Measurement of the density of moist air using gravimetric artefacts

James BerryNational Physical Laboratory

March 2007

Contents

• Background• Air density measurement using artefacts

– Artefact development at NPL– Current generation of NPL artefacts– Air convection effects– Experimental results and uncertainties– Conclusions

Background

• Primary requirement for precise air density measurement is for the dissemination from Pt-Ir to stainless steel

• An air density uncertainty of 1 part in 105 would give an uncertainty contribution of 1 µg in Pt-Ir / stainless steel comparisons

• Conventional air density measurement is limited by the accuracy with which P, t and DP can be determined

• and ultimately by the uncertainty in the CIPM equation to no better than 5 parts in 105

Artefact development at NPL

• First generation artefacts – hollow sphere and cup– Developed because no weighing in vacuum facility existed– Artefact mass could only be determined before evacuation and sealing

• Large volume difference –approximately 760 cm3

• Sealing of artefacts proved problematical

• Poor mass stability resulted in little improvement in air density uncertainty

Current NPL air density artefacts

• One set of large air density artefacts (volume difference approximately 510 cm3)

• One set of small air density artefacts (volume difference approximately 105 cm3)

Air convection effects

• Previous work by Gläser states that convection effects can occur at a weights surface due to heating or cooling

• Computational fluid dynamics (CFD) models of the air flow over the surface of each shape of air density artefact were constructed

• CFD models indicated that tube shapes are a better design for the small volume artefact than bobbin shapes (confirmed by weighing data)

Artefact shape effects on weighing stability

1.65

1.652

1.654

1.656

1.658

1.66

1.662

1.664

1.666

1.668

1.67

0 5 10 15 20 25 30 35 40

Time (hours)

mas

s di

ffere

nce

(mg)

-0.295

-0.293

-0.291

-0.289

-0.287

-0.285

-0.283

-0.281

-0.279

-0.277

-0.275

mas

s di

ffere

nce

(mg)

tube

bobbin

19.35

19.4

19.45

19.5

19.55

19.6

19.65

0 5 10 15 20 25 30 35 40

Time (hours)

Tem

pera

ture

(°C

)

Hollow air density artefact

Tube shape air density artefact

Bobbin shape air density artefact

Experimental results

Air density artefacts vs. CIPM method

1.196 50

1.196 55

1.196 60

1.196 65

1.196 70

1.196 75

1.196 80

29/04/200514:24

30/04/200504:48

30/04/200519:12

01/05/200509:36

02/05/200500:00

02/05/200514:24

Time

Air

dens

ity (k

g/m

3) CIPM

88H-88T

88DH-88DT

88H-88DT

88DH-88T

Uncertainty budget

1.2 ×10-5

(10.5 ×10-5 )Relative combined uncertainty, uc

(kg m-3)

0.8 ×10-50.004 21Volume uncertainty (cm3)

0.3 ×10-51.8Weighing scheme

Air mass uncertainty (µg)

0.2 ×10-5

0.0 ×10-5

0.5 ×10-5

1.40.003.10

Weighing schemeSorption correctionVacuum mass stability

Vacuum mass uncertainty (µg)

Relative influence,ui (ρ)/ρ

Standard uncertainty, ui

Parameter

Table 8: Uncertainty budget of air density evaluation using the artefact method. All uncertainties are reported at the 1 σlevel. The relative combined uncertainty in brackets is NPLs best uncertainty using the conventional method.

Conclusions

• Factor of 10 improvement in air density uncertainty compared with conventional (parametric) method

• Good agreement between new method and conventional method corrected for proposed change in Argon content of equation (within uncertainty limits)

• Some small offsets were found between the two methods

• CFD analysis highlighted tubes as a better design of artefact than bobbins