XXI
IMEKO World Congress “Measurement
in Research and Industry”
August
30 - September 4, 2015,
Prague, Czech Republic
VOLUME MEASUREMENT OF PISTON Prover CYLINDER BY gravimetric METHOD
FOR VALIDATION OF WATER FLOW RATE traceability AT METROLOGY LIPI
Jalu A. Prakosa, Nur Tjahyo Eka D, Bernardus H.S, Hafid
Research Center
for Metrology - Indonesian Institute of Sciences (LIPI)
Kawasan PUSPIPTEK Serpong, Banten 15314,
Indonesia
ABSTRACT
One way to validate the volume measurement of
the piston prover cylinder is using gravimetric method called water draw. The
purpose of this study is to measure the volume of piston prover cylinder with gravimetric
method for validation of its water flow rate measurement value and also to achieve the uncertainty
target. The measurement results of piston prover
cylinder volume are 92.43 litre and expanded uncertainty of 0.09 litre or 0.09% in relative. The
largest contribution comes from the water mass measurement repeatability because of the possibility of evaporation
and error measurement in using three-way valve as diverter. The Data collecting
methods should be improved in the future.
Keywords: cylinder volume, piston prover, gravimetric, water flow rate, traceability.
Introduction
Piston prover is one type of standard
that is used for water flow rate quantity measurement. This system is worked based on the principle
of positive displacement, when a volume of fluid that is located inside the cylinder, is moved by a piston. Flow
rate is measured by volumetric method that the piston displacement is
proportional to the volume that has been moved per unit time or it’s flow [1].
The displacement of piston at Metrology LIPI as Indonesian National Metrology
Institute, the brand of “Flow Technology Incorporated”, is measured by linear encoder so flow rate can
be calculated from the data of encoder pulses[2] and collecting time as shown
in Fig. 1 and 2. Frequency from linear encoder
is also proportional to flow rate. This standard can calibrate many kinds of
flow meter such as turbine, water meter, variable area, ultrasonic, electromagnetic
flowmeters, etc [3].
Piston prover is the standard of volume flow rate
quantity so it derive the quantity from volume and time. This paper will
discuss about how to validate the measurement and traceability of cylinder
volume of piston prover. There are some methods to measure volume of piston prover cylinder : volumetric
dimentional method, gravimetric method and using flow meter. In this study,
gravimetric method in water draw would be used to determine the cylinder volume
of piston prover [4]. To measure water mass that moved from piston cylinder, we
use electronic balance “sartorius F150S*D2” with capacity of 151 kg and 1 g resolution in Fig.3 [5]. This balance
was calibrated to weights E2 that have been traceable to SI units through mass laboratory of Metrology
LIPI. That water
draw of piston prover can build traceability chain of water flow rate
measurement in Metrology LIPI to SI units.
Piston prover facilities at Flow
Laboratory of Metrology LIPI has done
peer review by KRISS expert in November
2011 then the results are the measurement range of 4 ~ 1300 L/min with
uncertainty of 0.12% [6]. To achieve this uncertainty target, the uncertainty
measurement of each components at mathematical model also should be achieved to
minimum specific value. The
purpose of this study is to measure the volume of piston
prover cylinder with gravimetric method for validation of its water flow rate measurement value and also to achieve the uncertainty
target.
Figure. 1 Piston prover schema [1]
Figure. 2 Piston prover in Metrology LIPI
Figure. 3 Electronic balance[5]
THEORY OF WATER
VOLUME FLOW RATE MEASUREMENT USING PISTON PROVER
Piston
prover is a system that serves to calibrate flow meter as flowmeter calibrator. This system also
works on the principle of positive displacement, where the calibrated volume of
fluid located in the cylinder, is moved by a piston. To drive the piston,then
used compressed air from the compressor. Piston displacement are correlated with
the fluid volume that has been moved.
Therefore, this system is also called piston prover [1]. In Flow Laboratory of
Metrology LIPI, water has been used as fluid. See again in fig.2 for the piston prover picture.
This system
used linear encoder to measure piston displacement. The number of pulses from
linear encoder is proportional to the distance of the piston displacement that
recorded in the data acquisition of computer. To convert pulses into volume
quantity of fluid, it can use K-factor value that has unit of pulses per volume
unit. The number of encoder pulses per unit time or frequency of encoder is also proportional to the volume
flow rate that generated on the piston prover systems.
The volume
flow rate define as volume unit per time unit so the mathematical model of
water volume flow rate measurement using piston prover can be derived as this
following :
(1)
There are
effect of temperature and pressure as correction factor to the equation (2)
below.
(2)
Information :
QV = Water
volume flow rate.
ΔV =
Water volume changes.
Δt =
Travelling time.
K20,0=
K-factor value corresponding to 20 oC dan 0 Mpa.
αg = Linear thermal expansion coefficient of encoder.
tE = Encoder temperature when do
calibration.
βs = Volumetric thermal expansion coefficient of piston
cylinder.
ts = Piston cylinder temperature when do
calibration.
Ea = Water compressibility coefficient.
Pa = Water pressure when do calibration.
rs = Radius of piston cylinder.
ds = Width of piston cylinder.
Es = Constant of elasticity modulus for
piston cylinder.
Ps = Pressure at piston cylinder when do
calibration.
fE = Frequency of linear encoder
MEASUREMENT METHOD
The volume of piston
cylinder is equal to the volume of displaced
water from it. The displaced
water volume can be calculated from its meaures mass and density. Apply
pressure about 0.14 Mpa to the piston so it will push the water to flow out to
weighing tank for mass measurement. [7] Collection data of water mass measurement will be
done by 23 times repeatability.
Figure. 4 Water draw diagram
Figure.5 Pipe connection between piston and tank
To control when start
and stop for collecting data of water mass as diverter, three-way valve is used
in Fig. 6
Figure. 6 Three-way valve as water flow diverter
Cylinder volume of
piston prover can be calculated as this following (3) :
(3)
There are air buoyancy
corection, so the formula should be as in (4)
(4)
We also calculate
expansion of cylinder according to temperature and pressure and water compressibility
in the cylinder so the mathematical model would be as in (5).
(5)
Information :
Vc
= Cylinder volume of piston prover.
Vc,20 = Cylinder volume
of piston prover corresponding
to temperature of 20 ℃.
mw
= Water mass that displaced from piston.
ρe = Density of E2weight standard.
ρw = Water density.
ρa = Air density.
βc = Volumetric thermal expansion coefficient.
Tc = Temperature of cylinder.
Xc
= Constant of elasticity modulus for piston cylinder.
Pc
= Pressure in the cylinder.
Zw=
Water compressibility coefficient.
Pw=
Water temperature.
RESULTS AND DISCUSSION
Water draw is done at Flow Laboratory of Metrology LIPI in
November 2013 with room temperature of (22±2)°C and room humidity of (44±3)%RH
also room pressure of (1003±5) hPa. The results is in (7)
Figure. 7 Cylinder volume of piston
The uncertainty budget and data analysis[8]
for cylinder volume of piston prover measurement results are desribed as in
Table.1
Table. 1 Uncertainty budget for cylinder
volume of piston prover
|
Components of uncertainty
|
ci.u(xi)/xi
(%)
|
(ci.u(xi)/uc)2
(%)
|
|
Water mass, mw
|
0.04
|
93.8
|
|
Density of E2 weight, ρe
|
0.00
|
0.2
|
|
Water density, ρw
|
0.01
|
5.9
|
|
Air density, ρa
|
0.00
|
0.0
|
|
Temperature of cylinder, Tc
|
0.00
|
0.1
|
|
Pressure of cylinder, Pc
|
0.00
|
0.0
|
|
Water pressure, Pw
|
0.00
|
0.0
|
|
Combined uncertainty, uc
|
0.04
|
|
|
Expanded uncertainty(k=2), U
|
0.09
|
This is the
contribution of uncertainty diagram that consist of squared value of standard
uncertainty multiplied by sensitivity coefficient(ui.ci) in relative for each
component that form the mathematical model as shown in Fig. 8.
Figure. 8 Uncertainty contribution
From the table 1 and fig. 8, shown that the
largest contribution came from repeatability of water mass collection data
about 93.8% and the second came from repeatability of water density collection
data about 5.9%. The uncertainty from electronics balance traceablity is very
small that only have 2 gram or 22 ppm relative
because its is calibrated to excellent standard of E2 weight. The other contributor components is
neglected because their contribution is below 0.5%.
The cylinder volume of piston prover are measured and calculated at 92.43 litre and expanded uncertainty
of
0.09 litre so its relative uncertainty is 0.09%. This result are out of factory
specification that they claim the uncertainty of 0.05% for their product. In
November 2011, Dr Jong Seung Paik from KRISS Korea suggest flow laboratory of Metrology
LIPI to re-estimation our uncertainty for volume flow rate then the value of
0.12 % considered appropriate.
|
MUT : Turbine, turbine, water meter, variable area, ultrasonic,
electromagnetic flowmeters, etc
|
|
Piston prover
Estimated 0.12%
Factory 0.05%
|
|
|
|
Volume
0.09%
|
|
Mass Lab.
|
|
Density, temperature and pressure Lab.
|
|
Time and frequency Lab.
|
|
SI Units
|
|
E2Weight
|
Figure. 9 Traceability chart for water flow rate
in Metrology LIPI
Although the uncertainty measurement
value of the cylinder volume is large enough but it has been traceable to SI
units as shown in Fig. 9
There are some reason that maybe cause
the repeatability of water mass collection data is large enough. As shown in
Fig.2, the window is exposed directly to
the sunlight and in Fig.5, the weighing tank is freely open to the atmosphere so the effect of water
evaporation should be considered [9]. The use of three-way valve in Fig.6 to control when start and stop to collect data
also possibility cause measurement error [10].
CONCLUSIONS
Flow Laboratory of Metrology
LIPI has successfully validate the measurement traceability for cylinder volume
of piston prover as standard of water flow rate to SI units. From the results of measurement as much as 23 times repeatability
and the data analysis obtained that volume of piston prover cylinder are (92.43±0.09) litre. The expanded uncertainty is 0.09% in relative that has out of factory specification of
0.05%. The largest contribution of 93.8% comes from the uncertainty of mass measurement repeatability of water displaced
from the piston cylinder. The some possibility cause the large repeatability
of water mass collection data are :
1) The window position that exposed directly to the sunlight and the weighing tank is freely open to the atmosphere so the water evaporation may
be occurred.
2) The use of three-way valve to control when start and stop to collect
data as diverter also possibility cause measurement error.
Data collecting
methods of water draw needs to be improved so the target of water flow rate measurement uncertainty can be better in the future.
ACKNOWLEDGMENTS
Thank you to
management of research center for Metrology LIPI for supporting this research.
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