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Measurement of the pressure losses in a positive displacement flowmeter


Experimental investigation of an oscillating circular piston positive displacement flowmeter: I - piston movement and pressure losses 

3rd Submission

Charlotte E Morton, Ian M Hutchings  & Roger C Baker

Institute for Manufacturing, Department of Engineering, University of Cambridge, 17 Charles Babbage Road, Cambridge CB3 0FS

Corresponding author: Roger C Baker e-mail: rcb29@cam.ac.uk

Abstract

Tests of an oscillating circular piston positive displacement flowmeter are described which focused on the effect on pressure drop across the meter of variation in key parameters. These included flow rate, liquid density and viscosity, mass of piston and length of connecting pipes. In addition to the average pressure loss, the pressure loss variation during the oscillation cycle was measured and found to vary with an amplitude dependent on the various parameters. A companion paper reviews data on leakage and wear.

Keywords: positive displacement flowmeter, oscillating circular piston flowmeter, pressure losses, piston movement.

 

1. Introduction

This paper describes the pressure losses which were measured in an oscillating circular piston flowmeter. This is a type of positive displacement (PD) flowmeter. PD flowmeters measure the volumetric flow rate of a wide range of clean or well filtered liquids including water, hydrocarbons, other chemicals and liquid foods. These meters all work on the same basic principle: they measure the flow rate of a continuous stream of liquid by momentarily trapping a small volume of the liquid in a chamber of known volume and subsequently releasing it on the outlet side of the meter. The flow rate is obtained by counting the number of entrapments in a known period of time. The oscillating circular piston flowmeter, the subject of this paper, differs from virtually all other designs in having a bearingless piston held in position by contact with the measuring chamber. 

PD meters absorb a small amount of energy from the flowing liquid to overcome the friction in driving the meter, resulting in a pressure loss across the meter. This differential pressure provides the driving force for the internal mechanism of the meter. Baker [1] described the factors which could affect the volumetric flow rate for a fixed frequency of oscillation: temperature, pressure, viscosity, wear, solid deposits and gas in the liquid. Wear on meter surfaces can cause the displacement volume to increase, and decrease the long term repeatability of the meter. In contrast deposits on the meter surfaces will decrease the displacement volume. Factors which contribute to the pressure loss across the meter [2] are fluid friction, turbulence of the flow and changes in direction and velocity of the flow. The "fill-up characteristic" [3] for the measuring chamber is a function of the angle of rotation, and is generally not linear; the angular velocity will, therefore, vary. Baker & Morris [4] gave a simple theoretical explanation of some features of the operation of larger types of PD meter.

The oscillating circular piston flowmeter is capable of very low flow rates, and this has proved to be a valuable feature for precise measurement of additives in oil production. The meter is also widely used for domestic water measurement and a suitable design has also been used for liquid foods. 

1.1 Oscillating circular piston flowmeter

The oscillating circular piston flowmeter consists of a circular piston which is confined to move in a cylindrical measuring chamber. A diagram of the measuring chamber and piston are shown in figure 1. The measuring chamber consists of a cylindrical hub, pin and radial partition (also known as the web). The centre of the piston, the peg, is constrained to move within the annulus between the hub and pin. The orientation of the piston and chamber in these tests was with their axes, hub and pin, vertical. The piston profile allows the piston to slide along the partition which also prevents the piston from rotating. Liquid enters the measuring chamber through the inlet port and this causes the piston to move. The oscillation of the piston carries liquid through the meter in essentially self-contained compartments to the outlet port. Figure 2 illustrates the flowmeter mechanism and the positions of the piston during an oscillation and also defines the angle θ, used to describe the angular position of the piston’s peg in the chamber as it rotates in the hub.  

Since the oscillating circular piston flowmeter was patented by Nash [5] in 1884 it has become one of the most widely used positive displacement flowmeters. Since then, over a hundred patents have been filed relating to details of its design.

Cloran [6] reported that pressure losses in the oscillating circular piston flowmeter were likely to arise from the restrictions at the inlet and outlet. Baker [1] confirmed this but also 

partition

lubrication holes

profile

    slots

skirt

magnet

outlet

measuring chamber

inlet

hc

piston

pin height hpin

radius rpin

Dc

(b)

hh

hub outer radius

roh

peg

ror (outer height hor)

rir (inner height hir )

           (a)                (c)

Figure 1 The oscillating circular piston flowmeter (in these tests the pin was vertical): (a) the measuring chamber (housing): (b) the moving piston from above, (c) the piston from below.

noted that at low flow rates the main cause of pressure loss was the work needed to overcome the internal friction. Plank [7] reported that under certain conditions fluid slips through the clearances (leakage) but the meter does not register. Barnes [8] noted the sensitivity of error to viscosity, and since fluid temperature has an effect on the viscosity this source of error will vary with temperature [9]. Parry [10] presented a model for the meter using computational fluid dynamics (CFD) software. The dynamic interaction between the moving parts and the flow in the flowmeter was outlined. The movement of the piston was compared with the movement of a slider-crank mechanism. 

1.2 Research reported in this paper

The oscillating circular piston flowmeter which was studied in this work was a model MF30 1.5, supplied by Litre Meter, North Marston, UK. The body and cap were made from 316 stainless steel (SS) and the piston was made from either carbon or 316 SS depending on the application and flow range required. Materials and dimensions are given in Tables 1 & 2. 
 

Table 1 Dimensions of oscillating circular piston flowmeter (Litre Meter MF30 1.5)


Flowmeter component Material Diameter

(radius)

mm

Height

mm

Mean vertical clearances
Chamber 316 SS

(stainless steel)

Dc=34.00

(rc)

hc=7.06 chamber – piston = 60�m
Hub 316 SS external

Doh=15.00

(roh)

internal

Dih=11.00

hh=5.07  
Pin 316 SS Dpin=4.00 hpin=5.07  
Cap 316 SS

PMMA

     
Piston see Table 2 external Dor=26.50

(rop)

internal

Dir=22.60

(rip)

external

hor=7.00

internal

hir=5.10

internal height – hub = 30�m
Peg as for piston      
Inlet and outlet ducts   6.0    
 
 
 
 

Table 2 Material, density and mass of oscillating pistons used in this research


Material Density

ρp

(kg/m3)

Mass

m

(g)

carbon 2000 6
316 stainless steel 8000 24
PMMA 1200 3.6

The flowmeter could measure flow rates up to 90 litres/hour. An additional piston was made for this research from polymethyl methacrylate (PMMA, Perspex). Piston materials, density and mass are given in Table 2. Figure 1 indicates the position of lubrication holes which were found to affect the performance. In addition some pistons have slots in the skirt near to the partition to release trapped liquid. These also affect the performance of the meter.  

In earlier work [11] the measurement of vertical movement of the piston by a fluorescence technique was described. This paper considers the effect of a number of different parameters: flow rate, piston mass and material, liquid viscosity and density and the length of pipework before and after the flowmeter. To examine the effect of friction and the possible benefits of a low friction coating, Molykote (molybdenum disulfide MoS2) was applied to the 316SS piston for some tests.

The paper examines further the motion of the piston and then discusses the pressure losses and the pressure pulsations that exist in this flowmeter due to the varying flow rate as the piston oscillates. In a further paper [12] the authors report measurements of the leakage flows and wear.

The uncertainties in the results to a 95% confidence level are given as error bars on some of the graphs.

 

    (a) θ = 0

    (b) θ = π/2

 
 
 
 
 
 
 
 

    (c) θ = 3π/2

    (d) θ = π

 

Figure 2 Illustration of the flowmeter mechanism as the piston oscillates within the chamber: (a) θ = 0 rad (TDC), (b) θ = π/2 rad, (c) θ = π rad (BDC), (d) θ = 3π/2 rad.

2. Experimental methods

2.1 Flowmeter installation

A flow circuit supplied the test liquid from a header tank at an adjustable height, from where it passed through the meter and into a sump tank (Figure 3). The height difference between the surface levels in the two tanks, together with the valve at the outlet from the meter, were used to control the flow rate, which was measured from oscillation of the piston. The liquid temperature was measured in the header tank. The flow circuit was situated in a laboratory with an approximately constant temperature during each set of tests and the temperature changes in the test fluid during each experiment were negligible 
Table 3  Liquid combinations of white spirit and fully formulated multigrade motor oil (grade 15W40) used in varying proportions to assess the effect of variation of dynamic viscosity, , with approximately constant density, ρ. (Note that 1cP=1mPas)


Dynamic viscosity

μ (mPas)

(�0.1 uncertainty as claimed by instrument manufacturer)

Density

ρ (kg/m3)

(�1)

1.0 780
5.0 820
10.1 824
19.9 834
 

Table 4 Liquids used to assess the effect of variation of density, ρ, at approximately constant dynamic viscosity, �


Liquid Density

ρ (kg/m3)

(�1)

Dynamic viscosity

μ (mPas)

(�0.1 uncertainty as claimed by instrument manufacturer)

white spirit +motor oil 780 1.0
water 1000 1.0
salt water 1200 1.0
 

 

pressure sensor

adjustable height

flowmeter

header tank Tank

sump tank

plastic tubing

valve

 
 
 
 
 
 

Figure 3 Schematic diagram of the flow rig.

The liquids used to assess the effect of viscosity variation are given in Table 3 and those to assess the effect of density variation in Table 4. The viscosities were measured using a portable viscometer, Viscolite 700, with an uncertainty of � 0.1 mPas and the densities using a Paar DMA35 digital density meter which had an uncertainty of � 1 kg/m3

The height of the header tank set the total head, the maximum value being 1.5 m. Plastic tubing was used with internal diameter of 15 mm, to match the diameter of the connections to the flowmeter.  

2.2 Measurement of piston position

In order to determine the angular position of the oscillating piston a non-intrusive optical method was used to measure the motion of the piston within the measuring chamber as a function of time.  

The original 316 SS cap was replaced with a transparent one made from PMMA. The behaviour of the piston was found to be unaffected by using this transparent cap. This was confirmed by measuring the pressure losses over the meter with both the PMMA and 316 SS caps; they were found to be unchanged within experimental error.  A Fastcam 1024 pci high speed camera with a frame rate of 1,000 Hz was used, and the resulting images were processed using Image J [13], a public domain Java image analysis programme, to derive information about the position of the piston over time.

The camera images were used to measure the angular motion of the piston

2.3 Pressure sensor

A Honeywell 26PC differential pressure sensor was installed to measure the pressure between the inlet and outlet ducts of the flowmeter. The pressure tappings were directly before and after the meter. The pressure tappings were small holes (2.5 mm diameter) in the inlet and outlet pipework which were perpendicular to the direction of flow. It should be noted that the dynamic pressure, ρV2/2 (where ρ is density and V is velocity), was of order 20 Pa and the static pressure across the meter was up to about 4kPa. The tappings were smooth with no burrs and provided negligible disturbance to the flow. The tappings and the pressure sensor ports were connected by plastic tubing, with both the inlet and outlet taps having the same length of piping. The tubes connecting the pressure sensor were bled to ensure there was no air in the tubes. A schematic diagram of the pressure tapping is given in figure 4. 

The sensor was temperature compensated between 0 �C and 50 �C and could measure pressure differences between 0 and 7 kPa. The dynamic response of the sensor was 1,000 Hz for pressure variations between 10-90% of its range. Generally, when measuring dynamic pressures, the frequency response of the pressure sensor should be five times the maximum frequency of interest. The maximum frequency of oscillation was 5 Hz, and assuming there were five small fluctuations in pressure within each oscillation, then the dominant frequency of interest for the system was 25 Hz, requiring a frequency response of 125 Hz which was well within the capabilities of the sensor, and sufficient to allow for higher frequencies of small amplitude.  
 

The pressure losses were obtained from continuous recording of the output voltage from the pressure sensor using an oscilloscope. The output voltage was sampled at 1,000 Hz. At high flow rates this corresponded to 200 readings per oscillation. The raw voltages were converted to values of pressure loss across the flowmeter using the calibration defined below. Thus the pressure loss could be expressed as either time-averaged or time-varying over an oscillation. The time-varying pressure loss gave detailed information about the pressure losses over the rotation/oscillation cycle. A magnet was embedded in the centre of the piston and a digital Hall sensor positioned above the centre of the piston at top dead centre (TDC), where θ = 0 rad, sensed complete rotations/oscillations.

 

to pressure sensor

flow direction to flowmeter

plastic tubing

15 mm

pressure tapping

2.5 mm

 
 
 
 
 
 

Figure 4 Schematic diagram of pressure tapping.

2.4 Calibration of the pressure sensor

The short term drift was checked by calibrating the sensor every hour during an eight hour period. The long term drift was checked by calibrating the sensor twice per week for a ten week period. The results from these tests confirmed the stability of the sensor. 

Static calibration was carried out by using a manometer with a water column to give the pressure at each port of the sensor. The output voltage was recorded against the height difference between the columns. The pressure difference Δp was obtained, using Equation 1, from the height difference, Δh, between the columns.

                                                      (1)

The calibration covered ten points across the full range of pressures to be measured and was repeated three times. The calibration curve showed a linear response and is given in figure 5. The uncertainty was estimated as 1.5% of reading, or better, at 3000 Pa and above, and rose to about 8% at 500 Pa [14, 15]. The uncertainties are given based on reading.

 

 
 
 
 
 
 

Figure 5 Calibration curve for the pressure sensor. 

3. Measurement of the piston motion

3.1 Measurement of angular motion of the piston

The variation in normalised angular velocity in figure 6 is for the carbon piston. The normalised value is the ratio of the instantaneous velocity to the average velocity for a complete oscillation. The angular velocity was calculated from the gradient of the angular position. It had a maximum value at top dead centre (TDC θ=0 rad) and a minimum at bottom dead centre (BDC θ=π rad). The uncertainty was of order 2% at TDC and less elsewhere for the highest flow rate. The angular velocity was greatest just after TDC. The angular velocity was measured for a range of different flow rates to cover the full flow range for the meter. As the flow rate was reduced (Figure 6) the range of angular velocities decreased. Changes in the pattern of oscillation were most noticeable at 8 litres/hour where additional variations in the angular velocity occurred. As the flow was reduced the uncertainty of the results increased to order 10%. 

 

0                π/2               π                 3π/2              2π             5π/2              

80 l/h

32l/h

16 l/h

8 l/h

 
 
 
 
 

Figure 6 Variation in normalised angular velocity of the centre of the carbon piston at four water flow rates.

The behaviour was similar for changes in the mass, when using stainless steel, carbon and PMMA pistons. At lower flow rates the mass of the piston had a greater effect and for the heavier pistons the range in the angular velocity decreased. The effect of friction on the angular velocity was investigated using pistons of 316 SS both with and without the Molykote low friction coating.  The motion of the 316 SS piston without the Molykote coating was very irregular at 16 litres/hour and had some similarity to that of the carbon piston at 8 litres/hour shown in Figure 6. The most notable change was a much smoother motion at low flows with the coated piston. These results suggested that friction and drag were occurring due to contact between the piston and measuring chamber across the full flow range of the meter.

The angular velocity variation was measured with and without lubrication holes (shown in Fig 1b) in the top of the piston, and the changes were found to be small for the carbon piston. In contrast, the inclusion of slots in the piston skirt close to the partition appeared to relieve trapped fluid and to allow a higher rotational speed at TDC  at higher flow rates. A further effect which was investigated was the influence of the combined length of up- and downstream piping with the carbon piston at 80 litres/hour. The combined length of the piping affected the variation in angular velocity during the oscillation.  As the pipe length was increased from 0.2 m to 20 m there was an increase in maximum angular velocity at 80 litres/hour of about 20 %. The results suggest that due to this variation in the angular velocity, the instantaneous flow rate also varied, hence although the flow was between two constant head tanks, this suggested that the pressure across the meter varied [15]. 

3.2 Vertical motion of the piston

The vertical motion of the piston was determined by measuring the liquid film thickness above the piston of water doped with fluorescence as described previously [11, cf 15]. The film thickness, combined with knowledge of the meter chamber and piston heights, enabled the clearance between the bottom of the piston and the bottom of the chamber to be deduced. The measurements also allowed the tilt of the piston to be obtained. Figure 7(a) shows the variation with θ of the minimum, maximum and mean clearance for the carbon piston, while Figure 7(b) shows the tilt of the piston as it rotated.

The largest value for the minimum clearance was 2.8 μm, supporting the observation that some contact occurred between the bottom of the piston and the measuring chamber throughout the whole oscillation. The angular position at which the maximum, mean and minimum clearances were greatest was θ = π (BDC).

The angular tilt is defined as

                                        (2)

where cbmax and cbmin are the maximum and minimum clearances under the piston skirt respectively and ror is the outer radius of the piston.

Figure 8 illustrates the variations in mean vertical clearance and angular tilt with flow rate for a carbon piston. A similar trend was found with both the 316 SS and PMMA pistons (as shown in figure 9). It is apparent from Figure 8(a) that as the flow rate was reduced, there was less movement of the piston in the vertical direction. At 16 litres/hour the piston did not lift off. At higher flow rates (80 litres/hour) the piston tilted for all angular positions. As the flow rate was reduced, the amount of tilting was less until the piston did not tilt during the whole oscillation, but sat parallel to the measuring chamber.

Figure 9 illustrates the effect of piston mass on piston lift (see Table 2). Results in Figure 9 are for 80 litres/hour. As the mass of the piston increased, there was less movement in the vertical direction and at 16 litres/hour there was essentially no lift-off for the carbon piston, hence no tilting occurred. The 316 SS piston moved vertically by only a small amount for the whole flow range of the meter, and did not lift off below 32 litres/hour.

Blocking the lubrication holes in a carbon piston resulted in a film thickness approximately twice the value seen with open lubrication holes at 80 litres/hour. This was typical of the changes found. The presence of lubrication holes reduced the amount of movement in the vertical direction. As the flow rate was reduced, the lubrication holes continued to reduce the amount of movement in the vertical direction and at 16 litres/hour the piston did not lift off with lubrication holes, although some lift-off occurred without lubrication holes.  The angular position at which maximum lift-off and tilting took place was at about θ = π rad for higher flow rates, but at about θ = 3π/4 rad, for the carbon piston with no lubrication holes at lower flow rates.

 

The effects of other parametric variations on vertical motion: surface coating of the 316 SS piston, slots in the piston skirt, and the length of the pipework, were found to be less than the uncertainty of the tests.

3.3 Motion of the piston around the partition (web)

The position of the piston relative to the partition was found to be important and images were taken to obtain the precise position of contact of the piston and the partition and the consequent film thickness (Figure 10). The reason for this contact was due to a turning force on the piston, and the piston was prevented from turning by the presence of the partition. The direction of this turning force changed every π radians. This contact contributed to the frictional drag on the movement of the piston.

 

0                        π/2                  π                   3π/2                     2π                  5π/2   

 
 
 
 

                                          (a)

0                       π/2                      π                   3π/2                 2π                  5π/2   

 
 
 
 
 
 

                                          (b)

Figure 7 Motion of the carbon piston in the vertical direction with a water flow rate of 80 litres/hour: (a) Variation in minimum, mean and maximum clearance along the bottom of the piston in the vertical direction (uncertainty �1 �m), (b) Variation in angular tilt during the rotation/oscillation (uncertainty �2.5 x 10-5  rad)

 

0                        π/2                     π                   3π/2                   2π                    5π/2   

(a)

0                        π/2                     π                   3π/2                 2π                    5π/2   

80 l/h

32 l/h

16 l/h

80 l/h

32 l/h

16 l/h

 
 
 
 
 
 
 

(b)

Figure 8 Variation in motion in the vertical direction with the carbon piston for three water flow rates : (a) mean clearance, (b) angle of tilt 
 

 

(b)

(a)

0                        π/2                  π                   3π/2                   2π                  5π/2   

0                        π/2                    π                   3π/2                      2π                  5π/2   

316 SS

316 SS

 
 
 

PMMA

 
 
 
 
 

PMMA

 

Figure 9 Variation in motion in the vertical direction with mass of the piston in a water flow of 80 litres/hour: (a) minimum clearance, (b) angle of tilt. 
 
 

 

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Figure 10 Motion of the piston around the partition (piston moving anticlockwise).

 

4.  Measurement of pressure losses

The following results represent the average from ten tests with five different carbon pistons and five different 316 SS pistons in the same measuring chamber. The results for each piston material were in close agreement. The average pressure losses were plotted against the flow rate, and the variation during an oscillation was plotted against the angular position of the piston. 

4.1 Effect of flow rate

Oscillation of the piston allows flow rate to be deduced. We note that the ideal flow rate was derived as follows. The theoretical discharge volume was the sum of the volumes within the piston and between the piston and the chamber:

                                          (3)

where hir and hor were the internal and external heights of the piston, rc was the radius of the measuring chamber, roh was the outer radius of the hub and rir and ror were the inner and outer radii of the piston. The volume of the partition did not affect the total volume because it had no effect on the volume of fluid in the inner or outer chamber. Combined with oscillation frequency, this gave the ideal flow rate. This differed from the actual flow rate by the leakage quantity [12]. 

Figure 11 shows the average pressure loss against flow rate for water, for the carbon piston. The pressure loss varied during each oscillation and the variation is shown for the carbon piston at a flow rate of 80 litres/hour in figure 12. At 80 litres/hour, the pressure loss varied by more than 2,000 Pa over the oscillation, with the maximum pressure loss (4500 Pa) occurring at θ =0 rad. 

 

 
 
 
 

(l/h)

 

Figure 11 Average pressure losses for the carbon piston against the flow rate of water.

0                     π/2                    π                   3π/2                   2π                    5π/2

 
 
 
 
 
 
 

Figure 12 Pressure losses during one oscillation for the carbon piston in a water flow of 80 litres/hour.

 

      4.2 Effect of piston mass and surface coating

As the mass of the piston increased the pressure loss increased, figure 13. The pressure losses in the meter consisted predominantly of those due to flow losses and those due to frictional losses. This suggested that the frictional losses increased with a heavier piston, since the flow losses would be approximately constant for the two different pistons, so that either fluid friction (resulting from the shearing of the fluid between the surfaces of the piston and the measuring chamber) or contact friction between the piston and the chamber (if asperity contact took place) or both were higher. Both fluid friction and contact friction are dependent on the size of the clearances between the piston and measuring chamber, and these will depend on factors including the differential pressure across the piston and the piston mass..  

To investigate the effect of this, a thin low friction coating of Molykote was applied to a 316 SS piston. The pressure losses for pistons of carbon, 316 SS and 316 SS with Molykote are given in figure 13, which demonstrates that they were a function of both piston mass and surface coating. The smaller pressure losses for the coated 316 SS piston suggested that some contact friction occurred at all flow rates. At lower flow rates the coating had the greatest effect and reduced the minimum flow rate for which the meter could still operate from 20 litres/hour to 7 litres/hour.  

Figure 14(a) compares the variations, during one oscillation, in pressure loss at 80 litres/hour for the carbon piston and the 316SS piston coated with Molykote. As the mass increased the variation in pressure followed the same general pattern, but the variation increased with an increase in piston mass.

 

 
 
 
 
 

(l/h)

(with

Molykote)

 

Figure 13 The effect of mass and surface finish on the pressure losses showing the carbon piston and 316 SS piston with and without Molykote in a water flow 

It is instructive to note, from Figure 14(b), the effect of Molykote in reducing the pressure loss fluctuations as the piston oscillated although the general shape of the curve remained the same. The comparison indicates that the coating resulted in a smoother motion and a lower amplitude variation (Figure 14b). 

 

(a)

0                     π/2                    π                      3π/2                 2π                  5π/2

0                      π/2                     π                    3π/2                 2π                   5π/2

(with Molykote)

(with Molykote)

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

(b)

Figure 14 Variations during one oscillation in the pressure loss in a water flow of 80 litres/hour: (a) Carbon and 316 SS with a coating of Molykote, (b) 316 SS (with Molykote) and 316 SS.

 

4.3 Effect of lubrication holes in top of piston and slots in piston skirt

The average pressure loss for both carbon and coated 316 SS pistons was unaffected by the presence of lubrication holes, but the variation during one oscillation indicated that lubrication holes reduced the variation. However, the uncoated 316 SS piston had greater pressure losses without lubrication holes.  

The piston was tested with and without slots in the skirt near the partition. These appeared to release trapped liquid near TDC (θ = 0 rad) and BDC (θ = π rad). This trapped liquid increased the pressure amplitude within an oscillation and retarded the rotation. It was found that slots decreased the average pressure loss at maximum flow by about 7%. The reduction in pressure loss was most noticeable just before and after TDC (θ = 0 rad) where more fluid was trapped.

4.4 Effect of liquid viscosity and density

To investigate the effect of the viscosity of the liquid on pressure losses, a mixture of white spirit and motor oil was used in varying proportions, giving liquids with viscosities of 1.0 mPas, 5.0 mPas, 10.0 mPas and 20 mPas (Table 3). The density remained approximately constant. The average pressure losses for the carbon piston are shown in figure 15. The fluid frictional losses are proportional to the viscosity: hence the pressure losses increased with an increase in viscosity as shown in figure 15.  

To investigate the effect of liquid density, three liquids (Table 4) were used with the same viscosity but with densities of 780 kg/m3, 1000 kg/m3 and 1200 kg/m3. The average pressure losses with the carbon piston for the three liquids are shown in figure 16.The pressure losses increased with increase in liquid density.  

The variations in pressure during an oscillation were measured for each of these viscosities and densities and the results were found to be similar to the data in figure 12, apart from amplitude, with a maximum pressure loss occurring at TDC (θ = 0 rad).   
 

  
 
 
 
 

(l/h)

20mPas

10mPas

1mPas

5mPas

Figure 15 Pressure losses with the carbon piston with liquids of different viscosities and densities in the range 790 to 820 kg/m3.  

 
 
 
 

(l/h)

 

Figure 16 Pressure losses with the carbon piston with liquids of different densities and with viscosity 1 mPas.

 

 4.5 Effect of combined up- and downstream pipe length

The average pressure loss across the meter was unchanged by variation in the combined length of the up- and downstream pipework. However, the pressure losses during a single oscillation did change. Figure 17 gives the results for combined pipe lengths of 0.2 m, 2m and 20 m at 80 litres/hour, which demonstrate the increase in variation in the pressure loss with increased combined length of pipework. With the longer pipework the velocity of the liquid in the pipe responded less to the oscillation and the reduced variation in flow rate caused an increased pressure variation across the meter. For a combined length of pipework of 0.2 m, the pressure loss varied by 800 Pa during the oscillation, whereas with a combined length of pipework of 20 m the variation was almost 3,000 Pa.

It is useful to note that, although the flowmeter was run between two constant head tanks for all the tests reported in this paper, the pressure difference across the flowmeter varied.

It was considered that any effect of inlet pipe length (a minimum of about 6 diameters of straight pipe) on the inlet flow profile would have a negligible effect on flowmeter performance since, in addition, the inlet flow passed through a bend and a contraction in the meter’s inlet pipe, before discharging into the measuring chamber perpendicular to the primary direction of piston movement. This consideration appeared to be confirmed by the constancy of the average pressure losses for various lengths of inlet pipe. 

0                    π/2                     π                  3π/2                  2π                5π/2

 
 
 
 
 
 
 

Figure 17 Pressure loss variation during an oscillation with the carbon piston in water flow of 80 litres/hour with three different lengths of pipework

 

4.6 Pressure losses over inlet and outlet ducts

In order to compare the relative contributions for the pressure loss from flow and friction, the pressure losses were also measured across the flowmeter with no piston in the chamber. A second flowmeter was connected in series with the original flowmeter to measure the flow rate. The pressure losses are shown in figure 18 for the normal flowmeter (with a piston) and for the chamber without a piston. These curves illustrate that the proportion of losses from the inlet and outlet ports alone accounted for almost 60% of the total losses. However, these losses do not take into account the reduced cross-sectional area of the measuring chamber and the dividing and combining flow which takes place when the bottom of the piston covers a part of the inlet or outlet ports. These effects are likely to increase the flow losses.  
 
 

 
 
 
 
 

(l/h)

 

Figure 18 Pressure losses with piston (total losses) and without piston (inlet/outlet losses) in a water flow.

 

5.  Discussion

The motion of the piston around the chamber was measured, figure 6, and the movement around the partition was tracked, figure 10. These motions resulted from the varying forces required to cause the oscillation. These forces resulted from the pressure acting across the oscillating piston, and the friction and liquid film behaviour retarding the motion. It was observed that while lubrication holes in the top of the carbon piston had little effect on the motion, the slots in the piston skirt near to the profile had a significant effect on reducing the velocity variation by, apparently, releasing trapped liquid. In a subsequent paper the authors intend to describe a model which elucidates these forces in more detail. However, it is instructive to note how the forces caused the piston to impinge on the partition on each side alternately. This resulted in wear on the flat regions of the profile at the outer radius of the piston, and wear was also observed along the length of the partition. 

The pressure losses followed a similar pattern to the cyclical motion, since they determined the motion. The results of measurements of the pressure drop for the oscillating circular piston flowmeter under various conditions have been described. The two main sources of pressure losses across the flowmeter have been identified as frictional losses and flow losses. Frictional losses comprised the losses due to both fluid friction and contact friction. Flow losses were related to the turbulence of the flow, flow in the inlet and outlet ports and the losses as the liquid passed through the flowmeter including changes of direction.  

The pressure losses varied during each oscillation, with the maximum pressure loss occurring at TDC (θ = 0 rad), where the angular velocity was greatest. The variation in pressure loss observed during one oscillation was dependent on a number of factors including flow rate, mass of piston, viscosity and density of liquid, surface coating, inlet and outlet ducts and the presence or otherwise of lubrication holes, slots in the skirt and combined length of up- and downstream pipework. 

The pressure losses increased with flow rate. They are related to both Reynolds number and density of the liquid being metered. The pressure loss is approximately proportional to the density of the liquid being metered as shown in figure 16.  One important finding, already referred to, was the effect of up- and downstream pipe length on the pressure variation during an oscillation of the piston. For increasing length the amplitude of the fluctuation increases since the liquid in the line responds less to the fluctuating flow while for short lengths the liquid is able to respond more readily, figure 17. 

Increased mass of the piston resulted in higher pressure losses, but it was apparent that when the friction between piston and chamber was approximately the same for the carbon and 316 SS (coated) pistons the pressure increase was significantly reduced. A friction-reducing coating capable of lasting the life of the meter is clearly of value. Without coating, as the mass of the piston increased, the pressure loss increased. This suggests that the frictional losses increased with a heavier piston, and since the flow losses will be constant for the two different pistons, either fluid friction or contact friction or both were higher. 

The results have clearly indicated that increase in liquid viscosity and liquid density resulted in an increase in pressure difference.  

It can be seen that the variation in pressure loss observed during each oscillation was significant and could result in an increase in the pressure loss of 70% at some angular positions. It has also been shown that a major component of the pressure losses was due to flow losses resulting from varying cross-section and flow direction, particularly at the inlet and outlet. One area of design which could greatly reduce the flow losses is, therefore, the inlet and outlet ducts. If these flow ducts could be made with fewer bends and fewer changes in diameter, it is likely that a useful reduction in pressure loss would be achieved. 

This research [15] has had two objectives: to provide high quality data on the performance of this design of flowmeter, and to develop a numerical design method, to provide the tools for optimising the design. In reporting the research, it appeared appropriate to start by setting out the data, and the intention is to report the analytical/numerical solution in further papers which are in preparation for submission shortly. While dimensional analysis would give some similarity considerations, the need for a precise model has resulted in a full solution of the dynamic equations, which takes account of the detailed dimensions of the internals of the meter, and which can provide precise designs for future meters (and which has now been applied in this way). 

6. Conclusions

  1. The velocity variation of the piston during one oscillation was found to depend on: flow rate, mass of piston, surface finish, combined length of up- and downstream pipe work and the presence or otherwise of lubrication holes and slots in the skirt.
  2. The vertical motion of the piston and the angle of tilt was affected by flow rate, mass of the piston and the presence of lubrication holes, but less by other parameters. It was noted that the piston appeared never to lift off completely and, for the heavier piston at lower flows, not to tilt.
  3. The average pressure loss was dependent on a number of factors including flow rate, mass of piston, viscosity and density of liquid, surface finish of the piston and the presence or otherwise of slots in the skirt.
  4. The pressure loss across the meter does vary during the period of the piston oscillation and this variation can be significant. Reduction of contact friction can reduce the effect and can, possibly, be achieved by the use of low friction coatings.
  5. The pressure losses from flow in the inlet and outlet may account for as much as 60% of the total losses in the meter, and should be reducible with careful duct design.
  6. Lubrication holes have some benefit for pistons where the friction is not low.
  7. Slots in the skirt appear to reduce average pressure loss, and also reduce the amplitude of pressure fluctuation during each cycle.

Acknowledgements

CEM was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) and Litre Meter through an Industrial CASE Studentship. RCB received support from the Gatsby Charitable Foundation. The authors gratefully acknowledge support from departmental colleagues: Mick Harding, Stuart Fordham, Giles Hainsworth and Simon Sennitt.

References

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  3. Hahn BV. Theory of the sliding vane meter. Siemens Rev 1968;XXXV(9): 362-6.
  4. Baker RC, Morris MV. Positive displacement meters for liquids. Trans Inst Meas Control 1985; 7: 209-20.
  5. Nash LH. Oscillating Meter. U. S. Patent Office. USA. 300,625: 1884.
  6. Cloran EM. Rotary oil meters of the positive displacement and current types. Trans ASME 1938; 617-24.
  7. Plank N. Slippage errors in positive displacement liquid meters. Proc Third World Petroleum Congress Section 1951;1: 100-24.
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  11. Morton CE, Baker RC, Hutchings IM. Measurement of liquid film thickness by optical fluorescence and its application to an oscillating piston positive displacement flowmeter. Measurement Science & Technology 2011; 22: 125403 (11pp).
  12. Morton CE, Hutchings IM, Baker RC. Experimental investigation of an oscillating circular piston positive displacement flowmeter: II - leakage flows and wear tests. 2013; Submitted for publication to JFMI with this paper.
  13. Rasband WS. Image J. U. S. National Institutes of Health, Bethesda, Maryland, USA, http://rsb.info.nih.gov/ij/  1997-2009  [cited].
  14. Coleman HW, Steele WG. Experimentation and Uncertainty Analysis. 2nd ed. Wiley Inter Science; 1999.
  15. Morton CE. Performance and modelling of the oscillating piston flowmeter. PhD Thesis, Department of Engineering, University of Cambridge; 2009.
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