Abstract:
Disclosed is a bi-directional piston displacement type volumetric fluid flow rate delivery and metering system (calibration standard) and operational method for calibration of fluid flowmeters. The present invention provides reduced uncertainty of delivered volumetric fluid flow rate at meters under test relative to the uncertainty of volumetric fluid flow rate at meters under test provided by prior art bi-directional piston displacement type volumetric fluid flow rate standards given the same nominal cylinder diameters and working fluid and equal dimensional, timing and temperature measurement uncertainties by employing a plurality of metering pistons and cylinders to minimize the connecting volume piping between the metering piston cylinder outlet and meters under test, providing open access to one side of each metering piston to accomplish installation of temperature probes through the pistons into the working fluid and by operational method which minimizes the connecting volume to standard volume ratio.

Description:
1. FIELD OF THE INVENTION  
       [0001]    The present invention relates to a laboratory calibration system and operational method for characterization of fluid flowmeters. Specifically, the present invention is an improved system and operational method over prior art bidirectional piston displacement type volumetric fluid flow rate standards providing reduced uncertainty of volumetric fluid flow rate delivered to a meter under test over what can be achieved with prior art bi-directional piston displacement type volumetric fluid flow rate standards given the same nominal cylinder diameter and working fluid and equal dimensional, timing and temperature measurement uncertainties. 
       2. BACKGROUND OF THE RELATED ART  
       [0002]    Delivering volumetric fluid flow to a meter under test by metering the flow via timed displacement of a piston moving in a cylinder of known cross section has been an accepted method of flowmeter calibration for many years. Edward E. Francisco, Jr. disclosed a system and method for such an apparatus in U.S. Pat. No. 3,403,544 and in U.S. Pat. No. 3,492,856. Francisco, Jr. teaches the use of a plurality of pistons in a single cylinder to save time by sending first one then a second piston and so on through the calibrated cylinder to accomplish a plurality of test runs before having to return the pistons to the starting end of the cylinder. These earlier disclosed devices are unidirectional piston displacement type volumetric flow rate standards. Fluid flow to a meter under test is metered as the piston moves in the cylinder in one direction. The present invention utilizes timed piston displacement in a cylinder of known cross section to meter volumetric fluid flow rate as do these prior art inventions, but differs substantially from them by virtue of metering the fluid flow rate via bidirectional piston movement and the use of a plurality of cylinders, each with a metering piston therein. 
         [0003]    J. H. Hoffman et al disclosed a bi-directional piston displacement type flow and other hydraulic parameter test device in U.S. Pat. No. 3,098,382. A plurality of pistons and cylinders comprise the system disclosed by Hoffman et al. One cylinder with a piston functions as an actuator while the second cylinder with a piston is the test cylinder. The present invention differs from that disclosed by Hoffman et al in that the plurality of pistons and cylinders of the present invention are all standards or test cylinders as denoted by Hoffman et al, each cylinder having a metering piston and functioning collectively to reduce the connecting volume of piping required to couple a meter under test to the flow being delivered by a bi-directional piston displacement type volumetric flow rate standard. Additionally, working fluid is applied to both sides of each piston in the cylinders of the invention of Hoffman et al. The present invention applies working fluid to only one side of each piston in the plurality of cylinders differing substantially again from the invention of Hoffman et al. 
         [0004]    Francisco, Jr. later disclosed a piston displacement type volumetric flow rate standard in U.S. Pat. No. 4,152,922 which consists of a plurality of cylinders with pistons. One piston in a larger cylinder is identified as the measuring piston and the second piston in a smaller cylinder is identified as the retracting piston which is coupled to and utilized to return the measuring piston to the starting position after it has completed a measuring run to the opposite end of the measuring cylinder. The plurality of pistons and cylinders disclosed in U.S. Pat. No. 4,152,922 differ substantially in function and purpose from the plurality of pistons and cylinders disclosed in the present invention in that the plurality of pistons and cylinders of the present invention all are utilized for metering of fluid flow. 
         [0005]    Mathieu discloses in U.S. Pat. No. 4,507,952 a bi-directional piston displacement type volumetric flow rate standard with a jacket over the cylinder to provide a passage through which a flow of working fluid around the cylinder takes place during operation to equalize the temperature of the metering cylinder with the fluid. This process additionally provides near equal pressure on both sides of the metering cylinder wall which reduces the effect of fluid pressure on cylinder cross sectional area. Mathieu also discloses a pressurization means to the downstream side of a meter under test to avoid vaporization of the working fluid during flowmeter calibrations when the working fluid is liquid. Preferred embodiments of the present invention incorporate these teachings of Mathieu. Temperature equalization, control of liquid fluid pressure above the vapor point throughout the flow circuit and pressure equalization on both sides of the metering cylinder wall are best practices in the art. The present invention represents an improvement in the accuracy of delivered flow rate to a meter under test over what can be accomplished in the disclosed invention of Mathieu. The improvement is achieved by quantifying and accounting for the thermal effects to fluid density passing through the connecting volume between the metering piston and meter under test during standard volume delivery and by significantly reducing the connecting volume to standard volume ratio by both operational method and physical reduction of the required connecting volume piping for a bidirectional piston displacement type volumetric flow rate standard as well as by providing temperature measurement of the working fluid adjacent to the metering pistons. 
         [0006]    Cohrs et al disclose a piston displacement type volumetric fluid flow rate standard in U.S. Pat. No. 4,627,267 which incorporates a plurality of pistons and cylinders in the process. As in both U.S. Pat. No. 3,098,382 and U.S. Pat. No. 4,152,922 the plurality of pistons and cylinders comprise first a single measuring cylinder and secondly what is referred to as an actuating cylinder, retracting piston or control piston. The present invention incorporates a plurality of pistons and cylinders each of which functions as a metering device and which work collectively to reduce the connecting volume between the metering piston and the meter under test. The plurality of pistons and cylinders disclosed in the present invention function substantially different from the plurality of pistons and cylinders disclosed in U.S. Pat. No. 4,627,267. 
         [0007]    U.S. Pat. No. 4,627,267 further discloses a metering piston displacement measurement process incorporating a shaft attached to and moving with the metering piston and carrying an optical encoder head which moves relative to an inscribed linear ruler surface to produce a pulsed electrical signal with the number of pulses representing directly the linear axial displacement of the metering piston. Preferred embodiments of the present invention incorporate the use of such an optical encoder as the means to accurately measure the metering piston displacement during flowmeter calibration operations. Also disclosed in U.S. Pat. No. 4,627,267 is a position sensor. This position sensor relates to the position of a seal leak detection device and is substantially different from the position sensor disclosed in the present invention. The position sensor of the present invention is utilized to determine the position of the metering piston relative to the discharge end of the cylinder in which it is traveling for the purpose of positioning the metering piston to a proper starting position, traversing the metering piston to the discharge end of the cylinder during delivery of a standard volume and determining the fluid volume in the cylinder between the piston and cylinder discharge (dead volume) at the end of a standard volume delivery. 
         [0008]    Halpin discloses in U.S. Pat. No. 4,854,154 and again in U.S. Pat. No. 5,111,682 a piston displacement type volumetric fluid flow rate standard for flowmeter calibration. The systems disclosed by Halpin are for unidirectional piston displacement operation and differ substantially from the present invention. Halpin does disclose in U.S. Pat. No. 4,854,154 the use of a reservoir means with pressurized gas over liquid fluid therein to maintain a near constant fluid pressure. This being similar to the pressurization means disclosed by Mathieu in U.S. Pat. No. 4,507,952 to prevent liquid fluid pressure from falling below vapor pressure. Preferred embodiments of the present invention include the pressurized reservoir means to prevent vaporization of liquid working fluid at any location in the process and in particular the prevention of liquid fluid vaporization at the trailing edges of turbine flowmeter blades when such flowmeters are meters under test. Avoiding fluid vaporization when the working fluid is a liquid is required for proper calibration operation. The teachings of Mathieu and Halpin are best practices in the art. 
       SUMMARY OF THE INVENTION 
       [0009]    Fluid flowmeters require characterization of their response to flowing fluid in order to be properly utilized. Simply put, in order for a flowmeter to be used to accurately measure the flow rate of a given fluid, the flowmeter must first be subjected to a characterization process (calibration) which determines how the subject flowmeter responds to the particular fluid type to be metered over a range of flow rates. The level of uncertainty to which a flowmeter can be calibrated depends on a number of factors including the uncertainty of the fluid flow rate delivered by the standard used in the calibration process. As a rule of thumb, the calibration standard should be 4 times more accurate than the flowmeter being calibrated to provide a 95% confidence in readings taken from the flowmeter when it is placed into service. With extensive knowledge of the process applied and rigorous uncertainty analysis thereof, rules of thumb regarding the test uncertainty ratio (TUR) between the calibration standard and process and the flowmeter calibrated can be downwardly adjusted. However, in no case can the uncertainty of measurement for a given flowmeter be considered better than the standard and process against which it has been calibrated. As fluid flowmeters are improved and made to be capable of lower measurement uncertainty, the need for improved fluid flow rate calibration standards and processes grows. 
         [0010]    Prior art bidirectional piston displacement type volumetric fluid flow rate standards for calibration of fluid flowmeters do not provide optimization of calibration method to minimize the uncertainty of flow rate at meters under test for each delivered standard volume of fluid. Prior art bi-directional piston displacement type volumetric fluid flow rate standards for calibration of fluid flowmeters do not determine the total connecting volume value and calculate the connecting volume to standard volume ratio and all thermal effects associated with the connecting volume during standard volume delivery. Prior art bidirectional piston displacement type volumetric fluid flow rate standards for calibration of fluid flowmeters do not control the standard volume value on the basis of temperature measurement uncertainty, connecting volume value and fluid and connecting volume piping thermal expansion coefficients and other physical parameters contributing to uncertainty to assure that each delivered standard volume achieves a predetermined level of uncertainty for the average volumetric fluid flow rate at the meter under test. 
         [0011]    Accordingly, the present invention has been made to overcome the above mentioned shortcomings arising from conventional prior art technologies, and the objective of the present invention is to provide improved calibration results for fluid flowmeters over what can be provided by the prior art bi-directional piston displacement type volumetric fluid flow rate calibration system technologies. The present invention provides the means for reduced uncertainty of delivered fluid volumetric flow rate to a meter under test (MUT) and a method of improved fluid flowmeter calibration over what is now provided by prior art bidirectional positive displacement piston type fluid flowmeter calibration systems by reducing the connecting volume piping between the metering cylinder outlet and meters under test, provision to measure fluid temperature at the metering pistons, controlling the standard volume delivery process to minimize the dead volume in the cylinder through which the metering piston traverses for each standard volume delivery, quantifying the connecting volume thermal stability effects factor during standard volume delivery and controlling the standard volume quantity to assure the achievement of a predetermined level of uncertainty for the average volumetric fluid flow rate at the meter under test. 
         [0012]    Piston displacement type fluid flow rate standards work by movement of a fluid barrier piston in a cylinder of known cross sectional area. The displacement distance of piston movement times the cross sectional area of the cylinder determines a displaced volume. From the measured time required for the piston movement and known displaced volume, the average flow rate of fluid at the metering piston is derived. Bi-directional piston displacement type fluid flow rate standards deliver flowing fluid uni-directionally to a meter under test regardless of the direction of piston movement in the cylinder. This is accomplished by employing valves which appropriately block and direct flow depending on the direction of the metering piston movement. An arrangement of piping between the cylinder ends, valves and MUT is also involved. The interior volume of the piping and valves between the cylinder end discharging fluid and the meter under test summed with the volume in the cylinder between the metering piston and cylinder discharge at the end of standard volume delivery is referred to as the connecting volume. 
         [0013]    Uncertainty in the flow rate of fluid generated by the axial movement of the metering piston in the cylinder is derived from a combination of the uncertainties of cylinder cross sectional area, piston displacement distance measurement and the measurement of time of piston travel. The volumetric flow rate of fluid at the meter under test is related to the volumetric flow rate of fluid at the metering piston by a number of factors including any leakage of fluid around the piston or into or out of the volume between the metering piston and meter under test. These leakage parameters are considered detectable and cause to stop operation and administer repairs prior to continuing with any calibration operations using a positive displacement piston type flow rate standard. When calculating delivered fluid flow rate to a meter under test, leakage of fluid will not be considered since inspection for and correction of any leaks is considered to be the only acceptable operational practice with a fluid flow rate standard of the type being considered here. Without consideration for fluid leakage, the equation relating average volumetric fluid flow rate at a meter under test to the average volumetric fluid flow rate at the metering piston is given in Equation 1 below. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         V 
                         . 
                       
                       _ 
                     
                     MUT 
                   
                   = 
                   
                     
                       
                         
                           V 
                           . 
                         
                         _ 
                       
                       STD 
                     
                      
                     
                       { 
                       
                         
                           
                             
                               1 
                               + 
                               
                                 β 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         T 
                                         _ 
                                       
                                       MUT 
                                     
                                     - 
                                     
                                       
                                         T 
                                         _ 
                                       
                                       PIST 
                                     
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   V 
                                   CV 
                                 
                                 
                                   V 
                                   STD 
                                 
                               
                             
                           
                         
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       
                                         β 
                                          
                                         
                                           ( 
                                           
                                             
                                               〈 
                                               
                                                 T 
                                                 CVEf 
                                               
                                               〉 
                                             
                                             - 
                                             
                                               〈 
                                               
                                                 T 
                                                 CVFi 
                                               
                                               〉 
                                             
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     
                                       3 
                                        
                                       
                                         
                                           α 
                                           S 
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               〈 
                                               
                                                 T 
                                                 CVMf 
                                               
                                               〉 
                                             
                                             - 
                                             
                                               〈 
                                               
                                                 T 
                                                 CVMi 
                                               
                                               〉 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
       
         
           
             Where 
             {dot over (  V   MUT =The time average volumetric fluid flow rate at the meter under test during delivery of the standard volume 
             {dot over (  V   STD =The time average volumetric fluid flow rate at the metering piston during delivery of the standard volume 
             β=the volumetric thermal expansion coefficient of the fluid in the calibration system about the nominal operating temperature at constant pressure as determined by equation 2 below 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   β 
                   = 
                   
                     
                       
                         
                           1 
                           V 
                         
                          
                         
                           
                             ∂ 
                             V 
                           
                           
                             ∂ 
                             T 
                           
                         
                       
                        
                       
                         | 
                         P 
                       
                     
                     = 
                     
                       
                         
                           
                             - 
                             1 
                           
                           ρ 
                         
                          
                         
                           
                             ∂ 
                             ρ 
                           
                           
                             ∂ 
                             T 
                           
                         
                       
                        
                       
                         | 
                         P 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
       
         
           
             V CV =The connecting volume between the meter under test and the piston, equal to the sum of the piping volume from the cylinder discharge port to the meter under test and the volume in the cylinder between the piston at the end of standard volume delivery and the cylinder discharge port 
             V STD =The standard volume derived from piston displacement in the cylinder of known cross section 
               T   MUT =The time average temperature at the meter under test during the delivery of the standard volume 
               T   PIST =The time average temperature at the piston during the delivery of the standard volume 
             &lt;T CVFf &gt;=The spatial average fluid temperature in the connecting volume at the end of standard volume delivery 
             &lt;T CVFi &gt;=The spatial average fluid temperature in the connecting volume at the initiation of standard volume delivery 
             α S =The linear thermal expansion coefficient of the steel comprising the connecting volume structure 
             &lt;T CVSf &gt;=The spatial average temperature of the steel comprising the connecting volume structure at the completion of standard volume delivery 
             &lt;T CVSi &gt;=The spatial average temperature of the steel comprising the connecting volume structure at the initiation of standard volume delivery
 
Prior art bi-directional piston displacement type fluid flow rate standards do not employ the last term of Equation 1 in the calculation of average volumetric flow rate at the meter under test. The last term in Equation 1 is referred to as the connecting volume thermal stability effects term. If the spatial average temperature of the fluid in the connecting volume and steel comprising the connecting volume are equal at the initiation of and end of standard volume delivery representing no net gain or loss of thermal energy therein, the term has a value of zero. In that case Equation 1 is simplified to Equation 3 below.
 
           
         
       
     
         [0000]        {dot over (  V     MUT   ={dot over (  V     STD {1+β(   T     MUT   −  T     PIST )}  (3) 
         [0000]    It can be shown that the {1+β(  T   MUT −  T   PIST )} term of Equation 3 equals the ratio of the average fluid density at the metering piston to the average fluid density at the meter under test during the period of standard volume delivery. Equation 3 then becomes Equation 4 below. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         V 
                         . 
                       
                       _ 
                     
                     MUT 
                   
                   = 
                   
                     
                       
                         
                           V 
                           . 
                         
                         _ 
                       
                       STD 
                     
                      
                     
                       ( 
                       
                         
                           
                             ρ 
                             _ 
                           
                           PIST 
                         
                         / 
                         
                           
                             ρ 
                             _ 
                           
                           MUT 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Equations 3 or 4 are utilized in conventional prior art bi-directional piston displacement type fluid flow rate standards to quantify the average volumetric flow rate of fluid at the meter under test from the average volumetric flow rate at the metering piston. Thermal stability in the fluid is controlled to the extent possible in these systems in an effort to reduce the connecting volume thermal stability effects term which is not quantified by equation 3 or 4. Observation of operating bi-directional piston displacement type fluid flow rate standards leads to the conclusion that in fact there typically can be a net loss or gain of thermal energy in the fluid traversing the connecting volume and the steel comprising the connecting volume structure during standard volume deliveries. The present invention provides the ability to calculate and apply all terms of Equation 1 to the determination of average volumetric fluid flow rate at the meter under test from the average volumetric fluid flow rate at the piston during delivery of a standard volume of fluid. 
         [0027]    Temperature measurement is uncertain to some level. By reducing the ratio of connecting volume to the delivered standard fluid volume, a means of reducing the impact on uncertainty of average volumetric flow rate of fluid at the meter under test during standard volume delivery derived from temperature measurement uncertainty is achieved. The method of the present invention controls the piston to both minimize the dead volume in the cylinder after each standard volume delivery and to supply a standard volume quantity sufficient to produce a ratio of connecting volume to standard volume that assures a predetermined level of uncertainty of fluid flow rate at the meter under test given the uncertainty of temperature measurement and the thermal volumetric expansion coefficients of the working fluid and connecting volume piping material of construction. Additionally, preferred embodiments of the present invention utilize a plurality of metering pistons and cylinders to reduce the connecting volume piping between the metering cylinder outlet and the meter under test by 80% to 90% relative to the connecting volume piping required with prior art bi-directional piston displacement type fluid flow rate standards further reducing the ratio of connecting volume to standard volume and thus reducing the uncertainty of average volumetric flow rate at the meter under test. 
         [0028]    Preferred embodiments of the present invention provide direct open access to one side of each metering piston for the installation of temperature measurement probes through the pistons into the fluid. Measuring the working fluid temperature at the metering pistons provides improved determination of the standard volume fluid density as well as the spatial average fluid temperature in the connecting volume and the cylinder wall temperature derived from the fluid temperature contained therein. Prior art bi-directional piston displacement volumetric fluid flow rate standards do not provide a means to measure the fluid temperature at the metering piston. Fluid temperature measurement at the metering piston as achieved in the present invention provides an improved means of determining average volumetric fluid flow rate at the meter under test during standard volume delivery over what is now possible with prior art bi-directional piston displacement type volumetric fluid flow rate standards. In prior art bi-directional piston displacement type fluid flow rate standards, access to working fluid adjacent to the sides of the metering piston for temperature measurement is not practical. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0029]    The above and other aspects, features and advantages of the present invention will be more apparent from the following detailed description taken in conjunction with the accompanying drawing, in which 
           [0030]      FIG. 1  is a view into the open end of one of the cylinders of the preferred embodiment of the present invention from which the sectional view part of  FIG. 2  is selected; 
           [0031]      FIG. 2  is a sectional view as denoted on  FIG. 1  of the cylinders, pistons and shaft with an added plumbing schematic diagram for the preferred embodiment of the present invention; 
           [0032]      FIG. 3  is a basic process diagram of prior art bi-directional piston displacement type volumetric fluid flow rate standards with the required connecting volume piping highlighted by enclosure in dashed lines; 
           [0033]      FIG. 4  is a basic process diagram of the present invention with the required connecting volume piping highlighted by enclosure in dashed lines for comparison with the prior art required connecting volume piping; 
           [0034]      FIG. 5  is a graphical comparison of typical 95% confidence interval uncertainty of delivered volumetric flow rate at meters under test between prior art bi-directional piston displacement type volumetric fluid flow rate calibration systems and methods, that achieved by the method of the present invention applied to prior art systems and the present invention system and method; all versus delivered standard volume as percent of total metering cylinder volume given equal dimensional, timing, temperature measurement and other operational parameter uncertainties and equal fluid volumetric thermal expansion coefficient, β. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0035]    In the preferred embodiment of the present invention for liquid service, two cylinders  6  and  19 , each containing a fluid barrier piston  9  and  17 , are axially aligned. The two pistons  9  and  17  are mechanically coupled via an interconnecting shaft  13  and move in unison as directed by the force of fluid being pumped into the cylinder chamber  10  or  16  receiving said fluid via three-way valve  4  after said fluid has passed under pressure through the jacketed volumes  3  and  5  surrounding the exteriors of both cylinders  6  and  19 . The interconnecting shaft  13  passes through end plates  11  and  15  on the fluid chamber  10  or  16  end of the cylinders  6  or  19  via fluid barrier sealing mechanisms  12  and  14  around the outer surface of the shaft  13 . The pressure of the fluid acting on the piston  9  or  17  in the cylinder fluid chamber  10  or  16  receiving the pumped fluid creates a motive force on the piston  9  or  17  in the second cylinder  6  or  19  via the mechanical coupling of the interconnecting shaft  13 . The motive force on the second piston  9  or  17  causes the fluid in said cylinder fluid chamber  10  or  16  to flow through three-way valve  22  and further through three-way valve  23  where said fluid is directed either to by pass the meter under test  28  or into the flow conditioner  26  and piping directing fluid flow to the meter under test  28 . After passage through the meter under test  28 , the fluid, being pressurized by the gas pressure applied over the fluid in reservoir  29 , passes into the inlet of positive displacement pump  33  which forces said fluid into the jacketed volumes  3  and  5  surrounding the exterior of both cylinders  6  and  19  then through three-way valve  4  and into the cylinder chamber  10  or  16  receiving fluid. Fluid flow rate is varied under computer control between test conditions by varying the speed of motor  30  driving the positive displacement pump  33 . 
         [0036]    When the pistons  9  or  17  reach the end of allowed travel in the cylinders  6  or  19 , contact is made with limit switch  20  at the end of cylinder  19  or limit switch  21  at the end of cylinder  6  either of which cause the control system to actuate and switch the open paths in both three-way valves  4  and  22  to reverse the direction of piston travel by swapping which cylinder fluid chamber  10  or  16  is receiving fluid from the positive displacement pump  33  and which cylinder fluid chamber  10  or  16  is discharging fluid to the meter under test  28  during meter calibration. When required to accommodate the delivery of a standard volume of fluid which is much smaller than the total volume of one cylinder  6  or  19  to a meter under test  28  and to additionally cause the delivery of said volume to end with the metering piston  9  or  17  at the discharge end of the cylinder  6  or  19  in which it travels, three-way valve  23  can be actuated to provide a low resistance path for fluid flow around the meter under test  28  and the pumping flow rate increased to cause the pistons  9  and  17  to move quickly to optimum starting points for the standard volume delivery at which time the pumping rate is reduced to the desired test flow rate and three-way valve  23  reversed to direct a standard fluid flow rate through the meter under test  28 . Metering piston  9  or  17  position in cylinders  6  or  19  is determined by position sensor  24 . Direction of piston travel is determined by derivation of the position sensor  24  output during piston  9  and  17  travel. Alternately, monitoring the actions of end of travel limit switches  20  and  21  and counting pulses from optical encoders  1  provides a measure of the positions of pistons  9  and  17 . However, end of travel limit switches  20  and  21  could be manually actuated at will to reverse the direction of piston travel and lead to confused status of actual piston position. Use of position sensor  24  to determine meter piston  9  or  17  position and direction of travel is the preferred method of the present invention. 
         [0037]    The standard volume of fluid is determined by measuring the displacement of the metering piston  9  or  17  via optical encoders  1  and sensing head  2  which moves with the metering pistons  9  and  17  via connecting rod  7 . Knowing from dimensional calibration the cross sectional area of the cylinders  6  and  19  and adjusting according to temperature measurements from probes  8  or  18 , the measured displacement of the metering piston  9  or  17  provides calculation of the standard volume. The measured time to displace the standard volume provides the additional parameter required for calculation of the average fluid flow rate generated at the piston  9  or  17  of the discharging cylinder  6  or  19  during the standard volume delivery. Determining the average fluid flow rate at the meter under test  28  during the standard volume delivery requires the employment of Equation 1 which takes into account the thermal effects on fluid density and connecting volume piping during the time that the standard volume is being delivered. Fluid temperature measurement probes  8 ,  18 ,  27  and  32  provide the fluid temperature profile during standard volume delivery with which the data acquisition and control computer can make the required calculations to determine average fluid flow rate at the meter under test  28  relative to the average standard fluid flow rate at the metering piston  9  or  17 . Fluid pressure measurements are made on both the upstream and downstream sides of the meter under test  28  using pressure transducers  25  and  31 . Reservoir  29  is charged to supply a fluid pressure above the vaporization point of liquid working fluids at all points in the process and in particular at the outlet of the meter under test  28  during calibration operations. 
         [0038]      FIG. 3  depicts a basic process diagram of prior art bidirectional piston displacement fluid flow rate delivery and metering systems. The connecting volume piping of the prior art with the piston moving left to right is identified as  34  and outlined by dashed lines. Had the delivery of a standard volume ended with the piston in the position shown, the remaining volume of fluid in the cylinder to the right of the piston summed with the connecting volume piping volume would comprise the total connecting volume for the given standard volume delivered. 
         [0039]      FIG. 4  depicts the basic process diagram of the preferred embodiment of the present invention. The connecting volume piping of the present invention with the pistons moving left to right is identified as  35  and outlined by dashed lines. The method of the present invention requires the delivery of a standard volume to end with the metering piston at the discharge end of the cylinder. In that case, only the volume of the connecting volume piping  35  comprises the connecting volume. The much reduced required connecting volume piping of the present invention  35  and the operational method of the present invention contribute to enhanced uncertainty of delivered flow rate at meters under test relative to that achieved by the prior art.  FIG. 5  displays as plot  36  the typical uncertainty of prior art bi-directional piston displacement fluid flow rate delivery and metering systems. These prior art systems do not control the starting and ending locations of the metering piston relative to the discharge end of the metering cylinder. Given the additional uncertainty of a number of dimensional, timing and temperature measurement parameters along with the thermal expansion coefficient of the working fluid, plot  36  does represent typical uncertainty of delivered fluid flow rate at meters under test for the prior art. Plot  37  displays the typical improvement in uncertainty of delivered fluid flow rate at meters under test to be gained by implementing the method of the current invention on prior art bi-directional piston displacement type fluid flow rate delivery and metering systems. Finally, plot  38  displays the additionally improved uncertainty of delivered fluid flow rate at meters under test achieved by the present invention with dimensional, timing and temperature measurement uncertainties equal to the prior art denoted in plots  36  and  37 . These graphed uncertainties are all relative to the percent of metering cylinder volume delivered as fluid standard volume. As is apparent in  FIG. 5 , the present invention provides enhanced uncertainty of fluid flow rate at meters under test with the additional advantage of requiring a smaller delivered standard volume and thus less time for meter calibration while achieving a best level of said uncertainty. 
         [0040]    The above description of the preferred embodiment of the present invention is not the only embodiment which achieves the advantages in the claims. One additional embodiment suited to both gaseous and liquid fluids can be configured by replacing the fluid pump  33  with a linear drive mechanism to drive the pistons back and forth in the cylinders with the pistons being mechanically coupled as denoted in this description of the preferred embodiment. The linearly driven pistons would then serve to both move the fluid and with the optical encoders and known cylinder cross sectional area, meter the delivered standard volume. Yet other embodiments with a plurality of pistons and cylinders configured to achieve a reduced connecting volume piping requirement are possible.