z)を持っている。ボイド率の違いは水の量の違いであるから核燃料と中性子との反応の結果生じる出力に変化をもたらし、逆に出力の変化はボイド率に違いをもたらす。冷却材流量が多く冷却材出口側も水だけであれば、上下端からの中性子漏洩により出力Pの高さｚに関する出力分布P(z)は中央が最大になる上下対称なコサイン分布状である。しかし、冷却材入口側である核燃料棒（１）の下部ではボイド率がゼロであるため核燃料の反応が活発であるが、冷却材出口側である核燃料棒（１）の上部ではボイド率が高いため核燃料の反応が不活発である。したがって、出力分布P(z)の最大は核燃料棒（１）の中央から下方に移動する。核燃料棒最高温度は当然核燃料棒（１）の下方で生じる。
このような挙動をする原子炉の運転では、核燃料棒最高温度等が設定値と比べて余裕があることを確認しながら運転する必要がある。また経済的な原子炉を設計するには、核燃料棒最高温度等の安全性にかかわる値が設定値内で、炉心の大きさをできるだけ小さくすることが必要である。そのためには、炉心内出力分布を平坦化して、最大出力と平均出力の比を小さくするようにする必要がある。
このように炉心全体でボイド率に分布の存在する沸騰水型原子炉では、ボイド率分布α(z)と出力分布P(z)の計算は取分け重要である。
図3は従来の計算機に内蔵されている従来のボイド率式を組み込んだソフトウエアを示すフローチャートである。
ステップ１
二相流の全質量流量GTは冷却材循環ポンプ性能等により決まる一定の値とし、高さゼロからの総熱出力Qを一定の値とする。出力分布はどの高さｚでも一定と仮定する。
ステップ２
高さzでの出力分布P0(z)が求まる。
ステップ３
高さzでの熱出力分布ｑ(z)=Q×P0(z) が求まる。
ステップ４
二相流の流路断面に含まれる蒸気流量を表す蒸気含有率χの高さｚでの蒸気含有率分布χ(z)は、水が下部から高さｚ迄流れる間に核燃料から得た全熱量にほぼ比例するからGTと熱出力分布ｑ(z)とで求まる。流路断面を通る単位時間当たり高さzでの質量流量において、飽和蒸気の質量流量Gg(z)、飽和水の質量流量Gl(z)から、流路断面を通る単位時間当たりの二相流の全質量流量GTはGT＝Gg(z)＋Gl(z)であるから、蒸気含有率はχ(z)＝Gg(z)/GTと表される。
ステップ５
χ(z)に対する従来のボイド率分布α(z)の相関式。飽和蒸気の速度Vgと飽和水の速度Vlとに差があるため、すべり比R＝Vg/Vlを実験により定め、この定数を使って、
α(z)を計算する。
ステップ６
高さｚでの核燃料の組成が決まっていると、水の組成はボイド率分布α(z)により決められるため、高さｚ位置毎の物質反応断面積が求まる。
ステップ7
拡散方程式を解いて出力分布P1(z)を計算する。
ステップ8
新たに計算された出力分布P1(z)と前回の出力分布P0(z)を比較して所定の誤差d1内でなければ、このP1(z)をP0(z)と置き換えてχ(z)を計算し再度出力分布P1(z)を計算する。新たに計算された出力分布P1(z)と前回の出力分布P0(z)を比較して所定の誤差d1内になったらそれが最終出力分布であるとする（非特許文献１）。
ステップ9
核燃料棒（１）の健全性の指標となる核燃料棒（１）の温度や限界出力比等を計算表示する。核燃料棒（１）の温度は熱伝達率から計算される。
核燃料棒（１）を多数本結束しチャンネルボックスで包囲してなる核燃料集合体（特許文献１）が多数ある場合は、ボイド率と抵抗係数との関係式等から核燃料集合体毎の圧力降下を計算し核燃料集合体毎の全質量流量を配分する繰り返し計算する部分がある。 In a boiling water reactor, heat generated by nuclear fuel in the nuclear reactor is transferred to water, which is a coolant, and liquid water is boiled in the nuclear reactor to generate steam. The steam is guided to the turbine to generate electricity. A boiling water nuclear power plant centered on a boiling water reactor is composed of many equipment systems, just like a thermal power plant. Many measurement and control devices are required for operation. Computers that efficiently handle large amounts of data are widely used.
FIG. 1 shows the main performance calculation items of a conventional computer in a boiling water nuclear power plant. Based on the measured values, plant performance calculation and core performance calculation are performed, displayed and recorded.
Plant performance calculations are similar to those calculated at thermal power plants. Calculate, display, and record the performance and heat balance of various devices that make up a nuclear power plant, such as feedwater heater performance.
In the core performance calculation, the reactor thermal output is calculated, displayed and recorded in order to safely manage the reactor operation. The reaction of nuclear fuel uranium and plutonium with neutrons depends on the neutron velocity, and the neutron velocity depends on the amount of moderator water. In the boiling water reactor, as shown in FIG. 2, the liquid water (11) flowing from the lower part of the nuclear fuel rod (1) containing the nuclear fuel is heated from the nuclear fuel as it goes to the coolant outlet at the upper part of the nuclear fuel rod (1). In response, a portion of the liquid becomes vapor (12). (Area occupied by steam) per unit height in the cross section of the two-phase flow channel in which water (11), which is liquid, and steam (12), which is gas, coexist, ÷ (water that is steam and liquid Occupied channel cross-sectional area) is called void fraction and is expressed as α. The void ratio α is zero at the lower part of the nuclear fuel rod (1), reaches 70% at the upper part of the nuclear fuel rod (1), and becomes larger as the height z increases, and has a void ratio distribution α (z). . The difference in the void ratio is the difference in the amount of water, which causes a change in the output resulting from the reaction between the nuclear fuel and the neutron, and conversely, the change in the output causes a difference in the void ratio. If the coolant flow rate is large and the coolant outlet side is only water, the power distribution P (z) related to the height z of the power P due to neutron leakage from the upper and lower ends is a vertically symmetric cosine distribution with the maximum at the center. . However, since the void ratio is zero at the lower part of the nuclear fuel rod (1) on the coolant inlet side, the nuclear fuel reaction is active, but at the upper part of the nuclear fuel rod (1) on the coolant outlet side, the void ratio is high. Therefore, the reaction of nuclear fuel is inactive. Therefore, the maximum of the power distribution P (z) moves downward from the center of the nuclear fuel rod (1). The maximum temperature of the nuclear fuel rod naturally occurs below the nuclear fuel rod (1).
In the operation of a nuclear reactor that behaves in this way, it is necessary to operate while confirming that the maximum temperature of the nuclear fuel rods has a margin compared to the set value. In order to design an economical nuclear reactor, it is necessary to make the size of the core as small as possible while the safety-related values such as the maximum nuclear fuel rod temperature are within the set values. For this purpose, it is necessary to flatten the power distribution in the core so as to reduce the ratio between the maximum power and the average power.
As described above, in the boiling water reactor in which the void ratio is distributed throughout the core, the calculation of the void ratio distribution α (z) and the power distribution P (z) is particularly important.
FIG. 3 is a flowchart showing software incorporating a conventional void ratio formula built in a conventional computer.
Step 1
The total mass flow rate GT of the two-phase flow is a constant value determined by the coolant circulation pump performance, etc., and the total heat output Q from a height of zero is a constant value. The output distribution is assumed to be constant at any height z.
Step 2
The output distribution P0 (z) at the height z is obtained.
Step 3
The heat output distribution q (z) = Q × P0 (z) at the height z is obtained.
Step 4
The vapor content distribution χ (z) at the height z of the vapor content χ, which represents the flow rate of the steam contained in the cross section of the two-phase flow, is the total obtained from the nuclear fuel while the water flows from the bottom to the height z. Since it is almost proportional to the amount of heat, it can be obtained from GT and heat output distribution q (z). Two-phase flow per unit time through the channel cross section from the mass flow rate Gg (z) of saturated steam and mass flow rate Gl (z) of saturated water at a mass flow rate at a height z per unit time through the channel cross section. Since the total mass flow rate GT is GT = Gg (z) + Gl (z), the vapor content is expressed as χ (z) = Gg (z) / GT.
Step 5
The correlation formula of the conventional void ratio distribution α (z) with respect to χ (z). Since there is a difference between the saturated steam velocity Vg and the saturated water velocity Vl, the slip ratio R = Vg / Vl is determined by experiment, and using this constant,
α (z) is calculated.
Step 6
If the composition of the nuclear fuel at the height z is determined, the composition of water is determined by the void fraction distribution α (z), and therefore the mass reaction cross section for each height z position is obtained.
Step 7
Solve the diffusion equation to calculate the output distribution P1 (z).
Step 8
If the newly calculated output distribution P1 (z) and the previous output distribution P0 (z) are not within the predetermined error d1, this P1 (z) is replaced with P0 (z) and χ (z) And the output distribution P1 (z) is calculated again. When the newly calculated output distribution P1 (z) is compared with the previous output distribution P0 (z) and falls within a predetermined error d1, it is assumed that it is the final output distribution (Non-patent Document 1).
Step 9
The temperature, limit output ratio, etc. of the nuclear fuel rod (1), which are indicators of the soundness of the nuclear fuel rod (1), are calculated and displayed. The temperature of the nuclear fuel rod (1) is calculated from the heat transfer coefficient.
If there are many nuclear fuel assemblies (Patent Document 1) in which a large number of nuclear fuel rods (1) are bundled and surrounded by a channel box, the pressure drop for each nuclear fuel assembly is calculated from the relational expression between the void ratio and the resistance coefficient. There is a part to calculate and repeatedly calculate and distribute the total mass flow rate for each nuclear fuel assembly.

ボイド率αは、蒸気含有率χと、飽和蒸気の速度Vgと飽和水の速度Vlの比であるすべり比R＝Vg/Vlと、飽和蒸気密度ρgと飽和水密度ρlの比であるM=ρg/ρlから、
α=1/( 1- R×M×(1 - 1/χ) ) (非特許文献２)
と表される。Mは運転圧力が一定であるから蒸気表から求められ、χはGTと当該位置までの総出力から求まる。しかし、すべり比Rは今までαとχに関する実験により定数を定めていた。したがって、運転状態が大きく変わりボイド率が大きくなった場合には新たな実験をしてすべり比Rを求めねば適切なボイド率αが求まらないし、式そのものが適用できるとは実証されていない。したがって、出力分布が正しく求まるとは限らない。
沸騰水型原子炉の最近の動向として、ウランとプルトニウムの混合酸化物MOX燃料を導入しようとしている。プルトニウムを有効に利用するためには中性子速度を落とさないで燃焼させるほうがよいとされている。そのために、ボイド率αが高くなるような運転を想定した原子炉が望ましいとされている。ボイド率αの適切な求め方が求められている。 The void ratio α is the ratio of the steam content χ, the ratio of the saturated steam velocity Vg to the saturated water velocity Vl, R = Vg / Vl, and the ratio of the saturated steam density ρg to the saturated water density ρl, M = From ρg / ρl,
α = 1 / (1−R × M × (1 −1 / χ)) (Non-patent Document 2)
It is expressed. M is obtained from the steam table because the operating pressure is constant, and χ is obtained from GT and the total output up to that position. However, the slip ratio R has been determined by experiments on α and χ. Therefore, if the operating conditions change greatly and the void ratio increases, a new experiment must be performed to determine the slip ratio R, and an appropriate void ratio α cannot be obtained, and it has not been proven that the formula itself can be applied. . Therefore, the output distribution is not always obtained correctly.
A recent trend in boiling water reactors is to introduce mixed oxide MOX fuel of uranium and plutonium. In order to effectively use plutonium, it is said that it is better to burn without reducing the neutron velocity. Therefore, it is considered desirable to use a nuclear reactor that assumes an operation that increases the void ratio α. There is a need for an appropriate method for obtaining the void ratio α.

上記課題に鑑み、蒸気含有率χに関するボイド率αの新たな相関式を作成した。
以下に、説明に使われる記号の一覧を示した。
ρl：飽和水密度。規定されている運転圧力と蒸気表から求まる。
ρg：飽和蒸気密度。規定されている運転圧力と蒸気表から求まる。
M：ρgとρlの比。M=ρg/ρl。
A：流路断面積。
GT：流路断面を通る単位時間当たりの二相流の全質量流量。ポンプ性能等で求まっている液体の水の流入質量流量に等しい。
Vlh：飽和水初速度。Vlh＝GT / (ρl×A）と求められる。
Vg100：二相流が蒸気１００％になった時の飽和蒸気の速度。Vg100＝Vlh / M。
Gg：飽和蒸気の質量流量。
Gl：飽和水の質量流量。
χ：蒸気含有率。χ＝Gg/GT。
α：ボイド率。流路断面を通る単位時間当たりの二相流における単位高さ当たり、（蒸気が占める面積）÷（蒸気と液体である水が占める流路断面積）。
Vg：飽和蒸気の速度。
Vl：飽和水の速度。
ｋ：飽和蒸気の速度Vgにおけるαに対するχの重み。最適値を50とする正の値。
記号一覧終了。
E1=( M-1 ) / ( k+1 ) とし、重みｋをパラメータとしてχが0から1.0の範囲で本発明のボイド率αを、
α＝ ( ( M - E1×χ×k ) - ( ( M - E1×χ×k )2 - 4×χ×E1 )1/2 ）/ ( 2×E1 )
とする。
飽和蒸気の速度Vgをαとχ両方に依存するとして、
Vg＝Vlh＋（（α＋ｋ×χ）/（ｋ＋１））×（Vg100 - Vlh）
とする。
飽和水の速度Vlを、
Vl = ( Vlh - M×Vg×α ) / ( 1 - α )
とする。αが１では無限大になるがαが0.9999程度であれば有限な値になる。
飽和蒸気の質量流量Ggと飽和水の質量流量Glを、
Gg = ρg×Vg×α×Ａ
Gl = ρl×Vl×（1-α）×A
とする。
図４は計算機に内蔵せる、本発明のボイド率式を組み込んだ本発明のソフトウエアを示すフローチャートである。図３に示す従来との違いは、計算ステップ５では以下のようにした。
E1=( M-1 ) / ( k+1 ) とし、重みｋをパラメータとしてχが0から1.0の範囲で蒸気含有率分布χ(z)から、二相流のボイド率分布α(z)を、
α(z)＝( ( M - E1×χ(z)×k ) - ( ( M - E1×χ(z)×k )2 - 4×χ(z)×E1 )1/2 ）/ ( 2×E1 )
とした。
飽和蒸気の速度分布Vg(z)を、
Vg(z)＝Vlh＋（（α(z)＋ｋ×χ(z)）/（ｋ＋１））×（Vg100-Vlh）
とした。
ステップ９では以下のようにした。最終結果のα(z)とχ(z)から、
飽和蒸気の速度分布Vg(z)を、
Vg(z)＝Vlh＋（（α(z)＋ｋ×χ(z)）/（ｋ＋１））×（Vg100-Vlh）
飽和水の速度分布Vl(z)を、
Vl(z) = ( Vlh - M×Vg(z)×α(z) ) / ( 1 - α(z) )
とした。αが１では無限大になるがαが0.9999程度であれば有限な値になる。
飽和蒸気の質量流量分布Gg(z)と飽和水の質量流量分布Gl(z)を、
Gg(z) = ρg×Vg(z)×α(z)×Ａ
Gl = ρl×Vl(z)×（1-α(z) ）×A
とした。
核燃料棒（１）の健全性の指標となる核燃料棒（１）の温度や限界出力比等は従来通りに限界出力比を表示するか、飽和水の速度分布Vl(z)と( 1 - α(z) )から変換した水膜厚さとによる実験から限界熱流束に関わる式を定め最小限界熱流束比（MCHFR）を求め表示する。核燃料棒（１）の温度は熱伝達率から計算される（非特許文献３）。
核燃料集合体が多数ある場合は従来同様圧力降下を従来通りに、α(z)と抵抗係数との関係式等から求めるか、飽和水の速度分布Vl(z)から水のみの単相流から求めることにより各核燃料集合体毎の全質量流量GTも繰り返し計算により求める。
図5は、蒸気含有率χに対する本発明のボイド率αの相関式による、重みｋをパラメータとしたボイド率αの計算結果である。k=1000は従来のボイド率の相関式ですべり比が1.0に相当する。k=50は従来の相関式ですべり比が2.0に相当する（非特許文献４）。k=0はα増加による蒸気流路断面積の増加による蒸気流動抵抗の減少により蒸気流速が速くなると想定した場合の計算結果である。
図６，７，８は上記本発明の計算式による、運転圧力が70気圧、飽和水初速度Vlhが1m/sの場合の、重みｋによる蒸気含有率χ対飽和蒸気の速度Vg、飽和水の速度Vlの挙動を示す。縦軸速度の単位はm/sである。χが大きくなればVlもVgも速くなるため除熱効果は高いように見受けられる。
図９は、図1に示す沸騰水型原子力発電所における計測値を元にした従来の計算機での主要な性能計算項目（非特許文献５）のうち、炉心性能計算を図4に示した本発明のボイド率の計算式を組み込んだ本発明のソフトウエアを内蔵した本発明の計算機の主要な性能計算項目である。
：昭61-37591、「核燃料集合体」 ：理工学社、著者三神他「核燃料管理の方法と解析」２３１頁。 ：著者三神他「核燃料管理の方法と解析」２２０頁。 ：日本機械学会「伝熱工学資料」。 ：コロナ社、赤川著「気液二相流」52頁。横軸は対数目盛。 ：オーム社、浅田他監修「原子力ハンドブック」215頁。 In view of the above problems, a new correlation formula of the void ratio α with respect to the vapor content χ was created.
Below is a list of symbols used in the explanation.
ρl: saturated water density. It is obtained from the specified operating pressure and steam table.
ρg: saturated vapor density. It is obtained from the specified operating pressure and steam table.
M: Ratio of ρg and ρl. M = ρg / ρl.
A: Channel cross-sectional area.
GT: Total mass flow rate of two-phase flow per unit time through the channel cross section. It is equal to the inflow mass flow rate of liquid water determined by pump performance.
Vlh: Initial saturated water speed. Vlh = GT / (ρl × A).
Vg100: Saturated steam velocity when the two-phase flow reaches 100% steam. Vg100 = Vlh / M.
Gg: Mass flow rate of saturated steam.
Gl: Mass flow rate of saturated water.
χ: steam content. χ = Gg / GT.
α: Void ratio. Per unit height in the two-phase flow per unit time passing through the channel cross section, (area occupied by steam) / (channel cross-sectional area occupied by vapor and liquid water).
Vg: Velocity of saturated steam.
Vl: Speed of saturated water.
k: χ weight for α at the velocity Vg of saturated steam. A positive value with an optimal value of 50.
End of symbol list.
E1 = (M-1) / (k + 1), with the weight k as a parameter, the void ratio α of the present invention in the range of χ from 0 to 1.0,
α = ((M-E1 × χ × k)-((M-E1 × χ × k) 2-4 × χ × E1) 1/2 ) / (2 × E1)
And
As the saturated vapor velocity Vg depends on both α and χ,
Vg = Vlh + ((α + k × χ) / (k + 1)) × (Vg100-Vlh)
And
Saturated water speed Vl,
Vl = (Vlh-M × Vg × α) / (1-α)
And When α is 1, it becomes infinite, but when α is about 0.9999, it becomes a finite value.
Saturated steam mass flow rate Gg and saturated water mass flow rate Gl,
Gg = ρg × Vg × α × A
Gl = ρl × Vl × (1-α) × A
And
FIG. 4 is a flowchart showing the software of the present invention incorporating the void ratio formula of the present invention, which is built into the computer. The difference from the prior art shown in FIG. 3 is as follows in calculation step 5.
E1 = (M-1) / (k + 1), with the weight k as a parameter, the vapor content distribution χ (z) in the range of χ from 0 to 1.0, and the void fraction distribution α (z) of the two-phase flow ,
α (z) = ((M-E1 × χ (z) × k)-((M-E1 × χ (z) × k) 2-4 × χ (z) × E1) 1/2 ) / (2 × E1)
It was.
Velocity distribution Vg (z) of saturated steam,
Vg (z) = Vlh + ((α (z) + k × χ (z)) / (k + 1)) × (Vg100−Vlh)
It was.
In Step 9, the following was performed. From the final result α (z) and χ (z),
Velocity distribution Vg (z) of saturated steam,
Vg (z) = Vlh + ((α (z) + k × χ (z)) / (k + 1)) × (Vg100−Vlh)
Saturated water velocity distribution Vl (z)
Vl (z) = (Vlh-M × Vg (z) × α (z)) / (1-α (z))
It was. When α is 1, it becomes infinite, but when α is about 0.9999, it becomes a finite value.
Saturated steam mass flow distribution Gg (z) and saturated water mass flow distribution Gl (z)
Gg (z) = ρg × Vg (z) × α (z) × A
Gl = ρl × Vl (z) × (1-α (z)) × A
It was.
The temperature and limit power ratio of the nuclear fuel rod (1), which is an indicator of the soundness of the nuclear fuel rod (1), is displayed as usual, or the saturated water velocity distribution Vl (z) and (1-α (z) The formula related to the critical heat flux is determined from the experiment with the water film thickness converted from), and the minimum critical heat flux ratio (MCHFR) is obtained and displayed. The temperature of the nuclear fuel rod (1) is calculated from the heat transfer coefficient (Non-Patent Document 3).
When there are a large number of nuclear fuel assemblies, the pressure drop is obtained from the relational expression between α (z) and the resistance coefficient as before, or from the saturated water velocity distribution Vl (z) from a single-phase flow of water only. By determining the total mass flow rate GT for each nuclear fuel assembly, the calculation is repeated.
FIG. 5 is a calculation result of the void ratio α using the weight k as a parameter according to the correlation formula of the void ratio α of the present invention with respect to the vapor content χ. k = 1000 is a conventional correlation formula of void fraction, and the slip ratio is equivalent to 1.0. k = 50 corresponds to a slip ratio of 2.0 in the conventional correlation equation (Non-patent Document 4). k = 0 is a calculation result when it is assumed that the steam flow velocity becomes faster due to the decrease in the steam flow resistance due to the increase in the cross-sectional area of the steam channel due to the increase in α.
6, 7, and 8 are the steam content χ by the weight k versus the saturated steam velocity Vg and the saturated water when the operating pressure is 70 atm and the saturated water initial velocity Vlh is 1 m / s according to the calculation formula of the present invention. Shows the behavior of the velocity Vl. The unit of the vertical axis velocity is m / s. As χ increases, Vl and Vg become faster, so the heat removal effect seems to be high.
FIG. 9 shows the core performance calculation shown in FIG. 4 among the main performance calculation items (non-patent document 5) in the conventional computer based on the measured values in the boiling water nuclear power plant shown in FIG. This is a main performance calculation item of the computer of the present invention incorporating the software of the present invention incorporating the calculation formula of the void ratio of the present invention.
: Sho 61-37591, "Nuclear Fuel Assembly" : Science and engineering company, author Mikami et al. “Method and analysis of nuclear fuel management” on page 231. : Author Mikami et al., “Method and analysis of nuclear fuel management”, p. 220. : The Japan Society of Mechanical Engineers "Heat transfer engineering data". : Corona Co., Akagawa, “Gas-liquid two-phase flow”, p. 52. The horizontal axis is a logarithmic scale. : 215 pages of "Nuclear Handbook" supervised by Ohmsha and Asada et al.

近年、沸騰水型原子炉において、従来のウラン核燃料同様に、流路断面積が広く運転時の平均ボイド率が40%程度と低くして減速材たる水を十分にして、低速な熱中性子によりプルトニウムを燃焼させることが考えられている。しかし、プルトニウムは高速な高速中性子で燃焼させると効率が良い。そこで、流路断面積が狭く運転時の平均ボイド率を60%程度に高め減速材たる水が少ない低減速炉が検討されている。
従来のボイド率相関式は、原子炉実運転時と同程度の出口蒸気含有率χが0.2近傍での実験により約2.0と定めた、すべり比R＝Vg/Vlを用いていた。低減速炉のように平均ボイド率が60%にもなるとχが0.5以上にもなり新たに大掛かりな実験をしてすべり比Rを求めねばならない。その上Rを一定としても良いのかどうか不明であった。また、VgやVlは顕には表されていなかった。
本発明のボイド率相関式では、１００％蒸気での蒸気の理論的速度を考慮しているため、χが0から1.0の範囲で正確に、αは元より飽和蒸気の速度Vg、飽和水の速度Vl、飽和蒸気の質量流量Gg、飽和水の質量流量Glを求めることができる。その結果出力分布P(z)も精度良く求めることができるため、プルトニウムを効率よく燃焼させることができて、経済性向上に役立つ低減速炉を精度よく設計することができる。VgやVlの値は熱水力に関する種々の物理的解釈に役立ち、新たな原子炉設計や高度な原子炉運転に役立つ。
特に、Vlが顕に表されるため核燃料棒（１）の表面からの除熱が精度良く計算されるため核燃料棒（１）の健全性に関して精度良く検討できるため、低減速炉の経済性向上に役立つ。
原子炉の運転に関しても計算精度が向上するため、信頼性が増し原子炉運転員の負担が減るため人員減が可能となり管理コストが下がり、結果として発電コスト低下になる。 In recent years, in boiling water reactors, like conventional uranium nuclear fuel, the flow rate is wide and the average void fraction during operation is as low as 40%, so that the water as the moderator is sufficient, It is considered to burn plutonium. However, plutonium is efficient when burned with fast fast neutrons. In view of this, a reduced-speed reactor is being studied in which the channel cross-sectional area is narrow and the average void ratio during operation is increased to about 60% and the amount of water as a moderator is small.
The conventional void ratio correlation equation used the slip ratio R = Vg / Vl, which was determined to be about 2.0 by an experiment in which the outlet steam content χ, which is about the same as that in actual reactor operation, was around 0.2. When the average void fraction reaches 60% as in a low-speed slow reactor, χ increases to 0.5 or more, and a new large-scale experiment must be performed to determine the slip ratio R. In addition, it was unclear whether R could be constant. In addition, Vg and Vl were not clearly expressed.
In the void ratio correlation of the present invention, the theoretical speed of steam at 100% steam is taken into account, so χ is precisely in the range of 0 to 1.0, α is the speed of saturated steam Vg, saturated water from the beginning. The velocity Vl, the saturated steam mass flow rate Gg, and the saturated water mass flow rate Gl can be obtained. As a result, the power distribution P (z) can also be obtained with high accuracy, so that plutonium can be burned efficiently, and a reduced-speed furnace that is useful for improving economic efficiency can be designed with high accuracy. The values of Vg and Vl are useful for various physical interpretations of thermal hydraulics, and are useful for new reactor designs and advanced reactor operations.
In particular, since Vl is clearly expressed, the heat removal from the surface of the nuclear fuel rod (1) is calculated with high accuracy, so that the soundness of the nuclear fuel rod (1) can be examined with high accuracy. To help.
As the operation of the reactor is also improved, the calculation accuracy is improved, the reliability is increased, the burden on the reactor operator is reduced, the number of personnel can be reduced, the management cost is lowered, and the power generation cost is lowered as a result.

以下に、説明に使われる記号の一覧を示した。
ρlin ：未飽和水密度。
ρl：飽和水密度。規定されている運転圧力と蒸気表から求まる。
ρg：飽和蒸気密度。規定されている運転圧力と蒸気表から求まる。
M：ρgとρlの比。M=ρg/ρl。
A：流路断面積。
GT：流路断面を通る単位時間当たりの二相流の全質量流量。ポンプ性能等で求まっている液体の水の流入質量流量に等しい。
Vlin：未飽和液体の水の流入速度。
Vlh：飽和水初速度。Vlh＝GT / (ρl×A）と求められる。
Vg100：二相流が蒸気１００％になった時の飽和蒸気の速度。Vg100＝Vlh / M。
GH ：流路断面を通る単位時間当たりの二相流が蒸気１００％になった時の飽和蒸気の質量流量。GH＝ρg×Vg100×A。
Gg：流路断面を通る単位時間当たりの飽和蒸気の質量流量。
Gl：流路断面を通る単位時間当たりの飽和水の質量流量。
χ：蒸気含有率。χ＝Gg/GT。
α：ボイド率。流路断面を通る単位時間当たりの二相流の流路断面における単位高さ当たり、（蒸気が占める面積）÷（蒸気と液体である水が占める流路断面積）。
Vg：飽和蒸気の速度。
Vl：飽和水の速度。
ｋ：飽和蒸気の速度Vgにおけるαに対するχの重み。
記号一覧終了。
規定されている運転圧力と蒸気表から飽和水密度ρl 、飽和蒸気密度ρgが求まる。
二相流の全質量流量GTはポンプ性能等で求まっている液体の水の流入質量流量に等しく流路断面積Aは一定の値で決まっているから、液体の水の流入速度をVlin とし液体の水が飽和温度まで上昇したときの飽和水初速度をVlhすると、
GT=ρlin×Vlin×A＝ρl×Vlh×Aと表せるから飽和水初速度は、
Vlh＝GT / (ρl×A）と求められる。
二相流が蒸気１００％になった時の飽和蒸気の速度をVg100その質量流量をGHとすると、
GH＝ρg×Vg100×Aと表せる。質量保存則からGH =GTであるから、
ρg×Vg100×A＝ρl×Vlh×AよりVg100＝Vlh×ρl/ρg＝Vlh / MであるからVg100は求められる。
飽和蒸気の質量流量GgはGg＝ρg×Vg×α×Ａであるから蒸気含有率χは、今までは、
χ＝Gg/GT＝ρg×Vg×α×Ａ/（ρg×Vg×α×Ａ＋ρl×Vl×（1-α）×A）から変形してα=1/( 1-R×M×(1-1/χ) )としていた。本発明では、
χ＝Gg/GT＝ρg×Vg×α×Ａ/（ρl×Vlh×A）＝（ρg/ρl）×α×（Vg/ Vlh）と表せるからχ＝M×α×（Vg/ Vlh）と表せる。
Vgは今まであらわには表されていなかったが第一の近似として、
Vg＝Vlh＋χ×（Vg100 - Vlh）＝Vlh＋χ×（Vlh / M -Vlh）とχに関する線形近似とした。蒸気は燃料棒（１）を覆う液の表面から蒸発する近似とした。核燃料棒(1）の下部で飽和蒸気の初速度を飽和水初速度と同じVg＝Vlhとし、核燃料棒(1）の上部でχが100％蒸気になるとVg＝Vg100になるとした。
Vg＝Vlh＋χ×（Vlh / M -Vlh）＝Vlh×（１-χ×(1-1/ M) ）と表せるから、
χ＝M×α×（Vg/ Vlh）＝M×α×Vlh×（１-χ×(1-1/ M) ）/ Vlh
χ＝M×α×（１-χ×(1-1/ M) ）。これを変形すると、
α=1/( 1 - M×( 1 - 1/χ ) )となる。これは、従来のボイド率に関する相関式において飽和蒸気の速度Vgと飽和水の速度Vlの比であるすべり比R＝Vg/Vl＝１としたことになる。核燃料棒(1）の下部でχがゼロの時α＝0で、χが1になるとα＝1となり、χが0.5になるとαは約0.96である。
第二の近似として、
Vg＝Vlh＋α×（Vg100-Vlh）＝Vlh×（１-α×(1-1/ M) ）とαに関する線形近似とした。蒸気は蒸気通路が広くなれば抵抗が少なくなり速度を増すとした近似とした。すると蒸気含有率χは、
χ＝M×α×（Vg/ Vlh）＝M×α×Vlh×（１-α×(1-1/ M) ）/ Vlh
χ＝M×α×（１-α×(1-1/ M) ）。これを変形すると、
α＝( M - ( M2 - 4×χ×( M - 1 ) )1/2 ）/ ( 2×( M - 1) )となる。これは核燃料棒(1）の下部でχがゼロの時α＝0で、χが1になるとM<1だからα＝1となり、χが0.5になるとαは約0.7である。
実際の飽和蒸気の速度Vgは、上記２つの近似を同時に含むと想定できるため重みをｋとしたαとχの線形近似とした。
Vg＝Vlh＋（（α＋ｋ×χ）/（ｋ＋１））×（Vg100-Vlh）これを変形すると、
Vg＝Vlh×( 1+ （（α＋ｋ×χ）/（ｋ＋１））×（ (1/M) -1 ）)
上記と同様に、
χ＝M×α×（Vg/ Vlh）だからE1=( M-1 ) / ( k+1 ) と置くと、
α＝ ( ( M - E1×χ×k ) - ( ( M - E1×χ×k )2 - 4×χ×E1 )1/2 ）/ ( 2×E1 )
となる。
飽和水の速度VlはGg+Gl=GTより、
ρg×Vg×α×Ａ＋ρl×Vl×（1-α）×A =ρl×Vlh×A だから、
Vl = ( Vlh - M×Vg×α ) / ( 1 - α ) と求められる。
したがって、飽和蒸気の質量流量Ggと飽和水の質量流量Glは、
Gg = ρg×Vg×α×Ａ
Gl = ρl×Vl×（1-α）×A
と求められ、和は常にGTになる。
図5に示す本発明のボイド率αの相関式においてk=50の場合は、従来のボイド率αの相関式において蒸気含有率χが0.3以下の運転時ボイド率が低い原子炉において比較的良く合うとされているすべり比が2.0の場合に相当する。本発明のボイド率αの相関式は、蒸気含有率が低い状態でも従来のボイド率αの相関式と同等の値を示し、高蒸気含有率でも精度の良い相関式であることは１００％蒸気になった時の飽和蒸気の速度Vgが理論値Vg100になることが保証されていることからわかる。
図６，７，８は本発明のボイド率αの相関式において同時に求められる飽和蒸気の速度と飽和水の速度のk=0,50,1000の場合の挙動である。蒸気含有率χが1.0の時飽和蒸気の速度Vgは理論値になり、χが0.3以上になっても精度が保証されている。ボイド率αの相関式が保証されているということは、出力分布のボイド率に依存する計算も保証されるということであるから、原子炉挙動を高精度に解析できることが期待できる。したがって、運転状態の監視に高い信頼が持てる。計算された出力分布と炉心内核計側装置との比較において差が生じた場合においてもkの値を修正することにより精度が向上する。
プルトニウムを沸騰水型原子炉に適用する場合、ボイド率αが高い状態を想定した低減速炉の設計が望ましく、設計計算の際、ボイド率αの高い時にも高精度である式を使うことが必須である。
本発明のボイド率αの相関式において同時に求められる飽和蒸気の速度と飽和水の速度は、核燃料棒（１）の温度を求める際重要な熱伝達率を検討するのに使われる。核燃料棒（１）表面は液体の水で覆われているとして熱伝達率が求められる。ボイド率が1.0に近い場合でも高速な飽和蒸気と飽和水により除熱できることが計算可能になったため高度な炉心設計が可能となる。
また、多数の核燃料集合体を持った原子炉において、流速が解れば流動抵抗が解り流量分布も正確に求めることができて、炉心設計計算精度の向上につながる。
本発明のボイド率αの相関式中のパラメータkは、予め実験により定めることができる。即ち、想定した核燃料棒（１）の材料、配列形状、寸法を模擬した熱流動実験
によりkを定めることができる。 Below is a list of symbols used in the explanation.
ρlin: Unsaturated water density.
ρl: saturated water density. It is obtained from the specified operating pressure and steam table.
ρg: saturated vapor density. It is obtained from the specified operating pressure and steam table.
M: Ratio of ρg and ρl. M = ρg / ρl.
A: Channel cross-sectional area.
GT: Total mass flow rate of two-phase flow per unit time through the channel cross section. It is equal to the inflow mass flow rate of liquid water determined by pump performance.
Vlin: Water inflow rate of unsaturated liquid.
Vlh: Initial saturated water speed. Vlh = GT / (ρl × A).
Vg100: Saturated steam velocity when the two-phase flow reaches 100% steam. Vg100 = Vlh / M.
GH: Mass flow rate of saturated steam when the two-phase flow per unit time passing through the channel cross section becomes 100% steam. GH = ρg × Vg100 × A.
Gg: Mass flow rate of saturated steam per unit time through the channel cross section.
Gl: Mass flow rate of saturated water per unit time through the channel cross section.
χ: steam content. χ = Gg / GT.
α: Void ratio. Per unit height in the channel cross section of the two-phase flow per unit time passing through the channel cross section, (area occupied by steam) / (channel cross-sectional area occupied by vapor and liquid water).
Vg: Velocity of saturated steam.
Vl: Speed of saturated water.
k: χ weight for α at the velocity Vg of saturated steam.
End of symbol list.
Saturated water density ρl and saturated steam density ρg are obtained from the specified operating pressure and steam table.
The total mass flow rate GT of the two-phase flow is equal to the inflow mass flow rate of the liquid water determined by the pump performance, etc., and the channel cross-sectional area A is determined at a constant value. When the saturated water initial velocity when the water of the water rises to the saturation temperature is Vlh,
GT = ρlin × Vlin × A = ρl × Vlh × A
Vlh = GT / (ρl × A).
Vg100 is the velocity of saturated steam when the two-phase flow becomes 100% steam, and the mass flow rate is GH.
It can be expressed as GH = ρg × Vg100 × A. Because GH = GT from the law of conservation of mass,
From ρg × Vg100 × A = ρl × Vlh × A, Vg100 = Vlh × ρl / ρg = Vlh / M.
Since the mass flow rate Gg of saturated steam is Gg = ρg × Vg × α × A, the steam content χ has been
Modified from χ = Gg / GT = ρg × Vg × α × A / (ρg × Vg × α × A + ρl × Vl × (1-α) × A), α = 1 / (1−R × M × (1 -1 / χ))). In the present invention,
Since χ = Gg / GT = ρg × Vg × α × A / (ρl × Vlh × A) = (ρg / ρl) × α × (Vg / Vlh), χ = M × α × (Vg / Vlh) I can express.
Vg has not been represented so far, but as a first approximation,
Vg = Vlh + χ × (Vg100−Vlh) = Vlh + χ × (Vlh / M−Vlh) and a linear approximation for χ. The vapor approximated to evaporate from the surface of the liquid covering the fuel rod (1). The initial velocity of the saturated steam at the bottom of the nuclear fuel rod (1) is set to Vg = Vlh, which is the same as the initial velocity of the saturated water, and Vg = Vg100 when χ becomes 100% vapor at the upper portion of the nuclear fuel rod (1).
Vg = Vlh + χ × (Vlh / M-Vlh) = Vlh × (1-χ × (1-1 / M))
χ = M × α × (Vg / Vlh) = M × α × Vlh × (1-χ × (1-1 / M)) / Vlh
χ = M × α × (1-χ × (1-1 / M)). If this is transformed,
α = 1 / (1−M × (1-1 / χ)). This means that the slip ratio R = Vg / Vl = 1, which is the ratio of the saturated steam velocity Vg to the saturated water velocity Vl, in the conventional correlation equation regarding the void fraction. At the bottom of the nuclear fuel rod (1), α = 0 when χ is zero, α = 1 when χ is 1, and α is about 0.96 when χ is 0.5.
As a second approximation,
Vg = Vlh + α × (Vg100−Vlh) = Vlh × (1−α × (1-1 / M)) and a linear approximation for α. The approximation of steam was such that the larger the steam path, the lower the resistance and the speed. Then the steam content χ is
χ = M × α × (Vg / Vlh) = M × α × Vlh × (1-α × (1-1 / M)) / Vlh
χ = M × α × (1-α × (1-1 / M)). If this is transformed,
alpha = a (M - (M 2 - 4 × χ × (M - - 1)) 1/2) / (1) 2 × (M). This is α = 0 when χ is zero at the bottom of the nuclear fuel rod (1). When χ is 1, α = 1 because M <1, and when χ is 0.5, α is about 0.7.
Since the actual saturated steam velocity Vg can be assumed to include the above two approximations at the same time, it was assumed to be a linear approximation of α and χ with a weight of k.
Vg = Vlh + ((α + k × χ) / (k + 1)) × (Vg100−Vlh)
Vg = Vlh × (1+ ((α + k × χ) / (k + 1)) × ((1 / M) −1))
As above,
χ = M × α × (Vg / Vlh), so if you set E1 = (M-1) / (k + 1),
α = ((M-E1 × χ × k)-((M-E1 × χ × k) 2-4 × χ × E1) 1/2 ) / (2 × E1)
It becomes.
Saturated water velocity Vl is Gg + Gl = GT,
ρg × Vg × α × A + ρl × Vl × (1-α) × A = ρl × Vlh × A
Vl = (Vlh-M × Vg × α) / (1-α).
Therefore, the mass flow rate Gg of saturated steam and the mass flow rate Gl of saturated water are
Gg = ρg × Vg × α × A
Gl = ρl × Vl × (1-α) × A
The sum is always GT.
When k = 50 in the correlation equation of the void ratio α of the present invention shown in FIG. 5, it is relatively good in a reactor with a low operating void ratio where the steam content χ is 0.3 or less in the conventional correlation formula of the void ratio α. This corresponds to a slip ratio of 2.0. The correlation formula of the void ratio α of the present invention shows a value equivalent to the correlation formula of the conventional void ratio α even when the steam content is low, and it is 100% steam that is a highly accurate correlation formula even at a high steam content. It can be seen from the fact that the saturated vapor velocity Vg is guaranteed to be the theoretical value Vg100.
FIGS. 6, 7 and 8 show the behavior of the saturated vapor velocity and saturated water velocity k = 0, 50, 1000 simultaneously obtained in the correlation equation of the void ratio α of the present invention. When the steam content χ is 1.0, the saturated steam velocity Vg is a theoretical value, and accuracy is guaranteed even when χ is 0.3 or more. The fact that the correlation formula of the void ratio α is guaranteed means that the calculation depending on the void ratio of the power distribution is also guaranteed, so that it is expected that the reactor behavior can be analyzed with high accuracy. Therefore, it is possible to have high reliability in monitoring the operating state. Even when there is a difference in the comparison between the calculated power distribution and the in-core nuclear instrument side device, the accuracy is improved by correcting the value of k.
When applying plutonium to boiling water reactors, it is desirable to design a reduced-speed reactor that assumes a high void rate α, and it is necessary to use an equation that is highly accurate even when the void rate α is high in the design calculation. It is essential.
The velocity of saturated steam and the velocity of saturated water obtained simultaneously in the correlation equation of the void ratio α of the present invention are used to examine an important heat transfer coefficient when obtaining the temperature of the nuclear fuel rod (1). The heat transfer coefficient is calculated on the assumption that the surface of the nuclear fuel rod (1) is covered with liquid water. Even when the void ratio is close to 1.0, it has become possible to calculate that heat can be removed by high-speed saturated steam and saturated water, so that it is possible to design an advanced core.
In addition, in a nuclear reactor having a large number of nuclear fuel assemblies, if the flow velocity is solved, the flow resistance is solved and the flow distribution can be accurately obtained, which leads to improvement in the accuracy of the core design calculation.
The parameter k in the correlation equation of the void ratio α of the present invention can be determined in advance by experiments. That is, k can be determined by a heat flow experiment simulating the assumed material, array shape, and dimensions of the nuclear fuel rod (1).

沸騰水型原子力発電所は日本では約２０基以上建設され稼動している。核燃料の利用が進みプルトニウムが大量に蓄積されている。無駄でもよいから無理やり消耗させようとするのではなく効率良く燃焼させるには、ボイド率が高い状態で運転する低減速原子炉が良いといわれている。沸騰水型原子炉は元々ボイドを発生させているため、ボイド率の程度の問題であるから検討が進んでいる。本発明のボイド率に関する式が適用されることにより、非常に高いボイド率を想定した原子炉を設計することができ、プルトニウムの効率的運用を通して発電コストの低減に寄与できる。
ボイド率の問題は沸騰水型原子炉だけでなく、加圧水型原子力発電所の蒸気発生器にもでてくる。また、火力発電所においてもボイラーで発生した熱を水管で蒸気にすることによりタービンを回転させるわけであるから、ボイド率の問題は重要である。 About 20 boiling water nuclear power plants have been built and are operating in Japan. The use of nuclear fuel has progressed, and a large amount of plutonium has accumulated. It is said that a reduced-speed reactor that operates with a high void ratio is good for efficient combustion instead of forcing it to be exhausted because it may be wasted. Since boiling water reactors originally generate voids, they are under investigation because of the problem of void fraction. By applying the formula relating to the void ratio of the present invention, it is possible to design a nuclear reactor assuming a very high void ratio, and to contribute to a reduction in power generation cost through efficient operation of plutonium.
The void fraction problem is not only in boiling water reactors but also in steam generators in pressurized water nuclear power plants. Also, in the thermal power plant, since the turbine is rotated by converting the heat generated in the boiler into steam through the water pipe, the void ratio problem is important.

沸騰水型原子力発電所における従来の計算機の主要な性能計算項目。Major performance calculation items of conventional computers in boiling water nuclear power plants. 沸騰水型原子炉の二相流の概観図。Overview of two-phase flow in a boiling water reactor. 沸騰水型原子力発電所における従来の計算機に内蔵せる、従来のボイド率式を組み込んだソフトウエアを示すフローチャート。The flowchart which shows the software which incorporated the conventional void ratio formula to be built in the conventional computer in a boiling water nuclear power plant. 沸騰水型原子力発電所における計算機に内蔵せる、本発明のボイド率式を組み込んだ本発明のソフトウエアを示すフローチャート。The flowchart which shows the software of this invention incorporating the void ratio formula of this invention built in the computer in a boiling water nuclear power plant. 蒸気含有率χに対する本発明のボイド率αの相関式による、重みkをパラメータとしたボイド率αの計算結果。The calculation result of the void ratio α with the weight k as a parameter, according to the correlation formula of the void ratio α of the present invention with respect to the steam content χ. 本発明の式による重みk=0での飽和蒸気の速度Vg、飽和水の速度Vlの計算結果。The calculation result of the velocity Vg of saturated steam and the velocity Vl of saturated water at the weight k = 0 by the formula of the present invention. 本発明の式による重みk=50での飽和蒸気の速度Vg、飽和水の速度Vlの計算結果。The calculation result of the velocity Vg of saturated steam and the velocity Vl of saturated water at a weight k = 50 according to the formula of the present invention. 本発明の式による重みk=1000での飽和蒸気の速度Vg、飽和水の速度Vlの計算結果。The calculation result of the velocity Vg of saturated steam and the velocity Vl of saturated water at a weight k = 1000 according to the formula of the present invention. 沸騰水型原子力発電所において、本発明のボイド率の計算式を組み込んだ本発明のソフトウエアを内蔵せる本発明の計算機の主要な性能計算項目。Main performance calculation items of the computer of the present invention in which the software of the present invention incorporating the calculation formula of the void ratio of the present invention is incorporated in a boiling water nuclear power plant.

符号の説明Explanation of symbols

１ 沸騰水型原子炉の核燃料棒
１１ 沸騰水型原子炉の二相流の液体である水
１２ 沸騰水型原子炉の二相流の気体である蒸気
DESCRIPTION OF SYMBOLS 1 Nuclear fuel rod 11 of boiling water reactor Water 12 which is the liquid of the two-phase flow of boiling water reactor 12 Steam which is the gas of the two-phase flow of boiling water reactor

Claims (5)

水と蒸気とからなる二相流において、以下の記号を使って、
ρl：飽和水密度。
ρg：飽和蒸気密度。
M：ρgとρlの比。M=ρg/ρl。
A：流路断面積。
GT：流路断面を通る単位時間当たりの二相流の全質量流量。
Vlh：流路断面を通る単位時間当たりの飽和水初速度。Vlh＝GT / (ρl×A）。
Vg100：流路断面を通る単位時間当たりの二相流が蒸気１００％になった時の飽和蒸気の速度。Vg100＝Vlh / M。
Gg：流路断面を通る単位時間当たりの飽和蒸気の質量流量。
Gl：流路断面を通る単位時間当たりの飽和水の質量流量。
χ：蒸気含有率。χ＝Gg/GT。
α：ボイド率。
Vg：流路断面を通る単位時間当たりの飽和蒸気の速度。
Vl：流路断面を通る単位時間当たりの飽和水の速度。
ｋ：飽和蒸気の速度Vgにおけるαに対するχの重み。
記号一覧終了。
χに対する本発明のボイド率αの相関式を、E1=( M-1 ) / ( k+1 )として、
α＝ ( ( M - E1×χ×k ) - ( ( M - E1×χ×k )2 - 4×χ×E1 )1/2 ）/ ( 2×E1 )
とし、
飽和蒸気の速度Vgを、
Vg＝Vlh＋（（α＋ｋ×χ）/（ｋ＋１））×（Vg100-Vlh）
とし、
飽和水の速度Vlを、
Vl = ( Vlh - M×Vg×α ) / ( 1 - α )
とし、
飽和蒸気の質量流量Ggと飽和水の質量流量Glを、
Gg = ρg×Vg×α×Ａ
Gl = ρl×Vl×（1-α）×A
としたことを特徴とする。 In a two-phase flow consisting of water and steam, use the following symbols:
ρl: saturated water density.
ρg: saturated vapor density.
M: Ratio of ρg and ρl. M = ρg / ρl.
A: Channel cross-sectional area.
GT: Total mass flow rate of two-phase flow per unit time through the channel cross section.
Vlh: Initial saturated water velocity per unit time through the channel cross section. Vlh = GT / (ρl × A).
Vg100: Velocity of saturated steam when the two-phase flow per unit time passing through the channel cross section becomes 100% steam. Vg100 = Vlh / M.
Gg: Mass flow rate of saturated steam per unit time through the channel cross section.
Gl: Mass flow rate of saturated water per unit time through the channel cross section.
χ: steam content. χ = Gg / GT.
α: Void ratio.
Vg: Velocity of saturated steam per unit time through the channel cross section.
Vl: Saturated water velocity per unit time through the channel cross section.
k: χ weight for α at the velocity Vg of saturated steam.
End of symbol list.
The correlation equation of the void ratio α of the present invention with respect to χ is E1 = (M-1) / (k + 1),
α = ((M-E1 × χ × k)-((M-E1 × χ × k) 2-4 × χ × E1) 1/2 ) / (2 × E1)
age,
Saturated steam velocity Vg,
Vg = Vlh + ((α + k × χ) / (k + 1)) × (Vg100-Vlh)
age,
Saturated water speed Vl,
Vl = (Vlh-M × Vg × α) / (1-α)
age,
Saturated steam mass flow rate Gg and saturated water mass flow rate Gl,
Gg = ρg × Vg × α × A
Gl = ρl × Vl × (1-α) × A
It is characterized by that. 沸騰水型原子力発電所における炉心性能計算において、水と蒸気とからなる二相流に関わる式として請求項１における式を組み込んだことを特徴とするソフトウエア及び当該ソフトウエアを内蔵する計算機。 In calculation of core performance in a boiling water nuclear power plant, software comprising the formula in claim 1 as a formula relating to a two-phase flow comprising water and steam, and a computer incorporating the software. 水と蒸気とからなる二相流に関わる式として請求項１における式を使ったことを特徴とする沸騰水型原子炉の炉心設計及び炉心管理。 A core design and core management of a boiling water reactor characterized by using the formula in claim 1 as a formula relating to a two-phase flow comprising water and steam. 水と蒸気とからなる二相流に関わる式として請求項１における式を使ったことを特徴とする加圧水型原子力発電所の蒸気発生器の設計及び火力発電所の水管の設計。 A design of a steam generator of a pressurized water nuclear power plant and a design of a water pipe of a thermal power plant characterized by using the formula in claim 1 as a formula relating to a two-phase flow comprising water and steam. 水と蒸気とからなる二相流に関わる実験において実験結果の整理式として請求項１における式を使ったことを特徴とする。
In an experiment relating to a two-phase flow composed of water and steam, the formula in claim 1 is used as a formula for organizing the experimental results.
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Publication number Priority date Publication date Assignee Title
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