1. Introduction:
Volumetric flowmeter, also known as positivedisplacement flowmeter (PD flowmeter), is the most accurate type of flow meter.
It uses mechanical measuring elements to continuously divide the fluid into individual known volume parts.
The flow volume is measured based on the number of times the measuring chamber is filled and emptied with these volume parts.
PD flowmeters generally do not have a time reference, and an additional time measurement device is required to obtain instantaneous flow rate values.
The fixed displacement measurement method can be traced back to the 18th century, and it entered widespread commercial application in the 1930s.
2. Principle:
In principle, a PD flowmeter is a hydraulic engine that absorbs a small amount of energy from the fluid to overcome the friction of the flow detection element and attachments, while forming a pressure drop at the inlet and outlet of the instrument.
The working principle of a typical PD flowmeter (elliptical gear type) is shown in Figure 1. Two elliptical gears have a special shape that allows them to roll and make contact with each other while rotating.
P1 and P2 respectively represent the inlet pressure and outlet pressure, where P1 > P2. In Figure 1(a), the gear at the bottom rotates counterclockwise due to the pressure difference on both sides, and is the active gear.
The gear at the top does not produce a rotating torque because the pressure on both sides is equal, and it is the driven gear that is driven by the bottom gear to rotate clockwise.
When the gears reach the position in Figure 1(b), both gears continue to rotate under the differential pressure. When they reach the position in Figure 1(c), the gear at the top becomes the active gear and the gear at the bottom becomes the driven gear. The gears continue to rotate until they return to the position in Figure 1(a), completing one cycle.
One cycle of operation discharges the fluid volume of four crescent-shaped cavities enclosed by the gears and the housing, which is called the “cycle volume” of the flowmeter.
Assuming the “cyclic volume” of the flowmeter is υ and the number of gear rotations within a certain period of time is N, the volume of fluid flowing through the flowmeter during that time can be calculated as V.
Therefore, V = Nυ (1)
The rotation of the elliptical gears is transmitted to the counter through a magnetic seal coupling and a transmission reduction mechanism, which directly indicates the total amount of fluid passing through the flowmeter.
With the addition of a transmitting device and an electric display meter, remote transmission of instantaneous flow rate or accumulated flow rate can be achieved.
Although there are many methods for dividing and forming various types of PDFs, most of them have similar basic characteristics.
The main reason for the errors in PDF production is the gap leakage between the movable measuring member that divides a single fluid volume and the static measuring chamber.
One reason for the leakage is to overcome the friction of the movable member, and the other is the pressure drop caused by the hydraulic resistance of the instrument.
3. Structure
There are many varieties of PDFs with various structures, but their main components are similar. The waist wheel flowmeter is used as an example to illustrate.
It consists of a measuring section and an accumulating section, and can be equipped with automatic temperature compensator, automatic pressure compensator, transmitter, high temperature extension (cooling) component, etc. if necessary.
1）Measuring Chamber
The waist wheel flowmeter consists of a pair of rotors with conjugate curves, called Roots wheels, and a shell.
The two rotors are driven by a driving gear which is coaxially installed with the waist wheels. The measured flow drives the rotors to rotate, and the rotors drive each other through the driving gear.
The waist wheels and the measuring chamber shell are generally made of cast iron, cast steel, or stainless steel, and the material should be selected according to the corrosiveness of the fluid and its working pressure and temperature.
The measuring chamber can also be made separately and separated from the instrument shell so that the measuring chamber does not bear static pressure, eliminating additional errors caused by deformation due to static pressure.
2）Transmission Mechanism
The transmission mechanism includes a magnetic coupling (or mechanical seal device) and a reduction gear mechanism. The speed adjustment mechanism is composed of gear pairs.
3）Accumulator and Indicator Head
There are many types, including pointer type and digital type indicators, with or without reset counters. Some models also have instantaneous flow rate indication, printers, and setting parts, etc.
4）Automatic Temperature Compensator
It provides continuous automatic compensation for the effect of temperature changes on the measured medium, and can be mechanical or electronic.
5）Automatic Pressure Compensator
It automatically corrects the influence of static pressure changes on the measured medium.
6）Transmitter
The transmitter comes in many forms, including contact and non-contact types.
4. Advantages
PDFs have high measuring accuracy, with a basic error of generally ±0.5%R, and can reach ±0.2%R or higher for special applications. They are usually used for expensive media or situations that require precise measurement.
PDFs do not affect the measuring accuracy in rotating flows and when the velocity field is distorted by flow obstructions in pipes, and do not require a straight pipe section upstream.
This is important in field use. PDFs can be used for measuring high viscosity fluids. The rangeability is wide, generally 10:1 to 5:1, and can reach 30:1 or higher for special applications.
PDFs are direct-reading instruments that do not require external power and can directly obtain cumulative total amounts, which are clear and easy to operate.
Compared with the derivation of volume flowmeters, such as velocity-type meters, in the indirect method of mass flow measurement using volume flowmeters, the volume measured by PDFs is a direct geometric quantity, and the factors affecting the volume are simpler.
In high-pressure natural gas measurement where density measurement is not feasible, PDFs can be used to indirectly determine the compressibility factor of the gas, which is difficult to handle.
5. Disadvantages
PDFs have a complex structure, large volume, and are bulky, especially for large-diameter PDFs, which are generally only suitable for medium and small diameters.
Compared with other types of flow meters, such as differential pressure, float, and electromagnetic meters, PDFs have greater limitations on the type and working conditions (temperature, pressure) of the measured medium, and are more limited in their adaptability.
Due to issues such as thermal expansion and deformation of parts at high temperatures, and embrittlement of materials at low temperatures, PDFs are generally not suitable for high and low-temperature applications.
The temperature range of use is currently approximately -30 to +160℃, and the maximum pressure is 10 MPa.
Most PDF instruments are only suitable for clean single-phase fluids. When the fluid contains particles or dirt, a filter needs to be installed upstream, which increases pressure loss and maintenance work.
For measuring liquids containing gas, a gas separator must be installed.
PDFs have poor safety. If the moving parts are jammed during operation, the fluid cannot pass through, and the flow system cannot be used.
However, some design structures (such as the Instromet waist wheel flowmeter) have a bypass installed in the shell. When the moving element is stuck, the fluid can pass through the bypass.
Some forms of PDF instruments (such as elliptical gear, waist wheel, and rotating piston) will cause flow pulsation during the measurement process, and larger diameter instruments will also produce noise and even vibrations in the pipeline.
6. Classification
PDFs come in many varieties and can be classified according to different principles. They can be classified into the following types based on the structure of the measuring element:
1）Rotor type
2）Scraper type
3）Rotary piston type
4）Diaphragm type, etc.
1 – Liquid inlet; 2 – Baffle; 3 – Liquid outlet; 4 – Piston shaft; 5 – Measuring chamber shaft; 6 – Measuring chamber; 7 – Rotary piston.
（4）Diaphragm Type
In contrast to the wet-type gas meter described above, the diaphragm-type meter is also known as a dry-type meter.
Due to its widespread use in household gas consumption measurement, it is also commonly known as a household gas meter, but in reality, larger meters in this series are used for industrial processes in factories and mines.
The working principle is shown in Figure 4, which consists of a measuring chamber with a flexible diaphragm that can freely expand and contract (1, 2, 3, 4), and a flow measuring element composed of a sliding valve linked to the measuring chamber.
Under the action of the diaphragm and sliding valve, gas is continuously sent from the inlet to the outlet, and the volume passed through can be obtained by measuring the number of cycles of this action.
According to the OIML International Recommendation No. 31 “Diaphragm Gas Flowmeters,” there are 14 specifications with a wide range of flow rates from 0.016 to 1000 m3/h and a rangeability of up to 100:1. The meter has medium measuring accuracy, with an error of ±(2-3)%R.
7. Considerations for Selection
7.1 Application Overview
PDFs are used in industrial sectors such as petroleum, chemicals, coatings, pharmaceuticals, food, and energy to measure the total amount or flow rate of expensive media.
In these process industries, they are used for metering the injection, extraction, or mixing ratio control of liquid medicines, the quantitative injection of additives such as catalysts, hardeners, and anti-polymerization agents in chemical fluids, the addition of fragrances to food fluids and cosmetics, and the quantitative supply of paint in coating lines.
The greatest use of PDFs is in the measurement of the storage, transportation, transfer, and distribution of petroleum products, which can serve as the basis for financial accounting or as the legal measurement for tax and contract execution by both buyers and sellers.
High-quality PDFs with high accuracy, long-term performance stability, and good repeatability are used as reference flow meters or master flow meters for flow value transfer in comparative flow standard devices.
While PDFs are relatively large and cumbersome, especially for large flow rates and diameters, they have gradually been replaced by turbine, electromagnetic, vortex, and Coriolis mass flow meters in some applications.
However, PDFs still maintain their performance advantages such as excellent repeatability and long-term performance stability, and will not be fully replaced by other meters in foreseeable future in many applications.
PDFs are also widely used for liquefied petroleum gas abroad and are in the initial stage of development in China.
7.2 Factors to Consider When Selecting
According to the characteristics of the PDF, the following factors should be considered:
1）Is the purpose for process control/engineering management or storage/transportation transfer/commercial accounting?
2）Is the operation continuous or intermittent measurement? What are the maximum flow rate, common flow rate, and minimum flow rate used?
3）What are the maximum, common, and minimum working temperatures and pressures, and what is the allowable pressure loss?
4）The type and characteristics of the measured medium, including viscosity, corrosiveness, the amount of entrained solids, and particle size.
5）What calibration method will be used for the flowmeter, offline or on-site calibration?
6）The type, capacity, and pulsation of the pipeline pump.
7）The available space for installation.
7.3 Flow Range, Turndown Ratio, Accuracy, and Repeatability
Manufacturers typically define the flow range based on the type of measured medium (with viscosity being the main differentiator), usage characteristics (continuous or intermittent), and measurement accuracy.
To maintain good instrument performance and longer service life, the maximum flow rate for continuous use is recommended to be set at 80% of the upper limit of the instrument’s highest flow rate.
If the manufacturer does not explicitly specify the suitable flow range according to the medium type and usage characteristics, the following principles can be used for selection:
- For instruments used for medium viscosity lubricating oil, the upper limit flow rate is set at 100%;
- For low viscosity liquids without lubrication (such as gasoline and liquefied petroleum gas), the upper limit flow rate is reduced to 70%-80%;
- For water at around 100℃, it is 40%-60%; for high viscosity liquids, it is 75%-85%.
The maximum flow rate for intermittent use can be set at 100% of the upper limit flow rate, while for continuous use, it is 80% for medium viscosity liquids, 50%-60% for low viscosity liquids, and 50%-60% for high viscosity liquids.
For most structural types of liquid flowmeters, the basic error is ±0.5% R; for higher accuracy instruments, the basic error is ±(0.1~0.2)% R, such as elliptical gear type, and a few manufacturers claim that it can reach ±0.05% R (such as Dresser Wayne’s scraper type).
The basic error for lower accuracy instruments is ±(1-1.5)% R (such as elastic scraper type). The accuracy of gas flowmeters is slightly lower, with most structural types being ±(1-1.5)% R (such as the waist wheel type and CVM type), the higher accuracy ones being ±0.5% R (such as the same conversion type), and the lower accuracy ones being ±(2-2.5)% R.
The repeatability error is generally 1/5 to 1/2 of the basic error.
In all flowmeters, the PDF is the highest accuracy type. The basic error specified in the manufacturer’s specifications is obtained through calibration under laboratory reference conditions. Actual usage conditions often deviate from the reference conditions, inevitably causing additional errors.
The actual error should be the composite of the basic error and the additional error. Measures should be taken in selection and use to address potential problems in the field to maintain good measurement accuracy. The turndown ratio is typically between 5:1 and 100:1, with most falling between 10:1 and 20:1.
When an instrument is rated at a higher accuracy level, the turndown ratio obtained is lower. To achieve a larger turndown ratio, the accuracy level must be lowered. For example, the basic error for a range of 5:1 for various rotor-type liquid flowmeters is ±0.2% R, while for a range of 10:1, it drops to ±0.5% R.
7.4 Pressure Loss
The PDF relies on fluid energy to drive the measuring element, resulting in a relatively high pressure loss. The pressure loss of the PDF is higher than that of the same caliber and flow rate of a turbine or other flowmeter that impedes flow.
For liquid flowmeters, at maximum flow rate with a viscosity of 1-5 mPa.s, the pressure loss is between 20-100 kPa.
For low-pressure gas flowmeters, the waist wheel type is 200-500 Pa, and the membrane type is 130-400 Pa.
To select the correct instrument, it is important to avoid unacceptable pressure loss, especially when measuring high vapor pressure liquids. Excessive pressure drop can cause cavitation, which can damage the components.
For instruments that allow short-term overflows up to 120% of the measuring upper limit, this issue should be given special attention.
7.5 Fluid Corrosivity
The corrosivity of the fluid is the main factor in determining the material of the instrument.
Cast steel and cast iron are used for various petroleum products, copper alloys are used for slightly corrosive chemical liquids and cold and hot water, and stainless steel is used for pure water, hot water, crude oil, asphalt, high-temperature liquids, chemical liquids, food, or food raw materials.
The corrosion resistance of the PDF is not its strong suit.
In the food and biopharmaceutical industries, flowmeters require frequent cleaning, disinfection, and sterilization to meet hygiene requirements.
Parts in contact with the fluid must be made of stainless steel or other materials that meet hygiene requirements, and the structure should be easy to disassemble and have no liquid retention areas.
Elliptical gear and rotary piston flowmeters have already been developed for the food industry in China.
7.6 Impact of Liquid Viscosity on Instrument Performance
The viscosity of various gases is similar and does not vary much, so it has little impact on instrument performance.
However, if the viscosity of the liquid varies significantly, it will have a certain impact on instrument performance.
Some PDFs are designed with larger clearances to accommodate liquids with viscosities as high as 500 mPa.s.
PDFs have extensive experience in high viscosity liquids and are widely used in flow meters.
Although PDFs are affected by some liquid viscosities, the impact is much smaller than that of differential pressure, float, and turbine flow meters.
Viscosity has three main effects on PDF performance: measurement error, pressure loss, and flow range.
(1) Impact on Measurement Error
PDF has a different characteristic from many other flowmeters, in that as viscosity increases, clearance leakage decreases, which improves performance.
(2) Impact on Pressure Loss
As liquid viscosity increases, PDF’s pressure loss also increases. The relationship between pressure loss Δp and flow rate q can be expressed as Δp = kqn (where k is a coefficient and n is an index).
When viscosity is below 0.005 Pa.s (= 5 mPa.s), n = 2; when it is above 0.5 Pa.s (= 500 mPa.s), n = 1; and when it is between these two values, n = 1.9 to 1.1.
When the movable measuring element is used in high viscosity liquids, the load increases, and the pressure loss increases.
Special flowmeters for high viscosity liquids typically use larger clearances, up to 0.5 mm.
Elliptical gear flowmeters reduce the load on the liquid between gear teeth by adding grooves to the gear teeth (when viscosity is ≥150 mPa.s).
For viscosity greater than 500 mPa.s, elliptical gears with fewer teeth are used.
(3) Impact on Flow Range
As viscosity increases, pressure loss increases, and the upper limit of flow rate must be lowered to limit pressure loss in locations where pressure loss is limited.
Flow rate lower limits decrease with increasing viscosity, which expands the flow range.
As a rough estimate, as viscosity increases by a factor of 10, the lower limit of flow rate decreases to 1/10 to 1/3 of its original value.
7.7 Pressure and Temperature
All flow meters have a specified working temperature range and maximum working pressure.
The maximum working pressure refers to the pressure that the flow meter can withstand at room temperature and under shock pressure.
When used at higher temperatures, the maximum working pressure level must be reduced. Some product manuals do not specify this.
Rapid valve closing or opening can produce water hammer effects and other shock pressures, which may exceed the working pressure and even cause reading errors.
In this case, a buffer tank should be installed to reduce the impact of this defect.
Temperature affects flow meters not only by the pressure strength but also by the thermal expansion of the measuring element, which changes the size of the measuring chamber and gaps, affecting measurement accuracy, reducing gaps, and even causing the moving parts to jam.
Therefore, special gap sizes must be reserved for use at higher temperatures to compensate, especially when using different material combinations, which need to consider the differences in thermal expansion coefficients.
Temperature changes can also change the viscosity of the liquid and cause changes in the flow indication.
The size change of the measuring element caused by temperature changes changes the volume of the measuring chamber.
For example, for an elliptical gear flow meter with a measuring chamber and gears made of cast iron, the measurement value changes by +0.33% per 10°C, and for a measuring chamber made of cast iron and gears made of cast aluminum, it changes by +0.14% per 10°C.
Automatic temperature compensation can be used to adjust the change in measuring chamber volume to a designated standard temperature (such as 20°C) by using an output transmission ratio adjusting device.
When a high-temperature fluid enters a cold flow meter and is started before reaching thermal equilibrium, it may increase measurement errors due to the large gap. If the temperature exceeds the specified value, the moving measuring element may be jammed.
Therefore, appropriate preheating time should be provided before use, and observation should be made to ensure that the flow meter operates normally.
7.8 Compression Factor
Usually, the compressibility of liquids can be ignored, but it should not be neglected when measuring oil with high precision.
The compressibility coefficient of oil products listed in API Standard 1101 is between (5-20) × 10-4 / MPa.
For example, the volume compression is 0.45% when heavy oil pressure is increased from 0.5 MPa to 6 MPa. The compressibility of liquefied petroleum gas is even greater.
Gases have a high compressibility. At low pressure, their volume decreases in proportion to the increase in pressure, and most PDFs are applied under low-pressure conditions and can be directly converted.
However, at high pressures, the volume decrease is not proportional to the increase in pressure, and the rate of change decreases, so the compressibility factor of the gas should be considered.
8. Installation Precautions
8.1 Installation Location
The flowmeter installation should be in a suitable location, and the following points should be considered:
1）The ambient temperature and humidity should meet the manufacturer’s specifications, with a temperature range of -10 (-15) to 40 (50) ℃ and humidity of 10% to 90%.
2）Direct sunlight can cause temperature increases in the summer, and locations close to radiant heat can also cause temperature increases. Sun shading or heat insulation measures should be taken in such locations.
3）Non-dust-proof and non-waterproof instruments should avoid corrosive or humid environments, as components such as the odometer reduction gear can be damaged by corrosive gases and temperature fluctuations. If it cannot be avoided, clean air can be blown into the internal cavity to maintain a slight positive pressure.
4）Avoid locations with vibration and shock.
5）Adequate space should be available for installation and routine maintenance.
8.2 Installation Orientation, Flow Direction, and Pipe Connection
The installation orientation of PDF must be level and vertical, with the rotor axis parallel to the ground (except for vertical structure rotor axis design).
Other models should be installed according to the instructions, usually horizontal.
If installed vertically, it should be installed in a bypass pipe to prevent dirt from falling into the flowmeter from above the pipeline.
The actual flow direction should be consistent with the direction indicated on the flowmeter housing. PDF generally can only measure the flow in one direction.
If necessary, a check valve should be installed downstream to prevent damage to the flowmeter.
To prevent the flowmeter from being subjected to pipeline expansion, contraction, deformation, and vibration, it is necessary to prevent vibration generated by the system due to unreasonable valve and pipeline design, especially to avoid resonance.
During installation, the flowmeter should not be subjected to stress, such as when the flange surfaces of the upstream and downstream pipelines are not parallel, the flange surface distance is too large, the pipeline is not concentric, and other unreasonable pipeline layouts.
Especially for PDF with no separated measuring chamber, but with a pressure-resistant shell and measuring chamber integrated, attention should be paid to the installation orientation because excessive installation stress may cause deformation, affecting measurement accuracy, and even causing the movable measuring element to jam.
8.3 Preventing the entry of foreign phase fluids into the instrument
The measuring chamber and the moving detection parts of the PDF have very small clearances, and impurities in the fluid can affect the normal operation of the instrument, causing jamming or premature wear.
A filter must be installed upstream of the instrument and cleaned regularly when measuring liquid flow.
When measuring gas flow, protective equipment such as sediment traps or water absorbers should be considered if necessary.
When measuring liquid flow, gas entering the pipeline system must be avoided, and a gas separator should be installed if necessary.
8.4 Reducing the harm of pulsating flow, shock flow, or overload flow
Although there are successful examples of installation at the suction end of the pump, the instrument should be installed at the outlet end of the pump.
Pulsating and shock flows can damage the PDF, and the ideal flow source is a centrifugal pump or high-level tank. If it is necessary to use a reciprocating pump, or the pipeline is prone to overload shock, water hammer shock, or other shock flows, protective devices such as buffer tanks, expansion chambers, or safety valves should be installed.
Overloading and overspeed operation of the PDF can cause irreparable harm. If the pipeline system is likely to exceed the flow rate, protective facilities such as a flow limiter, a fixed flow valve, or a flow controller should be installed downstream.
8.5 Continuous flow installation
Due to the drawback of pipeline interruption caused by the damage of the PDF measuring element, in continuous production or in places where flow interruption is not allowed, automatic switching devices should be equipped with redundant systems connected in parallel, or the instruments can be operated in parallel so that one can still be used if the other fails.
8.6 Field calibration
If a PDF needs to be calibrated with standard flow devices such as standard volume tubes or standard meters on-site, branch pipes, connecting fittings, and stop valves should be pre-installed at appropriate locations on-site.
9. Usage Precautions
1）Cleaning pipelines:
New pipelines should be cleaned before operation, often followed by flushing with real flow to remove residual weld slag and scale.
At this time, the front and rear shut-off valves of the instrument should be closed, and the fluid should flow through the bypass pipe. If there is no bypass pipe, a short pipe should be installed in place of the instrument.
2）Exhausting gas:
Usually, after the actual liquid flow sweep, there is still a lot of air in the pipeline. As the pressure increases during operation, the air flows through the PDF at a high velocity, and the moving measuring element may rotate too quickly, damaging the shaft and bearings.
Therefore, the flow rate should be gradually increased at the beginning to gradually release the air.
3）Switching order of bypass pipe:
When the liquid flow is switched from the bypass pipe to the instrument, the opening and closing should be slow, especially on high-temperature and high-pressure pipelines.
When starting up, the first step is to slowly open valve A, and the liquid first flows in the bypass pipe for a period of time.
The second step is to slowly open valve B, followed by slowly opening valve C in the third step.
In the fourth step, slowly close valve A. When closing, operate in reverse order.
After starting up, confirm that the excessive flow has not been reached through the lowest pointer or dial and stopwatch, and the optimum flow rate should be controlled at (70~80)% of the maximum flow rate to ensure the service life of the instrument.
4）Checking the filter:
The filter screen is most likely to be broken when a new line is started, and the screen should be checked for integrity in time after trial operation.
At the same time, when the filter screen is clean and free of dirt, record the pressure loss under normal flow rate, and the degree of pressure loss increase in the future can be judged to determine if it needs to be cleaned, without removing and checking the blocked condition of the screen.
5）Measuring high-viscosity liquid:
For high-viscosity liquids, they are generally heated to make them flow. When the instrument is stopped, the internal liquid cools and thickens.
When it is started again, it must be heated first and wait for the viscosity of the liquid to decrease before allowing it to flow through the instrument, otherwise the moving measuring element may be stuck and damage the instrument.
6）Adding lubricating oil:
For gas-used PDF, lubricating oil must be added before starting up, and the oil level gauge for the lubricating oil quantity should be checked frequently during normal operation.
7）Avoid sharp flow rate changes:
When using a gas turbine flow meter, sudden changes in flow rate (such as using a fast-opening valve) should be avoided.
Due to the inertia of the turbine, sudden changes in flow rate will produce significant additional inertia forces, which may damage the rotor.
When used as a measuring instrument for a control system, if the downstream control suddenly shuts off the flow, the rotor cannot stop for a while, producing a compressor effect, causing the downstream pressure to rise, and then flow backward, resulting in an error signal.
8）Flushing pipelines with steam should not pass through the PDF.
