SUBJECT: Estimate of Critical Mass
A new estimate of the critical and operating mass of the
based on the more recent version of the
In summary: It is recommended that the reactor core be made with inside
diameter 10 3/4", inside height 11" (1.08" clearance at top), to accommodate
900 grams of U-235 at a hydrogen ratio of 400 (anhydrous uranyl sulfate l0% by
weight) solution density [~=] 1.1 g/cm³.
The main differences between SUPO and our reactor are as follows:
|Spherical shape||Cylindrical shape|
|Cooling Coil length 60 ft.||Cooling Coil length 27 ft.|
|Nitrate solution||Sulfate solution (tentative)|
The number and dimensions of exposure tubes, control rod sheaths, etc., are
enough alike so that it is unprofitable to estimate differences due to them.
An analysis of the effects of changes listed above is given.
Shape. The critical volume (and mass) of a bare cylindrical reactor of given
hydrogen ratio is theoretically 1.14 times that of a bare spherical reactor. The
effect of a reflector is to reduce this discrepancy somewhat, so that this can be
considered as an upper limit.
Cooling Coil. In the conversion at
made of the worth of cooling coils that turned out to be quite accurate. The
addition of 157" (13.1') of cooling coil made an 80 gram increase in U-235
cooling lengths is 33 ft., giving a predicted 200 gram charge. This value may be
high because a linear extrapolation may be incorrect.
Solution. The critical mass for a nitrate solution is quoted to be 70 grams
higher than that for a sulfate solution at 14.7% U-235 concentration.
Estimate of Mass. Starting with the experimental critical mass of SUPO of 870
grams of U-235, the change to sulfate would bring it down to 800 grams. A change
in shape brings it to 1.14(800) = 915 grams, but the cooling coil difference
cuts it back to 215 - 200 = 715 grams for the critical mass. Adding 60 grams a for
the temperature coefficient and 15 grams for excess reactivity, gives a final
value of 790 grams for the operating mass.
In the design of the core provisions should be made for the possibility that
the effect of cooling length reduction is not as high as linear extrapolation
would predict, that the extra void at the top and the void between the bottom of the
solution and the graphite introduces loss of reactivity, and that nitrate may be
used instead of sulfate.
Since it is preferable to err in the direction or too large a container size,
requiring that the actual solution used be of lower concentration, it is
Estimate of Reactor Size. The volume of container will be the sum of the necessary
tubing voids and the solution itself.
By the applicable chemical relations, the solution volume is
|Cooling coils 27.1' of 5/16" O.D. pipe||408 cm³|
|Control rods 2 x 9.7" of 13/16" O.D. pipe||165 cm³|
|Reentrant tube 8" of 1 1/8" O.D. pipe||130 cm³|
|Thermocouple 6.1" of 3/16" O.D. pipe||3 cm³|
For a bare cylindrical reactor, the optimum height is 1.8475 times the radius,
so that the volume is
A space of approximately 1" between the solution and the inside of the top
of the container is proposed.
The recommended fixed dimensions of the core are--Inside Diameter 10 3/4",
Inside Height 11".
Volume of top space
|weight of steel in walls.||A=2([pi]R²) + 2[pi]RH|
|=2[[pi](5.375)²] + 2[pi](5.375)(5)|
|=2[[pi]][28.8 + 26.8]|
|=(6.28)(45.6) = 286 in²|
|V=(286)(1/16)=17.9 in³ = (17.9)(16.387) = 282 cm³|
|M=V[rho]=(28.2)(8.0)(assumed) = 2340 g = 2.34 kg|