Pressure Calibrations Using Piston Gauge Standards

1 Page 1 NIST Special Publication 250-39 2009 NIST Calibration Services for Pressure Using Piston Gauge Standards Douglas A. Olson Open at page → 2 Page 2 NIST Special Publication 250-39 2009 NIST Calibration Services for Pressure Using Piston Gauge Standards Douglas A. Olson Chemical Science and Technology Laboratory Process Measurements Division Pressure and Vacuum Group... Open at page → 3 Page 3 Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or... Open at page → 4 Page 4 NIST Calibration Services for Pressure Using Piston Gauge Standards Table of Contents 1 Introduction.................................................................................................................... 1 2... Open at page → 5 Page 5 v 5.1.9 Uncertainty due to TEST piston circumference............................................... 48 5.1.10 Uncertainty due to acceleration of gravity..................................................... 48 5.1.11 Unce... Open at page → 6 Page 6 1 Introduction The National Institute of Standards and Technology (NIST) is responsible for realizing, maintaining, and disseminating the derived SI unit of thermodynamic pressure, the pascal (Pa). Pressure is an intrins... Open at page → 7 Page 7 Calibrations are performed using a range of piston gauge standards. Typically, the customer's instrument is calibrated against the NIST standard that best matches the desired pressure range and media. An item can be cali... Open at page → 8 Page 8 requires recording the output of the pressure instrument at the pressure points established by the piston gauge standard, but no incremental adjustment of the mass on the NIST piston gauge. 3 NIST piston gauge pressure s... Open at page → 9 Page 9 Cylinder Piston Column Masses Fluid pressure Figure 1. Schematic of free deformation piston gauge. 4 Open at page → 10 Page 10 the temperature changes. Thermal expansion is accounted through the expansion coefficients, or ( )()( )(,) 1 eepc ATp A T T αα=++ − r , (2) with A e is the effective area at pressure p and reference temperature T r; α p... Open at page → 11 Page 11 3.1 NIST gas primary standards PG38 and PG39 are gas primary piston gauge standards that operate from 20 kPa to 1 MPa. They were acquired by NIST from Ruska Instrument Corporation in 1989. They are deemed primary standar... Open at page → 12 Page 12 Cylinder 36 mm 75 mm CapPiston Figure 2. Schematic diagram of the PG38 and PG39 piston/cylinder assembly with the piston in upright (left) and inverted (right) orientations. The cap on the right is used to support the we... Open at page → 13 Page 13 Figure 3. Picture of PG39 cylinder (left), piston (right), an d mass set (top). Closed end of piston is shown. 8 Open at page → 14 Page 14 estimated as 10x10 -6 . In 1999, PG39 was dimensioned by Physikalisch Technische Bundesanstalt (PTB) using a state-of-the art diameter and form comparator in which a calibrating laser interferometer is integral to the ap... Open at page → 15 Page 15 3.0x10 -6 for both PG38 and PG39. The largest A0 occurred for the viscous flow model, and the smallest A0 occurred for the interpolated flow model in absolute mode. The value for the pressure distortion coefficient, b1,... Open at page → 16 Page 16 0.999990 0.999995 1.000000 1.000005 1.000010 1.000015 0 200 400 600 800 1000 1200 Pressure / kPa A 38 /A 39 Up-Up Dn-Dn Dn-Up Up-Dn TWF 5 ppm Figure 4. The ratio of the effective area for PG38 to that of PG39 ( A38/A39).... Open at page → 17 Page 17 3.1.4 Final result for effective area and uncertainty The final result for the primary standards for Ae in m 2 with p in Pa at a temperature of 23 ºC is: PG38: ( ) 31 1.0079497 10 1 8.97 10 e Ap −− =×+× 2 , (5) PG39: ( )... Open at page → 18 Page 18 Piston Cylinder Jacket pressure Column System pressure Figure 5. Schematic of controlled clearance piston gauge. 13 Open at page → 19 Page 19 determined by using the following equation: ()( )() () ()()0 1 11 1 a i i mi pp zj pc r mg C p Abpdpp TT ρ γ ρ αα⎛⎞ −+⎜⎟ ⎝⎠ = ++−++− ∑ . (9) The reader should note the similarity to eq. (3); the forces due to mass and su... Open at page → 20 Page 20 ( )13 p p b E μ−− = . (11) The Poisson’s ratio, μ, and modulus of elasticity, E p, are material properties of the piston. Typical values for b p are -5x10 -13 Pa -1 to -7x10 -13 Pa, and the standard uncertainty u(b p) is... Open at page → 21 Page 21 0 20 40 60 80 100 120 140 160 180 200 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 v 1/3 / (mm/s) 1/3 p j / MPa 200 180 160 140 120 100 80 60 40 20 p / MPa: Figure 6. Fall rate (v) of a typical CCPG over p j/p = 0 t... Open at page → 22 Page 22 The definition of d follows from taking the partial derivative of both sides of eq. (9) with respect to p j, holding the load (mass) constant and neglecting higher order terms. p is measured by cross-float calibration of... Open at page → 23 Page 23 Table 1. Characteristics of NIST controlled clearance piston gauge primary standards, in terms of HW model. Pressure p in Pa. Relative standard uncertainty in pressure given at maximum operating pressure. ( ) ( )( )0 11... Open at page → 24 Page 24 http://www.ngs.noaa.gov/cgi-bin/grav_pdx.prl. For further information on both of these services, contact National Oceanic and Atmospheric Administration, National Ocean Survey, Office of the National Geodetic Survey, Geo... Open at page → 25 Page 25 3.3.4 Density of masses The density of the masses is required for the buoyancy correction. When the piston gauge is used in the gauge mode, the values of the densities of the masses used in eq. (3) must be identical to t... Open at page → 26 Page 26 3.3.7 Thermal expansion Coefficients of thermal expansion are material properties for the piston and cylinder. The reference temperature for piston gauge measurements at NIST is 23 ºC, and the coefficients of thermal exp... Open at page → 27 Page 27 Table 2. Pressure range, medium, and effective area coefficients of NIST transfer standard piston gauges. A 0 / m 2 b 1 / Pa -1 b 2 / Pa -2 PG22 10 kPa to 150 kPa gas 336 3.357224x10 -4 00 PG36 10 kPa to 150 kPa gas 336... Open at page → 28 Page 28 standard given by eq. (3), substituted into eq. (18) and rearranged, the unknown is the effective area of the transfer standard, Ae,T: () ()() () ()() () , ,,, ,, ,, , , 1 12 3 1 . 12 3 1 a iT T pR cR R fami T eT e R TT... Open at page → 29 Page 29 PG42 26 PG41 140 PG21 280 PG20 140 PG27 28 PG67 280 Primary Standards Figure 7. NIST pressure scale for oil primary and transfer standard piston gauges. Circles represent piston gauge standards; the number in a circle is... Open at page → 30 Page 30 Figure 8. NIST pressure scale for gas primary and transfer standard piston gauges. Circles represent piston gauge standards; the number in a circle is maximum pressure in MPa. Lines between circles represent comparisons... Open at page → 31 Page 31 Table 3. Coefficients for Type B relative standard uncertainty in effective area in gauge mode of NIST transfer standard piston gauges. For absolute mode, add uncertainty of 2x10 -6 in quadrature. Relative standard uncer... Open at page → 32 Page 32 0 5 10 15 20 10 100 1000 10000 100000 Pressure / kPa u(A e )/A e x 10 6 PG38 PG22 PG28 PG34 PG13 PG23 PG87 Figure 9. Operating ranges and relative standard uncerta inties of NIST gas piston gauges. 27 Open at page → 33 Page 33 0 5 10 15 20 0 50 100 150 200 250 300 Pressure / MPa u(A e )/A e x 10 6 PG42 PG41 PG21 Figure 10. Operating ranges and relative standard uncertainties of NIST oil transfer standard piston gauges. 28 Open at page → 34 Page 34 The relative standard uncertainty for the transfer standard piston gauges is given by the function: () ()() 1/ 2 2 2 2 21 23 4 , () Be ave B e uA c ccpcpp Ap ⎛⎞ ⎛⎞ ⎜⎟=++ − ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ . (21) The coefficients c 1, c2, c3,... Open at page → 35 Page 35 , , , 1 (, ) a iT T i mi T eT T T T mg C ATp p ρ γ ρ ⎛⎞ −+⎜⎟ ⎜⎟ ⎝⎠ = ∑ (22) p T is determined by the NIST piston gauge and the difference in reference levels between it and the customer’s gauge. When these expressions ar... Open at page → 36 Page 36 Test piston gauge Reference piston gauge MT M R Figure 11. Schematic diagram for fluid circuit for crossfloat calibration of two piston gauges, when pressure equilibrium is established using a differential pressure cell.... Open at page → 37 Page 37 Screw pump or volume changer CVV1 Reference piston gauge Test piston gauge CVV2 Pressure transducer h MR Reservoir or gas tank MT TR TT Screw pump (optional) SV1 SV2 SV3 Piston Cylinder Figure 12. Schematic diagram for f... Open at page → 38 Page 38 provide leveling screws to assure that the piston is vertical. With many designs, a level can be placed temporarily on the top of the cylinder. The test piston gauge and the NIST reference piston gauge are connected thro... Open at page → 39 Page 39 Although the DP Cell is convenient in determining pressure equilibrium, it is not essential. The fall rate method can be used with the circuit shown in Fig. 12. Although the circuit is shown with CVV2, a pressure transdu... Open at page → 40 Page 40 4.1.2 Reference levels in a crossfloat For piston gauges with straight pistons, the reference level is normally defined as the lower end of the piston. For pistons with an irregular shape of the submerged part, an adjust... Open at page → 41 Page 41 The pressure at any other location in the fluid line that connects to the NIST piston gauge is given by the standard hydraulic formula (eq. 18), with the convention that the elevation change, h, is positive when the leve... Open at page → 42 Page 42 4) remove all remaining lint before assembly. It may be necessary to repeat the cleaning process to obtain satisfactory performance. The only way to judge how clean is “clean enough” is by the performance of the gauge. 4... Open at page → 43 Page 43 For gas piston gauges below 17 MPa, pressure coefficient b 2 is usually insignificant, and b 1 may be insignificant below 1 MPa. For oil piston gauges, b 1 is nearly always significant. A computer program developed by th... Open at page → 44 Page 44 Reservoir or gas tank SV2 Reference piston gauge h M T Piston Cylinder SV4 SV3 SV1 Bell jar, p V Test pressure instrument Vacuum pump Screw pump or volume changer Figure 14. Schematic diagram for fluid circuit for sensin... Open at page → 45 Page 45 rotated using a drive motor, which is then turned off and the masses allowed to rotate freely. The piston is lowered to its reference level. The residual vacuum is measured with a vacuum gauge. After about 5 minutes to a... Open at page → 46 Page 46 uncertainty components that are given are typical for routine calibrations at NIST. Reduced uncertainty values may be possible for special calibrations. 5.1 Uncertainties in a crossfloat calibration The standard uncertai... Open at page → 47 Page 47 42 ( ) ,12 , ,..., eT N Afxxx= . (42) with x1, x2,…., xN the N variables (called components) on the right hand side of eq. (40). i f x ∂ ∂ is the partial derivative of Ae,T with respect to variable (component) xi, referr... Open at page → 48 Page 48 Table 4. Type B component standard uncertainties for gauge mode oil piston gauge calibration at 5 MPa, REF piston gauge is PG42, TEST piston gauge of nominal area 8.4x10 -5 m 2 , and Spinesstic oil as pressure fluid. All... Open at page → 49 Page 49 44 Table 5. Type B component standard uncertainties for gauge m ode gas piston gauge calibration at 200 kPa, REF piston gauge is PG34, TEST piston gauge of nominal area 8.4x10 -5 m 2 , and nitrogen gas as pressure flui d... Open at page → 50 Page 50 5.1.1 Uncertainty due to reference area, ,eR A u The sensitivity coefficient is given by: ,, ,, eT eT eR eR AA AA ∂ = ∂ . (45) The standard uncertainty, u(Ae,R), is a function of the specific NIST piston gauge used. Equa... Open at page → 51 Page 51 where ,TiT M m=∑ . As in the REF masses, the standard uncertainty, u(MT) is more precisely the uncertainty of all the individual masses placed on the NIST piston gauge. The same considerations for assumed correlation app... Open at page → 52 Page 52 ( ),, , 2 ,, acal aeT eT MR MRA A ρρ ρρ−∂ = ∂ . (52) Here, ρa,cal is the density of the air at the time the masses were calibrated. To be conservative, the air density difference is taken as 0.03 kg/m 3 . We again assume... Open at page → 53 Page 53 Standard uncertainty, u(ρM,T): We use similar arguments as for the REF masses, so the standard uncertainty is therefore 0.0058 ρM,T. The term is negligible for gauge mode and less than 1x10 -6 in absolute mode calibratio... Open at page → 54 Page 54 Standard uncertainty, u(g): The standard uncertainty in g, based on measurements in the NIST calibration laboratory, is 2x0 -6 m/s 2 . g u is negligible for all crossfloats. 5.1.11 Uncertainty due to thermal expansion of... Open at page → 55 Page 55 , ,eT eT R R A A T α ∂ = ∂ . (62) The standard uncertainty, u(TR) is determined assuming a rectangular distribution of possible errors of 0.1 ºC, so u(TR) = 0.058 ºC. A good-quality calibrated thermometer will have an un... Open at page → 56 Page 56 The sensitivity coefficient is: , , () faeT eT T gA A hp ρρ−∂ = ∂ . (65) Standard uncertainty, u(h): The height difference between the gauges is the sum of the difference in the reference levels, hT0-hR0, and the differe... Open at page → 57 Page 57 The Type B combined relative standard uncertainties for typical crossfloat calibrations of a customer’s piston gauge are shown in Tables 4 and 5. For the oil calibration at 5 MPa, the Type B relative standard uncertainty... Open at page → 58 Page 58 53 Hence the Type B combined standard uncertainty can be written as 6 : () 222222222222 eaM f BT A M C g T h p up u u u u u u u u u u u u ρρ γ α ρ = + + + ++++++ ++ 2 V . (72) Table 6 summarizes the Type B component unce... Open at page → 59 Page 59 Table 6. Type B component standard uncertainties for pressure-s ensing instrument calibration, abso lute mode with nitrogen gas. NIST piston gauge is PG22 at 100 kPa. A ll uncertainty terms s hown for completeness. Relat... Open at page → 60 Page 60 5.2.3 Uncertainty due to ambient density, a u ρ The sensitivity coefficient is: TT am pp gh ρρ ∂ =−+ ∂ . (76) The first term in the sensitivity coefficient is the effect of the ambient density on the masses, and the seco... Open at page → 61 Page 61 The same mass density uncertainty has a larger effect on absolute mode calibrations than it does on gauge mode calibrations. Standard uncertainty, u(ρ M): The possible error in the mass density is assumed to have a recta... Open at page → 62 Page 62 This sensitivity coefficient becomes larger as the temperature of the NIST piston gauge departs from 23 ºC. Standard uncertainty, ()uα: NIST uses the manufacturer’s stated thermal expansion for the transfer standard pist... Open at page → 63 Page 63 our data reduction program. As long as h is less than 0.1 m, the uncertainty term is less than 0.2x10 -6 . 5.2.11 Uncertainty due to reference height difference, uh The sensitivity coefficient is: () T fa p g h ρρ ∂ =− −... Open at page → 64 Page 64 6 Quality system The calibration services performed by the piston gauge standards which are described in this document are support by the NIST quality system. The NIST quality system documentation consists of tiered qual... Open at page → 65 Page 65 7 References 1. NIST Calibration Program, Calibration Services Users Guide SP250 Appendix (2009). 2. Dadson, R.S., Lewis, S.L., and Peggs, G.N., “The pressure balance: theory and practice”, Her Majesty’s Stationery Offic... Open at page → 66 Page 66 Appendix A. Recommended formula for the calculation of the density of moist air and its uncertainty A.1 The CIPM-2007 equation The following is a summary of the method described in [9] for the calculation of the density... Open at page → 67 Page 67 Substituting eq. (89) and values of the quantities into eq. (88), the formula for ρa in kg/m 3 becomes: () () 2 3 CO 3.483740 1.4446 0.0004 1 0.3780 10 a v p xx ZT ρ − ⎡⎤=+⋅−⋅−× ⎣⎦ . (90) Using the formula is: 2 CO 0.000... Open at page → 68 Page 68 81 72 1.00062 , 3.14 10 Pa , 5.6 10 K . α β γ −− −− = =× =× t is the temperature in ºC. A.3 Calculation of compressibility factor, Z The equations for Z and its constants are given by: ()() () 2 22 01 2 01 01 2 1 vv pp 2... Open at page → 69 Page 69 64 Appendix B. Sample calibration report of a customer piston gauge Report follows on next page Open at page → 70 Page 70 UNITED STATES DEPARTMENT OF COMMERCE NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY GAITHERSBURG, MARYLAND REPORT OF CALIBRATION Pressure & Vacuum Group Bldg 220, Room B43 Requester: No One In Particular 123 Main Street... Open at page → 71 Page 71 The test gauge was cross-floated against the NIST standard. The calibration data are given in Table 1. The pressures (P) are at the reference level of the test gauge as determined by the NIST standard gauge. The temperat... Open at page → 72 Page 72 two standard deviation level (k=2). When normal statistical distributions apply, the expanded uncertainty defines an interval having a level of confidence of approximately 95%. The Type A component is due to random error... Open at page → 73 Page 73 Table 1. Calibration data of the crossfloat. Listed are pressure (P) on the test gauge at its reference level, force (F ) on the test gauge, and effective area (A) of the test gauge. Obs. PFA No. (MPa) (N) (m 2 ) 1 1.432... Open at page → 74 Page 74 69 Table 2. Effective area of the test gauge calibration fit (A fit) and its uncertainty, over the pressure range of the calibration. Listed are Type A relative standard uncertainty (u A/A), Type B relative standard unce... Open at page →