Numerical and Experimental Study of the Hydrostatic Pressure Correction in Gas Thermometry: A Case in the SPRIGT


Single-pressure refractive index gas thermometry (SPRIGT) is a new type of primary thermometry, which needs an extremely stable working pressure (stability < 4 ppm). In practice, the pressure control system at room temperature is located above the cold resonator at 5 K to 25 K, and a long pressure tube is used to connect them, which entails a hydrostatic pressure correction (HPC). To this end, a three-dimensional (3D) Computational Fluid Dynamics (CFD) simulation model of the pressure tube has been developed and compared with experimental results. First, to verify the simulation results, the helium-4 gas pressure in the center of the resonator was measured using a determination of the refractive index by microwave resonance coupled with the knowledge of the temperature. Results of simulation and experiment showed good agreement. Thereafter, based on this CFD simulation, the non-linear temperature distribution in the vertical pressure tube and the uncertainty caused by this non-linear phenomenon were calculated. After this, the validity of the isothermal assumption to simplify the calculation of the HPC was verified. Finally, the effect of heating on the pressure was studied and its impact found to be negligible. To the best of our knowledge, this is the first time experimental and simulation results have been compared for the HPC. The results are expected to be more generally applicable to the accurate determination of pressure in cryostats.

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    The exponent T in Eq. 2 denotes the transpose of the matrix.

  2. 2.

    The reason for simulating VT-3 is that it is connected to the second flange of the cryostat and contributes greatly to the HPC, as shown in Table 2.


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This work was supported by the National Key R&D Program of China (Grant No. 2016YFE0204200), the National Natural Science Foundation of China (Grant No. 51627809), the International Partnership Program of the Chinese Academy of Sciences (Grant No. 1A1111KYSB20160017) and the European Metrology Research Programme (EMRP) Joint Research Project 18SIB02 “Real-K”. Changzhao Pan was supported by funding provided by a Horizon 2020 Marie Skłodowska Curie Individual Fellowship 2018 (No. 834024). The authors thank Duowu Su from NIM for the measurement of g at TIPC (Technical Institute of Physics and Chemistry, Chinese Academy of Sciences) in Langfang.

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Uncertainty Budget for the Determination of the HPC at the Temperature of the Neon Triple Point

References to the literature are given for the electromagnetic and density virial coefficients.

Working pressure 30 kPa 60 kPa 90 kPa
Pressure in the resonator/Pa
Uncertainty component, type B
T of neon triple point 0.527 0.998 1.530
\(A_{\varepsilon }\) [29] 0.003 0.007 0.01
\(B_{\varepsilon }\) [30] 0.048 0.187 0.422
\(C_{\varepsilon }\) [25] 0.001 0.004 0.014
\(A_{\mu }\) [31] 0.002 0.001 0.001
B [32] 0.001 0.005 0.012
C [32]
D [32]
\(\kappa_{T}\) [26,27,28] 0.051 0.105 0.157
Uncertainty component, type A  
\(f + g_{0} /f + g_{p}\) 0.035 0.032 0.104
T stability 0.012 0.025 0.037
Pressure at room temperature/Pa
Uncertainty components, type B
p calibration 0.306 0.606 0.903
Uncertainty components, type A
p stability 0.003 0.003 0.004
Combined standard uncertainty/Pa
HPC 0.617 1.188 1.836
  1. The symbol “–” means the value lies below 0.001 Pa

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Pan, C., Chen, H., Han, D. et al. Numerical and Experimental Study of the Hydrostatic Pressure Correction in Gas Thermometry: A Case in the SPRIGT. Int J Thermophys 41, 108 (2020).

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  • CFD
  • Hydrostatic pressure correction
  • Primary thermometry
  • Refractive index gas thermometry