A New iston Gauge to Improve the Definition of High Gas ressure and to Facilitate the Gas to Oil Transition in a ressure Calibration Chain ierre Delajoud, Martin Girard DH Instruments, Inc. 4765 East Beautiful Lane hoenix, Arizona 85044 USA +1.602.431.9100, mgirard@dhinstruments.com Abstract A new piston gauge for direct operation in gas up to 100 Ma has been developed. Its design seeks to make pressure deformation of the piston-cylinder more predictable and reproducible as well as making high pressure gas operation more practical. The piston-cylinders operate directly in gas but with a liquid lubricating the piston-cylinder gap. They are integrated into interchangeable modules that include all the components that affect the pressure deformation coefficient and a dedicated lubricating liquid reservoir. The modules mount the piston-cylinder in negative free deformation in which the measured pressure is applied to the full working length of the cylinder without abrupt pressure changes. Finite element analysis has been used to compare the new design to previous approaches. The new piston gauge has been crossfloated with reference oil piston gauges to determine the agreement between theoretical and experimental values of pressure deformation. In addition to operating in gas, the piston gauge platform and piston-cylinder modules can be completely liquid filled and operated hydraulically. This facilitates its calibration and makes it a useful tool for the transition from lower pressure gas to higher pressure oil in pressure calibration chains. 1. Introduction The derivation of pressure from the base units and the maintenance of reference pressure values across the pressure scale are highly dependent on the knowledge and transfer of the effective area of piston-cylinders. The value of effective area for piston-cylinders used at low pressure has been determined from direct dimensional measurement of relatively large piston-cylinders and/or by pressure based comparisons with mercury manometers. Typically, to define higher pressures, the known effective area of large, low pressure piston-cylinders is transferred by pressure based crossfloat to smaller piston-cylinders. However, as pressure increases, the uncertainty in effective area due to the uncertainty in the change in effective area with pressure becomes significant. The change in effective area with pressure can be determined experimentally. The uncertainty in this determination is dependent on the range of pressure over which it can be made. A wider range and higher pressure yields greater pressure deformation that is easier to measure. While the best values of effective area are determined at low pressure (a few ka to 1 Ma) and transferred upwards, the best values of the change in effective area with pressure are determined at high pressure (100 to 500 Ma) and transferred downwards. The coherence of measurement throughout the pressure scale and minimizing uncertainty, particularly in the intermediary range, is therefore dependent on methods used to accomplish the transfers. One of the challenges in connecting the low and high ends of the pressure scale is that, for a number of metrological and practical reasons, the highest quality measurements are traditionally made with instruments operated with gas at low pressure and oil at high pressure. Due to its low viscosity, gas works well as the lubricant of the piston-cylinder gap at low pressure. On the other hand, its high compressibility and low change in viscosity with pressure make gas a poor choice for operation at higher pressures. The positive free deformation mounting system, in which the piston-cylinder gap increases with pressure, results in drop rates that are too great with high pressure gas. To achieve an acceptable drop rate at high pressure, the piston-cylinder must have a very small gap, which requires a counteracting pressure on the outside of the cylinder and/or a relatively limited operating range. iston-cylinders with very small gaps are also highly sensitive to piston-cylinder geometry. At DH Instruments, Inc. (DHI) it is generally considered that the best measurements are made with gas operated, gas lubricated piston-cylinders up to about 5 Ma, and then with oil operated, oil lubricated piston-cylinders. The precision with which piston-cylinder effective area and pressure deformation coefficient values can be transferred
upwards and downwards between low pressure gas and high pressure oil has traditionally been limited by the need to use gas/oil interfaces and the relatively small overlapping range over which both work well. The significance of the quality of these transfers has increased as the uncertainty in effective area and deformation coefficients has continued to be reduced and the demand for lower uncertainties at higher pressures has increased. 2. A new high pressure gas operated piston gauge Although gas lubrication of piston-cylinders is not ideal above about 5 Ma, there are requirements for very low uncertainty standards operating in gas up to much higher pressure. DHI offers gas lubricated piston-cylinders commercially for use up to 11 Ma but there are many applications to 20, 40 and even 100 Ma. A new piston-gauge designed to meet this demand operates directly up to 100 Ma with gas as the pressurized medium. In addition to its normal role as a high pressure gas calibration device, it can be a very useful tool in assuring the connection of the high and low ends of the pressure scale. Due to the limitations of gas lubrication of the pistoncylinder gap at high pressure, the new piston gauge uses piston-cylinders that operate directly with gas under the piston but whose gap is lubricated with a liquid. Gas operated, liquid lubricated piston-cylinders were first introduced in the 1970s with the objective of operating directly with natural gas as the pressurized medium. 3. Conventional high pressure gas operated piston gauge The conventional gas operated, liquid lubricated pistoncylinder is represented in Figure 1. The gas pressure to be measured is applied beneath the piston-cylinder and to the top of a liquid filled reservoir. The liquid from the reservoir is connected to the outside of the cylinder where it is contained by two O-rings around the cylinder. The liquid enters the piston-cylinder gap through two lateral holes in the cylinder. The liquid reservoir is higher than the cylinder, so the pressure of the liquid, l, is always higher than the pressure of the gas, g, by the amount of the column of liquid, ρ l g h. This assures that there is always a flow of liquid out of the piston-cylinder gap towards the pressurized gas and that the gas cannot enter the space. This liquid flow is the minute amount resulting from a differential pressure of a couple of centimeters of liquid through an annular gap of less than 1 micron. As the differential pressure and gap size are roughly constant, this flow does not change appreciably with measured pressure. In fact, it tends to decrease due to the increase in viscosity of the fluid with pressure. Of course, there is also a larger flow of liquid, of a magnitude dependent on the gas pressure, upward through the gap towards atmosphere. Figure 1. Conventional gas operated, liquid lubricated piston-cylinder This system has been used extensively with little change since its original introduction. However, it was originally designed to achieve measurement uncertainty on the order of 1 x 10-4 and repeatability around 1 x 10-5. Today, needs at the highest levels are roughly an order of magnitude better and the system s metrological limitations have become noticeable. Note that the piston-cylinder is mounted in what is referred to as a reentrant system. The measured pressure is applied to the outside of the cylinder wall part way up the length of the cylinder. This type of mounting system was originally designed to limit pressure deformation of the cylinder and reduce expansion of the gap to limit the drop rate at high pressure. There was also some hope of achieving zero deformation with a perfectly placed O-ring. However, the reentrant design causes an abrupt change in stress along the outside of the working zone of the cylinder, which leads to complexities in modeling that increase the uncertainty in the prediction of deformation. Also, movement of the upper O-ring relative to the cylinder can change the deformation of effective area with pressure, affecting repeatability. Finally, note the retaining nut at the top of the cylinder. The nut s threads determine the vertical alignment of the cylinder. Torque on the nut and thus vertical mounting stress on the cylinder is dependent on the operator. Figure 2 visualizes Von Mises stress by finite element analysis in a conventional gas operated, liquid lubricated piston-cylinder in the case of a 5 mm diameter (500 ka/kg) cylinder at 20 Ma measured pressure. The abrupt change in stress on the outside of the cylinder at the level of the O-ring is apparent. This causes the calculation of deformation to be highly influenced by the geometry of the gap and the level of the stress point, which can change with movement of the O-ring. Below the O-ring, the stresses on the cylinder are balanced, as the pressure is the same on the inside and outside of the cylinder wall. Above the O-ring the cylinder tends to open. Axial
force from the pressure on the bottom of the cylinder pushes the cylinder up on the nut and the main contact of the nut with the cylinder is on the outside of the nut as it deforms. CYLINDER O-RING LOCATION complete module is threaded on and off the piston gauge platform mounting post when piston-cylinders are changed (Figure 4). The module concept allows all the parts associated with pressure deformation to be married to a piston-cylinder. The mounting system design can then be specialized for different piston-cylinder sizes, which is not possible when common mounting hardware that is part of the platform must accommodate all the piston-cylinder sizes. It also addresses the fact that, inevitably, individual mounting components with conventional mechanical tolerances of 20 or 30 micron have individual effects on an individual pistoncylinder with tolerances on the order of 0.1 micron. Marrying the parts keeps these individual effects constant, improving repeatability. Figure 2. Von Mises stress in a reentrant cylinder The reentrant mounting system was favored for high performance piston gauges in general until the early 1980s. At that time improvements in piston-cylinder materials and geometry along with a better understanding of deformation with pressure led to its replacement by the free deformation mounting system. In free deformation, the measured pressure is sealed at the bottom of the cylinder and the cylinder is allowed to deform freely with no O-rings and abrupt pressure changes along its working length. This results in deformation that is more predictable and repeatable. 4. New high pressure gas operated piston gauge design Figure 4. Installation of piston-cylinder module Figure 5 shows the implementation of gas operated, liquid lubrication in a piston-cylinder module. The lubricating liquid reservoir is contained within the module. This allows the liquid to conveniently be specialized for a piston-cylinder size (for example, lower viscosity for larger piston sizes) and eliminates loss of liquid when removing and installing piston-cylinders in the platform. The interface between the module and the mounting post is away from the pistoncylinder and does not contribute to its deformation. The cylinder s alignment is defined by a single part and is not dependent on threading. The tolerance of the parts is such that there is no metallic preload on the cylinder, only precompression of the O-rings. Figure 3. iston-cylinder modules The new design of the new gas operated, liquid lubricated piston gauge overcomes the metrological and practical limitations of the original. Central to the design is the concept of the piston-cylinder module, which is used throughout the DHI G7000 family of piston gauges. The module is an integrated assembly that includes the pistoncylinder and dedicated mounting components (Figure 3). The
RESERVOIR CYLINDER INTERFACE TO MOUNTING OST Figure 5. Gas operated, liquid lubricated module H in ositive Free Deformation From a practical standpoint, integrating the reservoir into the module allows piston-cylinders to be changed on the platform quickly and cleanly. In the conventional design, removing the cylinder required disassembly and opened the connection from the liquid reservoir to the mounting post. The reservoir in the module is filled with 8 cc of fluid, which allows roughly 50 hours of continuous operation at maximum pressure. Normal procedure is to refill the module at a regular time interval. An O-ring on the bottom face of the cylinder separates the liquid in the reservoir from the gas pressure under the cylinder. Two O-rings at the top of the cylinder seal the measured pressure from atmospheric pressure. The measured pressure is applied to the active length of the cylinder, which is completely surrounded by the measured pressure with no boundary stresses other than on its top surface. Since the pressure inside the cylinder decreases from the measured pressure to atmospheric pressure from the bottom to the top of its bore while the measured pressure outside the cylinder remains constant, the cylinder contracts at the top. This causes the pressure deformation coefficient to be negative as effective area is reduced with measured pressure. This type of mounting system can be referred to as negative free deformation as opposed to positive free deformation in which the constant pressure on the outside of the cylinder is atmospheric pressure, the cylinder expands at the bottom as measured pressure increases and the pressure deformation coefficient is positive (Figure 6). H 0 H x L x/l Negative Free Deformation Graphs of pressure in gap, (x)/, applies if Symbol (x) H ip H in L Note that Description Measured pressure H > H in ip ressure in the gap at height x 1 H H Initial gap for positive free deformation Initial gap for negative free deformation Length of cylinder H 0 Gap at top of cylinder (x = L, (x) = 0) H Gap at base of cylinder (x = 0, (x) = ) η 0 Viscosity of fluid at pressure (x) = 0 η x Viscosity of fluid at pressure (x) = Distance from bottom of cylinder (x)/ 3 η 0 η0 Figure 6. ositive and negative free deformation piston-cylinder behavior with pressure 1
The objective and results of negative and positive free deformation mounting systems at maximum pressure are the same in terms of gap profile. The objective of a piston-cylinder and its mounting system for operation with oil in the gap is to obtain, at maximum pressure, a cubed ratio of the bottom and top gap that is equal to the ratio of the viscosity of the fluid in the same positions. This results in nearly linear pressure distribution along the gap and therefore nearly linear deformation with pressure. A piston-cylinder with linear pressure distribution in its gap conforms most closely to theoretical models and has the best behavioral characteristics (high sensitivity, low drop rate) at a given pressure. The manner in which the two different mounting systems achieve the desired profile, leads to different initial gap sizing and makes them useful for different applications. In the case of positive free deformation, the gap size increases with pressure so the initial gap must be small enough to avoid excessive drop rates at maximum pressure. In the case of negative free deformation, the gap size decreases with pressure so the initial gap must be large enough to avoid closure of the top of the cylinder at maximum pressure. In practice, a large initial gap is attractive as it improves the sensitivity of the piston-cylinder at low pressure, however, the starting gap must not be so large as to make the drop rate unacceptably high. For these reasons, negative free deformation lends itself well to mid-range pressure (with oil in the gap) where the initial gap size can be large enough to give very good mobility with a reasonable drop rate but the maximum pressure is not so high that it will close the gap. Negative free deformation is also useful when gas, whose viscosity is nearly constant with pressure, is the fluid in the gap and reducing the gap size is necessary to prevent excessive increases in drop rate as measured pressure increases. Negative free deformation can provide the benefits of the old reentrant design, reducing gap with pressure, without the mechanical disadvantages of abrupt stress changes in the working zone of the cylinder wall. For higher pressure, positive free deformation is necessary so that the initial gap can be small enough for the drop rate to be acceptable at the low end of the piston-cylinder s range where viscosity is lowest. CYLINDER Figure 7. Von Mises stress in a negative free deformation cylinder Figure 7 visualizes Von Mises stress by finite element analysis in the new gas operated, liquid lubricated pistoncylinder module in the case of a 2.5 mm (2 Ma/kg) diameter piston at 100 Ma measured pressure. Note the very different condition of the cylinder, despite a measured pressure about 5 times higher, when compared to the conventional gas operated, liquid lubricated cylinder in Figure 2, (the representation of the hole from the screw in the top of the cylinder retaining flange is not meaningful due to mesh size). There is a very smooth transition of Von Mises stress along the height of the cylinder exactly as desired. The result of the progressive drop of pressure in the gap can be seen clearly. In this situation, the analytical prediction of deformation coefficient is much more accurate and the actual deformation more repeatable. Direct operation of a piston-cylinder in high pressure gas, without compromise in metrological performance relative to conventional oil piston-cylinders mounted in free deformation mounting systems, becomes possible. Kn H nom. [µm] Ø eff. [mm] Ø c [mm] Λ [Ma -1 ] 100 [ka/kg] 1.20 11.17 20-2.91E-6 200 [ka/kg] 1.00 7.901 20-2.48E-6 500 [ka/kg] 0.80 4.997 20-2.31E-6 1 [Ma/kg] 0.7 3.533 20-2.25E-6 2 [Ma/kg] 0.6 2.498 20-2.23E-6 Table 1. G7202 piston-cylinder modules Table 1 lists the different piston-cylinder sizes used in the new gas operated liquid lubricated modules by Kn, the nominal mass to pressure conversion coefficient. The table lists the nominal values of the gap between the piston and the cylinder (H nom. ), the effective diameter (Ø eff ), the cylinder diameter (Ø c ) and the calculated pressure deformation coefficient (Λ). The magnitude of the deformation is about
double that of positive free deformation piston-cylinders. This results in a relative change in effective area when going from null pressure to 100 Ma of -2 x 10-4 for the 2 Ma/kg piston-cylinder. With a typical uncertainty (k=2) of ± 1 x 10-1 in the value of deformation, the contribution of pistoncylinder pressure deformation uncertainty to the measured pressure uncertainty at 100 Ma is ± 2 x 10-5. The calibration of gas operated, liquid lubricated piston-cylinder modules by comparison to DHI calibration chain hydraulic piston-cylinder modules indicates that the actual pressure deformation is typically within 10 % of the calculated value when the piston-cylinder initial gap is within 10 % of the nominal value. The pressure deformation coefficients assigned to the hydraulic calibration chain piston-cylinder modules were measured directly by national measurement institutes equipped with methods to determine deformation experimentally [1]. 5. Application of the new high pressure gas operated piston gauge The main role of the new gas operated, liquid lubricated standard is to act as a convenient means of performing very low uncertainty day to day calibrations of transfer standards directly with gas as the pressurized medium. The typical pressure measurement uncertainty specification (k=2) is ± 2 x 10-5 at 10 Ma and ± 4.5 x 10-5 at 100 Ma [2]. recision is at least 10 times better than measurement uncertainty. The new piston gauge can also be very useful in a pressure calibration chain for making the transition between gas operated piston gauges at the low end and oil operated piston gauges at the high end. As discussed above, this transition is difficult due to the uncertainties associated with gas to oil interfacing techniques and because of the relatively small pressure range over which gas and oil operated piston gauges both behave well and can be compared precisely. The piston gauge platform is designed to be filled with either gas or oil. Both gas operated, liquid lubricated piston-cylinder modules and oil operated modules can be installed in it. In addition, the gas operated, liquid lubricated modules can be operated filled entirely with oil. As the fluid in the gap and the application of forces to the piston-cylinder are identical whether working with gas or oil under the piston, the effective area and pressure deformation are consistent with both media. This feature can allow a single pistoncylinder module to be crossfloated directly with a gas operated piston gauge at lower pressure and then directly with an oil operated piston gauge at higher pressure. For example, a pair of 11.2 mm diameter (100 ka/kg) gas operated, liquid lubricated modules are being used to assure the gas/oil link in the DHI pressure calibration chain. The highest pure gas level in the calibration chain is a pair of 16 mm diameter (50 ka/kg) piston-cylinder modules that operate between 0.05 and 5 Ma. The lowest oil level is a pair of 7.9 mm diameter (200 ka/kg) oil piston-cylinder modules that operate between 0.2 and 20 Ma. In the past, these have been crossfloated between 0.4 and 5 Ma through a direct gas/oil interface. The gas/oil interface and 4:1 effective area ratio make the crossfloats difficult and very technique dependent. The process is improved by using the gas operated, liquid lubricated piston-cylinders. First they can be crossfloated directly in gas over the full 5 Ma range of the 16 mm diameter pure gas piston-cylinder modules. Then, they are filled with oil and crossfloated directly with the oil piston-cylinder modules up to 10 Ma. Use of the gas/oil interface is eliminated and the crossfloat effective ratios are only 2:1. The ability of the gas operated, liquid lubricated piston-cylinders to operate in oil is also exploited for the calibration of new modules produced for customers. It allows them to be filled with oil and calibrated by direct crossfloat with oil piston-cylinder modules from the calibration chain that have very well known deformation coefficients determined by national measurement institutes. 6. Conclusions The new gas operated, liquid lubricate piston gauge offers significant practical and metrological improvements over previous designs. These make it possible to work directly in gas up to 100 Ma without compromises in performance or uncertainty relative to oil piston gauges. The excellent metrological performance combined with the ability to operated in gas or oil, make the new piston gauge a unique tool for filling the critical link between lower pressure gas and higher pressure oil standards in high level pressure calibration chains. This should make the transfer of effective area value upwards from large gas pistons to smaller pistons easier and more precise. In addition, it can improve the transfer downwards of pressure deformation coefficient values from high pressure oil piston gauges to improve the knowledge of deformation coefficient at high end of the pure gas range. References [1] Bair M., Improvements in the Determination of Effective Area Through a iston-cylinder ressure Calibration Chain, roceedings of NCSLI Conference, Anaheim, CA, USA, 2002, August. [2] Bair M., Delajoud., Uncertainty Analysis for ressure Defined by a G7601, G7102, G7202 or G7302 iston Gauge, DH Instruments, Inc. Technical Note 7920TN01C, 2003, June.