FEA calculation of pressure distortion coefficients of gas-operated pressure balances

Project Description

Objective
Establish FEA methods for gas-operated pressure balances

• Minimise uncertainty contribution produced by a pressure dependence of the effective area in the range up to 7 MPa which is important e.g. for Boltzmann constant experiments

Available information
Real dimensional data and material elastic constants with associated uncertainties

Conditions
Absolute and gauge operation mode with nitrogen and helium

Expected results
Zero-pressure effective areas and their uncertainties

• Pressure distortion coefficients and their uncertainties
• Radial distortions and pressure distributions, piston fall rates

Schedule and objects
1st phase, 2008, existing piston-cylinder units and dimensional data

• PTB 10 cm² 1 MPa unit 288
• PTB 5 cm² 2 MPa unit 6222

2nd phase, 2009, new piston-cylinder units 

• 20 cm² 0.75 MPa new units to be available in April 2008
• 2 cm² 7.5 MPa units to be available in August 2008

intended for pressure measurements in the experiments for re-determination of the Boltzmann constant.

Final Reports 2010-03-25

FEA methods were developed and applied to gas-operated pressure balances with piston-cylinder assemblies (PCAs) of piston- and cylinder-floating configuration: 10 cm2 (1 MPa), 5 cm2 (2 MPa), 20 cm2 (0.75 MPa) and 2 cm2 (7.5 MPa), the two later PCAs to be used for pressure measurements in experiments to re-determine the Boltzmann constant. Zero-pressure and pressure-dependent effective areas (A0 and Ap), pressure distortion coefficients (l), piston fall rates (Vf) with associated uncertainties were determined. Real dimensional properties of the PCAs were used, gauge and absolute pressure operation modes considered, effect of the pressure medium being the ideal gas, nitrogen and helium investigated.Main results, conclusions, problems:

• A₀, A_p and l are independent of gas (ideal, N₂, He) within the viscous flow model.
•  Better results agreement for real than for ideal gap, for floating piston than for floating cylinder, at higher than at lower pressures.
•  Largest effect on l comes from: (1) real vs. ideal gap profile model, (2) operation mode, (3) uncertainty of dimensional data, (4) uncertainty of elastic constants.
• Piston cap does not effect l.
• Most differences in l are due to A₀-discrepancies caused by numerical procedures.
• Very good agreement of uncertainty budgets for l.
• Agreement in pressure up to 2 MPa is within 0.5 ppm; up to 7 MPa within 0.3 ppm - this meets uncertainty required in Boltzmann constant experiments..
• Improvement of numerical procedures for A₀ and A₀(p) calculation is required.
•  Singularity of 1/density(p) in absolute mode with real gases at p ® p₂=0 is to be solved by taking 0<p₂<<p₁.