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Observations on the design and development of a water flow rig related to calibration in the manufacturing process
Flow Measurement and Instrumentation 17 (2006) 171–178 www.elsevier.com/locate/flowmeasinst
Observations on the design and development of a water flow rig related to calibration in the manufacturing process Roger C. Baker a,∗ , Tao Wang a , Pamela I. Moore a , Andy Nurse b a Institute for Manufacturing, University of Cambridge, United Kingdom b Quadratic Consulting Limited, Troon, Camborne, Cornwall, United Kingdom
Abstract In the development of a flow test rig as a tool for investigating manufacturing variation, we encountered various problems. We suspect that we were not unique and that our observations would be of interest to others. In this paper we concentrate on the hydraulic engineering aspects of the rig, referring to the uncertainty only as required to understand the discussion. In particular we consider the consequences of selecting a standing start and stop system, and the errors which may result. We review the likely effects of entrained air, and we consider the error which may result from the ramp up and down at the start and end of each run. Further aspects will be discussed in subsequent papers. We aim to provide a source of guidance for manufacturers and others who need to install a calibration rig for their manufacture or research. c 2006 Elsevier Ltd. All rights reserved. Keywords: Flowmeter; Calibration; Uncertainty
1. Introduction This paper describes aspects of the design and commissioning of a flow calibration rig at the Cambridge University Engineering Department (CUED). The objective of this work was to develop a water flow rig with reasonable uncertainty and high instrument stability to: (a) identify [1] and measure the effect of manufacturing variation on the performance of high precision flowmeters; (b) provide guidance to manufacturers who wish to invest in a flow calibration rig. This paper widens the discussion from the specifics of one rig, to identify the key points and some of the decisions to be made when designing such a rig. The paper examines the reasoning behind aspects of the design of the flow system, and the mounting for the flowmeters. We explore the causes of uncertainty which result from some of these decisions. ∗ Corresponding address: Cambridge University, Engineering Department, Institute for Manufacturing, Mill Lane, CB2 1RX Cambridge, United Kingdom. Tel.: +44 1223 766 403. E-mail address: [email protected] (R.C. Baker).
c 2006 Elsevier Ltd. All rights reserved. 0955-5986/$ - see front matter doi:10.1016/j.flowmeasinst.2006.01.005
2. Choice of flow rig type We required two modes of operation from our rig: (i) the ability to test and evaluate flowmeters to very high levels of accuracy and repeatability; (ii) the ability to run flowmeters under test continuously against a master meter. Within these requirements were a low level of uncertainty (an achieved uncertainty better than 0.2% would have been acceptable), stability of flow rate, average values over a selectable period of one to five minutes and data in a form allowing recording and analysis. The period of measurement was not critical, although for a manufacturing unit it would be, and should be capable of automation. There are various types of rig [2] for calibration. We opted for a gravimetric system with a standing start and stop (where the flow is zero at the beginning and end of the run) as the most economical to achieve the uncertainty we sought. An advantage of the standing start and stop over the flying start and stop (in which the flow is diverted for a brief period into a weigh tank) is that the diversion uncertainty is removed and the weight is the only measurement with uncertainty. The
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disadvantage is that the flow is not at constant rate throughout the test. Initially we proposed to use transfer standards between our rig and manufacturers’ laboratories. We found that there was too much variation and installed a weighbridge. A weighbridge provides a convenient method for weighing the water and an independently traceable uncertainty. Without a constant head tank, the flow steadiness will depend on the steadiness of the pump supply, but may also be affected by the water level, for instance when water is diverted into the weigh tank for a period the level in the sump tank drops, and the pump will operate against a changed head. The circuit is shown in Fig. 1. It consisted of the main tank, a pump, a bypass after the pump to allow water to be dumped straight back into the tank if necessary, but with the main flow route passing through up to six flowmeters before dividing into three test lines and finally back into the main tank. One of the test lines allowed the flow to be diverted into a weigh tank and the water from this was then dumped back in the main tank once the weight had been recorded. 2.1. Calculation of losses in the flow circuit
Fig. 1(a). Schematic diagram of the flow rig for testing variation in flowmeters: although the successive runs of pipe were above each other and anchored to the central concrete base, they are shown in this diagram spread out to make the arrangement clearer. Following the tank and the pump the pipework spiralled up through an electromagnetic flowmeter (EMFM), the first Coriolis flowmeter, a second EMFM, second, third and fourth Coriolis flowmeters. It then broke into three separate selectable runs across the top of the concrete base before discharging into the tank once more. The centre run could be diverted into the weigh tank, which sat over the main tank.
Pressure losses are calculated by considering the contribution of each component in the circuit, including bends, valves, straight pipe etc. The loss in the circuit is a function of the flow rate and the flow rate and losses must be matched with the pump characteristic. The source used for this calculation was Miller [3]. The pressure loss caused by each component is calculated and the sum will give the loss through the circuit for a particular flow rate. The basic equation for the loss coefficient in a straight pipe is K = f L/D
(1)
where f is the friction coefficient, L is the length of pipe and D is the pipe diameter. Care should be taken in the use of f as there are two definitions with resulting values differing by a factor of four [4]. For other components the loss coefficients are obtained from empirical data which is set out in the form of charts and correlations [3]. The total pressure loss is then given by the summation of all the losses in the circuit: (2) p = K V 2 /2. The value of V , the velocity, is that which relates to the particular loss coefficient. The total pressure drop indicated the requirements for pump size. An allowance was made for additional losses due to flow conditioners etc. A pump with a maximum pressure characteristic of 14 bar was chosen. For 226 kg/min which gives about 7.4 m/s in the 25.4 mm pipe, the total loss calculated was about 13 bar. However, it should be noted that this figure was high due to the losses across one meter which was operating well above its design range. 2.2. Choice of main tank capacity Dissipation of the energy imparted to the water by the pump results in temperature increase. To ensure approximately
Fig. 1(b). Photograph of the flow rig.
constant temperature, therefore, the main tank needs to be large enough to contain the temperature rise for typical lengths of calibration run. Temperature could be controlled with a water cooler, but this would be an added cost and inconvenience. The temperature rise of the water must be negligible compared with the operating temperature range of the meter, and have no unwanted effects on the uncertainty of the rig. The effect of density change where volumetric meters are being calibrated will need to be assessed and allowed for. The temperature rise can be estimated from the pressure loss expected through the system and the flow rates to be used. Thus in the system under consideration, the volume of the tank selected was 3 m3 . At 226 kg/min, the power loss predicted was about 4.8 kW and, allowing for inefficiency in the pump at the operating point, this was increased to 7.6 kW. The temperature rise will be
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Tend − Tstart Average power dissipated × Run time . = Specific heat capacity of water × mass of water
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2.5. Pipework (3)
This was estimated to result in a temperature rise of about 0.036 ◦C/min of run. Comparing this with the actual rig, at 226 kg/min and for a period of 22 min, the temperature rise was 0.89 ◦C, or 0.04 ◦C/min. For an extended test with flow rate increasing over a 10:1 range, since the power consumed increases as the square of the flow rate, the average rise per minute of run for flows from low to full flow rate will be about one third of the maximum. For a run of 210 min, from about 60 kg/min to about 190 kg/min in a 25 mm pipe, this led to a water temperature rise of about 2 ◦ C. Eventually the rig should settle at an equilibrium temperature, but this would have been considerably higher and inappropriate. 2.3. Pump and inverter It was decided to purchase an inverter to control the pump speed, and to allow flow control by this means as well as by use of a flow control valve. The decision was fully justified in the event. The main benefits of the inverter were: (i) The speed of the pump was controlled by a remote set point. (ii) The additional temperature rise, resulting from the energy dissipation when using a bypass and control valve, was avoided. Otherwise this could have required a cooler in the circuit to hold the temperature constant. (iii) The inverter allows pump operation to be automated if required. The pump size chosen had the capacity to deliver over 10 m/s in 25 mm pipe, about 10 m/s in 40 mm pipe and about 5 m/s in 50 mm pipework. The pump was predicted to be capable of delivering a pressure larger than the initial calculations, but this allowed for added flow and flowmeter components, and particularly the possibility of incorporating flow straighteners if required with loss coefficients [4] ranging up to of order 5. 2.4. Supports and working area As the rig was to be used for testing Coriolis flowmeters it was decided to minimise external vibration by basing the rig on a concrete block. This was cast in position to provide a very solid and massive base, and special supports were made to hold the meters. The pipe work wound round this block with the meters mounted on each side and at one end. Finally the pipe split into three test runs to allow investigation of three different meters before the water was ducted back to the main tank system. The footprint of the rig can be an important aspect of the design. In the case of the Cambridge rig the pipe configuration allowed the maximum length of pipe within the space. The possibility of short-term use of larger pipe sizes could be accommodated without permanent use of space. The vertical spacing between the pipes on successive passes round the concrete block should be sufficient to allow instruments with larger readout heads to be accommodated.
The maximum pressure achievable by the pump was 14 bar, and the pipework had to be capable of withstanding this pressure, it was decided to use ABS pipework capable of this. Some ball valves for isolating sections of the rig were made of ABS and others of metal. Block and bleed valving was incorporated at the start of each of the three test lines, to allow leakage to be checked from time to time. Adequate support for the meters at inlet and outlet required stainless steel pipe. The cost difference between stainless steel and ABS may not be sufficient to make this a prime consideration in the choice of pipework. More important may be the versatility, selfsupporting capability, pressure rating etc. and also the different skills required to manufacture and to install the pipework. Careful thought should be given to the relative benefits of each type of pipework. With standing start and stop it was necessary to run the rig against a closed valve. This results in full pressure in the pipework, and the danger of shock loading if the valves are opened or closed too quickly. Shock loading can cause short pulses of higher pressure which might result in pipe or joint failure. For a rig in a manufacturing line, the justification for electrically controlled pneumatically powered valves is that the calibration cycle can be automated with the pump and the weigh tank. The value of such valves is also that they are likely to give a greater repeatability of closure pattern than is possible from hand operated valves. Obviously they will require a source of pressurised air. Electrically activated and powered valves are an alternative, but the level of control and repeatability compared with electro-pneumatic valves should be checked. Initially hand operated valves were used, and care was taken to turn them smoothly in as short a time as was deemed safe while avoiding shock loading. This resulted in a change of flow rate in about one second. The shortest run using the weigh tank was about 60 s. One concern with this rig layout relates to the profile distortion and the possibility of swirl creation. However, the relative angle of successive 90◦ bends was less than 5◦ and bend–bend interaction should have been negligible [3]. We ensured that the upstream straight run of pipe before each electromagnetic flowmeter was greater than 60D. Distortion due to the previous bend should, therefore, have been negligible. The possibility of swirl creation would have been at two points. The first was at outlet from the pump. Here the distance from the pump outlet to the first bend consisted of about 14D of 2 in. pipe followed by a contraction down to 1 in. and about 18D of 1 in. pipe. We deduce from the data (cf. Ref. [3]) that distortion due to the exit bend from the pump would have decayed sufficiently by the time the flow reached the first bend so that the 66D from the first bend to the electromagnetic flowmeter would ensure negligible swirl. In practice we did not use this flowmeter for any precision measurements. The second possible swirl creation point was before the test section. Here flow straightening will be necessary where meters sensitive to swirl are to be tested.
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3. Water quality
indicate that this will be sufficient to remove all bubbles with diameter greater than 0.02 mm. Alternatively the terminal velocity for a gas bubble in liquid given by Clift et al. [7] as
3.1. Air in water — existence, problems and elimination There was concern about the possibility of air entrained in the flow not being removed during the passage through the tank. One method of increasing the residence time for the water in the tank is to install baffles in the tank to increase the length of flow path. Thus, in our rig, the flow was dumped back in the tank under the water surface near the bottom of the tank, rose over the first baffle, then down to the bottom of the tank to pass under the second baffle. It finally flowed over the third baffle before leaving the tank through a pipe at the bottom of the tank, which led to the pump inlet. The maximum flow rate was less than 10 m/s in the 25 mm line. The cross-section of the tank above or below the baffles was about 0.75 m2 . This resulted in a velocity of about 6 mm/s, or a time to traverse the tank of about 10 min minimum. This is also equivalent to a minimum water exchange time of about 10 min. There are two mechanisms to be considered, in particular, in the discussion of air in water. (a) Diffusion of air into water According to Jones [5] “in flow measurement work, except in the rare case in which freshly distilled water is used, the water density of interest is the density of airsaturated water”. For temperatures in the range 5–40 ◦ C he gave the following equation: ρas = 999.84847 + 6.337563 × 10−2 t − 8.523829 × 10−3 t 2 + 6.943248 × 10−5 t 3 − 3.821216 × 10−7 t 4
(4)
where t is the temperature in ◦ C. However, Jones states that ‘At 20 ◦ C, the uncertainty in the density of airsaturated water for an uncertainty in temperature of 1 ◦ C is approximately 210 ppm or 0.21 kg m−3 ’. Kaye and Laby [6] state that ‘A kilogram of water saturated with air at a pressure of 101.325 kN m−2 contains the following volumes of dissolved oxygen, etc., in cm3 at 0 ◦ C and 101.325 kN m−2 ’. For 20 ◦C their data gives 6.4 cm3 of oxygen and 12.3 cm3 of nitrogen, argon etc., the sum of these being 18.7 cm3 . (b) Air bubbles in water The entrainment of bubbles in the flowing water can cause a larger effect. A source of these is likely to be due to the return water from, say, a weigh tank causing splashing and air entrainment. Thus, bubbles of a range of sizes may be introduced, and the mechanism for these to be removed will, in general, be to allow time for them to rise to the surface in the main tank. The rise time depends on the size of bubbles and the contamination of the water, since terminal velocity in pure water is higher. Taking the minimum time of 600 s calculated above to transit the tank, and assuming that the worst case will be a bubble which needs to rise one metre to the main tank surface, a terminal rise velocity of 0.002 m/s would suffice. Extrapolating experimental results quoted by Clift et al. [7] appears to
gd 2 ρ (5) 12μ can be used to obtain an order of magnitude of the diameter of air bubbles. For air bubbles in water, ρ will approximate to the value of density for water of 1000 kg/m3 and μ will be about 1.002 × 10−3 Pa s. For a velocity of 0.002 m/s, derived above, this results in a bubble diameter of order 0.05 mm. A crude estimate of the bubble population caused, presumably, by disturbed water, for instance the water returning from the weigh tank into the main tank, could assume that the distribution was normal with a mean diameter of order a few millimetres. However, apart from the intuitive perception that the volume contained in such small bubbles will be negligible, there would appear to be no more substantial confirmation. The mass ratio of a bubble would be about 10−15/m3 requiring 109 such bubbles per cubic metre to equal 1 ppm in density, or one such bubble per cubic millimetre. If this amount of air entrained is to be checked, then it will probably require special instrumentation, possibly optical, to sense the presence of the bubbles. VT =
3.2. Water filter In the initial rig circuit a filter was considered necessary to protect the pump. However, the filter used caused a substantial pressure drop before the pump, and it was decided that it was probably unnecessary, except for occasional use to clean out any larger particles in the water. However, when the tank was emptied to do some modifications, it was found that there was considerable sand-like sediment in the tank. The most likely source of this appeared to be the mains water. The tank was thoroughly cleaned out, and an inlet filter fitted to filter the mains water as the tank was filled. 3.3. Algae and other water problems It was found that the glass tube of a variable area (VA) meter under test became discoloured on the inside with a deposit. The contamination was probably due to an algal growth in the water when there was no flow in the circuit. To avoid this a black cover has been used to cover the VA meter when the rig is not in use, the theory being that without light there can be no photosynthesis, and therefore no algal growth. Palmer [8] suggested two approaches for dosing the water to prevent the growth of algae. Commercial additives are also available. If any treatment is contemplated, the user should give consideration to: • the safety of the resulting dosed water; • the legality of eventual discharge of the dosed water into the disposal systems;
R.C. Baker et al. / Flow Measurement and Instrumentation 17 (2006) 171–178 Table 1 Master meters compared with weigh tank Type of meter
Special features
Manufacturer
Coriolis Coriolis
Twin tube Single tube
Manufacturer 1 Manufacturer 2
• the corrosive effect of the dosed water on the meters and other pipe work components; • the validity of the resultant calibration if the water is dosed rather than pure. Because of the problems encountered in identifying satisfactory additives and the points above, our solution was to ensure, as far as possible, that no light reached the water by entirely enclosing the circuit, and the water quality appears to be retained.
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The weigh tank has a lid with access (but not contact) to the inlet flow line. Clearly splashing occurred during the fill period, but this was, essentially, contained by the tank and lid. The weir initiation process ensured that the starting and stopping conditions were the same, and the allowance for the excess water to drip (see Section 5.4) also ensured that any spray on the nozzle was allowed to drop into the tank. We consider, therefore, that any errors due to this were negligible. For very long low flow rate runs it may be necessary to allow for evaporation. An estimate of this can be made by allowing the weigh tank, with water in it, to stand for a long period, and the weigh scale change recorded. At the maximum flow rate used by us, the run time for filling the tank is about one minute. 5.1. Correction for weight of air in weigh tank and for humidity
Being cautious as to the likely achievable accuracy from a weighing system, the original plan was to use master meters as the standard with traceable calibrations. For the first few months of the rig, this was the situation, but it was found that there was a substantial discrepancy between some of the meters, which was outside the expected uncertainty brackets. We propose to discuss this in detail in a later paper. The decision was, therefore, taken to install a weigh tank system. For the purposes of this paper we shall summarise the agreement we achieved between the weigh tank and two of the flowmeters. The meters are given in Table 1.
It is important to allow for the buoyancy of the air in the calculation of the collected mass when using the weigh scale. When the scale is tared (zeroed before the calibration run) the tank is filled with air which will be displaced with water. The mass of this air must be taken into account. This is known as the buoyancy effect, since the water in the tank is being “buoyed up” by the surrounding air. In this procedure ambient temperature and pressure are recorded and used to obtain the density of the air on the day. We reproduce the standard derivation below for completeness and clarity (cf. Refs. [9,10]). Thus the mass reading on the scale, m s , may be equated to the difference between the mass of liquid, m l , in the tank and the mass of air displaced, m a :
5. Weigh system
ms = ml − ma .
4. Reference flowmeters
It was decided to install a weigh scale and modify the pipework to allow the flow to be diverted into a weigh tank. A scale with a range up to 300 kg was bought and installed. A weigh tank suitably sized (scale capacity + about 10%) and as light as possible to avoid using scale capacity, was acquired. It was of uniform cross-section. The approach pipework at inlet to the tank was specially constructed to include a swan neck and weir to ensure that the level was the same whenever the flow was stopped. The pipework should be rigid to prevent movement from detracting from the function of the weir plate. The tank sides and the jet from the inlet nozzle were vertical. It was decided to use hand operated valves. Before starting a run, some water was allowed to enter the weigh tank to ensure that the weir was full. It appeared that the weir sat at a slightly different height for each flow rate. The method used was, then, to set the flow rate as required, then to shut the valve and to take kilogram readings on the meters. The valve into the weigh tank was then opened and about 240 kg allowed to flow into the tank before the valve was closed again. Total mass readings on the meters and the weigh scale were then obtained and the flow valve, which allowed recirculation of the water, and the weigh tank drain valve were opened. Using the hand operated valves resulted in a change of flow rate in about one second compared with the shortest run of about 60 s.
(6)
Assuming that the air density remains constant and ρa is the density of air and ρl is the density of the liquid then m s = m l (1 − ρa /ρl )
(7)
resulting in the correction factor for the weigh tank value of ρa . (8) 1+ ρl − ρa Since the density of air, ρa , is about 1.2 kg/m3 , and the density of water, ρl , is about 1000 kg/m3 , the correction factor is about 1.0012 or an adjustment of about 0.12%. Assuming a worst case of 10 ◦C error in the temperature of the air, this would cause about 3% error in the adjustment and about 0.003% uncertainty in the correction factor. An additional effect which proves to be negligible is that due to humidity. This may be calculated using the empirical formula [9] ρa =
0.348444 pambient − h(0.00252Tambient − 0.020582) (9) 273.15 + Tambient
where pambient is the atmospheric pressure in millibars, Tambient is the ambient temperature in ◦ C and h is the relative humidity as a percentage. Assuming a relative humidity of 60% and a temperature range of 15–25 ◦C the effect of neglecting humidity in the
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Fig. 2. Diagram of the flow rate variation during a calibration run.
calculation of air density is less than 1%. The effect of this on the calculation of buoyancy correction is less than 0.002%. In order to obtain rig certification it will probably be necessary to demonstrate means to obtain the density of water and air at ambient conditions. 5.2. Error due to varying flow rate While the standing start and stop weigh system eliminated time measurement related to the diverter system, it introduces variation in the flow. This is unlikely to be acceptable for meters with significantly non-linear characteristics, but will also be viewed as unacceptable where a constant flow rate is preferred for some meters and certifications. Calibration of a non-linear meter can be achieved in this rig in two steps: (i) the calibration check of the master meter; (ii) the steady flow test against the master meter. It is, therefore, important to consider the likely errors introduced by the standing start and stop. If we take a ramped increase and decrease in flow rate as shown in Fig. 2, then we can assume that the time taken to open and close the valve is t (of order one second). Assuming that the ramp up and down is essentially linear, and that we can assume that the meters are linear down to the cut-off, then Ramp up flow = Qt/2 Steady region flow = QT Ramp down flow = Qt/2 Total flow passed = Q(T + t) Unrecorded flow (%) = y 2 Qt/[100Q(T + t)] = y 2 t/[100(T + t)]. Minimum run time is about 60 s, and the valve movement is about 1 s. With the cut-off at 0.2%, the unrecorded flow will be less than 7 × 10−6 %. Small changes in t will not be important. Manufacturers will need to consider whether a low flow cut-off is implemented and for which signals. However, were the characteristic of the flowmeter non-linear at very low flow then this would introduce an error which, as an extreme, could be taken as the value of the error above, but with y equal to, say, 2%. This could result in an error of 0.0007%. The characteristic of the flowmeter under test should be checked for linearity, and the low flow cut-off level should be checked to ensure that it is sufficiently low, to make standing start and stop calibration satisfactory.
Fig. 3. The effect of heated water from the pump passing through one of the flowmeters.
For manual operation variation in the rate and time of opening and closing for a non-linear flowmeter will also have an effect which should be calculated by introducing the non-linear characteristic into Fig. 2. 5.3. Effect of temperature change due to closed valve operation The effect of running the pump against closed valve, as required in the standing start and stop procedure, could damage the pump if it continued for more than a minute or so. It will also lead to the water in the pump heating up. Taking the volume of water in the pump as approximately 50% of the impeller casing volume (50 cm long and 20 cm diameter), or 0.0075 m3 , and the closed valve period as one minute, then at a power level of 3.7 kW, the temperature rise of the pump contents will be about 7.2 ◦ C. This should have a negligible effect on the calibration. With a flow rate of 7.44 m/s the warm water should pass through each of the meters in about 2 s. Fig. 3 shows some experimental results from one of the flowmeters. The pump was held against closed valve for periods up to 10 min. The resultant temperature profile as the warm water flowed through the meter is shown. There will be an error due to the transient temperature measurement which may be of order 1 ◦ C or greater. The flow rate for these tests was 118 kg/min, about half that in the calculation above, so that the heating effect in the pump would be about 1/8 of that in the example above or about 1 ◦ C/min. This is compatible with the values in Fig. 3. However, one possible problem with the water heating, apart from the fact that mass meters will be operating with a density variation, though brief, is the danger that it could cause the cavitation boundary to be shifted enough to cause problems where the pressure is low, for instance near the outlet of the flow circuit. Cavitation was noted when two electromagnetic flowmeters with reduced bores were positioned in the final test section of the rig. Brief temperature increase could trigger cavitation in such circumstances (cf. Ref. [2] for appropriate formulae). Meters that use sensors mounted directly on to the measuring tube for measuring temperature or strain may start to apply large temperature compensations in software as a result of the increased output of the sensor. Increasingly, calibration of flowmeters now includes “characterisation” with complex algorithms used to correct flow measurement for temperature
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7. Rig uncertainty
Fig. 4. Change of weigh scale reading due to water dripping from the inlet pipe.
effects on the meter. It may, therefore, be beneficial to switch a pump bypass in and out of circuit at the beginning of test batches to eliminate this slug of warmer water. 5.4. Dripping and meniscus variation in the weir pipe The pipe leading to the weigh tank can be a source of error if the cut-off water level at start and finish of the run is not well defined. An effective method of achieving the same initial and final level is by inserting a sharp edged weir across the swan neck at outlet to the pipe. However we noted two problems: (i) the level differs between various flow rates presumably due to the change in the meniscus at the weir: this we overcame by initialising the level according to the flow rate to be used; (ii) the inlet pipe continued to drip for some minutes after the valve closed, and this affected the weigh scale reading; this effect is indicated in Fig. 4. To deal with (i), an alternative may be to increase the time taken to ramp down, so that inertia of the water is reduced for all flow rate settings. This may increase the problem identified in Section 5.2. To deal with (ii) it was necessary to compromise between waiting a long time for the dripping to end, and accepting that the pattern at the start and end of the run was similar and that a reasonable cut-off time should be selected. Too long a delay could also be a problem, since if a meter’s zero cut-off is set too low, the meter may continue to record flow at zero flow. 6. Working sections and meters installed in them Once the flow has gone through the master meters, the pipework allowed three alternative runs to be selected on top of the concrete block. These have had the following meters installed: (a) a variable area meter for tests to identify the effect of manufacturing variation in the manufacture of tubes and floats (cf. Ref. [11]); (b) an averaging pitot meter (using ganged differential pressure cells to obtain the flow rate over the range of the rig flows); (c) Coriolis meters relating to manufacturing variation.
On the basis of a review of the weigh scale calibrations over the past three years, an uncertainty of ±0.02% for the weigh scale reading appears appropriate for our tests where the total load was usually of the order of 200 kg. The tank was placed centrally and the water allowed to stabilise, so that the eccentricity errors were not relevant. There is a reading uncertainty at start and finish which amounts to ±0.002%. However, there were other uncertainties in this measurement, such as the level at the weir, the draining of pipework after flow had stopped, the measurement of the temperature of the air and the displaced air during the weigh period and the ramped flow changes. This paper has focused on some special effects which need to be taken into consideration in the design of the flow rig. We restrict consideration of uncertainties to those addressed in this paper and plan to give a fuller discussion of this in a future paper. We indicate in Table 2 the likely effects of the individual components and the overall current estimate of uncertainty resulting from these components. In particular we have neglected the possible error due to evaporation, considered negligible in these tests, and the uncertainty due to the effect of temperature change and drift in weigh scale. We have not considered problems relating to signal and data processing. In compiling Table 2 which we include as a preliminary estimate pending further work, we have not allowed for differing probability distributions. We would emphasise that in seeking national accreditation for a rig to provide a calibration standard, all such factors should be taken into consideration. We note, from Table 2, that the two meters from different manufacturers, which gave greater confidence, appear to agree well with the weigh system which is used as the datum in Fig. 5. They agree over the range to within ±0.05%. It is important to reiterate that this paper does not attempt to give a full estimate of all possible errors, or of likely achievable uncertainty. We consider that it would be misleading to attempt this in a paper which is focused, only, on certain errors. The figure obtained in Table 2 represents, only, the root sum square of the specific errors identified. (The reader is referred to Ref. [2] for a fuller discussion on the estimate of flow rig uncertainty.) In addition the uncertainty in measurement for a flowmeter calibrated on this rig will need to allow for the uncertainties of data collection etc. In this paper we have not attempted to deal with these other issues. However, flow rigs of a similar construction to that built at Cambridge have achieved accreditations from UKAS to an uncertainty in the range 0.035%–0.1% for a batch as opposed to a mass flow rate. This would appear to be a reasonable guide to what is currently achievable in terms of optimising cost and complexity. While we have targeted the paper at manufacturers who may be building rigs we would not exclude users, who may be considering their own in-house checking facility. For them, an alternative is to test against a master meter, in which case the accuracy may not be better than of order 0.1%–0.15%.
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Table 2 Uncertainties based on the observations in this paper for 200 kg ignoring probability distribution variation Source of uncertainty
Estimate of variation
Current estimate of uncertainty % (95% confidence)
Flow profile distortion Air in water Weigh scale uncertainty Weigh scale readability Buoyancy calculation Humidity error Dripping Splashing Temperature changes Ramp up and down Combined uncertainty Flowmeter uncertainty Coriolis meter uncertainty
Profiles fully developed 2 ppm 0.02% 2g 0.003% 0.002% 20 g Negligible Negligible 0.0007%
0.0000 0.0002 0.0200 0.0020 0.0030 0.0040 0.0200 0.0000 0.0000 0.0014 ±0.029 Supplied by manufacturer ±0.1000
Typical claim
of their manufacturing process. We have identified possible answers. We emphasise that the discussion has focused on certain special effects, and that advice should be sought if setting up a calibration facility on other effects which should be evaluated. Acknowledgements
Fig. 5. Primary flowmeter calibration against the weigh system.
8. Conclusions The object of this paper has been to identify and discuss some of the considerations which should be reviewed when deciding to build a flow calibration facility. These have been focused on the mechanical and hydraulic aspects of the rig. We plan to discuss other aspects in a future paper. We have: • set out the approach to loss estimation for a new design of rig, noting that unseen factors may increase the loss, and a margin of safety should be built in by slight overspecification of the pump; • discussed the reason for the main tank size and the estimation of the temperature increase; • discussed the pump and inverter, pipework and supports; • considered the worrying matter for the precision of flow measurement of the existence of air in water; • discussed the factors which need to be considered in installing a weigh tank and the errors which can result from standing start and stop methods; • provided initial results on the agreement achieved between two of the Coriolis flowmeters and the weigh system. We have identified certain special effects which we have encountered, so as to alert manufacturers to the problems which may occur when setting up a calibration rig as part
The authors wish to acknowledge the work of Gerry Franklin and other members of the maintenance and technician staff of CUED for their great help in building the rig, Dr Yousif Hussain for advice on the design and the sourcing of some components of the rig, and Samuel Mumba who carried out experimental checks on the rig. The support for this work from the Gatsby Charitable Foundation, from manufacturers who lent flowmeters, and from the Knowledge Transfer Partnership which included funding from the industrial partner, Krohne Limited, is also acknowledged. References [1] Baker RC. Variation in flowmeter manufacture: some observations and lessons. Proc I Mech E Part B J Eng Man 2004;218:961–75. [2] Baker RC. Flow measurement handbook. New York: Cambridge University Press; 2000. [3] Miller DS. Internal flow systems. Cranfield: BHRA Fluid Engineering; 1990. [4] Baker RC. An introductory guide to industrial flow. Professional Engineering Publishing; 1996. [5] Jones FE. Techniques and topics in flow measurement. Florida (USA): CRC Press; 1995. [6] Kaye GWC, Laby TH. Tables of physical and chemical constants and some mathematical functions. 14th ed. Longman; 1973. [7] Clift R, Grace JR, Weber ME. Bubbles, drops, and particles. New York (USA): Academic Press; 1978. [8] Palmer CM. Algae and water pollution—the identification, significance, and control of algae in water supplies and in polluted water. Castle House Publications Ltd; 1980. [9] Buoyancy correction and air density measurement. National Physical Laboratory, 2002, http://www.npl.co.uk/mass/guidance/buoycornote.pdf. [10] Miller RW. Flow measurement engineering handbook. New York: McGraw-Hill; 1996. [11] Baker RC. The impact of component variation in the manufacturing process on variable area (VA) flowmeter performance. J Flow Meas Instrum 2004;15(4):207–13.
Observations on the design and development of a water flow rig related to calibration in the manufacturing process Roger C. Baker a,∗ , Tao Wang a , Pamela I. Moore a , Andy Nurse b a Institute for Manufacturing, University of Cambridge, United Kingdom b Quadratic Consulting Limited, Troon, Camborne, Cornwall, United Kingdom
Abstract In the development of a flow test rig as a tool for investigating manufacturing variation, we encountered various problems. We suspect that we were not unique and that our observations would be of interest to others. In this paper we concentrate on the hydraulic engineering aspects of the rig, referring to the uncertainty only as required to understand the discussion. In particular we consider the consequences of selecting a standing start and stop system, and the errors which may result. We review the likely effects of entrained air, and we consider the error which may result from the ramp up and down at the start and end of each run. Further aspects will be discussed in subsequent papers. We aim to provide a source of guidance for manufacturers and others who need to install a calibration rig for their manufacture or research. c 2006 Elsevier Ltd. All rights reserved. Keywords: Flowmeter; Calibration; Uncertainty
1. Introduction This paper describes aspects of the design and commissioning of a flow calibration rig at the Cambridge University Engineering Department (CUED). The objective of this work was to develop a water flow rig with reasonable uncertainty and high instrument stability to: (a) identify [1] and measure the effect of manufacturing variation on the performance of high precision flowmeters; (b) provide guidance to manufacturers who wish to invest in a flow calibration rig. This paper widens the discussion from the specifics of one rig, to identify the key points and some of the decisions to be made when designing such a rig. The paper examines the reasoning behind aspects of the design of the flow system, and the mounting for the flowmeters. We explore the causes of uncertainty which result from some of these decisions. ∗ Corresponding address: Cambridge University, Engineering Department, Institute for Manufacturing, Mill Lane, CB2 1RX Cambridge, United Kingdom. Tel.: +44 1223 766 403. E-mail address: [email protected] (R.C. Baker).
c 2006 Elsevier Ltd. All rights reserved. 0955-5986/$ - see front matter doi:10.1016/j.flowmeasinst.2006.01.005
2. Choice of flow rig type We required two modes of operation from our rig: (i) the ability to test and evaluate flowmeters to very high levels of accuracy and repeatability; (ii) the ability to run flowmeters under test continuously against a master meter. Within these requirements were a low level of uncertainty (an achieved uncertainty better than 0.2% would have been acceptable), stability of flow rate, average values over a selectable period of one to five minutes and data in a form allowing recording and analysis. The period of measurement was not critical, although for a manufacturing unit it would be, and should be capable of automation. There are various types of rig [2] for calibration. We opted for a gravimetric system with a standing start and stop (where the flow is zero at the beginning and end of the run) as the most economical to achieve the uncertainty we sought. An advantage of the standing start and stop over the flying start and stop (in which the flow is diverted for a brief period into a weigh tank) is that the diversion uncertainty is removed and the weight is the only measurement with uncertainty. The
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disadvantage is that the flow is not at constant rate throughout the test. Initially we proposed to use transfer standards between our rig and manufacturers’ laboratories. We found that there was too much variation and installed a weighbridge. A weighbridge provides a convenient method for weighing the water and an independently traceable uncertainty. Without a constant head tank, the flow steadiness will depend on the steadiness of the pump supply, but may also be affected by the water level, for instance when water is diverted into the weigh tank for a period the level in the sump tank drops, and the pump will operate against a changed head. The circuit is shown in Fig. 1. It consisted of the main tank, a pump, a bypass after the pump to allow water to be dumped straight back into the tank if necessary, but with the main flow route passing through up to six flowmeters before dividing into three test lines and finally back into the main tank. One of the test lines allowed the flow to be diverted into a weigh tank and the water from this was then dumped back in the main tank once the weight had been recorded. 2.1. Calculation of losses in the flow circuit
Fig. 1(a). Schematic diagram of the flow rig for testing variation in flowmeters: although the successive runs of pipe were above each other and anchored to the central concrete base, they are shown in this diagram spread out to make the arrangement clearer. Following the tank and the pump the pipework spiralled up through an electromagnetic flowmeter (EMFM), the first Coriolis flowmeter, a second EMFM, second, third and fourth Coriolis flowmeters. It then broke into three separate selectable runs across the top of the concrete base before discharging into the tank once more. The centre run could be diverted into the weigh tank, which sat over the main tank.
Pressure losses are calculated by considering the contribution of each component in the circuit, including bends, valves, straight pipe etc. The loss in the circuit is a function of the flow rate and the flow rate and losses must be matched with the pump characteristic. The source used for this calculation was Miller [3]. The pressure loss caused by each component is calculated and the sum will give the loss through the circuit for a particular flow rate. The basic equation for the loss coefficient in a straight pipe is K = f L/D
(1)
where f is the friction coefficient, L is the length of pipe and D is the pipe diameter. Care should be taken in the use of f as there are two definitions with resulting values differing by a factor of four [4]. For other components the loss coefficients are obtained from empirical data which is set out in the form of charts and correlations [3]. The total pressure loss is then given by the summation of all the losses in the circuit: (2) p = K V 2 /2. The value of V , the velocity, is that which relates to the particular loss coefficient. The total pressure drop indicated the requirements for pump size. An allowance was made for additional losses due to flow conditioners etc. A pump with a maximum pressure characteristic of 14 bar was chosen. For 226 kg/min which gives about 7.4 m/s in the 25.4 mm pipe, the total loss calculated was about 13 bar. However, it should be noted that this figure was high due to the losses across one meter which was operating well above its design range. 2.2. Choice of main tank capacity Dissipation of the energy imparted to the water by the pump results in temperature increase. To ensure approximately
Fig. 1(b). Photograph of the flow rig.
constant temperature, therefore, the main tank needs to be large enough to contain the temperature rise for typical lengths of calibration run. Temperature could be controlled with a water cooler, but this would be an added cost and inconvenience. The temperature rise of the water must be negligible compared with the operating temperature range of the meter, and have no unwanted effects on the uncertainty of the rig. The effect of density change where volumetric meters are being calibrated will need to be assessed and allowed for. The temperature rise can be estimated from the pressure loss expected through the system and the flow rates to be used. Thus in the system under consideration, the volume of the tank selected was 3 m3 . At 226 kg/min, the power loss predicted was about 4.8 kW and, allowing for inefficiency in the pump at the operating point, this was increased to 7.6 kW. The temperature rise will be
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Tend − Tstart Average power dissipated × Run time . = Specific heat capacity of water × mass of water
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2.5. Pipework (3)
This was estimated to result in a temperature rise of about 0.036 ◦C/min of run. Comparing this with the actual rig, at 226 kg/min and for a period of 22 min, the temperature rise was 0.89 ◦C, or 0.04 ◦C/min. For an extended test with flow rate increasing over a 10:1 range, since the power consumed increases as the square of the flow rate, the average rise per minute of run for flows from low to full flow rate will be about one third of the maximum. For a run of 210 min, from about 60 kg/min to about 190 kg/min in a 25 mm pipe, this led to a water temperature rise of about 2 ◦ C. Eventually the rig should settle at an equilibrium temperature, but this would have been considerably higher and inappropriate. 2.3. Pump and inverter It was decided to purchase an inverter to control the pump speed, and to allow flow control by this means as well as by use of a flow control valve. The decision was fully justified in the event. The main benefits of the inverter were: (i) The speed of the pump was controlled by a remote set point. (ii) The additional temperature rise, resulting from the energy dissipation when using a bypass and control valve, was avoided. Otherwise this could have required a cooler in the circuit to hold the temperature constant. (iii) The inverter allows pump operation to be automated if required. The pump size chosen had the capacity to deliver over 10 m/s in 25 mm pipe, about 10 m/s in 40 mm pipe and about 5 m/s in 50 mm pipework. The pump was predicted to be capable of delivering a pressure larger than the initial calculations, but this allowed for added flow and flowmeter components, and particularly the possibility of incorporating flow straighteners if required with loss coefficients [4] ranging up to of order 5. 2.4. Supports and working area As the rig was to be used for testing Coriolis flowmeters it was decided to minimise external vibration by basing the rig on a concrete block. This was cast in position to provide a very solid and massive base, and special supports were made to hold the meters. The pipe work wound round this block with the meters mounted on each side and at one end. Finally the pipe split into three test runs to allow investigation of three different meters before the water was ducted back to the main tank system. The footprint of the rig can be an important aspect of the design. In the case of the Cambridge rig the pipe configuration allowed the maximum length of pipe within the space. The possibility of short-term use of larger pipe sizes could be accommodated without permanent use of space. The vertical spacing between the pipes on successive passes round the concrete block should be sufficient to allow instruments with larger readout heads to be accommodated.
The maximum pressure achievable by the pump was 14 bar, and the pipework had to be capable of withstanding this pressure, it was decided to use ABS pipework capable of this. Some ball valves for isolating sections of the rig were made of ABS and others of metal. Block and bleed valving was incorporated at the start of each of the three test lines, to allow leakage to be checked from time to time. Adequate support for the meters at inlet and outlet required stainless steel pipe. The cost difference between stainless steel and ABS may not be sufficient to make this a prime consideration in the choice of pipework. More important may be the versatility, selfsupporting capability, pressure rating etc. and also the different skills required to manufacture and to install the pipework. Careful thought should be given to the relative benefits of each type of pipework. With standing start and stop it was necessary to run the rig against a closed valve. This results in full pressure in the pipework, and the danger of shock loading if the valves are opened or closed too quickly. Shock loading can cause short pulses of higher pressure which might result in pipe or joint failure. For a rig in a manufacturing line, the justification for electrically controlled pneumatically powered valves is that the calibration cycle can be automated with the pump and the weigh tank. The value of such valves is also that they are likely to give a greater repeatability of closure pattern than is possible from hand operated valves. Obviously they will require a source of pressurised air. Electrically activated and powered valves are an alternative, but the level of control and repeatability compared with electro-pneumatic valves should be checked. Initially hand operated valves were used, and care was taken to turn them smoothly in as short a time as was deemed safe while avoiding shock loading. This resulted in a change of flow rate in about one second. The shortest run using the weigh tank was about 60 s. One concern with this rig layout relates to the profile distortion and the possibility of swirl creation. However, the relative angle of successive 90◦ bends was less than 5◦ and bend–bend interaction should have been negligible [3]. We ensured that the upstream straight run of pipe before each electromagnetic flowmeter was greater than 60D. Distortion due to the previous bend should, therefore, have been negligible. The possibility of swirl creation would have been at two points. The first was at outlet from the pump. Here the distance from the pump outlet to the first bend consisted of about 14D of 2 in. pipe followed by a contraction down to 1 in. and about 18D of 1 in. pipe. We deduce from the data (cf. Ref. [3]) that distortion due to the exit bend from the pump would have decayed sufficiently by the time the flow reached the first bend so that the 66D from the first bend to the electromagnetic flowmeter would ensure negligible swirl. In practice we did not use this flowmeter for any precision measurements. The second possible swirl creation point was before the test section. Here flow straightening will be necessary where meters sensitive to swirl are to be tested.
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3. Water quality
indicate that this will be sufficient to remove all bubbles with diameter greater than 0.02 mm. Alternatively the terminal velocity for a gas bubble in liquid given by Clift et al. [7] as
3.1. Air in water — existence, problems and elimination There was concern about the possibility of air entrained in the flow not being removed during the passage through the tank. One method of increasing the residence time for the water in the tank is to install baffles in the tank to increase the length of flow path. Thus, in our rig, the flow was dumped back in the tank under the water surface near the bottom of the tank, rose over the first baffle, then down to the bottom of the tank to pass under the second baffle. It finally flowed over the third baffle before leaving the tank through a pipe at the bottom of the tank, which led to the pump inlet. The maximum flow rate was less than 10 m/s in the 25 mm line. The cross-section of the tank above or below the baffles was about 0.75 m2 . This resulted in a velocity of about 6 mm/s, or a time to traverse the tank of about 10 min minimum. This is also equivalent to a minimum water exchange time of about 10 min. There are two mechanisms to be considered, in particular, in the discussion of air in water. (a) Diffusion of air into water According to Jones [5] “in flow measurement work, except in the rare case in which freshly distilled water is used, the water density of interest is the density of airsaturated water”. For temperatures in the range 5–40 ◦ C he gave the following equation: ρas = 999.84847 + 6.337563 × 10−2 t − 8.523829 × 10−3 t 2 + 6.943248 × 10−5 t 3 − 3.821216 × 10−7 t 4
(4)
where t is the temperature in ◦ C. However, Jones states that ‘At 20 ◦ C, the uncertainty in the density of airsaturated water for an uncertainty in temperature of 1 ◦ C is approximately 210 ppm or 0.21 kg m−3 ’. Kaye and Laby [6] state that ‘A kilogram of water saturated with air at a pressure of 101.325 kN m−2 contains the following volumes of dissolved oxygen, etc., in cm3 at 0 ◦ C and 101.325 kN m−2 ’. For 20 ◦C their data gives 6.4 cm3 of oxygen and 12.3 cm3 of nitrogen, argon etc., the sum of these being 18.7 cm3 . (b) Air bubbles in water The entrainment of bubbles in the flowing water can cause a larger effect. A source of these is likely to be due to the return water from, say, a weigh tank causing splashing and air entrainment. Thus, bubbles of a range of sizes may be introduced, and the mechanism for these to be removed will, in general, be to allow time for them to rise to the surface in the main tank. The rise time depends on the size of bubbles and the contamination of the water, since terminal velocity in pure water is higher. Taking the minimum time of 600 s calculated above to transit the tank, and assuming that the worst case will be a bubble which needs to rise one metre to the main tank surface, a terminal rise velocity of 0.002 m/s would suffice. Extrapolating experimental results quoted by Clift et al. [7] appears to
gd 2 ρ (5) 12μ can be used to obtain an order of magnitude of the diameter of air bubbles. For air bubbles in water, ρ will approximate to the value of density for water of 1000 kg/m3 and μ will be about 1.002 × 10−3 Pa s. For a velocity of 0.002 m/s, derived above, this results in a bubble diameter of order 0.05 mm. A crude estimate of the bubble population caused, presumably, by disturbed water, for instance the water returning from the weigh tank into the main tank, could assume that the distribution was normal with a mean diameter of order a few millimetres. However, apart from the intuitive perception that the volume contained in such small bubbles will be negligible, there would appear to be no more substantial confirmation. The mass ratio of a bubble would be about 10−15/m3 requiring 109 such bubbles per cubic metre to equal 1 ppm in density, or one such bubble per cubic millimetre. If this amount of air entrained is to be checked, then it will probably require special instrumentation, possibly optical, to sense the presence of the bubbles. VT =
3.2. Water filter In the initial rig circuit a filter was considered necessary to protect the pump. However, the filter used caused a substantial pressure drop before the pump, and it was decided that it was probably unnecessary, except for occasional use to clean out any larger particles in the water. However, when the tank was emptied to do some modifications, it was found that there was considerable sand-like sediment in the tank. The most likely source of this appeared to be the mains water. The tank was thoroughly cleaned out, and an inlet filter fitted to filter the mains water as the tank was filled. 3.3. Algae and other water problems It was found that the glass tube of a variable area (VA) meter under test became discoloured on the inside with a deposit. The contamination was probably due to an algal growth in the water when there was no flow in the circuit. To avoid this a black cover has been used to cover the VA meter when the rig is not in use, the theory being that without light there can be no photosynthesis, and therefore no algal growth. Palmer [8] suggested two approaches for dosing the water to prevent the growth of algae. Commercial additives are also available. If any treatment is contemplated, the user should give consideration to: • the safety of the resulting dosed water; • the legality of eventual discharge of the dosed water into the disposal systems;
R.C. Baker et al. / Flow Measurement and Instrumentation 17 (2006) 171–178 Table 1 Master meters compared with weigh tank Type of meter
Special features
Manufacturer
Coriolis Coriolis
Twin tube Single tube
Manufacturer 1 Manufacturer 2
• the corrosive effect of the dosed water on the meters and other pipe work components; • the validity of the resultant calibration if the water is dosed rather than pure. Because of the problems encountered in identifying satisfactory additives and the points above, our solution was to ensure, as far as possible, that no light reached the water by entirely enclosing the circuit, and the water quality appears to be retained.
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The weigh tank has a lid with access (but not contact) to the inlet flow line. Clearly splashing occurred during the fill period, but this was, essentially, contained by the tank and lid. The weir initiation process ensured that the starting and stopping conditions were the same, and the allowance for the excess water to drip (see Section 5.4) also ensured that any spray on the nozzle was allowed to drop into the tank. We consider, therefore, that any errors due to this were negligible. For very long low flow rate runs it may be necessary to allow for evaporation. An estimate of this can be made by allowing the weigh tank, with water in it, to stand for a long period, and the weigh scale change recorded. At the maximum flow rate used by us, the run time for filling the tank is about one minute. 5.1. Correction for weight of air in weigh tank and for humidity
Being cautious as to the likely achievable accuracy from a weighing system, the original plan was to use master meters as the standard with traceable calibrations. For the first few months of the rig, this was the situation, but it was found that there was a substantial discrepancy between some of the meters, which was outside the expected uncertainty brackets. We propose to discuss this in detail in a later paper. The decision was, therefore, taken to install a weigh tank system. For the purposes of this paper we shall summarise the agreement we achieved between the weigh tank and two of the flowmeters. The meters are given in Table 1.
It is important to allow for the buoyancy of the air in the calculation of the collected mass when using the weigh scale. When the scale is tared (zeroed before the calibration run) the tank is filled with air which will be displaced with water. The mass of this air must be taken into account. This is known as the buoyancy effect, since the water in the tank is being “buoyed up” by the surrounding air. In this procedure ambient temperature and pressure are recorded and used to obtain the density of the air on the day. We reproduce the standard derivation below for completeness and clarity (cf. Refs. [9,10]). Thus the mass reading on the scale, m s , may be equated to the difference between the mass of liquid, m l , in the tank and the mass of air displaced, m a :
5. Weigh system
ms = ml − ma .
4. Reference flowmeters
It was decided to install a weigh scale and modify the pipework to allow the flow to be diverted into a weigh tank. A scale with a range up to 300 kg was bought and installed. A weigh tank suitably sized (scale capacity + about 10%) and as light as possible to avoid using scale capacity, was acquired. It was of uniform cross-section. The approach pipework at inlet to the tank was specially constructed to include a swan neck and weir to ensure that the level was the same whenever the flow was stopped. The pipework should be rigid to prevent movement from detracting from the function of the weir plate. The tank sides and the jet from the inlet nozzle were vertical. It was decided to use hand operated valves. Before starting a run, some water was allowed to enter the weigh tank to ensure that the weir was full. It appeared that the weir sat at a slightly different height for each flow rate. The method used was, then, to set the flow rate as required, then to shut the valve and to take kilogram readings on the meters. The valve into the weigh tank was then opened and about 240 kg allowed to flow into the tank before the valve was closed again. Total mass readings on the meters and the weigh scale were then obtained and the flow valve, which allowed recirculation of the water, and the weigh tank drain valve were opened. Using the hand operated valves resulted in a change of flow rate in about one second compared with the shortest run of about 60 s.
(6)
Assuming that the air density remains constant and ρa is the density of air and ρl is the density of the liquid then m s = m l (1 − ρa /ρl )
(7)
resulting in the correction factor for the weigh tank value of ρa . (8) 1+ ρl − ρa Since the density of air, ρa , is about 1.2 kg/m3 , and the density of water, ρl , is about 1000 kg/m3 , the correction factor is about 1.0012 or an adjustment of about 0.12%. Assuming a worst case of 10 ◦C error in the temperature of the air, this would cause about 3% error in the adjustment and about 0.003% uncertainty in the correction factor. An additional effect which proves to be negligible is that due to humidity. This may be calculated using the empirical formula [9] ρa =
0.348444 pambient − h(0.00252Tambient − 0.020582) (9) 273.15 + Tambient
where pambient is the atmospheric pressure in millibars, Tambient is the ambient temperature in ◦ C and h is the relative humidity as a percentage. Assuming a relative humidity of 60% and a temperature range of 15–25 ◦C the effect of neglecting humidity in the
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Fig. 2. Diagram of the flow rate variation during a calibration run.
calculation of air density is less than 1%. The effect of this on the calculation of buoyancy correction is less than 0.002%. In order to obtain rig certification it will probably be necessary to demonstrate means to obtain the density of water and air at ambient conditions. 5.2. Error due to varying flow rate While the standing start and stop weigh system eliminated time measurement related to the diverter system, it introduces variation in the flow. This is unlikely to be acceptable for meters with significantly non-linear characteristics, but will also be viewed as unacceptable where a constant flow rate is preferred for some meters and certifications. Calibration of a non-linear meter can be achieved in this rig in two steps: (i) the calibration check of the master meter; (ii) the steady flow test against the master meter. It is, therefore, important to consider the likely errors introduced by the standing start and stop. If we take a ramped increase and decrease in flow rate as shown in Fig. 2, then we can assume that the time taken to open and close the valve is t (of order one second). Assuming that the ramp up and down is essentially linear, and that we can assume that the meters are linear down to the cut-off, then Ramp up flow = Qt/2 Steady region flow = QT Ramp down flow = Qt/2 Total flow passed = Q(T + t) Unrecorded flow (%) = y 2 Qt/[100Q(T + t)] = y 2 t/[100(T + t)]. Minimum run time is about 60 s, and the valve movement is about 1 s. With the cut-off at 0.2%, the unrecorded flow will be less than 7 × 10−6 %. Small changes in t will not be important. Manufacturers will need to consider whether a low flow cut-off is implemented and for which signals. However, were the characteristic of the flowmeter non-linear at very low flow then this would introduce an error which, as an extreme, could be taken as the value of the error above, but with y equal to, say, 2%. This could result in an error of 0.0007%. The characteristic of the flowmeter under test should be checked for linearity, and the low flow cut-off level should be checked to ensure that it is sufficiently low, to make standing start and stop calibration satisfactory.
Fig. 3. The effect of heated water from the pump passing through one of the flowmeters.
For manual operation variation in the rate and time of opening and closing for a non-linear flowmeter will also have an effect which should be calculated by introducing the non-linear characteristic into Fig. 2. 5.3. Effect of temperature change due to closed valve operation The effect of running the pump against closed valve, as required in the standing start and stop procedure, could damage the pump if it continued for more than a minute or so. It will also lead to the water in the pump heating up. Taking the volume of water in the pump as approximately 50% of the impeller casing volume (50 cm long and 20 cm diameter), or 0.0075 m3 , and the closed valve period as one minute, then at a power level of 3.7 kW, the temperature rise of the pump contents will be about 7.2 ◦ C. This should have a negligible effect on the calibration. With a flow rate of 7.44 m/s the warm water should pass through each of the meters in about 2 s. Fig. 3 shows some experimental results from one of the flowmeters. The pump was held against closed valve for periods up to 10 min. The resultant temperature profile as the warm water flowed through the meter is shown. There will be an error due to the transient temperature measurement which may be of order 1 ◦ C or greater. The flow rate for these tests was 118 kg/min, about half that in the calculation above, so that the heating effect in the pump would be about 1/8 of that in the example above or about 1 ◦ C/min. This is compatible with the values in Fig. 3. However, one possible problem with the water heating, apart from the fact that mass meters will be operating with a density variation, though brief, is the danger that it could cause the cavitation boundary to be shifted enough to cause problems where the pressure is low, for instance near the outlet of the flow circuit. Cavitation was noted when two electromagnetic flowmeters with reduced bores were positioned in the final test section of the rig. Brief temperature increase could trigger cavitation in such circumstances (cf. Ref. [2] for appropriate formulae). Meters that use sensors mounted directly on to the measuring tube for measuring temperature or strain may start to apply large temperature compensations in software as a result of the increased output of the sensor. Increasingly, calibration of flowmeters now includes “characterisation” with complex algorithms used to correct flow measurement for temperature
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7. Rig uncertainty
Fig. 4. Change of weigh scale reading due to water dripping from the inlet pipe.
effects on the meter. It may, therefore, be beneficial to switch a pump bypass in and out of circuit at the beginning of test batches to eliminate this slug of warmer water. 5.4. Dripping and meniscus variation in the weir pipe The pipe leading to the weigh tank can be a source of error if the cut-off water level at start and finish of the run is not well defined. An effective method of achieving the same initial and final level is by inserting a sharp edged weir across the swan neck at outlet to the pipe. However we noted two problems: (i) the level differs between various flow rates presumably due to the change in the meniscus at the weir: this we overcame by initialising the level according to the flow rate to be used; (ii) the inlet pipe continued to drip for some minutes after the valve closed, and this affected the weigh scale reading; this effect is indicated in Fig. 4. To deal with (i), an alternative may be to increase the time taken to ramp down, so that inertia of the water is reduced for all flow rate settings. This may increase the problem identified in Section 5.2. To deal with (ii) it was necessary to compromise between waiting a long time for the dripping to end, and accepting that the pattern at the start and end of the run was similar and that a reasonable cut-off time should be selected. Too long a delay could also be a problem, since if a meter’s zero cut-off is set too low, the meter may continue to record flow at zero flow. 6. Working sections and meters installed in them Once the flow has gone through the master meters, the pipework allowed three alternative runs to be selected on top of the concrete block. These have had the following meters installed: (a) a variable area meter for tests to identify the effect of manufacturing variation in the manufacture of tubes and floats (cf. Ref. [11]); (b) an averaging pitot meter (using ganged differential pressure cells to obtain the flow rate over the range of the rig flows); (c) Coriolis meters relating to manufacturing variation.
On the basis of a review of the weigh scale calibrations over the past three years, an uncertainty of ±0.02% for the weigh scale reading appears appropriate for our tests where the total load was usually of the order of 200 kg. The tank was placed centrally and the water allowed to stabilise, so that the eccentricity errors were not relevant. There is a reading uncertainty at start and finish which amounts to ±0.002%. However, there were other uncertainties in this measurement, such as the level at the weir, the draining of pipework after flow had stopped, the measurement of the temperature of the air and the displaced air during the weigh period and the ramped flow changes. This paper has focused on some special effects which need to be taken into consideration in the design of the flow rig. We restrict consideration of uncertainties to those addressed in this paper and plan to give a fuller discussion of this in a future paper. We indicate in Table 2 the likely effects of the individual components and the overall current estimate of uncertainty resulting from these components. In particular we have neglected the possible error due to evaporation, considered negligible in these tests, and the uncertainty due to the effect of temperature change and drift in weigh scale. We have not considered problems relating to signal and data processing. In compiling Table 2 which we include as a preliminary estimate pending further work, we have not allowed for differing probability distributions. We would emphasise that in seeking national accreditation for a rig to provide a calibration standard, all such factors should be taken into consideration. We note, from Table 2, that the two meters from different manufacturers, which gave greater confidence, appear to agree well with the weigh system which is used as the datum in Fig. 5. They agree over the range to within ±0.05%. It is important to reiterate that this paper does not attempt to give a full estimate of all possible errors, or of likely achievable uncertainty. We consider that it would be misleading to attempt this in a paper which is focused, only, on certain errors. The figure obtained in Table 2 represents, only, the root sum square of the specific errors identified. (The reader is referred to Ref. [2] for a fuller discussion on the estimate of flow rig uncertainty.) In addition the uncertainty in measurement for a flowmeter calibrated on this rig will need to allow for the uncertainties of data collection etc. In this paper we have not attempted to deal with these other issues. However, flow rigs of a similar construction to that built at Cambridge have achieved accreditations from UKAS to an uncertainty in the range 0.035%–0.1% for a batch as opposed to a mass flow rate. This would appear to be a reasonable guide to what is currently achievable in terms of optimising cost and complexity. While we have targeted the paper at manufacturers who may be building rigs we would not exclude users, who may be considering their own in-house checking facility. For them, an alternative is to test against a master meter, in which case the accuracy may not be better than of order 0.1%–0.15%.
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Table 2 Uncertainties based on the observations in this paper for 200 kg ignoring probability distribution variation Source of uncertainty
Estimate of variation
Current estimate of uncertainty % (95% confidence)
Flow profile distortion Air in water Weigh scale uncertainty Weigh scale readability Buoyancy calculation Humidity error Dripping Splashing Temperature changes Ramp up and down Combined uncertainty Flowmeter uncertainty Coriolis meter uncertainty
Profiles fully developed 2 ppm 0.02% 2g 0.003% 0.002% 20 g Negligible Negligible 0.0007%
0.0000 0.0002 0.0200 0.0020 0.0030 0.0040 0.0200 0.0000 0.0000 0.0014 ±0.029 Supplied by manufacturer ±0.1000
Typical claim
of their manufacturing process. We have identified possible answers. We emphasise that the discussion has focused on certain special effects, and that advice should be sought if setting up a calibration facility on other effects which should be evaluated. Acknowledgements
Fig. 5. Primary flowmeter calibration against the weigh system.
8. Conclusions The object of this paper has been to identify and discuss some of the considerations which should be reviewed when deciding to build a flow calibration facility. These have been focused on the mechanical and hydraulic aspects of the rig. We plan to discuss other aspects in a future paper. We have: • set out the approach to loss estimation for a new design of rig, noting that unseen factors may increase the loss, and a margin of safety should be built in by slight overspecification of the pump; • discussed the reason for the main tank size and the estimation of the temperature increase; • discussed the pump and inverter, pipework and supports; • considered the worrying matter for the precision of flow measurement of the existence of air in water; • discussed the factors which need to be considered in installing a weigh tank and the errors which can result from standing start and stop methods; • provided initial results on the agreement achieved between two of the Coriolis flowmeters and the weigh system. We have identified certain special effects which we have encountered, so as to alert manufacturers to the problems which may occur when setting up a calibration rig as part
The authors wish to acknowledge the work of Gerry Franklin and other members of the maintenance and technician staff of CUED for their great help in building the rig, Dr Yousif Hussain for advice on the design and the sourcing of some components of the rig, and Samuel Mumba who carried out experimental checks on the rig. The support for this work from the Gatsby Charitable Foundation, from manufacturers who lent flowmeters, and from the Knowledge Transfer Partnership which included funding from the industrial partner, Krohne Limited, is also acknowledged. References [1] Baker RC. Variation in flowmeter manufacture: some observations and lessons. Proc I Mech E Part B J Eng Man 2004;218:961–75. [2] Baker RC. Flow measurement handbook. New York: Cambridge University Press; 2000. [3] Miller DS. Internal flow systems. Cranfield: BHRA Fluid Engineering; 1990. [4] Baker RC. An introductory guide to industrial flow. Professional Engineering Publishing; 1996. [5] Jones FE. Techniques and topics in flow measurement. Florida (USA): CRC Press; 1995. [6] Kaye GWC, Laby TH. Tables of physical and chemical constants and some mathematical functions. 14th ed. Longman; 1973. [7] Clift R, Grace JR, Weber ME. Bubbles, drops, and particles. New York (USA): Academic Press; 1978. [8] Palmer CM. Algae and water pollution—the identification, significance, and control of algae in water supplies and in polluted water. Castle House Publications Ltd; 1980. [9] Buoyancy correction and air density measurement. National Physical Laboratory, 2002, http://www.npl.co.uk/mass/guidance/buoycornote.pdf. [10] Miller RW. Flow measurement engineering handbook. New York: McGraw-Hill; 1996. [11] Baker RC. The impact of component variation in the manufacturing process on variable area (VA) flowmeter performance. J Flow Meas Instrum 2004;15(4):207–13.