Oct 15, 2014

E-Cat長期試験報告 010

For each cap, we applied (2), to each of the three areas attributed to each cap (A = 16.7 ∙ 10–4 [m²], D = 0.04 [m]).

各キャップのために、私たちは(2)を適用した、各キャップに帰属する3つの領域のそれぞれに、 (A = 16.7 * 10 ^ –4 [m ^ ²], D = 0.04 [m])。

For instance, for cap Area 1a, by consulting Plots 2, 3, and 4, and taking into account Tf = 453.05 [K], we get the following values:

例えば、キャップ領域1aのため、プロット2、3、および4を調べることにより、Tf = 453.05 [K] を考慮して、私たちは、以下の値が得られます。

k = 37 ∙ 10 –3 [W/mK], ν = 32 ∙ 10 –6 [m²/s] and α = 47 ∙ 10 –6 [m²/s].

k = 37 * 10 ^ –3 [W/mK], ν = 32 * 10 ^ –6 [m ^ ²/s] and α = 47 * 10 ^ –6 [m²/s]。

In this case, the Rayleigh number and coefficient h become:


Ra = (gβ(Ts– Ta)D ^ ³) / να = 292803.67 (19)

h = (kCRa ^ ⁿ) / D = 10.33 [W/m ^ ²K] (20)

Heat emitted by convection by cap Area 1a alone is thus:


Q = hA(Ts– Ta) = 5.50 [W] (21)

Table 3 below shows, for each area, the values obtained for average temperature, power emitted by radiation, and power emitted by convection, when the appropriate emissivity is assigned;


the last four columns give only the results relevant to the sum total of watts emitted by radiation and convection when emissivity is made higher or lower by uncertainty.


(訳注 クリックすると拡大します)

Table 3.For each one of the areas that the caps and the body of the dummy reactor have been divided into, the table shows, subsequently:


 actual emissivity value, average temperature, power emitted by radiation, power emitted by convection, the sum of the last two values, emissivity minus uncertainty,

実際の放射率値、平均温度、放射線により放出された電力、対流によって放出された電力、最後の二つの値の合計、放射率 マイナス 不確実性、

 the sum total of watts emitted if one sets “emissivity minus uncertainty”, 


emissivity plus uncertainty, and the sum total of watts if one sets “emissivity plus uncertainty”.


(訳注 ここで17ページの終わり)

The total power emitted by the dummy reactor is 316.50 W, and the percentage error to be associated to this value is:

ダミー反応装置によって放出される総電力は316.50 Wです、この値に関連付けられるパーセント誤差は次のようになります。

(318.65 – 314.67) / 316.50 = 0.0126 = 1.26% ≈ 1.3% (22)

The very same process used for the dummy reactor body was used to calculate the power emitted through radiation and convection by the rods.


During the test, the rods were heated by conduction, from their being in contact with the reactor, and from the heat yielded to them by the lengths of Inconel cable external to the caps.


Not only do the cables dissipate heat by Joule heating, they also subtract it from the reactor by conduction.


Here too, the thermal images of each rod were divided into 10 areas.


Because the rods were placed in overlapping positions,


each one of them was capable of dissipating heat to the environment for only 2/3 of its surface;


moreover, whereas the temperature of the two lower rods was more or less the same,


the upper rod always indicated higher temperatures.


For this reason, we decided to perform calculations on a thermography file corresponding to a side view,


in which only one upper and one lower rod were visible,


and to attribute to the third rod which was not framed by the camera the same values of the lower visible rod (Figure 11).


Lastly, we found that the three rods connected to the cap on the right of the dummy reactor indicated slightly higher temperatures than those connected to the cap on the left,


and that this difference was within the associated error margin.


We therefore decided to perform the calculations for only one set of three rods (the cooler ones) and multiply the result by a factor of 2.


Figure 11.Thermography image of the set of three rods on the left of the reactor. 


To the third rod hidden behind the other two, we attributed the temperatures appropriate to the lower rod.


The dimensions of each area are given by:


(2π * Rrod * Lrod) / 10 = 4.71 * 10 ^ –3 m^2 (23)

where R and L are the radius and the length of each rod, respectively.


To each area, formulas (14) for calculating radiation and formula (18) convection were applied, substituting the appropriate values.


Table 4 shows all the results obtained for the areas of the upper rod (indicated by u)


and one of the lower rods (indicated by d) of a set of three rods.


In the columns from left to right, the first values found are relevant to the upper rod (subsequently: emissivity, average temperature, radiation power, convection power, and the sum of the last two values), followed by the values relevant to the lower rod.


The sum of the results obtained for each area appears in the last line.


Finally, the bottom cell of the last column of the table records the watts emitted by one entire set of three rods,


a value obtained by adding the total watts produced by the upper rod, to the total watts, multiplied by two, produced by the lower rod.


(訳注 ここで18ページの終わりから19ページの最初二行まで)

(訳注 クリックすると拡大します)

Table 4.The values in the table refer to one of the two sets of three dummy reactor rods. 


Subscript “u” refers to the uppermost rod of the set, subscript “d” to one of the two lower rods (the same results apply to the second lower rod). 


Each rod has been divided into 10 areas. 


For each area, the table indicates, subsequently: 


assigned emissivity, average temperature, power emitted by radiation, power emitted by convection, the sum of the last two values. 


The last cell of the table gives the total watts emitted by one whole set of three rods, 


reckoned by multiplying the results relevant to the lower rod by 2, 


and adding them to those of the upper rod.


We can now calculate the total heat emitted from both sets of three rods, 


bearing in mind how much of their surface is actually emitting heat, and the associated error percentage (estimated at ca. 5%):


(97.40 * 2/3) * 2 = 129.86 ± 5% [W] (24)

In the previous paragraph, we have seen that the copper cables running through the rods emit a total of 0.4 W through Joule heating.

前の段落では、棒を通る銅ケーブルは、ジュール加熱により0.4 Wの合計を放出することを見てきました。

This value should be subtracted from (24) because, contrary to the power calculated with that equation,


it does not derive from heat generated by the reactor and transmitted to the rods by conduction, but from electric power supplied by the mains.


However, as it is a very small value, it may be considered part of the error associated to (24).


Note also that part of the power produced by the rods is also due to Joule heat emitted by the short lengths of Inconel resistors connected to the copper cables inside the rods after leaving the caps.


All the characteristics of these resistors, however, such as their geometric dimensions and the exact makeup of the alloy they are made of, are covered by trade secret.


Though we are unable to furnish an exact calculation of their contribution to the heat emitted by the rods,


the short lengths of Inconel cable inside the rods allow us to reasonably consider it as lying within the error percentage associated to the measurements.


By adding the watts emitted directly by the dummy reactor to watts released by conduction to the rods,


we get the dummy’s thermal power output:


(316.50 ± 4.11) + (129.86 ± 6.49) = 446.36 ± 10.60 = 446 ± 2.4% [W] (25)

(訳注 ここで19ページの終わり)

Let us now compare this dissipated power with the power supply,


the average of which over 23 hours of test is = (486 ± 24) W (uncertainty here is 5% of average, calculated as standard deviation).

試験の23時間にわたる平均は、 = (486 ± 24) W (不確かさは、ここでは、標準偏差として計算し、平均値の5%である)。

Keeping in mind the Joule heating of the power cables discussed in paragraph 4.3, we have the following results:


Power supply (W) Joule heating (W) Actual input (W) Output (W)

電力供給 (W) ジュール加熱 (W)  実入力 (W)  出力 (W) 

486 ± 24        7    486 – 7 = 479 ± 24       446 ± 10

If we take error percentages into account, we will see that where input is at minimum possible value (455 W) and output at maximum possible value (456 W),

もし私たちが誤差の割合を考慮する場合、わかることは、入力が可能な最小値である(455 W)、さらに、出力が、可能な最大値(456 W)であると、

our method overestimates by about 1 W, i.e. 0.2%.

私たちの方法は、約1 W、すなわち0.2%過大評価である。

Vice versa, where input is at maximum possible value (503 W) and output at minimum possible value (436 W) our method underestimates the power supplied to the reactor by about 67 W, i.e. 14%.

逆に、入力を可能な最大値である、(503 W)とし、さらに、出力を最小可能値(436 W)とすると、私たちの方法は、約67 Wにより反応器に供給される電力を過小評価しています、すなわち14%。

We can therefore rely on the fact that applying the very same procedure to data gathered from the E-Cat test does not lead to any significant overestimation; rather,


there is a good chance that the power actually generated by the reactor is underestimated.


(訳注 ここで 5章(20ページの中央)の終わり)