What Are Positive Displacement Flow Meters?

What is positive displacement flow meter?

Positive Displacement Flowmeter, also known as a PD flowmeter, is one of the most accurate types of flow measurement instruments. It operates by using mechanical measuring elements to continuously divide the fluid into discrete, known volume segments. The total volume of fluid is measured based on the number of times these segmented volumes are successively and repeatedly filled and discharged from the metering chamber. PD flowmeters typically do not have an inherent time reference; thus, an additional time-measuring device is required to determine the instantaneous flow rate. The positive displacement measurement method dates back to the 18th century and became widely adopted for commercial use in the 1930s.  

Featured PD Flow Meters

What is Principle of positive displacement flow meter ?

From a working principle perspective, a Positive Displacement flowmeter essentially functions as a hydraulic motor that extracts a small amount of energy from the fluid. This energy is utilized to overcome the frictional resistance of the rotating measuring element and associated components, while simultaneously creating a pressure drop between the inlet and outlet of the meter.

The working principle of a typical PD FLOW METER (oval gear flow meter) is illustrated in Figure 1. The two oval gears have a unique profile that allows them to rotate in rolling contact with each other. Here, p₁and p₂represent the inlet and outlet pressures, respectively, with p₁> p₂under normal operation.

     In Figure 1(a):

     The lower gear is subjected to a pressure differential, generating a counterclockwise torque and acting as the drive gear.

The upper gear experiences equal pressure on both sides, producing no rotational torque and thus functions as the driven gear, rotating clockwise under the lower gear’s motion.

     In Figure 1(b):

     Both gears develop rotational torque due to the pressure difference, continuing their motion.

     In Figure 1(c):

     The upper gear now becomes the drive gear, while the lower gear turns into the driven gear.

Upon completing a full cycle (returning to the position in Figure 1(a)), the gears discharge four crescent-shaped fluid volumes formed between the gears and the chamber wall.

This discharged volume per cycle is termed the “displacement volume” of the flowmeter.

Let v be the displacement volume (cycle volume) of the flowmeter, and N be the number of gear rotations within a given time period. The total fluid volume V passing through the flowmeter during that period is then calculated as:

The rotation of the oval gears is transmitted to the counter through a magnetic coupling and gear reduction mechanism, directly displaying the total volume of fluid that has passed through the flowmeter. When equipped with a signal transmitter and paired with an electronic display instrument, the system can enable remote indication of either instantaneous flow rate or cumulative total flow.

Although various Positive Displacement Flowmeters (PD flow meters) employ different segmentation methods, most share similar fundamental characteristics. As shown in Figure 2, curve c represents the flowrate-error profile common to most PD flow meters (excluding rotary wet gas meters). The primary source of measurement error in PD flow meters stems from clearance leakage between the moving measuring element and stationary measuring chamber.

 Mechanisms of Leakage Formation:

     1.Friction-Induced Leakage:

• Required to overcome frictional resistance of moving parts
• At zero flow (p₁= p₂), leakage initiates when downstream valve opens slightly
• Fluid bypasses through clearances until pressure differential overcomes static friction

     2.Hydraulic Resistance Leakage:

• Proportional to flowrate due to increasing pressure drop (Δp ∝ Q)
• Dominates at higher flowrates as shown by curve b

     Quantitative Example:

     For a DN40 oval gear flowmeter measuring 3–4 mPa·s viscosity liquid:

• Maximum rated flow: 15 m³/h
• Friction-induced leakage: 60 L/h (constant)
• Hydraulic leakage increases linearly with flow

     Error Compensation:

• Curve a: Friction error diminishes with flowrate (leakage becomes negligible at higher flows)
• Curve c: Composite error (a + b) forms the characteristic “saddle-shaped” profile
• Calibration adjusts gear ratio to shift reference line (O’-O’ → O-O), confining errors within specified tolerance

If the frictional leakage of the flowmeter increases, curve a shifts rightward to a’; if clearances widen, the hydraulically-induced leakage rises, causing line b to steepen as shown by b’. The composite characteristic curve consequently deteriorates with increased error. This explains how prolonged use degrades meter performance due to:

     1.Increased friction from aging components

     2.Enlarged clearances from wear/corrosion

Changes in fluid (typically liquid) viscosity will also alter the characteristic curves. If viscosity decreases: curve a shifts rightward to position a’, and line b tilts downward as shown by b’. If viscosity increases: curve a shifts leftward, and line b becomes flatter. This demonstrates how liquid viscosity affects the measurement performance of the flowmeter.

Structure of positive displacement flow meter

Positive Displacement Flowmeters (PD flow meters) exhibit a wide variety of models and structural designs, yet their core components remain fundamentally similar. This section uses the Roots-type flowmeter as a representative example for illustration.

Structural Overview

As shown in Figure 3, the Roots flowmeter consists of two primary assemblies:the measuring unit and totalizing unit.Optional accessories may include:automatic temperature compensators , automatic pressure compensators, signal transmitters, high-temperature extension (heat dissipation) modules.

1) Measuring Chamber:

The Roots-type flowmeter consists of a pair of lobe rotors and a housing.These two lobe rotors are conjugate-curve rotors, known as Roots rotors.Drive gears are mounted coaxially with the lobe rotors.The measured fluid drives the rotors to rotate, while the rotors are mutually synchronized through these drive gears.The lobe rotors and measuring chamber housing are typically constructed from cast iron, cast steel, or stainless steel.

Material selection depends on the fluid’s corrosivity, operating pressure, and temperature requirements.Some designs feature an independently manufactured measuring chamber that is structurally isolated from the main meter housing.This configuration prevents the measuring chamber from bearing static pressure, thereby eliminating measurement errors caused by pressure-induced deformation.

2) Transmission Mechanism:

The transmission system consists of magnetic coupling (or mechanical seal assembly) and gear reduction unit. Speed adjustment mechanism is composed of gear pairs.

3) Totalizer & Indicator Head:

Multiple configurations are available, including analog (pointer-type) indicators and digital (numeric) displays, configurations with non-resettable totalizers and resettable counters.There are also Instantaneous flow rate display, integrated ticket printers, programmable preset units, and so on.

 4) Automatic Temperature Compensator:

Provides continuous real-time compensation for measurement errors induced by process fluid temperature variations,including mechanical and electrical electronic types.

 5) Automatic Pressure Compensator:

Automatically corrects measurement deviations caused by static pressure variations in the process fluid.

 6) Signal Transmitter:

There are various forms of transmitters, including contact and non-contact types.

Advantage of positive displacement flow meter

• Positive Displacement Flowmeters (PD flow meters) exhibit high metrological accuracy, with a fundamental error typically within ±0.5% of reading (R). Specially calibrated models can achieve ±0.2%R or better, making them ideal for high-value fluids or custody transfer applications requiring precision.

• PD flow meters maintain metrological accuracy unaffected by swirling flows or flow profile distortions caused by pipeline obstructions (e.g., valves, elbows), requiring zero upstream straight pipe runs—a critical advantage in field installations.

• PD flow meters are suitable for high-viscosity fluid measurement, offering a turndown ratio typically ranging from 10:1 to 5:1, with specialized models achieving 30:1 or higher. We can see positive displacement flow meter can measure high viscosity fluids, like bitumen, resin, paint, molasses and so on.

• PD flow meters are direct-reading instruments that require no external power, providing instantaneous cumulative totals with unambiguous readability and user-friendly operation.

In indirect mass flow measurement using a combination of volumetric flow meters, compared with velocity derived volumetric flow meters, PD FLOW METER yields a direct geometric quantity of volume, and the factors affecting the volume quantity are simpler. In high-pressure natural gas measurements that are not suitable for density measurement, the compressibility coefficient of gases that are difficult to handle can be indirectly obtained using PD FLOW METER.

Disadvantages

• Positive Displacement Flowmeters (PD flow meters) feature complex mechanical structures and large physical dimensions, with particularly bulky designs in larger sizes, thus primarily recommended for small-to-medium pipe diameters.

• Compared to other general-purpose flowmeters (e.g., differential pressure, variable area flow meters, electromagnetic flow meters), PD flow meters demonstrate more restrictive applicability in measured fluid types (limited to clean, lubricating liquids/gases) ; process conditions (narrower temperature/pressure ranges) and pipe diameter options , resulting in a significantly smaller operational applications. For example , we can make 20 inches magnetic flow meters, but the max size for PD flow meter is around 12 inches.

• Due to thermal expansion and deformation of components under high temperatures and material embrittlement issues at low temperatures PD flow meters are generally not recommended for extreme temperature applications .The current operable temperature range is approximately -30°C to +160°C with a maximum pressure rating of 10MPa.

• Most PD flow meter instruments are exclusively suitable for clean, single-phase fluids. For fluids containing particulates/contaminants, upstream filtration is mandatory. This introduces both additional pressure loss and maintenance workload; for gas-entrained liquid measurement, installation of a gas eliminator is compulsory.

Positive displacement flow meter types

Rotary-type meters are the most widely used in positive displacement flow meters, with representative models including oval gear flow meters, Roots flow meter, round gear flow meters, helical screw, and sliding vane types, as illustrated in Figure 4.

The operational principle of the oval gear type (Figure 1) has been previously discussed. The remaining configurations are illustrated in Figure 4. Among rotary-type meters, all designs except oval gear and round gear types require a pair of drive gears (refer to Figure 3) for synchronized rotation. These rotor type PD flow meters measuring elements with drive wheels maintain clearance between the rotors without direct contact, and have good resistance to particle interference, unlike elliptical gear type and circular gear type measuring elements that are prone to abrasion when in direct contact.

In addition to the radial inflow perpendicular to the rotor axis shown in Figure 4 (where fluid enters at 90°to the shaft),helical screw PD flowmeters also feature axial inflow parallel to the screw axis (Figure 5).

 Two additional screw-type configurations exist (Figure 6):

(a) Radially-fed rotors with asymmetric profiles (one grooved, one ribbed),

(b) Axially-fed matched rotor pair. Radial inflow is typically used for smaller lines (DN15-DN80), while axial inflow suits larger pipes.

The current production flow sensor sizes range in China: oval gear type flow meter is 6-250mm ( that is 1/4 “ to 10 inches) ; lobe-type is 15-500mm, gas type is 25-600mm; screw-type liquid type is 40-400mm.