Gas flow through the multiopening orifices
Martin Vičar, Tomáš Gronych, Martin Jeřáb, LadislavPeksa, Dominik Pražák, Jiří Tesař, Zdeněk Krajíček, František Staněk
Czech Metrology InstituteBrno, Czech Republic
Faculty of Mathematics and PhysicsCharles University in PraguePrague, Czech Republic
Why multiopening orifice? Main goal of metrology:
calibration of measuring devices
Pressure standard – device for pressure unit reproducing
Primary pressure standard – device for the generation / measuring pressure using the basic principles.
Why multiopening orifice? Some primary pressure standards:
liquid piston orifice flowcolumn gauge system
p2-p1 ≈ h··g p ≈ m·g/S p ≈ q/C
Why multiopening orifice?
bRRbRRbR
RMRTC
N
NONON
22 222
[Pa m3 / s]
[m3 / s]
[Pa]
Why multiopening orifice?Orifice flow system
molecular regime:
orifice diameter d
d >> 500 λ
(Knudsen numberd / λ >> 500 )
Why multiopening orifice? For the new standard built we need:
pressure range 10-6 to 10-1 Pa
at 10-1 Pa λ ~ 6 cm (N2)
→ maximum d ~ 1 mm
Why multiopening orifice?→ maximum d ~ 1 mm
Additional restrictions:Minimum precisely generatedflow from constant volumeflowmeter: 10-7 Pa m3/s
and Minimum pressure required:~ 10-6 Pa→ aproximate orificeconductance: 0,1 m3/s
Why multiopening orifice?molecular regime
↓diameter maximum ~ 1 mm (conductance ~ 10-4 m3/s)
aproximate orificeconductance 0,1 m3/s
↓circular orifice withdiameter minimum 33 mm(calculated for nitrogen N2)
Why multiopening orifice?33 mm orifice cannot be used (molecular regime)
Possible solution:About 1000 small orifices1000 x 10-4 m3/s = 0,1 m3/s
Possible problems:- Practical: measuring, solved.- Theoretical: Are the flowsthrough orifices independent?
Are the flows independent?Are the flows through the individual small orifices mutually independent?
Mutual interference of flows(at higher pressures)
↓Orifices total conductancediffers from the sum of theirtheorethical molecularconductances (total conductance is higher due to the interference)
Are the flows independent?For which distance of small orifices the flows are really independent?
1. LiteratureHans Wolfgang Liepmann:Gaskinetics and gasdyna-mics of orifice flow:There is a region abovethe orifice with the disturbedMaxwell distribution:He consider hemisphere with diameter 2 x greater than the orifice diameter, with the centre at the orifice center.
Are the flows independent?For which distance of small orifices the flows are really independent?
If two openings are very close and the mentioned hemispheres overlaps, we can expect the different behaviour in the transitional regime.
d d
L
d d
L
Are the flows independent?Except the Liepman‘s considerations, we haven‘t found relevant literature describing this problematics.
2. Calculations
Another possibility couldbe studying this questiontheorethically using theBoltzmann transport equation.Unfortunatelly our involved colleague has left the team before problem resolution.
Are the flows independent?For which distance of small orifices the flows are really independent?
3. Experiment
We had need of answeringthe question urgentlyto be able to continuethe primary standard construction.
So we decided to set up the experiment.
ExperimentThe typical opening conductance
The conductance starts to increase at p0.
laminartransitionalmolecular regime
p0
Experiment
The particular question:
At which mutual distance of the openings the flow starts to be transitional at the different pressure (lower pressure) than in the case of one single opening?
In praxis: Flow starts to be transitional = the conductance increases e. g. 5 % above the molecular conductance.
laminartransitionalmolecular regime
p0
Experiment
Small orifices were prepared, each with 7 openings.
D0 = 0.4 mm of diameter
Mutual distances of the openings:
1.25 D0
1.5 D0
1.75 D0
2 D0
2.5 D0
3 D0
4 D0
5 D0
Experiment
ResultsRelative conductance dependence to the pressure
ResultsThe pressure at which the conductance deviationis 5 % (10 %) from the molecular conductanceand the pressure for the inflex point
ConclusionAccording to the theorethical presumptions (Liepman), the experiment shows that the noticeable mutual interaction of the flows through the particular openings occur at the mutual openings distance between 3 and 2 opening diameters.
Liepman, H. W.:
Thanks
Thank youfor your attention.
Liepman, H. W.:
