Calorimetric Flow Meters – Measurement Principle, Applications, and Selection

A calorimetric flow meter or calorimetric flow monitor is a device used to measure or monitor the flow of liquids and gases. The measuring principle of calorimetric flow meters is based on heat transfer between a heated sensor and the flowing medium.

In this process, a sensor in the measuring tube or pipeline is specifically heated. The flowing medium carries heat away from the sensor, thereby cooling it.
The higher the flow rate, the more heat is removed by the flowing medium.
The resulting cooling—or the heating power required to maintain a defined temperature— serves as a measure of the flow rate.

Depending on their design and application, calorimetric measurement methods can be divided into various methods and device classes:

• Calorimetric flow meters and flow monitors
  for measuring and monitoring liquids and gases
• Thermal mass flow meters and controllers
  for the direct measurement of mass flow, particularly of gases
• Thermal anemometers
  for determining the flow velocity of gases

The devices have no moving parts in the measuring tube and are characterized by high reliability and low maintenance requirements.

Measuring Principle of a Calorimetric Flow Meter

The measuring principle of a calorimetric flow meter is based on heat transfer between a heated sensor and the flowing medium.
Thermal flow measurement utilizes the physical property that a body with a higher temperature transfers heat to its cooler surroundings. In the case of a flowing medium, the heat emitted by the sensor is carried away by the flow.

The heat output of a heated sensor depends, among other things, on the temperature difference between the sensor and medium, the thermal properties of the medium (thermal conductivity, specific heat capacity, density), and the flow. As the flow rate increases, more heat is dissipated from the sensor.
This relationship is detected by the evaluation electronics and used to determine or monitor the flow rate.

The basic principle of calorimetric and thermal flow measurement can be explained in three simple steps:

1. Heating
   A sensor or heating element is heated electrically.
2. Heat dissipation
   The flowing medium absorbs heat from the sensor and carries it away.
3. Evaluation
   The cooling, the temperature difference, or the required heating power is measured, and the flow rate or mass flow rate is determined from this.

Evaluation Methods for Calorimetric Flow Measurement

Various methods are used to evaluate the heat transfer caused by the flow. Depending on the sensor design and the electronic evaluation system, methods used include measurement at constant heating power , measurement at constant temperature difference, and the interval or heating method.

Measurement with Constant Heating Power

In the method using constant heating power, two sensors are used.

• Sensor 1
  measures the temperature of the flowing medium and serves as a reference sensor
• Sensor 2
  is heated with a constant electrical power.

Because it is heated, Sensor 2 is warmer than the surrounding medium. This creates a temperature difference between the two sensors. The flowing medium carries heat away from the heated Sensor 2.
As the flow velocity increases, more heat is carried away from the heated sensor. At a constant heating power, this causes the temperature of the heated sensor to drop, and thus the temperature difference between Sensor 1 and Sensor 2.
The measured temperature difference is therefore a measure of the flow velocity or flow rate.
However, the relationship between the temperature difference and flow rate is not strictly linear and depends, among other factors, on the sensor design and the thermal properties of the medium.
The method can be implemented with a relatively simple design. Since the measurement is influenced by the temperature of the medium and its thermal properties, appropriate compensation or calibration is required for the specific application. In older calorimetric flow meters, the two temperature-dependent resistance sensors were part of a Wheatstone bridge circuit for signal evaluation. In this configuration, the bridge signal is evaluated directly to determine the temperature change or temperature difference caused by the flow.
In modern sensors, the Wheatstone bridge is often replaced by integrated electronic circuits and digital signal processing.

Measurement at a constant temperature difference

In the constant-temperature method or when measuring with a constant temperature difference , two sensors are also used.

• Sensor 1
  measures the temperature of the medium and serves as a reference.
• Sensor 2
  is electrically heated.

The evaluation electronics continuously measure the temperature difference between the two sensors. An electronic control loop regulates the heating power of Sensor 2 so that the specified temperature difference between Sensor 1 and Sensor 2 remains constant.
If the flow velocity increases, the flowing medium carries more heat away from Sensor 2.
To keep the set temperature difference constant despite this, the heating power must be increased.
The heating power required to maintain the constant temperature difference is thus a measure of the flow velocity and flow rate.
The greater the flow rate, the more electrical heating power must be supplied to the heated sensor.
The constant-temperature method enables a rapid response to changes in flow and is used in particular with thermal flow sensors and thermal mass flow meters. The actual measurement characteristics depend on the sensor design, the medium, and the operating conditions. In older calorimetric flow meters, the two temperature-dependent resistance sensors were part of a Wheatstone bridge circuit for signal evaluation. The bridge signal serves as the actual value for a control loop that adjusts the heating power so that the specified temperature difference remains constant
In modern sensors, the Wheatstone bridge is often replaced by integrated electronic circuits and digital signal processing.

Interval Method – Periodic Heating and Cooling

This method requires only one sensor, which is alternately heated and then cooled again by the flow of the medium.
During the heating phase, the sensor is specifically brought to an elevated temperature. The heater is then turned off. The flowing medium now carries the stored heat away from the sensor and cools it down again.
The cooling rate of the sensor depends on the flow velocity.
At higher flow rates, more heat is carried away from the sensor per unit of time. The sensor therefore cools down faster and reaches its initial temperature or a defined temperature value in a shorter amount of time.
The evaluation electronics record the temporal progression of the cooling process. For this purpose, for example, the cooling time, the temperature change within a defined time interval, or the slope of the cooling curve can be evaluated.
To determine the relationship between cooling behavior and flow velocity, under defined conditions and for various temperatures, characteristic curves or maps are determined and stored in the evaluation electronics. During subsequent measurements, the actual measured cooling curve is compared with these stored characteristic values. From this, the electronics calculate the flow velocity or flow rate.
Since cooling is also influenced by the thermal properties of the medium, the determined curves apply only to a specific medium.

Comparison of Evaluation Methods

Thanks to modern sensor and microprocessor technology, measurement signals can now be digitally analyzed and corrected using characteristic curves or maps. This allows calorimetric flow meters to be adapted to different media and operating conditions and reliably used for flow measurement and flow monitoring.

Bypass Method for Thermal Mass Flow Meters

The bypass method for thermal mass flow meters is used to measure even larger gas flows with a comparatively small thermal sensor. In this method, a defined portion of the main flow is routed through a bypass containing a thermal sensor. The thermal measurement is therefore not performed directly in the entire main flow, but in a precisely defined partial flow.

The main pipe contains a laminar flow element (LFE). It consists of a large number of small, parallel flow channels. The laminar flow element creates a defined pressure drop between the pressure side upstream of the LFE and the pressure side downstream of the LFE.

The differential pressure that develops between the two sides of the laminar flow element generates a partial flow through the bypass tube. With proper design, there is a reproducible relationship between the pressure drop across the laminar flow element and the volumetric or mass flow rate. This allows a defined portion of the total flow to be directed through the thermal measurement channel.

The actual thermal mass flow sensor is located in the bypass. A heating element transfers heat to the medium flowing through the bypass. Two temperature sensors, T1 and T2, measure the temperature of the medium upstream and downstream of the heating element.

When the medium is stationary, i.e., with no flow, the heat generated by the heating element is distributed through the measurement channel by thermal conduction. After steady-state conditions are reached, no permanent temperature difference exists between the two temperature sensors. The temperatures of T1 and T2 approximate each other.

When there is a mass flow, the heat introduced by the heating element is carried away by the flowing medium. This results in a measurable temperature difference ΔT between temperature sensor T1 upstream of the heater and temperature sensor T2 downstream of the heater. The magnitude and time variation of this temperature difference depend on the mass flow rate and the thermal properties of the medium.

In a downstream evaluation electronics unit, the partial flow rate calculated from the temperature difference is converted to the total flow rate. In this process, sensor-specific properties, properties of the medium, etc., are taken into account via calibration curves, characteristic maps, and mathematical corrections.

Advantages and Disadvantages

Advantages

• No moving parts—therefore virtually wear-free
• Low pressure loss
• Low-maintenance operation
• Fast response time
• Measurement and monitoring of liquids and gases

Disadvantages

• Dependence on the thermal properties of the medium
• Sensitivity to contamination and deposits on the sensor
• Effect of medium temperature and thermal properties on the measurement
• Adjustment or calibration required when media change
• Impact of unfavorable flow conditions on measurement accuracy
• Electrical power required for sensor heating

Applications

• Machinery and Plant Engineering
• Process Monitoring in Cooling Circuits
• Water and Wastewater Technology
• Monitoring and Consumption Tracking for Gas and Compressed Air Systems

Historical Development of Thermal Flow Measurement

The history of thermal flow measurement is closely linked to research on heat transfer between a heated body and a flowing fluid.

An important foundation for the development of thermal flow measurement was laid in the early 20th century through studies on heat transfer at thin, electrically heated wires. Of particular significance in this context was the work of the Canadian physicist and professor Louis Vessot King (L. V. King) from McGill University in Montreal.

In 1914, Louis V. King published a seminal scientific paper on heat transfer from small cylinders and thin platinum wires to flowing fluids. Publication by Professor Luis V. King
The relationships described by King later became known as King’s Law or King’s law. In simplified form, the relationship describes the correlation between the heat dissipation of a heated sensor and the flow velocity. It became an important foundation for the development and calibration of hot-wire anemometers.

From Hot-Wire Anemometry to Thermal Flow Measurement

Hot-wire anemometry was initially used primarily to measure flow velocities. In this method, an electrically heated wire or sensor is surrounded by a flowing gas. The flow carries heat away from the sensor. The flow velocity is determined from the change in sensor temperature or the required heating power.

With advances in sensor and electronic technology, this principle has been increasingly used for industrial flow measurement. Increasingly robust sensors have been developed that are also suitable for industrial applications. Modern sensors consist, for example, of thin metallic layers or specially developed heating elements and temperature sensors.

Model Overview