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

Abstract

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 was developed and compared with experimental results.First, to verify the simulation results, the helium-4 gas pressure in the centre of the resonator was measured using a determination of the refractive index by microwave resonance coupled with a knowledge of the temperature.Results of simulation and experiment showed good agreement. Thereafter, based on this CFD simulation, the nonlinear 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.

Measurement of thermodynamic temperature between 5 K and 24.5 K with single-pressure refractive-index gas thermometry

“…The temperature distribution for each segment is assumed to be linear. The calculation was verified in a recent paper [47]. The hydrostatic head correction is thus…”

Refractive index gas thermometry between 13.8 K and 161.4 K

“…These posts are internally bored by 4 mm diameter ducts and heat-sunk to the experimental vessel and the two cooling stages of the cryostat. This system simplifies the calculation of the pressure correction accounting for the aerostatic weight of the gas column, as first suggested by Astrov et al [16] and recently discussed by Pan et al [17]. In our working conditions the pressure correction spans between a minimum of 5.1 Pa when He fills the apparatus at 80 kPa, 161 K, which is relatively equivalent to 63 ppm, and a maximum of 50.4 Pa at 280 kPa, 54.3 K or equivalently 180 ppm when Ne fills the apparatus.…”

“…vacuum recorded at the start and at the end of the sequence showed their consistency at the level of a few ppb. Among the various mathematical combinations of the raw microwave data which may be used for the estimate of κ T,eff (273.16 K), the following p j , n p j , 273.16 K f m p j , 273.16 K f m (0, 273.16 K) (17) can be fitted with a linear model a 0 + a 1 p with a 1 = κ T,eff (273.16 K). Figure 10 shows the residuals for this linear fit, which essentially estimates κ T,eff implementing an extrapolation to zero pressure.…”