Scattering Chamber Vacuum Failure

The scattering chamber will be leak checked before service but obviously the possibility of vacuum loss cannot be eliminated. The most likely sources of vacuum failure are:

Spectrometer Windows

Initially the scattering chamber will have two aluminum windows, one for each side of the beam line.

Target Cell Failure

This is a multiple loop system. If a target cell fails, the remaining targets will have their insulating vacuum spoiled.

The two spectrometer windows are both made from aluminum. Each window is seven $in$ high and subtends 170 $^\circ$ on the 43 $in$ outer diameter of the scattering chamber. This window is made of 0.016 $in$ thick 5052 H34 aluminum foil.

The scattering chamber was evacuated (and cycled several times) with both windows covered by the same 0.016 $in$ material. The foil forms regularly spaced vertical ridges when placed under load. The window had an inter-ridge spacing of 3 inches. If the window is treated as a collection of smaller rectangular windows which have the full vertical height of 7 inches and the inter-ridge spacing as a width, then stress formulas predict that the 0.016 $in$ material would reach ultimate stress at a pressure higher than 35 PSI. There is a gate valve between the scattering chamber and the beam entrance (exit) pipe. Both valves will be closed automatically in the event that the chamber vacuum begins to rise and an FSD will be caused ( this is done via a relay output of the scattering chamber vacuum gauge). If either valve is closed an FSD will result.

In the unlikely event of a catastrophic vacuum failure, it is important that the relief line of the targets be sized such that it can handle the mass flow caused by the sudden expansion of its cryogenic contents due to exposure to the heat load. A calculation has been performed which models the response of the system to sudden vacuum failure. That calculation indicates that the relief plumbing is sized such that the flow remains subsonic at all times and that the maximum pressure in the cells remains well below their bursting point.

The calculation was performed by following methods in an internal report from the MIT Bates laboratory [5]. The formulas and algorithm in the report were incorporated in two computer codes and those codes were able to reproduce results in the report (hence they represent an accurate implementation of the Bates calculation).

The calculation can be logically broken into two parts. First, the mass evolution rate is calculated from geometric information and the properties of both the target material and vacuum spoiling gas. The principal results of this first stage are the heat transferred per unit area, q, the boil off time, t$_b$, and the mass evolution rate, w. Second, the capability of the plumbing to handle the mass flow is checked. The principle result of this second step is the maximum pressure in the target cell during the discharge, P$_1$.

The formula involved will not be repeated (readers are referred to the Bates report for detail). The information that was used as input to the calculation is given in tables 3.3, 3.4 and 3.5.

For the calculation of the boil off rate the target was split into two pieces: the cells plus cell block, both aluminum; and the heat exchangers plus the connecting plumbing, all steel. The mass evolution rates for the two pieces were then added in order to find the total mass flow rate.

Table 3.3: The properties of the gases used to calculate the heat transferred to the target during a catastrophic vacuum failure.

Fluid and Phase	Property	Symbol	Value
Hydrogen/Liquid	Temperature	T(K)	22
	Density	$\rho$ (kg/m$^3$)	67.67
	Specific Heat	C$_p$ (J/(kg K))	11520
	Enthalpy of Vaporization	H$_v$ J/kg	428,500
Hydrogen/Vapor	Temperature	T(K)	22
	Density	$\rho$ (kg/m$^3$)	2.4991
	Viscosity	$\mu$ (kg/(s m))	1.29$*$10$^{-6}$
	Specific Heat	C$_p$ (J/(kg K))	13,550
	Thermal Conductivity	k (W/(K m))	0.02
	Volume Expansivity	$\beta$ K$^{-1}$	0.00366
Air	Temperature	T(K)	273
	Pressure	P (Torr)	760
	Density	$\rho$ (kg/m$^3$)	1.224
	Viscosity	$\mu$ (kg/(s m))	1.8$*$10$^{-5}$
	Specific Heat	C$_p$ (J/(kg K))	1005
	Thermal Conductivity	k (W/(K m))	0.0244
	Volume Expansivity	$\beta$ K$^{-1}$	0.00367

Table 3.4: The geometric quantities needed for and the results of calculations of the mass evolution rate after a catastrophic vacuum failure.

Quantity	Cell Block	Piping	Heat Exchanger	Total
D	2.5 in (0.063 m)	1.5 in (0.038 m)	7 in (0.1778 m)
k	55 W/(K m)	6.5 W/(K m)	6.5 W/(K m)
A	0.146 m$^2$	0.185 (m$^2$)	0.216 m$^2$	0.510 m$^2$
V	0.001 m$^3$	0.0019 (m$^3$)	0.002 m$^3$	0.0054 m$^3$
x	0.004 in (0.0001 m)	0.065 in (0.00165 m)	0.12 in (0.003 m)
q	14903 W/m$^2$	10526 W/m$^2$	11235 W/m$^2$
t$_{b}$	26.78 s	28.29 s	23.89 s	26.3 s
w	0.0038 kg/s	0.0045 kg/s	0.0056 kg/s	0.014 kg/s
				(0.03 lbs/s)

Table 3.5: Tubing sizes, and other information needed to analyze relief line response. The mass flow rate was 0.03 lbs/s.

Inner Diameter	Length	K (K$_{eff}$)
0.44 in tube	10 ft	4.64 (31.5)
0.88 in tube	10 ft	2.32 (0.98)
Quantity		Value
Minor Losses		7.4
K $^{total}_{eff}$		40
Average Diameter		0.71 in
xmax		0.890
w$_{sonic}$		0.065 lbs/s
m		0.323
x		0.748
P$_{2}$		14.7 PSIA
P$_{1}$		58.3 PSIA
P$_{1}$		43.6 PSIG

The calculation of the pressure drop includes all the plumbing up to the large relief valve. The calculation assumes that all the mass flow is carried out the relief side of the target gas handling system (no flow out of the fill line reliefs). The friction factor for each diameter was taken from a Moody plot. A typical value was $f = 0.017$. The effective K values, K$_{eff}$, were adjusted to the average tube inner diameter which was taken to be 0.71 in. The final K$_{eff}$ value was 40. The minor losses are from bends, expansions and contractions in piping.

The final result shows the cells subjected to 58 PSIA during the boil off, which is comparable to the 75 PSIA pressure that the assembled cell blocks were tested at, and is significantly below the tested pressure of the cell components.

The scattering chamber has a volume of about 2,100 $l$ with perhaps an additional 200 $l$ of volume in the bellows and the cryo can. If one target cell were to rupture and the chamber were unrelieved, the chamber pressure would rise to about 2 Atm. It takes approximately 150 seconds to bring 5 $l$ of 22 $^\circ$ K hydrogen to room temperature by conductive heat transfer with the scattering chamber walls. In order that the maximum pressure in the chamber stay near one atmosphere, it is necessary to vent one half of the target mass in approximately one half of the total expansion time. Therefore the relief valve for the scattering chamber should be capable of venting about three grams per second at a low pressure difference (say two PSIG). If one considers the case where all three targets fail at once, the vent must be capable of handling three times that amount. A four $in$ diameter relief valve placed near the top of the scattering chamber should be capable of handling this rate. A rise in the chamber vacuum will stop the beam, FSD, and cause the gate valves on either side of the scattering chamber to close.

In the unlikely event that a line which carries helium coolant were to rupture the four $in$ chamber relief valve is capable of handling the full coolant flow rate.