Pressure Measurement and Control

Pressure Measurement and Control

PRESSURE SEMINAR

Pressure Metrology

Using the

Piston Pressure Balance

(Deadweight Tester)

24 June 2003

Korea Power Plant Service Co. Ltd.

Sponsored by

SOTech


Agenda

Introductions – SO Tech and Ruska

Pressure Measurement

Measurement Philosophy

Primary Standards - Principle of Operation

- Instrumentation

Digital Transfer Standards

- Principle of Operation

- Instrumentation

Calibration Process – An example


ACCURACY

Components of ‘Accuracy’♦ Uncertainty of Standard

♦ Precision/Performance of Test Device

♦ Environment/Process

♦ User (Metrologist)

• Training/Experience/Tools


ACCURACY

CALIBRATING STANDARD

* NATIONAL * CORPORATE * WORKING

ACCURACY

USER TRANSFER STANDARD

* PROCESS * PRECISION* ENVIRONMENT * PERFORMANCE* PROCEDURES

Traceability Path


Pressure – 17 Decades


Pressure is Not a Fundamental Unit ofMeasure

Pressure is a derived quantity

Types of Reference StandardsLiquid Column (a.k.a. Mercury Column, Manometer, Mercury Barometer, etc.)

Deadweight Gauge (a.k.a. Piston Pressure Balance, Deadweight Tester, Piston Gauge)


Definition - Pressure

PressureForce = Mass x AccelerationArea

SI Unit ⇒ Pascal = Newton/m2

= (m • kg • s-2)/m2

FFPP == ________

AA


Reference Modes


Primary Devices – ReferenceStandards

Liquid Columns (Manometers) Mercury, H2O:0.0 to 50 psi (4 bar) [gauge / absolute]Accuracy: 0.1% to 0.0015% reading

Piston Gauges (Deadweight Gauges):0.003 to 1,000 psi (5 Pa to 7 MPa) [gauge / absolute]0 to 200,000 psi (1.4 GPa) [gauge]Accuracy 0.1% reading to 0.0010% reading

(1000 to 10 ppm)


Liquid Manometer, U-Tube


NPL-UK Fundamental Manometer


Fundamental Standard - NIST


Definition

FFP =P = ________

AA

PressureForceArea

SI Unit ⇒ Pascal = Newton/m2


Deadweight Gauge (Piston Gauge)


Deadweight Gauge - Floating


PISTON PRESSURE BALANCE

Ae

F1

F2

Pressurized FluidP

When F1 - F2 = 0

where F1 = ΣFi

F2 = P • Ae

∴ P = ΣFi / Ae


Piston Gauge - Ruchholz 1882


Piston Gauge

Ruska Model 2485 -Hydraulic


Piston/Cylinder Assembly - Details


Piston Gauge – Hydraulic

Ruska Model 2485


Model 2465 Autofloat System

PC w/ WinPrompt

software

Autofloat Controller

Deadweight Gauge


Piston Gauge - Hydraulic

Pressurements, LTD.Model M22xx


Influences on Force

Mass Load Local GravityAir BuoyancyVerticality (Level)Surface TensionOther (Environment)

-- Magnetism, Air Drafts, MassRotation

ΣΣ FFP =P = ________

AA


Deadweight Gauge - Floating

F1 = ma • gl

F2Pressure

Fb

Fst

θ

F2 = Ftotal• cos θ

= (F1 + Fst - Fb) • cos θ


Local Gravity

Force = Mass x Acceleration= Ma x gl

The deadweight gauge masses are accelerated in the downward direction by the gravitational attraction of the earth.


Effects of Local Gravity

Standard Gravity: 980.665 cm/sec2

Local Gravity:At Ruska In Houston = 979.278 cm/sec2

1-(979.2778/980.665) = 1- 0.998585

Uncorrected Uncertainty = 0.14% (1400 ppm)

Gravity surveys can be obtained resulting in uncertainty values of ≤ 1 ppm (0.0001%)


Air Buoyancy

Archimede’s PrincipleThe weight of an object submerged in a fluid is diminished

by the weight of the fluid displaced.‘Apparent mass’ was developed to simplify determining the mass value of an object, whose density is unknown while being weighedin air.The correction term for the buoyancy force contribution is

(1 - ρa/ρs)where

ρa = density of ambient air (nominally 0.0012 g/cm3)ρs = density of mass standard (brass = 8.4 g/cm3, St.Steel = 8.0 g/cm3)


Buoyancy

Magnitude of Error if Buoyancy is Ignored:For RH = 50%, T = 23°C, P = 760 mmHg;

ρa = 0.001186 cm/sec2

(1 - ρa/ρs) = (1 - 0.001186/8.4) = 0.9998588Uncorrected Uncertainty ≈ 140 ppm (0.014%)

Buoyancy Corrected within the following tolerance:RH = +/- 15%RH, T = +/- 1.5oC, P = +/- 2 mmHg

Corrected Uncertainty ≈ 0.9 ppm (0.00009%)


VERTICALITY


Error due to Verticality

θ (Minutes of Arc) Error (ppm)1 0.022 5 1.1 (0.00011%)15 9.5 (0.00095%)60 (1 degree) 152 (0.015%)120 (2 degrees) 609 (0.061%)


SURFACE TENSION

Due to the surface tension properties of liquids a meniscus is formed around the circumference of the cylinder at the point where the piston projects out ofits cylinder.

The resulting force is defined as

Fst = γ Cwhereγ = Surface tension in (dynes/cm or lbf/in)C = circumference of piston (cm or inches)


FORCE COMPONENT

Total Force ( ΣF) = (ma · gl) · cos θ · (1 - ρair/ρstd) + γ·C

Buoyancy Correction

VerticalitySurfaceTensionGravitational

Force


Influences on Area

Pressure DependenceDistortionOperating Fluid

FFP =P = ________

AA

• Temperature


Forces Acting on Cylinder (Simple)


Simple Cylinder - Area Increasing


Temperature Coefficient

Thermal Coefficient of Expansion for Piston/Cylinder Materials;Piston Cylinder CoefficientSteel Bronze 30 ppm/°C

Steel Steel 24 ppm/°C

Steel WC 15 ppm/°C

WC WC 9.1 ppm/°C

WC = Tungsten Carbide


Change in Area due to Temperature

Example: - 3oC Delta Temperature from Calibrated Temperature.

Change in Area (Uncorrected Error):Tungsten Carbide = 9.1 ppm/oC x 3oC = 27.3 ppmSteel/Bronze = 30 ppm/oC x 3oC = 90 ppm

Measuring and correcting the Area of the Piston/Cylinder for Temperature changes result in errors in the 1.3 ppm magnitude


EFFECTIVE AREA

Effective Area =Effective Area =

AA00••(1+b(1+b11••P+bP+b22••PP22))••(1+c(1+c••(t(t--ttrr))))

Distortion coefficient(s)

Thermal CoefficientArea @ 0

pressure


Piston Gauge Pressure Equation

FFP =P = ____ ____

AA∴ becomes

(ma · gl) · cos θ · (1 - ρair/ρm) + γ· ·C —————————————

Ao ·· (1 + b(1 + b1 1 ·· P + bP + b2 2 ·· PP22) ) ·· (1 + c (1 + c ·· ((tt--ttrr))))


REFERENCE PLANE

L1 = 2.867i i

D = 10.74i

Bench Top

PressurizedFluid

REFERENCE PLANE


Uncorrected Errors -- Example

Buoyancy 140 ppm (0.014%)Level (1 degree) 152 ppm (0.015%)Distortion 300 ppm (0.030%)Temperature (5 oC) 120 ppm (0.012%)Gravity 1400 ppm (0.140%)Total (Additive) 2112 ppm (≈ 0.201%) Total (RSS) 1482 ppm (≈ 0.15%)


Pressure Uncertainty at Reference Plane ofStandard

Error Source Uncertainty (ppm)

Effective Area (From Cal. Report) 9.0Mass (From Cal. Report) 3.7Local Gravity (1 mgal) 1.0Buoyancy (1.5oC, 0.25 kPa,15%RH) 0.9Level (5 min.) 1.1Temperature (0.14oC) 1.3

(K=2) Total (rss) 10.0 ppm


UNCERTAINTY ANALYSIS -- ExamplePISTON PRESSURE BALANCE (at 100kPa)

Influence Symbol Units Sens Coeff Approximate Rectangular Uncertainty Equivalent Numerical Pressure Variance

Quantity Value Distribution @ k=2 Sigma Standard Value of Std Dev.

(if fixed) Limits Deviation Sens Coeff

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Area P/C Ao m2 Ao -1 8.39863E-05 1.17581E-09 5.87904E-10 11906.705 7.000E-06 4.900E-11

Area Temp. Coef. (Tstd - Tref ) C 0.6 0.14 8.08290E-02 9.100E-06 7.355E-07 5.410E-13

Local Gravity gl m/sec2 gl -1 9.792778 9.79E-06 5.65386E-06 1.021E-01 5.774E-07 3.333E-13

Pressure P Pa 100000 3.50000E+02 0.000E+00 0.000E+00 0.000E+00

Distortion Coeff Pa-1 P 0 0 0.00000E+00 0.000E+00 0.000E+00 0.000E+00

Density of Air kg/m3 1.19 0.0082 4.73427E-03 1.282E-04 6.070E-07 3.684E-13

Mass Load Mload kg M-1 0.85778 3.00223E-06 1.50112E-06 1.166E+00 1.750E-06 3.063E-12

Density of Mass Load kg/m3 7800 46.8 2.70200E+01 1.956E-08 5.285E-07 2.793E-13

Density of Fluid kg/m3 Ao*h/M 5.05 0.0883 5.09630E-02 2.644E-05 1.347E-06 1.815E-12

Fluid Head Correction h m 0.27 0.00635 3.66617E-03 3.779E-04 1.386E-06 1.920E-12

Thermal Exp Coeff Std C-1 Tstd - Tref 0.0000091 0.00000091 5.25389E-07 6.000E-01 3.152E-07 9.937E-14

Level deg. 0 1.0577E-06 6.10663E-07 1.000E+00 6.108E-07 3.730E-13

P/C Serial Number: C-349 5.779E-11

Mass Set Serial Number: 52799 7.602E-06

15.2

Uncertainty in Units Pressure Variant Terms

Expanded Uncertainty k = "2" (ppm)

Uncertainty @ k="1",Square Root of Sum

Variance Sum

A0*(ρfluid -ρair)/M

αp + αc

λρair

λ

* 1 ∂P P ∂xi

ρload

ρf luid

αp + αc

ρload-1

ρair/ρload2

(σ) (1σ) (1σ) (σ2)

θ Cos θ -1


REFERENCE PLANE

L1 = 2.867i i

D = 10.74i

Bench Top

PressurizedFluid

REFERENCE PLANE


APPLICATION

DUT

STD hf

“Accuracy” (Uncertainty) of Calibration Standard

“Precision” (Performance) of Device Under Test


Pressure at Device Under Test

P1 : Pressure at Reference plane of source (STD)P2 : Pressure at Reference plane of Device Under Test (DUT)Pfh: Pressure Gradient of Fluid Column (Head)hfh: Vertical distance between two Reference planes (fluid)hah: Vertical distance between two Reference planes (ambient air)ρf : Density of compressed fluid (liquid or gas)ρa : Density of ambient air gl : Local Gravityar : Reference Acceleration

ar = 1 m/sec2 for Force in units of Newtonsar = 9.80665 m/sec2 for Force in units of mass (kgf, lbf)

P1

P2

hfhSTD.

DUT

hah

Pfh = (ρf • hfh • gl/ar), Pa = (ρa • hah • gl/ar)

P2 = P1 - (Pfh - Pah)

P2 = P1 - [(ρf • hfh • gl/ar) - (ρa • hah • gl/ar)]

if hfh ≈ hah = h then

P2 = P1 - (ρf - ρa) • h • gl/ar

Note: The sign of h may be plus or minus. The convention chosen for this example is for h to be positive when the DUT is above the STD.


Pressure “Head” - Pneumatic

∆Ph = ρa• gl • hAt 1 bar (100 kPa) barometric pressure

ρa ≈ 0.001201 gm/cm3

for 1 cm ‘gas head’, pressure gradient is≈ 0.1 Pa

∴ for 30 cm ≈ 3.0 Pa (1 foot, ≈ 0.001 in Hg)

0.0035% (of 100 kPa)


Pressure “HEAD” - Hydraulic

HYDRAULIC (oil) ∆Ph = ρo • gl • h

ρo ≈ 0.85 grams/cm3

for 10 cm oil head (h), pressure gradient is

≈ 800Pa

At Error, %rdg100 MPa 0.0008%50 MPa 0.0016%5 MPa 0.016%


Calibration Accuracy - Example

Primary Pressure Standard, Model 2465Accuracy: 0.0010% rdg

Secondary Transfer Standard, Model 7250Performance: Precision – 0.003% fs

Stability – 0.005% rdg/ 6 mos.

Device-Under-Test (DUT)


Total Uncertainty of DUT

TOTAL UNCERTAINTY

OF

DEVICE UNDER TEST (DUT)

************

⇒ Uncertainty of Calibrating Source, (Type B, UB)

combined with

⇒ Standard Deviation of DUT Data, (Type A, UA)


Combination of Type A & B Uncertainties

U = ±2 [ ∑(UAi)2 + ∑(UBi/2)2 ]½

(Coverage Factor, K = 2)

where UB = ‘accuracy’ of calibration standard

UA = ‘precision’ of DUT

* ISO Guide


Transducers- Performance

Basic Performance ParametersRepeatabilityHysteresis Precision (Accuracy)Linearity (Usually combined RSS)

Environmental Considerations (Temperature / Pressure Coefficients)Time Stability Drift -Zero and Span


Performance/Accuracy of 7250 Transfer Standard

Performance = Precision* + Time stability**

Accuracy = Performance + Uncertainty of the Calibration Standard

Example: Precision: ±0.003% fs ⎤

Stability: ±0.005% rdg/6 mos.⎦⇒ Performance

Cal. Std.: ±0.0010% rdg

Performance = ±(0.003% fs + 0.005% rdg)/6 mos.

Accuracy = ±([0.003% fs + 0.005% rdg] + 0.0010% rdg)/6 mos.

* Precision: Combined effects of linearity, repeatability, hysterisis

** Time Stability: Time stability of the calibration


Accuracy of 7250 at 100 kPa

Accuracy = ±([0.003% fs + 0.005% rdg] + 0.0010% rdg)/6 mos.

0.003% of 100 kPa = 3 Pa

0.005% of 100 kPa = 5 Pa

0.001% of 100 kPa = 1 Pa

Total Error = 9 Pa (linear summation)

Total Error = 5.9 Pa (RSS)


Calibration Source

Model 7250: Accuracy at 100 kPa = ± 5.9 Pa (0.0059 % fs)

DUT


EXAMPLE - Calibration of 100kPa DUT(using the 7250 as the transfer standard)

Test Gauge: Full Scale = 100 kPa

Standard DUT reading, x x-m (x-m)2

0.000 -0.003 -0.004273 1.826E-0510.000 -0.005 -0.006273 3.935E-0520.000 0.001 -0.000273 7.438E-0830.000 0.003 0.001727 2.983E-0640.000 0.005 0.003727 1.389E-0550.000 -0.002 -0.003273 1.071E-0560.000 0.008 0.006727 4.526E-0570.000 0.003 0.001727 2.983E-0680.000 -0.007 -0.008273 6.844E-0590.000 0.001 -0.000273 7.438E-08

100.000 0.010 0.008727 7.617E-05

mean (m) = 0.001272727

rss = 0.0053 kPa, Standard Deviation


TOTAL UNCERTAINTY

U = ±2 [ ∑(UAi)2 + ∑(UBi/2)2 ]½

UAi = 0.0053 % FSUBi = 0.0059 % FS

∴ UDUT = 0.0121% (2σ)


Thank You24 June 2003

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Pressure Measurement and Control