The cooling capabilities of C2F6/C3F8 saturated fluorocarbon blends for the ATLAS silicon tracker

We investigate and address the performance limitations of the ATLAS silicon tracker fluorocarbon evaporative cooling system operation in the cooling circuits of the barrel silicon microstrip (SCT) sub-detector. In these circuits the minimum achievable evaporation temperatures with C3F8 were higher than the original specification, and were thought to allow an insufficient safety margin against thermal runaway in detector modules subject to a radiation dose initially foreseen for 10 years operation at LHC. We have investigated the cooling capabilities of blends of C3F8 with molar admixtures of up to 25% C2F6, since the addition of the more volatile C2F6 component was expected to allow a lower evaporation temperature for the same evaporation pressure.A custom built recirculator allowed the in-situ preparation of C2F6/C3F8 blends. These were circulated through a representative mechanical and thermal setup reproducing an as-installed ATLAS SCT barrel tracker cooling circuit. Blend molar compositions were verified to a precision of 3.10−3 in a custom ultrasonic instrument.Thermal measurements in a range of C2F6/C3F8 blends were compared with measurements in pure C3F8. These indicated that a blend with 25% C2F6 would allow a reduction in evaporation temperature of around 9̂C to below -15̂C, even at the highest module power dissipations envisioned after 10 years operation at LHC. Such a reduction would allow more than a factor two in safety margin against temperature dependant leakage power induced thermal runaway.Furthermore, a blend containing up to 25% C2F6 could be circulated without changes to the on-detector elements of the existing ATLAS inner detector evaporative cooling system.

ABSTRACT: We investigate and address the performance limitations of the ATLAS silicon tracker fluorocarbon evaporative cooling system operation in the cooling circuits of the barrel silicon microstrip (SCT) sub-detector. In these circuits the minimum achievable evaporation temperatures with C 3 F 8 were higher than the original specification, and were thought to allow an insufficient safety margin against thermal runaway in detector modules subject to a radiation dose initially foreseen for 10 years operation at LHC.
We have investigated the cooling capabilities of blends of C 3 F 8 with molar admixtures of up to 25% C 2 F 6 , since the addition of the more volatile C 2 F 6 component was expected to allow a lower evaporation temperature for the same evaporation pressure.
A custom built recirculator allowed the in-situ preparation of C 2 F 6 /C 3 F 8 blends. These were circulated through a representative mechanical and thermal setup reproducing an as-installed AT-LAS SCT barrel tracker cooling circuit. Blend molar compositions were verified to a precision of 3.10 −3 in a custom ultrasonic instrument.
Thermal measurements in a range of C 2 F 6 /C 3 F 8 blends were compared with measurements in pure C 3 F 8 . These indicated that a blend with 25% C 2 F 6 would allow a reduction in evaporation temperature of around 9 • C to below -15 • C, even at the highest module power dissipations envisioned after 10 years operation at LHC. Such a reduction would allow more than a factor two in safety margin against temperature dependant leakage power induced thermal runaway.
Furthermore, a blend containing up to 25% C 2 F 6 could be circulated without changes to the on-detector elements of the existing ATLAS inner detector evaporative cooling system. KEYWORDS: Detector cooling and thermo-stabilization; Gas systems and purification; Materials for gaseous detectors 1 Introduction

Motivation
During initial operation of the ATLAS silicon tracker fluorocarbon evaporative cooling system a limitation in performance of the cooling circuits of the barrel silicon microstrip (SCT) subdetector was encountered. The minimum achievable evaporation temperatures with C 3 F 8 [octafluoropropane: R218; molecular weight (mw) = 188] were higher than the original specification due to greater than expected pressure drops in inaccessible regions of the exhaust vapour return tubing, and were thought to allow an insufficient safety margin against thermal runaway once the detector modules had been subjected to a radiation dose approaching that initially foreseen in their expected 10 year operational lifetime at LHC. Prior estimates of the evolution of depletion voltage and leakage current suggested that an evaporation temperature of -15 • C would be required for an adequate safety margin against thermal runaway under the expected operating profile. Since laboratory measurements in a representative cooling circuit demonstrated that this temperature could not be achieved with pure C 3 F 8 with return line parameters as in the installed ATLAS evaporative cooling system, we have investigated the cooling capabilities of blends of C 3 F 8 with molar admixtures of up to 25% C 2 F 6 [hexafluoroethane: R116; molecular weight (mw) = 138]. The addition of the lighter and more volatile C 2 F 6 -1 - component was expected to allow a lower evaporation temperature for the same evaporation pressure. Thermodynamic calculations suggested that a blend containing up to 25% C 2 F 6 could be circulated without changes to the on-detector elements or the inaccessible liquid delivery and vapour exhaust systems of the existing ATLAS inner detector evaporative cooling system.

The ATLAS inner detector C 3 F 8 evaporative cooling system
The ATLAS Inner Detector (ID) contains a multi-layer silicon tracker. In this tracker two independent subsystems are presently cooled by the evaporation of C 3 F 8 . Of these the Pixel detector is located close to the interaction point and comprises 3 cylindrical layers of silicon pixels with three disk-shaped layers at each end. The Semi-Conductor Tracker (SCT) surrounds the Pixel detector with 4 cylindrical barrel layers of silicon microstrip detectors, with a further nine disk-shaped layers at each end. These subsystems can collectively dissipate up to 60kW of heat after long term radiation damage as a result of operation at the CERN Large Hadron Collider (LHC). The evaporative cooling system circulates coolant through the Pixel and SCT detectors via 204 cooling circuits [1]. Figure 1 illustrates the principal components of the ATLAS C 3 F 8 evaporative cooling system.
-2 -Shared principal components of the system include compressors and a condenser. Individual circuit elements include liquid flow-defining pressure regulators (PRs), the on-detector capillaries and cooling tubes (or evaporators), followed -in order of fluid flow -by heat exchangers, electric heaters and evaporation pressure-defining back pressure regulators (BPRs).
In each cooling circuit, liquid refrigerant arrives through a 30 m uninsulated supply tube and is sub-cooled (segment D 2 D 3 in figure 1) in a heat exchanger by counter-flowing cold liquid/vapour exhausting from the on-detector cooling channel. The liquid PR is set to a fixed pressure to provide a mass flow of around 120% of that necessary for the maximum expected detector dissipation. Any liquid remaining at the output of the heat exchanger (point F in figure 1) must be evaporated in an electric heater (FF') and the exhaust vapour temperature raised above the expected cavern dew point of 12 • C to prevent condensation on the exterior un-insulated vapour exhaust tubing. The heaters are mounted close to the silicon tracker cold volume in the closed ID zone, which is flushed with dry CO 2 gas to prevent condensation. The evaporation pressure in the on-detector cooling tubes (and thereby the detector operating temperature) is set with a BPR located on a service platform around 30 m downstream of the heater.
The pressure drop in the exhaust system between the end of the on-detector cooling tube (E') and the input of the BPR (F') must be well understood and managed, or can result in an unacceptable increase in detector operating temperature, particularly at high power loads following operation at high accumulated radiation dose. The original design, in which the internal diameters of the exhaust tube, electric heaters and heat exchanges were chosen, assumed a maximum pressure drop over segment E'FF' of 470 mbar [1]. Operation with this exhaust pressure drop using C 3 F 8 would result in a thermodynamic cycle similar to that shown in the pressure-enthalpy diagram of figure 2.
The thermodynamic cycle is composed of several state transitions occurring between successive indices, as detailed table 1.
The operating temperatures of the SCT and Pixel silicon substrates affect long term annealing processes which determine the increase in depletion voltage and leakage current (I leak ) under irradiation.
These silicon substrates will remain thermally stable only if the coolant temperature and thermal resistance are low enough to allow the heat generated by the front end electronics and substrate leakage current to be removed. Failure to maintain a sufficiently low temperature can result in 'thermal runaway' [2], a self-destructive positive feedback phenomenon where the self-heating product of substrate leakage current and applied depletion voltage can further increase I leak .
It was believed that these concerns would be addressed by maintaining the temperature of the silicon substrates of the SCT and Pixel detectors below -7 • C [3,4] and 0 • C [5] respectively. Expected thermal impedances through the support structures attaching the silicon modules to the coolant channels predicated a typical evaporation temperature of ∼ -25 • C in the on-detector cooling channels for full power operation after the accumulation of radiation damage from 10 years of LHC operation under the original luminosity LHC assumptions [3][4][5]. This evaporation temperature was Figure 2. Target pressure-enthalpy diagram for the ATLAS ID evaporative cooling system operation with C 3 F 8 (table 1). the original design specification for the ATLAS silicon tracker cooling system [1], corresponding to an evaporation pressure of 1.67bar abs with C 3 F 8 , as illustrated in the pressure-enthalpy diagram of figure 2. More recent -and reduced -estimates of the 10 year integrated luminosity at LHC have suggested that a higher SCT silicon module substrate temperature of 10 • C could assure a safety factor of two against leakage power induced thermal runaway (as reported in [6]). These module operating temperatures would be maintained by a corresponding evaporation temperature of -15 • C in the SCT on-detector cooling channels.

Measured limitations of C 3 F 8 evaporative cooling for the SCT barrel bi-stave circuits
Previous studies made in a test structure representing an SCT cooling channel -(referred to hereafter as a "bi-stave") had shown [6] evaporation at the design pressure of 1.67 bar abs to be unachievable over a wide range of power dissipation in the currently-configured C 3 F 8 evaporative cooling system, due to higher than expected pressure drops in inaccessible regions of the exhaust vapour return system (segment E'FF' in figure 2). Figures 3 and 4 illustrate the test structure that was used to emulate a barrel SCT cooling circuit and which has been retained and extended for the present study. Spare parts for barrel SCT cooling circuits were used to build the bi-stave test structure, including the on-detector cooling tubes, the -4 - Table 1. Transition points on the enthalpy-pressure diagram of figure 1.

Transition
Physical State and location A→B Pressure and temperature rise from (1 bar abs , 20 • C) at the input of the oil-less two-stage compressor, 1 to (17 bar abs , 90 • C) at its output.
B→C Subsequent cooling and condensation of the C 3 F 8 vapour; Sub-cooling of the condensed C 3 F 8 liquid in a storage tank in the ATLAS technical cavern and along its 150m delivery path to flow division racks located on service platforms mounted on the detector.
Pressure drop over the PRs on the liquid distribution manifolds and delivery tubes to the inner detector cold volume.
Sub-cooling of the arriving C 3 F 8 liquid through counterflow heat exchange with exhausting liquid/vapour (segment EF), allowing the use of a greater fraction of the available enthalpy of evaporation to cool the detector.

F→F'
Evaporation of any liquid remaining at the output of the heat exchanger, and the raising of the vapour temperature to 20 • C 2 using an electric heater.

F'→A
Combined pressure drop across the BPR 3 defining the on-detector evaporation temperature and the tubing returning the vapour from the ATLAS service platforms to the compressor input. module attachment blocks [7], the heater, subcooling heat exchanger and capillaries, to which additional instrumentation was added for measurement of the temperature and pressure profiles.
The "on-detector" part of the test structure consists of two U-shaped "staves" sharing a common exhaust manifold, together with the local liquid delivery and exhaust tubing. In the installed detector such "on-detector" components lie within the pseudorapidity acceptance of the silicon tracker; their associated radiation length (%X0) must be reduced as far as possible, consistent with operating practicality, to minimise background and multiple scattering. Other elements, including liquid subcooling heat exchangers, exhaust heaters and the larger diameter liquid delivery and exhaust vapour tubing are positioned outside of this critical zone at larger radius.
-5 -In each stave two straight cupro-nickel tubes of 4.06 mm internal diameter and 70 µm wall thickness are attached in series with a 180 • turn at the midpoint. Liquid coolant flow is equally divided between the two staves through the use of a pair of capillaries of nominal internal diameter 0.76 mm and length 72 cm.
The cooling tube of each stave has a combined length of 300 cm and cools 24 dummy modules: ceramic substrates of length 6.2 cm and width 2.5 cm with deposited zig-zag metallic heating elements of resistance 161 ± 0.2 Ω. Heat from the dummy modules is directed through a film of GC-ELECTRONICS R 10-8108 4 thermal grease to standard SCT aluminium alloy coupling blocks [7] which are silver soldered to the cooling tubes.
Temperature sensors are attached at various positions in the liquid supply and vapour exhaust tubing, as indicated in figure 3 and to the Cu-Ni tubes of the staves at positions midway between modules. The overall uncertainty in temperature measurements was estimated to be ± 0.35 • C, based on the intrinsic sensor resolution, 5 ADC calibration and the standard deviation in measured temperature values under zero power operation with a flow of around 12.7 g.s −1 C 3 F 8 and a backpressure of 1.2 bar abs . 6 The latter uncertainty includes the effects of small variations in temperature sensor attachment to the cooling tube.
The pressures in the system were measured with electronic transducers. 7 The pressure upstream of the capillaries was measured to a precision of ± 15 mbar 7 by transducers with 30 bar full scale. Pressures downstream of the capillaries, at the half-way points on each stave, on the common exhaust and at the input of the BPR were measured to a precision of ± 5 mbar 7 by transducers with 10 bar full scale. In all tests both staves were run in parallel under identical flow and power conditions: the overall exhaust system pressure drop is thus determined by the combined exhaust flow, in the same way as in the installed SCT barrel bi-staves.
The SCT bi-stave test structure was housed in a plexiglass box externally insulated with 5 cm of Armaflex R insulation and flushed with dry air. As in the SCT detector, the liquid refrigerant delivered to each capillary was locally sub-cooled to a temperature of around -15 • C in a heat exchanger cooled by counter-flowing cold exhaust liquid/vapour. A combined fixed liquid flow of 12.7 ± 0.3 g s −1 8 was established with the upstream liquid PR set to 13bar abs and injected into the two capillaries, irrespective of the heat dissipation in the structure. The PR was followed by a heat exchanger operating with water at 17 • C to stabilise the liquid temperature at the input of the 4 Thermal conductivity 0.75 Wm −1 K −1 , similar to that of Dow Corning 340 used in the SCT detector (0.67 (1kΩ) at 25 • C. Resistance variation with absolute temperature T of the form where B= 4390 ± 1%. These two effects yield a combined intrinsic temperature error of ± 0.21 • C. 6 The difference in pressure measured between the inlet and exit of a stave ( figure 3) was around 100 mbar, implying a difference in saturation temperature of 1.5 • C. However in the zero power condition the thermal conductivity of the Cu-Ni tube was able to equilibrate the temperature to within ± 0.28 • C (standard deviation of around 100 measurements on each of 25 tube wall temperature sensors taken under stable flow conditions), masking the effect of the dynamic pressure drop seen at higher applied power levels. 7 Model PAA33X pressure transducer. Keller AG: St. Gallerstrasse 119 CH-8404 Winterthur Switzerland. Precision ± 0.05% of full scale. 8 Based on the standard deviation of around 400 flow measurements over a period of around 2 hours, during which thermal data were taken at 4 power ratings (0W, 6W, 9W and 10.5W per emulated module) at the same backpressure.
-6 -  -7 - Figure 5. Thermodynamic cycles on a pressure-enthalpy diagram for the evaporative cooling system operating with pure C 3 F 8 : at total power loads of 0 W, 288 W & 504 W in the SCT bi-stave thermal test structure [6].
sub-cooling heat exchanger against temperature variations in the test building. The injected flow represented 120% of that needed to cool the structure at the maximum on-detector power load of 504 Watts. Fluorocarbon refrigerant leaving the SCT test structure (containing a variable amount of unevaporated liquid, depending on the power dissipation in the preceding test structure) was evaporated in a downstream electrical heater, which also raised the exhaust vapour temperature to 20 • C (maintaining the same safety margin above the expected cavern dew point of 12 • C) as in the installed detector, for return to the blend machine compressor.
The evaporation pressure in the test structure was set by the BPR, located downstream of the heater, following ∼ 30 m of uninsulated copper pipe, as in the installed system [6].
The achievable thermodynamic cycles, based on measurements made in the test structure dissipating 0 W, 288 W and 504 W in total; respectively equivalent to 0 W, 6 W and 10.5 W per module are shown in figure 5. Table 2 details the various state transitions.
It can be seen from figure 5 -even with injection at around -15 • C -that the exhaust pressure drop E ' FF' exceeded the specification [1], with the greatest effect coming from the pressure drop in the exhaust heat exchanger (segment E'F). This pressure drop raised the evaporation temperature -8 - Table 2. Transition points on the enthalpy-pressure diagram of figure 5 for operation with C 3 F 8 in the test structure.

Transition
Physical State and location A→B C 3 F 8 vapour compressed from 1 to 17 bar abs , heated to 90 • C in a 2-stage compressor.
B→C C 3 F 8 vapour condensed inside the condenser at 53 • C and delivered to a storage tank. C→D 1 C 3 F 8 liquid cooled in the storage tank and along its delivery path to the liquid supply pressure regulator.
Pressure drop from 16 to 13 bar abs across the liquid supply pressure regulator and along the liquid delivery tubing to the SCT detector. -and with it the module operating temperature -by more than 10 • C (13 • C) from the -25 • C design figure when the bi-stave was operated at power dissipations of equivalent to 6 W and 10.5 W dissipation per module respectively. The temperature gradient along the on-detector evaporator EE' also exceeded the SCT specification of 5 • C [7].
The effects of these pressure drops are also manifested in differences between the maximum evaporation temperatures measured on the tube wall and that expected from the C 3 F 8 saturated vapour temperature corresponding to the pressure at the BPR, as illustrated in figure 6.
The abscissa of figure 6 is the pressure measured at the input of the BPR (P BPR in figure 3) around 30 metres downstream of the heater. The BPR is 'dome-loaded': a pneumatic command signal in the range 1-4 bar abs applied to its dome sets the pressure immediately upstream of the device, to which the evaporation pressure in the on-detector cooling tube is referenced via the incremental pressure drop in the preceding exhaust tubing, heater and heat exchanger (figure 1). Remote analogue pneumatic signals have been chosen for use in the high radiation zones of ATLAS due to the simultaneous presence of high magnetic fields.
From figure 6 it can be seen that at P BPR = 1.35 bar abs the maximum temperatures measured along the on-detector cooling tube were -11.8 • C, -15 • C and -17.5 • C for total power dissipations equivalent to 10.5 W, 6 W and 3 W per module. These temperatures respectively correspond to local ("on-detector" cooling tube) evaporation pressures of 2.75, 2.47 and 2.25 bar abs . The differences between these pressures and the BPR input pressure of 1.35 bar abs manifest the effect of pressure drop in the exhaust tubing linking the emulated bi-stave to the BPR. The increase is particularly pronounced at lower system pressures where the C 3 F 8 saturated vapour density is lower (resulting -10 -in a higher liquid → vapour expansion ratio and a consequently higher exhaust vapour volume flow). It can further be seen from figure 6 that an on-detector evaporation temperature of -15 • C cannot be reached at total dissipations equivalent to 9 W and 10.5 W per module.
The consequent perceived risk of leakage power-induced thermal runaway in SCT silicon sensors after extended operation at LHC motivated an investigation into the possible reduction of evaporation temperature through the circulation of blends of C 2 F 6 and C 3 F 8 within the existing SCT on-detector cooling tubes. This would in turn reduce the temperature-dependent leakage power and extend the safety margin against thermal runaway.
At the time of writing this paper updated LHC luminosity projections suggest that leakage power will be lower than previously foreseen, with the consequence that pure C 3 F 8 is likely to be sufficient. Nevertheless, the ability to use blends to lower the evaporation temperature provides a vital backup solution should requirements or projections change in the future.
1.4 C 2 F 6 /C 3 F 8 blends for lower evaporating temperatures in existing cooling structures Although from figure 6 it can be seen that an evaporation temperature of -15 • C is not achievable using pure C 3 F 8 in an SCT bi-stave at the highest module power levels, calculations with the NIST-REFPROP package [8] suggested that evaporation temperatures of -15 • C and below would be reachable by blending C 3 F 8 with a more volatile component of similar (radiation resistant, nonflammable and dielectric) chemical structure. This possibility stimulated the study reported in this paper.
Among the saturated fluorocarbons of structure C n F (2n+2) , hexafluoro-ethane (C 2 F 6 ; mw = 138) is the nearest neighbouring fluid of increased volatility. The addition of sufficient C 2 F 6 in a binary blend would be expected to reduce the evaporation temperature for the same evaporation pressure (or increase the evaporation pressure for the same evaporation temperature), allowing sufficient margin to overcome the pressure drops seen with pure C 3 F 8 .
In contrast to the case of pure C 3 F 8 , evaporation and condensation in C 2 F 6 /C 3 F 8 blends are not simultaneously isothermal and isobaric. Due to their similar chemical structure C 2 F 6 /C 3 F 8 blends can be considered as zeotropic mixtures manifesting "temperature glide" when evaporating and condensing. Temperature glide is illustrated in figure 7 for a molar blend of 85% C 3 F 8 / 15% C 2 F 6 , while table 3 compares the Saturated Liquid Pressure (S.L.P) and Saturated Vapour Pressure (S.V.P) for evaporation at temperatures of -25 • C and -15 • C in pure C 3 F 8 and a variety of C 2 F 6 /C 3 F 8 blends of thermodynamic interest. Also shown in table 3 is the maximum temperature glide assuming all the available enthalpy of evaporation is used. In practice, not all the enthalpy is available for use in the on-detector evaporator (cooling tube): the liquid sub-cooling temperature may be warmer than the evaporation temperature, while evaporation enthalpy may be shared between the on-detector evaporator and a downstream exhaust heat exchanger and heater (figure 1). Taking an example from figure 7; the use of only half of the ∼ 110 kJkg −1 of available enthalpy (illustrated in figure 7 using a violet band) in the on-detector cooling channel at an evaporation pressure of 1.94 bar abs and an injection temperature of -15 • C would result in a temperature rise of ∼ 6 • C (illustrated in red) from the injection point to the exit of the on-detector cooling channel. This temperature glide effect would be partially opposed however by the dynamic temperature gradient due to evaporation pressure drop with distance from the input of the channel. This dynamic -11 - Figure 7. Pressure-enthalpy diagram for a molar blend of 85% C 3 F 8 /15% C 2 F 6 (from NIST-REFPROP [8]). The curving evaporation isotherms illustrate the naturally anisobaric nature of the phase change. The use of half the available enthalpy (shown in violet in inset) at an evaporation pressure of 1.94 bar abs with injection at -15 • C would result in a temperature rise ("glide") of ∼ 6 • C (shown in red in inset). temperature gradient is readily observable in the evaporation of a pure coolant like C 3 F 8 -the exhaust end of an on-detector evaporator being colder than the input.

JINST 10 P03027
In operation with C 2 F 6 /C 3 F 8 blends it will be necessary to monitor the molar mixture ratio and if necessary to adjust it with the addition of either component. The C 2 F 6 /C 3 F 8 mixing station and recirculator is discussed in section 2.1, while the protocol used to create C 2 F 6 /C 3 F 8 molar blends is discussed in appendix A.
The C 2 F 6 /C 3 F 8 molar ratio is best monitored through measurement of sound velocity in the superheated (single phase) vapour state. In table 3 the sound velocities at 20 • C, 1 bar abs were calculated for various C 2 F 6 /C 3 F 8 blends using the NIST-REFPROP package [8]. The custom ultrasonic instrument developed for simultaneous on-line blend composition and vapour flow measurement [9] is discussed in appendix B.
Results from thermal studies with pure C 3 F 8 and in C 2 F 6 /C 3 F 8 blends in a test structure representing an SCT barrel bi-stave are presented in section 3.
2 The blend recirculation machine and cooling circuit 2.1 The blend recirculation machine Figure 8 illustrates the custom-built fluorocarbon blend recirculation machine, while figure 9 shows the schematic of the blend machine local components. The machine can be used to create and circulate molar blends of C 3 F 8 and C 2 F 6 .
The principal elements of the blend recirculator are: • a three-cylinder, single stage oil-less compressor 9 operating with a typical aspiration pressure of 1000 mbar abs and an output pressure of 9 bar abs ; • a high pressure condenser/reservoir tank cooled to operate in the range (-30 → 20 • C); by a refrigerator operating with R404A refrigerant; • a liquid pressure booster pump 10 located around 2.5 m below the condenser, which adds around 7 bar to the pressure of the liquid leaving the condenser; • weighing platforms for the condenser/reservoir tank and the C 2 F 6 and C 3 F 8 cylinders. These platforms allow molar blends of C 3 F 8 and C 2 F 6 to be created by mass addition in the liquid phase according to the protocol discussed in appendix A; • an ultrasonic vapour mixture analysis instrument for measurement of the molar C 2 F 6 and C 3 F 8 concentrations in superheated vapour. The instrument is discussed in appendix B.
The blend machine operation is highly automated: the main parameters of the system can be set and monitored remotely using the CERN UNICOS [10] distributed control system environment.
In the thermal studies with C 2 F 6 /C 3 F 8 blends it was intended to reproduce as far as possible the as-installed liquid delivery and vapour return configuration. However since no two-stage compressor could be spared for integration into the blend machine a booster pump was used to raise the liquid pressure to around 16 bar abs : a pressure sufficient to deliver the liquid via the 50 m of tubing linking the blend recirculator and the thermal test stand. The compressor output pressure was 9 Haug Model WTEGX80 LM-L, maximum nominal output (minimum nominal aspiration) pressures of 11(0.8) bar abs flow rate 17m 3 hr −1 C 3 F 8 at P in = 1.0 bar abs , P out = 7 bar abs . 10   limited to 9 bar abs ; around 2 bar lower than its maximum pressure in order to reduce mechanical strain. Fluorocarbon vapour (either pure C 3 F 8 or C 2 F 6 /C 3 F 8 blend) was condensed at this pressure. Liquid fluorocarbon leaving the condenser at 9 bar abs descended around 2.5 m to the liquid booster pump, which added around 7 bar relative to the output pressure of the condenser. The liquid descending to the pump passed through a heat exchanger which was counter-cooled with a water/glycol mix, leaving with a temperature in the range 15-17 • C. Together with the hydrostatic column of 2.5 m (plus the liquid height in the condenser) this ensured that the pump was always kept primed to avoid vapour-induced cavitation. The 50 m interlink tubing was insulated with 25 mm of Armaflex R foam and passed through an air-conditioned zone.
2.2 Examples of thermodynamic cycles in operation with C 3 F 8 and C 2 F 6 /C 3 F 8 blends Figure 10 illustrates the measured thermodynamic cycle on an enthalpy-pressure diagram for the blend recirculator operating with pure C 3 F 8 , the reference with which all thermal studies with blends are later compared. Figure 11 illustrates the measured thermodynamic cycle on an enthalpypressure diagram for the blend recirculator operating with a molar blend of 75% C 3 F 8 /25% C 2 F 6 .
Systematic differences due to the constraints of the blend recirculation machine can be seen relative to the thermodynamic cycle of figure 5; • the lower compression available in the single stage compressor (segment AB); • the increase in liquid pressure from the booster pump (segment CD 1 ).
Some differences between the thermodynamics of figures 10 and 11 are also readily apparent: • in the molar blend of 75% C 3 F 8 /25% C 2 F 6 the maximum evaporation temperature 'glide' (traversal of isotherms along the on-detector evaporation segment EE') of around 4 • C is seen for zero heat load; • in the same blend the condensation pressure is defined by the 9 bar abs output pressure of the compressor, causing the blend to condense over the 14 • C temperature 'glide' between 16 • C (incoming vapour) and 2 • C (bulk liquid) in the volume above the liquid in the condenser/reservoir tank.
• the fluid starts boiling in the capillary. Table 4 summarises and discusses the transition points on the thermodynamic cycles shown in figures 10 and 11 for circulation of pure C 3 F 8 and the molar blend of 75% C 3 F 8 /25% C 2 F 6 .
-15 -2015 JINST 10 P03027 Figure 10. Thermodynamic cycle on a enthalpy-pressure diagram for the blend recirculator operating with pure C 3 F 8 at power loads of 0, 288 & 504 W in the emulated SCT bi-stave; backpressure set to 1.2 bar abs .
3 Comparison of cooling performance in C 3 F 8 and C 2 F 6 /C 3 F 8 blends Thermal profiles were measured along the cooling tubes (staves) of the SCT test structure of figure 3, at power settings of 0 W, 3 W, 6 W, 9 W and 10.5 W per dummy module. The two identicallypowered staves of 24 thermal emulator modules shared a common output: the exhaust pressure drop was therefore comparable with that of an operational SCT barrel bi-stave.
These measurements were repeated for nominal C 2 F 6 molar concentrations of 0%, 1%, 3%, 5%, 10%, 20% and 25% in the C 2 F 6 /C 3 F 8 blend. These concentrations were "targets" for the blending protocol described in appendix A: the achieved concentrations were verified to a precision of ± 0.3% in the ultrasonic analyser discussed in appendix B. Figure 12 illustrates the complete temperature profile along one of the staves, read out by 25 sensors attached to the cooling tubes between the dummy modules. The upper plots show the temperature profiles at the different module power dissipations for pure C 3 F 8 coolant (solid lines) while the lower plots show temperature profiles at the same power dissipations for a blend containing 25%C 2 F 6 /75%C 3 F 8 (dashed lines). All data in figure 12 correspond to a back pressure (P BPR ) of 1.2 bar abs . Figure 13 illustrates the corresponding temperature profiles at the same power settings for P BPR = 2 bar abs . The liquid pressure at the capillary input was 13 bar abs for both backpressures.
-16 - Figure 11. Thermodynamic cycle on an enthalpy-pressure diagram for the blend recirculator operating with a molar blend of 75% C 3 F 8 / 25% C 2 F 6 at total power loads of 0, 288 & 504 W in the emulated SCT bi-stave; backpressure 1.2 bar abs .
It can be seen that the temperature profile along the stave in the 25%C 2 F 6 /75%C 3 F 8 blend increases toward the exit, in contrast to the reduction generally seen in pure C 3 F 8 . This effect is the result of the opposing effects of temperature glide and dynamic temperature gradient along the evaporator and is most apparent when almost the full enthalpy is used in the stave at a power of 10.5 W per module. Nevertheless at this power the maximum temperature on the tube remains no higher than -21 • C (-15 • C) with P BPR = 1.2 bar abs (2 bar abs ). Figure 14 illustrates the maximum temperature seen on the tubes of the emulated SCT bistave as a function of the ultrasonically-verified molar concentration of C 2 F 6 in the blend, for three different power (per module) levels, with P BPR = 1.2bar abs . As expected, the addition of the more volatile C 2 F 6 component reduced the evaporation temperature on the cooling tubes under the same operational "envelope"; the same liquid supply and exhaust backpressures. The improvements for 0 W, 6 W and 10.5W per module are respectively characterised by gradients of approximately -0.50, The addition of 25% C 2 F 6 was found to reduce the maximum evaporation temperature on the cooling tubes from -12 • C (-15 • C) at a dissipation of 10.5 (6) Watts per module to -21 • C (-25 • C) respectively when operating at the same backpressure. Figure 15 compares the maximum temperature seen on the tubes of the emulated SCT bi-stave with pure C 3 F 8 to that seen in a blend containing 25% C 2 F 6 , at P BPR values of 1.20, 2.26, 2.40, 2.60 and 2.78 bar abs .
-17 - Table 4. Transition points on the enthalpy-pressure diagram of figures 10 & 11 for blend recirculator operation with an emulated SCT barrel bi-stave operating with pure C 3 F 8 and a molar blend of 75%C 3 F 8 /25%C 2 F 6 .

Transition
Physical State and location A→B Refrigerant vapour is compressed from 1 bar abs to 9 bar abs and heated to 70 • C by a single stage compressor.

B→C
Refrigerant vapour condenses inside the condenser/storage tank (at 27 • C for pure C 3 F 8 and over the range 17 • C → 5 • C for 25% C 2 F 6 /75% C 3 F 8 ).

C→D 1
Refrigerant in liquid state from the condenser/storage tank is sub-cooled before the liquid booster pump to a temperature of 17 • C, and is raised in pressure to 16 bar abs by the pump. In the case of 25% C 2 F 6 /75% C 3 F 8 the refrigerant is warmed to 17 • C.
Pressure drop from 16 bar abs to 13 bar abs across the liquid supply pressure regulator and liquid delivery tubing to the emulated SCT bi-stave.
Liquid sub-cooling in the local liquid supply heat exchanger by counter-flow of remaining liquid/cold vapour in the exhaust line (to -15 • C for pure C 3 F 8 and -25 • C for 25% C 2 F 6 /75% C 3 F 8 ) Note: exact sub-cooling temperature (point D 3 ) depends on the total heat load in the emulated SCT bi-stave. A comparison of the left and right hand plots of figure 15 illustrates again that 25% C 2 F 6 in a C 2 F 6 /C 3 F 8 blend is capable of reducing the maximum temperature on the cooling tubes by 9 • C in operation at the highest power level of 10.5 W per module. Figure 15 further illustrates that in such a blend an evaporation temperature of -15 • C is achievable everywhere on the structure for operation at P BPR 2.38 bar abs . This cooling tube temperature would allow a safety factor of two in heat dissipation against thermal runaway in SCT silicon module substrates after 10 years of LHC operation, as outlined in section 1.1. Figure 16 compares the maximum temperature seen in operation with pure C 3 F 8 to that seen in a blend containing 25% C 2 F 6 for the corresponding pressures sensed at the 180 • half way points (figure 3). It can be seen that the temperature-pressure profiles for the different power levels become almost collinear with the C 3 F 8 saturation line. In the 25%C 2 F 6 /75%C 3 F 8 blend all the temperaturepressure profiles fall within the zone delineated by the saturated liquid pressure (lower) and saturated vapour pressure (upper) curves. As the power increases the temperature-pressure profiles migrate progressively toward the saturated vapour line as more vapour is produced by evaporation, and toward higher pressures as the dynamic pressure drop increases.
-19 -2015 JINST 10 P03027 Figure 13. Comparison of the temperature profile along an SCT Barrel staves in pure C 3 F 8 (solid lines) and with 25%C 2 F 6 / 75%C 3 F 8 blend (dashed lines) [6], at 2bar abs backpressure. Temperature measurement precision: ± 0.35 • C. Figure 17 illustrates the difference in maximum temperature seen on the tubes of the emulated SCT bi-stave between cooling with pure C 3 F 8 and a blend containing 25%C 2 F 6 /75%C 3 F 8 , for five different power (per module) levels. In each case the pressure upstream of the capillary is 13bar abs while P BPR varies between 1.2 and 3 bar abs . It can be seen that a reduction in operating temperature of at least 8.5 • C is possible for all power levels in a blend containing 25% C 2 F 6 .

Conclusion
We have constructed a custom thermodynamic recirculator that has been used for investigations of the cooling capabilities of C 2 F 6 /C 3 F 8 blends with molar admixtures of up to 25% C 2 F 6 . The cooling performance of these blends was studied in a representative test setup of an ATLAS barrel SCT bi-stave containing 48 thermal emulator modules. The test structure incorporated an exhaust heat exchanger, an electric heater, backpressure regulator and intervening tubing identical to those used in the installed SCT system. Fluorocarbon blend molar concentrations were verified in the superheated vapour phase using an ultrasonic instrument with a typical resolution of ± 0.3%.
-20 - Figure 14. Maximum temperature on a tube of the SCT bistave vs C 2 F 6 concentration in the blend, for three different power (per module) levels [6]. In each case the input pressure is 13bar abs upstream of the capillary and the back pressure is 1.2bar abs . Temperature (mixture) measurement precision: ± 0.35 • C (± 0.3%: appendix B). Figure 15. Maximum evaporation temperature on the cooling tubes between dummy modules in an SCT barrel bi-stave evaporator as a function of the pressure measured at the input of the back pressure regulator [6], for different applied detector power (per module: 48 modules total). Temperature (pressure) measurement precision: ± 0.35 • C (± 15 mbar) Left plot: pure C 3 F 8 , with C 3 F 8 saturation curve shown for comparison. Right plot: 25%C 2 F 6 /75%C 3 F 8 , with saturated vapour (upper) and saturated liquid (lower) curves.
-21 - Figure 16. Maximum evaporation temperature on the cooling tubes between dummy modules in an SCT barrel bi-stave evaporator as a function of the pressure measured at the half-way point between the two staves [6], for different applied detector power (per module: 48 modules total). Temperature (pressure) measurement precision: ± 0.35 • C (± 15 mbar) Left plot: pure C 3 F 8 , with C 3 F 8 saturation curve shown for comparison. Right plot: 25%C 2 F 6 /75%C 3 F 8 , with saturated vapour (upper) and saturated liquid (lower) curves. Figure 17. Reduction of maximum temperature on a tube of the SCT bistave vs pressure, by replacing pure C 3 F 8 with a blend containing 25% C 2 F 6 . Data are shown for five different backpressures and power (per module) levels [6]. The pressure upstream of the capillary is 13bar abs . Temperature measurement precision: ± 0.35 • C.
-22 -As expected, the addition of the more volatile C 2 F 6 component reduced the evaporation temperature measured on the cooling tubes of the emulated SCT bi-stave. These improvements are characterized by gradients of approximately -0.50, -0.45 & -0.37 • C.%[C 2 F 6 ] −1 respectively at power dissipations of 0, 6 and 10.5 W per emulated module. A new dedicated structure is being constructed for the measurement of absolute heat transfer coefficient in C 3 F 8 and C 2 F 6 /C 3 F 8 blends: measurements will be presented in a future work.
The addition of 25% C 2 F 6 was found sufficient to reduce the evaporation temperature on the cooling tubes of a barrel SCT bi-stave from -12 • C (-15 • C) to -21 • C (-25 • C) at a dissipation of 10.5 (6) Watts per module, respectively in operation with an exhaust backpressure set to 1.2bar abs . This temperature reduction would compensate for the pressure drops seen in inaccessible regions of the exhaust return tubing in operation with pure C 3 F 8 , and would be sufficient to allow the asinstalled barrel SCT bi-staves to be operated for 10 years under demanding previously-foreseen LHC luminosity conditions, equivalent to an integrated luminosity of around 700 fb −1 .
While more recent LHC projections suggest an integrated luminosity of only 300-400 fb −1 over 10 years of operation up to the LHC 3 rd long shutdown ("3LS": currently proposed for 2023), it is clear that operation with a blend containing 25% C 2 F 6 would provide a valuable safety net should the integrated luminosity accumulated before 3LS prove to exceed recent forecasts. Furthermore, a blend containing up to 25% C 2 F 6 could be circulated in the existing ATLAS inner detector evaporative cooling system. the individual vapour pressure for each component being: where p i is the partial pressure of the component i in the mixture, and x i is the mole fraction of the component i in the liquid mixture.
In the blend machine, illustrated in figures 8 and 9, the condenser also serves as a liquid reservoir tank and is fitted with a dynamometer for weight measurements, while the cylinders containing the C 2 F 6 and C 3 F 8 constituents stand on weighing platforms, allowing a redundancy in mass transfer measurements.
A prerequisite for making or modifying a blend is that all the fluorocarbon liquid -and as much of the vapour as possible -is first recovered from the ∼ 60m external piping -back into the condenser to give a new mass baseline. This recovery is made using the compressor, with the liquid in the delivery line either being allowed to boil through the thermal test stand or (more quickly) through a thermal load bypass. In practice a small amount of vapour (at the minimum compressor aspiration pressure of 800 mbar abs ) remains in the liquid supply and vapour return piping after this operation. This must be evacuated before resuming circulation through the thermal test stand, to avoid changing the mixture of the new blend.
The number of moles per kilogram of C 2 F 6 and C 3 F 8 in a liquid mixture, given by the reciprocals of their molar masses of 0.138 and 0.188 kg, are respectively 7.25 and 5.32 moles.kg −1 .
The resulting C 2 F 6 mole fraction, M C 2 F 6 ,obtained through adding X kg liquid C 2 F 6 and Y kg liquid C 3 F 8 is given by: To achieve a blend having desired molar C 2 F 6 & C 3 F 8 fractional concentrations M C 2 F 6 and M C 3 F 8, X kg of liquid C 2 F 6 is added to Y kg of liquid C 3 F 8 already in the condenser to arrive at a total liquid mass of Z kg of blended fluorocarbon liquid, such that: The total number of moles, M, in the liquid mixture is given by: As an example, for a desired molar ratio of 95%C 3 F 8 /5%C 2 F 6 , 386 g of liquid C 2 F 6 would need to be added to 10 kg liquid C 3 F 8 already in the condenser tank, for a total of 56 moles. The multi-step procedure used to create this blend is outlined below: • Step 1: the mass of 10 kg, equivalent to 53.2 moles of C 3 F 8 liquid transferred to the condenser of the blend machine is verified by subtraction of the tare weight of the C 3 F 8 cylinder and its flexible tubing from their combined gross weight).
• Step 2: the overall weight of the C 2 F 6 cylinder and its flexible tubing are noted; -24 -2015 JINST 10 P03027 • Step 3: the condenser temperature is reduced to around -30 • C, reducing the saturated vapour pressure of the C 3 F 8 fluid to ∼ 1.36 bar abs . This temperature is chosen to be significantly below the saturated vapour pressure of C 2 F 6 in its uncooled cylinder (∼ 27 bar abs at 15 • C) to allow the saturated vapour pressure in the condenser to be measured over a wide range of C 2 F 6 concentrations; • Step 4: 386 g of C 2 F 6 is progressively transferred into the condenser reservoir, noting the change in saturated vapour pressure of the fluid mixture in the condenser -according to a prepared curve of vapour pressure vs. C 2 F 6 concentration in C 3 F 8 , as illustrated on the left axis of figure 18 -together with the mass changes in the condenser and C 2 F 6 cylinder. The condenser pressure is measured with a transducer having a resolution of ± 15 mbar. Small additive steps, followed by pauses of a few minutes to allow the pressure to stabilise, are made to reduce the risk of overshoot. In practice we have found that the change in saturated vapour pressure -around 68 mbar.%[C 2 F 6 ] −1 -to be a more precise indicator than the change in mass in the cylinder and condenser which are measured by electronic balances with a precision of ± 100 g. Nonetheless all mixtures are considered "nominal" at this stage: absolute molar mixture ratio is measured in a custom ultrasonic gas mixture analyser (step 6); • Step 5: when C 2 F 6 transfer is complete and confirmed by the condenser pressure at -30 • C (figure 18), the condenser temperature is increased to raise the pressure to around 9 bar abs , a value chosen to be within the safe range of output pressure of the compressor. The temperature necessary to achieve this for different C 2 F 6 /C 3 F 8 molar mixtures is shown in figure 12 (right axis). The condenser pressure of 9 bar abs is insufficient to supply the thermal test structures; the liquid booster pump increases the liquid pressure to around 16 bar abs ; • Step 6: the compressor is started and the blended fluid circulated through a dummy load around a short closed loop on the blending machine (figures 6, 7). In this loop the superheated vapour mixture passes through a custom ultrasonic gas mixture analyser (section 4). The molar mixture of the circulating fluid is determined to a precision of ± 0.3% from the sound velocity, which is a unique function of the molar concentrations of the two components at the measured temperature and pressure; • Step 7: if the mixture corresponds to the desired ratio, circulation is started through the thermal test stand.
The mixing procedure detailed in the six preceding steps is extended when more C 2 F 6 or C 3 F 8 is added to an existing C 2 F 6 /C 3 F 8 blend.
• Step 8: the fluorocarbon blend is recovered into the condenser tank from the external piping using the compressor. Fluorocarbon vapour (at the minimum compressor aspiration pressure of 800 mbar abs ) remaining in the external tubing is evacuated to avoid changing the mixture of the new blend once it is dispatched through the thermal test stand; • Step 9: the mass, Z'(kg), of the fluorocarbon fluid in the condenser is noted by subtraction of the tare weight from the gross weight. Combining fluid lost in the evacuation procedure with any lost in the preceding thermal studies, (Z -Z') kg of blended fluid is determined to have been lost.
-25 - Figure 18. Saturated vapour pressure above liquid at -30 • C in the condenser (left axis) and condenser temperature for a vapour pressure of 9 bar abs (right axis), for a range of C 2 F 6 /C 3 F 8 mixtures: calculated using NIST-REFRROP [8].
Note: measurements with the ultrasonic gas analyser (section 4) have shown that the mixture molar ratio is maintained despite losses during circulation. The mixing protocol makes use of the observation that losses affect the two components in proportion to their molar concentrations in the blend.
The total number of moles remaining, M', after losses and recovery is given by: while the numbers of remaining moles of C 2 F 6 , M' C2F6 and of C 3 F 8, M' C3F8 , are given by: • Step 10: the condenser temperature is reduced to -30 • C. This allows the molar composition of the remaining mixture to be verified by measurement of saturated vapour pressure, and also prepares for the measurement of the molar composition of the new blend; • As an example, for a new desired molar ratio of 15%C 2 F 6 /85%C 3 F 8 , 805 g of liquid C 2 F 6 would need to be added to a tank containing a remaining total of 9.36 kg of blended C 3 F 8 and C 2 F 6 with previously-set molar ratio of 5%C 2 F 6 /95%C 3 F 8 corresponding to steps 1-4. This situation might correspond to the case where 10% of the previously blended liquid had been lost due to leaks and the evacuation loss in the long tubing connecting the blend machine to the thermal test stand.
Fluid is progressively transferred into the condenser, noting mass changes in the C 2 F 6 cylinder and the condenser. Small additive steps with stabilisation pauses reduce the risk of overshoot. The change in saturated vapour pressure of the fluid mixture in the condenser is verified after each step, according to a prepared curve illustrated on the left axis of figure 13. As in step 4, all mixtures are considered "nominal" at this stage: absolute molar mixture ratio is measured by the ultrasonic gas mixture analyser (step 13); • Step 12: the condenser temperature is increased to raise the condenser pressure to ∼ 9 bar abs ; • Step 13: the compressor is started and the blended fluid circulated through the dummy load and the ultrasonic gas mixture analyser of the blend machine The molar mixture is determined to ± 0.3% from the sound velocity; • Step 14: if the mixture corresponds to the desired ratio, circulation is started through the thermal test stand.

B The ultrasonic gas mixture analysis instrument
We have developed a custom on-line instrument for the simultaneous measurement of binary gas mixture molar composition measurement and flowmetry [9]. The instrument uses the phenomenon whereby the sound velocity in a binary gas mixture at known temperature and pressure is a unique function of the molar concentration of the two components of differing molecular weight. Ultrasonic gas analysis was first used in particle physics for the analysis of the N 2 /C 5 F 12 (dodecafluoropentane: mw = 288) Cherenkov gas radiator of the SLD Cherenkov Ring Imaging Detector [11], as a simpler alternative to on-line refractive index monitoring. Since then it has been adopted in all the major ring imaging Cherenkov detectors. The instrument is illustrated in figure 19. A pair of capacitative ultrasonic transducers are mounted face-to-face around 666 mm apart in a flanged stainless steel tube. The sounding volume includes a 'pinched' region of inner diameter 44.3 mm. Vapour is diverted around the ultrasonic transducers by flow-deflecting cones. The temperature in the analysis tube is monitored to a precision of better than ± 0.2 • C through the use of six internal NTC sensors. Pressure is monitored with a transducer having ±1 mbar precision.
-27 -2015 JINST 10 P03027 Figure 19. Internal construction of the custom ultrasonic gas mixture analyser showing the mounting of the ultrasonic transducers on their axial flow-deflecting cones. Six internal NTC thermistors are also installed (not shown). The perpendicular tubes allow pressure transducer attachment and the injection of calibration gas.
Two custom ultrasonic gas mixture analyser/flowmeters were constructed to measure the molar concentration of C 2 F 6 and C 3 F 8 in the blend. Identical instruments are installed at the blend recirculation machine and at a point in the return tube near the thermal test stand Sound velocity is calculated from the transit time of sound pulses over the known path length. The molar concentration of the two component vapours is determined from a comparison of online sound velocity measurements with velocity-composition look-up table data gathered from prior measurements in calibration mixtures or from theoretical data derived according to an appropriate equation of state. The NIST-REFPROP [8] package is based on the most accurate pure fluid and mixture models currently available for a wide range of fluid combinations. It currently implements three models for the thermodynamic properties of pure fluids: equations of state explicit in Helmholtz energy, the modified Benedict-Webb-Rubin (BWR) equation of state, and an extended corresponding states (ECS) model. Mixture calculations employ a model that applies mixing rules to the Helmholtz energy of the mixture components. Figure 20 illustrates the sound velocity measured in the instrument in varying C 2 F 6 /C 3 F 8 molar mixing ratios at a temperature of 19.2 • C and a pressure of 1.14 bar abs . These calibration mixtures span the region of thermodynamic interest in this work and were set up by partial pressure ratio in the previously-evacuated tube, to create molar mixtures. Component partial pressures were set using a MKS "Baratron R " capacitative absolute pressure gauge with a precision of ± 1 mbar. The transducer foil inter-distance had been previously established using the gas calibration procedure described in [9], to a precision of ± 0.1 mm.
Individual contributions (shown in parentheses below) to the overall 0.05 ms −1 sound velocity measurement error (equivalent to 0.042 % of the measured sound velocity of 118.3 ms −1 at 20 % C 2 F 6 concentration, for example) were due to: • ± 0.2 • C temperature stability in the sonar tube (equivalent to ± 0.044 ms −1 ); • ± 4 mbar pressure stability in the tube (± 0.012 ms −1 ) with blend circulation machine operating; -28 - Figure 20. Upper plot: comparison between measured sound velocity data and theoretical predictions in NIST-REFPROP [8] for molar C 2 F 6 /C 3 F 8 mixtures of thermodynamic interest, at 1.14 bar abs & 19.2 • C. The binary gas mixture measurement uncertainty of 0.3% is illustrated in red. Lower plot: differences between the measurements and the NIST-REFPROP predictions.
The average difference between measured sound velocity and the NIST-REFPROP [8] predicted sound velocities in mixtures with (0 to 30 %) C 2 F 6 in C 3 F 8 was around 0.03 % at pressures near 1 bar abs and temperatures around 19 • C.
The precision of mixture determination, ∂ (mix), at any concentration of the two components is given by; where m is the local slope of the sound velocity/concentration curve and ∂ c is the uncertainty in the sound velocity measurement. For example, in a blend of 20 % C 2 F 6 in C 3 F 8 the sound velocity uncertainty of 0.05 ms −1 yields a concentration uncertainty of ∼0.3 % at 20 %C 2 F 6 , where the slope is ∼0.18 ms −1 %.[C 2 F 6 ] −1 .