1. Working Principle of Vortex Flowmeters
Vortex flowmeters operate based on the Kármán vortex street principle. The core mechanism involves detecting the frequency of vortices generated in the fluid to calculate the flow rate.
Vortex Formation: In a pipeline, a non-streamlined body (such as a cylindrical or triangular pillar) is placed. As the fluid flows past the body, vortices are alternately generated on both sides of the body, rotating in opposite directions. This phenomenon is known as the Kármán vortex street.
Relationship between Frequency and Flow Velocity: The frequency (f) of the vortices generated is proportional to the average flow velocity (v) of the fluid, and inversely proportional to the characteristic size (d, such as diameter) of the vortex generator. The relationship is given by the equation:
where
is the Strouhal number (a dimensionless constant that depends on the shape of the vortex generator and Reynolds number, and is approximately constant within a certain range of Reynolds numbers).
Flow Calculation: By detecting the vortex frequency using sensors such as piezoelectric crystals or ultrasonic sensors, and knowing the cross-sectional area (A) of the pipe, the volumetric flow rate (Qv) can be calculated:
For a specific flowmeter,
,
, and
are constants, so the volumetric flow rate is linearly related to the vortex frequency.
2. The Need for Temperature and Pressure Compensation when Measuring Steam
Steam, especially saturated and superheated steam, has a density that is significantly influenced by temperature and pressure. Since vortex flowmeters measure volumetric flow, but industrial measurement often requires mass flow (or flow at standard conditions), temperature and pressure compensation is necessary to correct for density changes. The reasons for this are as follows:
Steam Density Variation with Temperature and Pressure:
Saturated Steam: As pressure increases, the saturation temperature rises, causing a significant increase in density (e.g., at 0.1 MPa, the density is around 0.58 kg/m³, while at 1.0 MPa, it increases to approximately 5.15 kg/m³, almost a 9-fold difference).
Superheated Steam: When pressure is constant, an increase in temperature reduces the density, while at constant temperature, an increase in pressure raises the density. The density of superheated steam needs to be calculated using a superheated steam equation (such as the ideal gas law correction).
Difference Between Volumetric Flow and Mass Flow:
Vortex flowmeters measure the volumetric flow rate (Qv) under operating conditions. However, the mass flow rate (Qm) is required in industrial applications. The relationship between the two is:where
is the density of steam at the operating temperature (T) and pressure (P). If no compensation is made, changes in temperature or pressure will cause density variations, leading to errors in mass flow measurement. For example, if pressure increases without compensation, the mass flow will be underestimated.
Accuracy Requirements for Trade Settlements and Process Control:
Steam is commonly used as an energy medium, and accurate measurement is crucial for trade settlements or energy consumption statistics, typically with accuracy requirements of ±1% to ±2%. Temperature and pressure fluctuations can lead to density deviations greater than 10%, which would significantly impact measurement accuracy (such as overestimating or underestimating steam usage), thus affecting economic settlements or process control parameters (such as mismatches between steam supply and reaction demand).
3. Implementation of Temperature and Pressure Compensation
Temperature and pressure compensation is implemented by installing temperature sensors (such as platinum resistance thermometers) and pressure transmitters on the pipeline of the vortex flowmeter. These sensors collect real-time steam temperature (T) and pressure (P) data. Based on the steam’s thermal properties (e.g., saturated steam density tables, superheated steam density formulas), the flowmeter’s controller or the DCS system automatically calculates the real-time density (
), and the volumetric flow is corrected to mass flow:
Where
is a constant determined by the flowmeter’s structure.
Conclusion
Vortex flowmeters measure volumetric flow based on the Kármán vortex street principle. However, steam’s density is significantly influenced by temperature and pressure. To obtain accurate mass flow (or standard volume flow), temperature and pressure compensation is essential to correct for density variations, ensuring that measurement accuracy meets industrial requirements.