Measurements of the Joule-Thomson coefficient in cryogenic fluids

Contributors

• Jakub Tkaczuk — 0000-0001-7997-9423 — design, data collection & analysis, writing
• Nicolas Luchier — 0000-0002-5852-4726 — supervision, review
• François Millet — 0000-0002-1240-0138 — supervision

Introduction

This repository contains the raw data, processed data, and code used to obtain and analyse measurements of the Joule-Thomson coefficient in pure gases and mixtures at temperatures between 65 K and 180 K. It is the supporting dataset for the article submitted to the Journal of Chemical & Engineering Data.

The measurements from this repository validate the earlier-developed equations of state in the single-phase region. Indirect measurements are first acquired for pure fluids, allowing for the experiment validation and then for mixtures, providing new results to the study. The expanded relative standard uncertainty is calculated along with the Monte Carlo analysis for the combined uncertainty. The impact of the composition uncertainty on the Joule-Thomson coefficient is quantified for mixtures using the Monte Carlo simulations.

System description

The fluid path starts at a 50 L high-pressure cylinder holding the pure fluid or the pre-mixed binary mixture. The cylinder is connected through the pressure-reducing valve RV004A to a 1 U.S. gallon (3.6 L) buffer volume that smooths out the manual adjustments of the reducer and absorbs the slow pressure decay of the supply cylinder, reducing the frequency of inlet corrections from seconds to minutes.

Inside the cryostat (dashed envelope in the P&ID below), a copper block with a brazed heat exchanger is mounted on the cold head of a Cryomech AL300 Gifford-McMahon cryocooler, capable of cooling the inlet flow from 300 K down to about 40 K. A 6 m helical capillary (304L stainless steel, 0.4 mm × 1 mm ID × OD, 0.365 mm equivalent ID) imposes the isenthalpic expansion. Two calibrated Lake Shore Cernox temperature sensors are placed upstream (TT101, T_in) and downstream (TT102, T_out) of the capillary, with their lead wires thermalised at the cold head. Pressure is measured at the same two stations with Mensor CPT 6100 absolute-pressure transducers (PT101, PT102; 0.01% FS, p_max = 13.7 MPa).

Two fine-control needle valves (HV013, HV015) are installed in parallel downstream of PT102 to give a broad range of flow regulation. The gas analyser GA016 (Stanford Research Systems BGA244HP) sits at the system outlet so that the speed-of-sound-based composition measurement always runs at atmospheric pressure (±0.1 mol-%).

The capillary is mounted in vacuum on a glass-fibre support inside a multi-layer-insulated radiation shield thermalised at the cold head, so that the residual heat exchange with the environment is dominated by axial conduction along the tube wall.

All raw and processed data files use the P&ID tag names below for sensor identification.

The principal sensors used for the Joule-Thomson analysis are:

• temperature: TT101 (upstream) and TT102 (downstream) Cernox sensors;
• pressure: PT101 (upstream) and PT102 (downstream) Mensor transducers;
• composition (mixtures only): GA016 binary gas analyser.

Equipment list

The components installed on the test bench, with their P&ID tag, function, and manufacturer/model, are listed below.

Control

P&ID tag	Equipment type	Manufacturer and model
RV001	Pressure regulator	Alphagaz LTH 400
PI001	Pressure indicator	Alphagaz LTH 400
HV002	Diaphragm sealed valve	Nupro SS-DSV51
HV003	Diaphragm sealed valve	Nupro SS-DSV51
RV004A	Pressure regulator	Alphagaz LTH 400
PI004A	Pressure indicator	Alphagaz LTH 400
HV004B	Diaphragm sealed valve	Nupro SS-DSV51
SV005	Safety valve	Swagelok SS-6R3A-MM
HV006	Diaphragm sealed valve	Nupro SS-DSV51
TT007	Platinum temperature sensor
TT008	Platinum temperature sensor
Q008	Resistive heater in copper mass
TT009	Platinum temperature sensor
TT010	Platinum temperature sensor
Q011	Resistive heater
HV012	Diaphragm sealed valve	Swagelok SS-DLVC04
HV013	Needle valve	Hoke Mili-Mite 1335G4Y
HV014	Diaphragm sealed valve	Swagelok SS-DLVC04
HV015	Needle valve	Hoke Micromite 1654G4YA
HV016	Needle valve	Swagelok SS-4BMW-VCR
HV017	Diaphragm sealed valve	Swagelok SS-DLVC04
NV018	Check valve	Swagelok
cryocooler	Gifford-McMahon refrigerator	Cryomech AL300

Measurement

P&ID tag	Equipment type	Manufacturer and model
GA016	Gas analyser	SRS BGA244HP
PT101	Absolute pressure transducer	Mensor CPT 6100
TT101	Cernox temperature sensor	Lake Shore CX-1080-CU-HT-20L
PT102	Gauge pressure transducer	Mensor CPT 6100
TT102	Cernox temperature sensor	Lake Shore CX-1050-SD-HT-1.4L

Vacuum

P&ID tag	Equipment type	Manufacturer and model
M301	Turbo-molecular pump	Alcatel
PT301	Vacuum pressure transmitter	Alcatel CF2P
M302	Roughing pump	Alcatel
HV303A	Diaphragm sealed valve	Nupro SS-DSV51
HV303B	Manual vacuum valve
M303	Roughing pump
PT303	Vacuum pressure transmitter	Adixen ACC2009-SP
HV304	Bellow sealed valve	Swagelok SS-4H-V71
PI304	Pressure indicator	Bourdon Haenni M1
M305	Turbo-molecular pump
M306	Roughing pump
PV306	Solenoid valve
PT307	Vacuum pressure transmitter	Pfeiffer IKR 251

Raw data

raw-data contains raw measurement data stored in CSV files. It contains:

• the pressure-temperature pairs used for indirect measurements of the Joule-Thomson coefficent in pure fluids (nitrogen, argon, helium-4);
• the pressure-temperature-composition values used for indirect measurements of the Joule-Thomson coefficient in fluid mixtures (helium-neon, helium-nitrogen).

Variable	Unit	Description
Date	yyyy-mm-dd	Measurement date
Time	hh:mm:ss	Measurement time
PT102	MPa	Pressure measured after the isenthalpic expansion
PT101	MPa	Pressure measured before the isenthalpic expansion
TT009	K	Themal shield highest temperature (point of the highest radiation heat loss)
TT010	K	Temperature at the outlet from the cryostat (before heater Q011)
TT008	K	Cold head temperature
TT101	K	Temperature measured before the isenthalpic expansion
RT101	$\Omega$	Resistance of the TT101 Cernox temperature sensor
TT102	K	Temperature measured after the isenthalpic expansion
RT102	$\Omega$	Resistance of the TT102 Cernox temperature sensor
Q008	W	Power of the cold head heater (automaticaly regulated)
x1	-	1st gas concentration (for mixture measurements)
x2	-	2nd gas concentration (for mixture measurements)
impurity	-	Gas impurity defined as $1 - purity$ (for single component measurements)
err(x)	-	Concentration/purity measurement uncertainty

The measurements for two dates do not contain values for Q008: 2020-11-27 and 2020-12-14.

The measurements are grouped in files by collection date. The Joule-Thomson coefficient was measured for the fluids below:

Date	Fluid	Average purity	Average molar composition
2020-11-27	${\rm N_2}$	0.9987	-
2020-12-09	${\rm N_2 - He}$	-	0.8497/0.1503
2020-12-10	${\rm N_2 - He}$	-	0.8909/0.1091
2020-12-11	${\rm N_2 - He}$	-	0.5641/0.4359
2020-12-14	${\rm N_2}$	0.9904	-
2020-12-15	${\rm Ar}$	0.9990	-
2020-12-16	${\rm N_2}$	0.9977	-
2020-12-17	${\rm N_2}$	0.9986	-
2021-01-12	${\rm He}$	0.9967	-
2021-01-13	${\rm He}$	0.9904	-
2021-01-14	${\rm He - Ne}$	-	0.7148/0.2852
2021-01-15	${\rm He - Ne}$	-	0.7385/0.2615
2021-01-25	${\rm N_2}$	0.9977	-
2021-01-26	${\rm He}$	0.9993	-
2021-01-27	${\rm He - Ne}$	-	0.3464/0.6536
2021-01-28	${\rm He - Ne}$	-	0.4084/0.5916
2021-03-03	${\rm He - Ne}$	-	0.2219/0.7781
2021-03-04	${\rm N_2}$	0.9987	-

Derived data

data/derived_data contains the products computed from the raw data, documented in data/derived_data/README.md:

• p_T_pairs/ — steady-state pressure–temperature(–composition) points extracted from the raw time series, one file per isenthalp;
• jt_coeffs/ — the derived Joule-Thomson coefficients with conventional and Monte Carlo uncertainties, a jt_coefficients_summary.csv, and a jt_coefficients_detailed.json;
• calculated_mass_flow_rate/ — capillary-sizing design calculations.

Cernox temperature-sensor calibration data are in data/cernox_calibration_data, and experiment metadata (timestamps, p–T pairs) in data/metadata.

Code

The src directory consists of the following sub-directories:

• data_acquisition — code running data acquisition and real-time visualization of collected data;
• data_analysis — code for data wrangling and analysis of results (see src/data_analysis/README.md).

Reproducing the analysis

Install the Python dependencies with pip install -r requirements.txt. The reference thermodynamic properties require REFPROP (accessed through the ctREFPROP bindings); the custom equations of state for the mixtures are provided in REFPROP/ and must be copied into REFPROP's HMX.BNC file. REFPROP is licensed separately, so the scripts that evaluate the equation of state (calculate_jt_coefficients.py, monte_carlo_uncertainty.py, and the theory_figures/ scripts) cannot be run without it; the remaining scripts (plot_paper_results.py, compare_theory_vs_experiment.py, theoretical_jt_uncertainty.py, plot_toc_graphic.py, generate_paper_tables.py) run from the committed derived data alone. Typical entry points:

python src/data_analysis/get_pT_pairs.py                 # extract p-T pairs from raw data        (REFPROP-free)
python src/data_analysis/calculate_jt_coefficients.py    # derive mu_JT with uncertainties         (REFPROP)
python src/data_analysis/monte_carlo_uncertainty.py      # Monte Carlo uncertainty bound           (REFPROP)
python src/data_analysis/generate_paper_tables.py        # LaTeX bodies of the result tables        (REFPROP-free)
python src/data_analysis/plot_paper_results.py           # per-fluid result figures                 (REFPROP-free)

The heat-loss and kinetic-energy corrections quoted in the manuscript (Table of mean corrections) are auxiliary bounding estimates and are not produced by the released scripts.

Citation

If you use this dataset or code, please cite it via the metadata in CITATION.cff.

License

This work is released under the Creative Commons Attribution 4.0 International(CC-BY-4.0) license.