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ATLAS NOTENovember 25, 2015
2
Gas Leak Test Prototype Setup for the NSW Micromegas Multiplets:3
Implementation and Calibration Technique4
T. Alexopoulosa, E. Gazisa, S. Maltezos1a5
aNational Technical University of Athens6
Abstract7
A prototype setup implemented for the Gas Leak Test of the NSW Micromegas Multiplets is8
described in this work. Because this test is crucial for the stable operation of the Micromegas9
modules, we have combined two methods: a conventional one based on the pressure decay10
rate (PDR) and an alternative, but novel one, based on the flow rate loss (FRL). Both methods11
have been tested by using emulated leak branches based on the idea of using home made12
impedances and specific-low cost medical hypodermic needles. The gas leak rate of a certain13
number of such leak branches have measured by connecting them to the flow stream pipe.14
The obtained measurements by both methods are also given and are compared by means15
of their consistency, and as well as, of their statistical and systematic errors. We present16
a phenomenon of volume expansion strain, observed during the gas leak test of a small17
size Micromegas. Its effect on the measured leak rate by the pressure decay method was18
unsuspectingly very high and has been deeply studied.19
20
1Corresponding author© Copyright 2015 CERN for the benefit of the ATLAS Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-3.0 license.
1 Introduction21
The mass production of the Micromegas modules (MM)[1] for the New Small Wheel (NSW) upgrade22
phase I of the ATLAS muon spectrometer [2] has to be include quality checking and quality assurance23
individual tests. One of them is the gas leak test (GLT) which is crucial for the stable operation of the24
detectors. According to the NSW requirements a general rule for the leak rates of the modules have25
specified: the leak rate has to be 10−5 × V per minute, where V is the volume of the module. The26
obtained limits differ because of the different volumes. However, the pressure (gauge pressure) of the27
main test schedule has to be specified. In addition, when a Multiplet (four modules in back-to-back28
orientation)is created, the gas mixture can flow among the four modules. This lead to the necessity for29
testing the complete Multiplet and not the Modules alone. This fact makes the GLT more complicate30
because the transient gas flow effects have to be taken into account. In this work we present the design31
and the instrumentation for implemented two methods, the conventional “Pressure Decay Rate” (PDR)32
and a new proposed method we call “Flow Rate Loss” (FRL) [3]. The former is based on the ideal gas33
law and the latter on the mass conservation law. The most noticeable difference concerns the flow rate34
during the tests. In PDR method, the Multiplet under test is isolated from the stream line for a certain35
time and thus the flow rate is by definition zero. In FRL the flow rate is different than zero, relatively36
low and stable (undisturbed) during the test. In both methods, the gauge pressure is the fundamental37
parameter in this test because its strong effect on the leak rate. In our prototype setup we have chosen as38
basis 1 mbar but we have also results in a wide range of pressures. The gas we used was air (nitrogen39
with 21 % oxygen)and also pure argon. The argon could be appropriate for the GLT because its leak rate40
is very close to the one expected with the nominal mixture, Ar + 7%CO2.41
2 Methodology of data analysis42
2.1 Model uncertainty in PDR method43
In PDR method the main idea is to measure experimentally the pressure decay rate and analyzing this as44
a function of time to determine the leak rate QL, due an hypothetical rate loss of gas molecules dn/dt. In45
Ref.[6], its application for the Muon MDT chamber gas tightness test, is described in details.46
According to Ideal Gas Law:47
d(PV)dt
= RsTdmdt⇒ V0
P0
dPdt= −QL (1)
where Rs is the specific gas constant and m is the mass of the gas in the volume V0. However, the48
leak rate QL depends only on the absolute pressures inside the unit under test (UUT) and the ambient’s49
pressure. In general, for constant ambient absolute pressure P0 is a function of the gauge pressure p ≡ pg50
of the UUT, that is, QL = g(P, P0) = g(P0 + p, P0), where p = P − P0 ⇒ dP = dp. If P − P0 ≪ P0 the51
leak rate depends approximately on the gauge pressure, that is QL = f (p). As a result, the above Eq. 1 is52
written:53
V0
P0
dpdt= − f (p)⇒ dP
f (p)= −P0
V0dt ⇒
! p
p0
dp′
f (p′)= −P0
V0t (2)
From the above integral we have to calculate the pressure p as a function of time (pressure decay),54
1
p(t), and then the leak rate at t = 0 as follows:55
QL,0 = f (p0) = f (p(0)) =V0
P0
"""""dpdt
"""""t=0
(3)
But the function QL = f (p) describing the flow by an unknown leak orifice or channel, by means56
of their geometrical shape and dimensions, is also unknown. Therefore, having the experimental57
data points for p(t) we have to fit the appropriate theoretical model without any hint for that.58
It is evident that a model uncertainty is unavoidable. To minimize the systematic error in the data59
analysis we have to fit the most probable to occurred theoretical models which are categorized as follows:60
61
a) Constant flow rate, independent of pressure, that is,QL = QL,0 = const. This is met only in62
“choked” flow cases (discussed in section 4) and it is the most simple theoretical model for determining63
the leak rate given by:64
QL,0 = |λa|V0
P0(4)
where λa is the constant slope of the pressure in time ∀t.65
66
b) The flow rate is a linear function of pressure, that is, QL = sb p. This is met in laminar flow67
cases, like the viscous leak channels with Reynolds number smaller than 2300. Substituting the function68
f (p) = sb p in the Eq. 2 and after integration we obtain the following exponential function:69
p(t) = p0e−P0V0
sbt (5)
and the leak rate is given by:70
QL,0 = |λb|V0
P0(6)
where λb = −sb p0P0V0
is the slope of pressure function at t = 0.71
If the leak rate is considerably low and in short time period the absolute value of the exponent in Eq.572
should be x = P0V0
sbt << 1. If it is the case we can apply the approximation e−x ≈ 1 − x for x << 1 and73
thus the Eq. 5 becomes:74
p(t) = p0
#1 − P0
V0sbt
$(7)
and the leak rate should be:75
QL,0 = sb p0P0
V0= |λb|
V0
P0(8)
The later expression is identical to that of Eq. 6 and it holds, not only for t = 0, but in a76
reasonable-short time period leading to faster and more simple data analysis.77
c) The flow rate is a function of pressure in n-th power, that is, QL = sc pn, where 0.5 ≤ n < 1.78
The value n = 0.5 is met in turbulent flow cases of viscous leak channels or orifices (quadratic79
relationship between pressure and flow rate) while a real building envelope will lie somewhere in80
between. Substituting the function f (p) = sc pn in the Eq. 2 and after integration we obtain:81
p1−n(t) = p1−no − scPo
Vot (9)
2
QL,0 = sc pn0 = |λc| pn
0V0
P0(10)
where λc = −scP0V0
is the constant slope of pressure function p1−n(t),∀t.82
83
However, the actual leaking mechanism should be more or less complicate with arbitrary geometrical84
and dynamical parameters. For this reason the optimal fitting model has to investigated in each tested85
Micromegas Multiplets. The associated model uncertainty should cause a systematic error. The case (a)86
pertains higher pressures than that we use. The cases (b) and (c)can be the basis of the data analysis87
procedure aiming to minimize the systematic error. Below, we calculate the model uncertainty if we88
assume the case (a) instead of the actual (b) and vice versa. Let us assume n = 1/2. Then, the ratio of89
the determined leak rates in (c) and (b) cases is:90
QcL,0
QbL,0=λc p0
P0V0
λbP0V0
=
√pp0 − p0
∆t% dp
dt
&t=0
(11)
For a derivative in finite time we can have, ∆t%dp
dt
&t=0≈ p − p0 ! 0 and the ration of the leak rates91
becomes:92
QcL,0
QbL,0=
√pp0 − p0
p − p0=
11 +
'p/p0
(12)
For an average derivative using a finite pressure variation tending to zero, we obtain the following93
limit or the ratio:94
re = limp→p0
√p0(√p − √p0
)
p − p0= lim
p→p0
12
*p0
p=
12
(13)
This result means that, if we analyze the data assuming a laminar flow, model of case (b) while95
the actual leak channel corresponds to a turbulent flow, model of case (c), the error factor tends to 1/2.96
Therefore, there is a risk to overestimate the leak rate by a factor of 2. A similar conclusion should97
be pointed out in the reverse hypothesis, analyzing the model of case (c) while the actual leak channel98
corresponds to model case (b) where the error factor tends to 2 having a risk to underestimate the leak99
rate by a factor of 1/2. Considering a general exponent n the limit of re is:100
δn = limp→p0
re = limp→p0
(1 − n)pn0 p−n = 1 − n (14)
The model uncertainty due to unknown leak source and mechanism is: δ(1−n) = ∓δn and for n = 1/2101
we obtain:102
limp→p0
re = ∓12
(15)
Based on the above investigation, the data analysis in PDR method is proposed to be performed103
following the steps described below:104
1. Perform a non-linear fit to the data (with error to each point) trying with the exponential model105
and then with the model of f (p) = sc√p.106
3
2. Calculate the resulting chi square per d.o.f. for both trials (models). Evaluate the goodness of the107
two fits and choose the best of them. If both models are not adequate (acceptable) continue with108
the last step. Otherwise keep the better of two and calculate the leak rate.109
3. Perform a non-linear fit to the data (with error to each point) trying with a polynomial110
second-degree model and evaluate the resulting chi square per d.o.f.111
The best fit, by means of the above criteria, is the most reliable for determining the leak rate by using112
the corresponding formula given by the optimal model found at t = 0, QL = f (p(0)) = f (p0).113
2.2 Temperature compensation in PDR method114
During a gas leak test by the PDR method a temperature variation is unavoidable and thus it is necessary115
to monitor it. Its variation affects on the pressure drop causing incorrect determination of the leak rate116
without a kind of its compensation. Let us consider the Ideal Gas Law and calculate the pressure drop117
assuming a simultaneous temperature variation:118
d(PV)dt
= RsTdmdt+ mRs
dTdt
(16)
Setting, P = p + P0 ⇒ p = P − P0 and RsT = P0ρ0
rearranging the terms in the equation we obtain:119
V0dpdt= RsTρ0
dVdt+ ρ0V0Rs
dTdt⇒ V0
P0
dpdt− V0
TdTdt=
dVdt= − f (p) (17)
Additionally, in practice, the variations of T are very small compared to the initial one, T0 and120
thus in the Eq. 17 we can set approximately T0 instead of T . Using also the equality θ in oC: dθ =121
d(T − 273.15) = dT , we obtain:122
V0
P0
dpdt− V0
T0
dθdt=
dVdt= − f (p) (18)
In addition, in order to have an approximate but applicable result, we assume that dθdt = constant in123
a short time period close to t = 0. Defining also, qθ = V0T0
dθdt and assuming that it is constant during the124
pressure drop, we have:125
V0
P0
dpdt− qθ = − f (p) (19)
Integrating by separating variables:126
! p
p0
dp′
f (p′) − qθ= −P0
V0t (20)
Assuming laminar flow and thus the flow rate being linear function of pressure, that is, QL = sp, we127
obtain:128
! p
p0
dp′
sp′ − qθ= −P0
V0t ⇒
! p
p0
dp′
p′ − qθs= −s
P0
V0t ⇒ p =
qθs+
+p0 −
qθs
,e−
sp0V0
t (21)
4
Finally, based on the measured pressure drop, the leak rate can be determined by the the following129
formula including the temperature compensation:130
QL,0 = f (p0) = f (p(0)) =""""""qθ −
V0
P0
-dpdt
.
t=0
"""""" (22)
If dθdt < 0 ⇒ qθ < 0 then, without temperature compensation the leak rate is overestimated. In131
contrary, if dθdt > 0⇒ qθ > 0 then, without temperature compensation the leak rate is underestimated.132
2.3 “Volume compliance” effect in PDR method133
If a testing chamber has a degree of elasticity, that is after its pressurization it appears a slight134
expansion/contraction. In this case the PDR method becomes noticeably risking for the measured leak135
rate. This can be explained based on the Ideal Gas Law:136
−P0QL =d(pV)
dt= V0
dpdt+ P0
dVdt
(23)
In the Eq. 1 we can use the quantity “volume compliance” defined as, cv = dVdt . But it should be more137
practical to normalize it in order to be dimensionless and thus measuring relative quantities. This can be138
done defining, c, (where 0c ≤ 1)in the following way:139
c =dpP0
dVV0
(24)
From Eq. 26 and 24 we obtain:140
−P0QL = V0 (1 + c)dpdt
(25)
or141
V0
P0
dpdt= − QL
(1 + c)(26)
142
143
From the last equation we can conclude that the pressure drop rate is much lower for a given leak144
rate by a factor 11+c which varies in the range [0, 1]. Let us now correlate the compliance with the Youngs145
modulus, E. According to the definition of c we have, c = P0E .146
Therefore, the is essentially the reciprocal of the Youngs modulus normalized to and measures a kind147
of “Volume Expansion Strain” (VES). During a gas leak test by the PDR method, even a slight volume148
expansion of the chamber, could cause an associated underestimation of the leak rate according to the149
above mechanism. The VES can be measured experimentally by the help of a calibration procedure by150
the FRL method.151
2.4 Systematic error in FRL method152
The FRL method and has been described in [3] together with its sensitivity and the statistical153
uncertainties. In this subsection we discuss the main source of the systematic error is the coefficient154
5
b of the calibration curve of the mass flow sensors. According the associated data analysis the leak rate155
is determined by:156
QL =1b1
-(VA
0,in − VA0,out
)− b1
b2
(VB
0,in − VB0,out
).(27)
The fraction b1/b2 has to be consider very close to 1 because the manufacturer gives only one set of157
calibration points. On the other hand, the comparison test given again by the manufacturer shows a slight158
difference among several samples of sensors. Thus, we can conclude that the difference between b1 and159
b2 has an upper limit equal to the repeatability upper bound (1 % F.S. in our case). Consequently, the160
ratio b1/b2 affects the systematic error at a level of 1 % F.S. while the b1 affects at a level of the absolute161
accuracy of the sensors which is 5 %. This systematic error can be further reduced if we calibrate the162
sensors by using more accurate mass flowmeters.163
Figure 1: The prototype setup for combined use of PDR and FRL methods. The abbreviations means,MFS: mass flow sensor, DM: differential manometer, DVM: digital voltmeter, FCR: flow controlregulator anv V: valve.
3 The overall prototype setup164
According to the [3], the design of the prototype GLT setup is based mainly on two mass flow sensors,165
OMRON D6F-P0001A1, appropriately selected to have low full scale flow rate, namely 0-6 L/h. In166
this range the repeatability given as 1% F.S. becomes sufficiently low, that is, 0.06 L/h. This value167
is given as an upper limit describing the behavior of a number of tested samples. According to our168
experience the repeatability of this MFS, calculated in rms, is in the level of 0.0006 L/h. The MFSs169
6
Figure 2: A photograph of a general view of theprototype setup. The two well-tight referencetubes are also shown at the top of the image.
Figure 3: A photograph of three medicalhypodermic needles, used for the gas leakcalibration, inserted to a pipe of polyethylene.By using the thinner needle, 32G, we canaccomplish any leak rate in the range ofinterest.
are insensible in temperature variations in wide the range, from -10 to 60 oC. Its systematic error could170
come only from slope b of its fitted calibration curve. For the differential sugnal from MFSs we use a171
Digital Multimeter, High Performance 6 1/2 digits from Keithley (Multimeter 2000). In the setup we172
use two digital differential manometers, Digitron 2021P, with two full ranges 0-20 mbar and 0-130 mbar,173
accuracy 0.03 mbar and precision 0.01 mbar. Two well tight stainless steel tube of 1.05 L in volume174
are used as a) control volume in PDR method and b) reference volume for recording the atmospheric175
pressure variations during the pressure decay. A diagram of the prototype setup is given in Fig. 2.176
The measurement procedure for both methods presuppose to reach a steady state condition of gas177
flow before starting the measurement. The required time period depends mainly on the UUT volume178
and has to be confirmed during the tests of the real Micromegas Multiplets. In PDR method, after the179
steady state and isolating the equilibrium along the isolated volumes (the UUT and the associated pipes180
and components) has to be accomplished. In FRL method which the steady state condition of gas flow is181
being accomplished the correct pressure of the test has to be adjusted.182
4 Evaluation and calibration technique183
4.1 Pressure dependence of the leak rate184
According to the theoretical calculations for the leak orifices and channels the leak rate, in principle,185
depends on the pressure difference between the tested volume and the ambient pressure (this difference186
constitutes the gauge pressure). Regardless of the detailed relationship of leak rate with gauge pressure,187
the important remark is that for low pressure values this dependence is strong. A study of this dependence188
has been done using medical needles (see how we use them in Fig. 3). The leak rate has been measured189
using a needle of type 28G (D = 184 µm) and the results are illustrated in Fig. 4. We also measured190
another type of needle, 27G, and an orifice (of D = 413 µm). In a narrow range of pressure variation191
we can assume approximately linear dependence and thus the relative variations in leak rate and pressure192
could be considered the same. Consequently, the GLT has to be defined according to the gauge pressure193
we choose. Because the gases are compressible fluids, increasing the absolute pressure will increase the194
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volume leak flow rate until the gas velocity reaches the speed of sound and the flow becomes “choked”.195
Beyond this critical point, further increase of the absolute pressure doesn’t increase the volume leak rate.196
This critical absolute pressure corresponds to a pressure ratio between the volume and the ambient equal197
to 1.886 bar. This can be translated to a gauge pressure of 1.886 − 1.0132 ≈ 0.873 bar.198
Figure 4: Experimentally obtained plot of the leak rate of a calibrated needle (28G) as a function of thegauge pressure. The leak rate of this needle is close to the acceptance limit set for the LM MP. The solidline is a polynomial fit to the data.
4.2 Calibration by individual medical needles199
We have performed two individual measurements of leak rate, with both methods, by using the two with200
smaller diameter calibrated needles, that is, the 31G-CN1 and 32G-CN1. By using PDR we obtained the201
pressure drop decay of 31G-CN, in conjunction with a well -tight reference tube having volume of 1.05202
L while the atmospheric fluctuations have been compensated by using a differential manometer. The203
resulting plot is shown in Fig. 5. By fitting a line, with errors, to the first five data points we found the204
line equation, p = −10.2t + 1.13, in the units used in the plot (s for time and mbar for pressure). The205
overall error in the slope is 10 %, as minimum, because of the model uncertainty. A similar measurement206
and analysis procedure has been used for the pressure decay of needle 32G-CN1 shown in Fig. 7. The207
corresponding line equation was p = −5.04t+1.13 with an overall error in the slope, 11 %, as minimum.208
We can see by inspection that both pressure decay curves, close to t = 0, exhibit a general trend of linear209
behavior as approximately might be happened in a viscous leak channel like a needle. The same needles210
has been also measured by the FRL method, see Fig. 6 and Fig. 8 respectively. In the plots the small211
positive difference in flow rate corresponds to the demanded leak rate loss. The results in leak rate are212
summarized in Table 1. We have to note that while the lasting time of PDR procedure was about 10 min,213
the lasting time of FRL procedure was only a few seconds.214
It is also interesting to observe the small fluctuations in the data points coming from the repeatability215
variation. The rms of these fluctuations (around 0.0006 L/h) is 100 times smaller than the upper limit216
8
Figure 5: Pressure decay plot obtained experimentally with the calibrated neeedle 31G-CN1. A line hasbeen fitted to the first five data points from 1 mbar and below.
Figure 6: The flow rates measured in the input and output with the calibrated neeedle 31G-CN1connected in the stream line.
9
Figure 7: Pressure decay plot obtained experimentally with the calibrated neeedle 32G-CN1. A line hasbeen fitted to the first five data points from 1 mbar and below.
Figure 8: The flow rates measured in the input and output with the calibrated neeedle 31G-CN1connected in the stream line.
given by the manufacturer (1 % F.S. or equivalently 0.06 L/h). In fact, this a is very promising result217
proved that when operating in very low flow rates we can profit a much better repeatability.218
10
Needle ID — Method PDR FRL31G - CN1 0.0107 ± 10% syst. (min) 0.0114 ± 8 stat. % ± 1.5% syst.32G - CN1 0.0053 ± 11% syst. (min) 0.0058 ± 15 stat. % ± 1.5% syst.
Table 1: Leak rate results obtained by both GLT methods, PDR and FRL by using emulated leak ofcalibrated needles.
5 Overview of experimental results - “Leak Ruler”219
The investigation of the detection limit of our setup was feasible by using medical (hypodermic) needles220
of the series 27G, 28G, 30G, 31G, 32G. Their precision in diameter is 19 µm (which corresponds to about221
from 9 % to 18 %). However, we are interesting only for their particular flow rate as we can measure222
with much better accuracy it by our setup. The needles are simply inserted in the side of a plastic pipe.223
As we confirmed experimentally, there is not any observable leak between the needle and the side of the224
tube. These needles constitute the emulated leak branches useful for calibration the gas GLT setup of225
Micromegas Multiplets (at CERN or at other test sites). We have measured them one-by-one with air and226
by the FRL method. The obtained results are illustrated in a plot which in the horizontal axis has the leak227
rate divided by the acceptance limit of LM1 Multiplet while in the vertical one has the obtained leak rate228
it self. This plot we call “Leak Ruler” because of its usefulness to give two information simultaneously.229
This plot is shown in Fig.9.230
Figure 9: The plot with the “Leak Ruler” in the region of acceptance limit and below this. The firstmeasured calibrated needles are indicated with N-XXCN where XX represents the corresponding Gcode.
A certain number of calibrated needles are going to be measured systematically with air, and as well231
as, with argon creating a complete calibration set.232
11
Conclusions233
In this work we implement the methods we considered as appropriate for the gas leak test of Micromegas234
Multiplets for NSW, that is, the pressure decay rate (PDR) and the flow rate loss (FRL). For evaluation235
and calibration of both method we introduced the technique of the Leak Branches based on medical236
needles. The combined gas leak methods have been implemented in a unified prototype setup.237
Our experimental measurements using the calibrated leak branches have been confirmed a sensitivity238
corresponding to leak rates much lower than the NSW acceptance limit. We also detected and explained239
the high sensitivity of the PDR method to the “volume compliance” of a small Micromegas chamber of240
TMM type. Furthermore, we investigated the data analysis model uncertainty of the PDR method having241
in mind the Micromegas Multiplets. The proposed FRL method has been successfully tested and seems242
reliable, fast, accurate and insensible to the temperature variations. A progress have been done in the243
noise reduction based on Lock-in Amplifier technique and the data acquisition and control subsystem244
dedicated to gas leak test. Our prototype setup, as first-level PDR/FRL configuration, can be used in245
the BB5 Lab. For a noticeable upgrade for a second-level configuration, more precise mass flowmeters246
found in the market, should be proposed.247
Acknowledgments248
We would like to thank our colleagues in MAMMA collaboration for the useful private communications249
and discussions for this project.250
The present work was co-funded by the European Union (European Social Fund ESF) and Greek national251
funds through the Operational Program ”Education and Lifelong Learning” of the National Strategic252
Reference Framework (NSRF) 2007-2013, ARISTEIA-1893-ATLAS MICROMEGAS.253
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