Thermal flow measuring principle

As a distinct class of flowmeters, thermal mass devices can be divided into two main types:

The “thermal dispersion” (aka anemometric) principle (Fig. 1):
A heated element is exposed to the flow. The rate of cooling is a measure of local specific mass velocity and therefore flow.

The “calorimetric” principle (Fig. 2):
Heat is applied to a limited area in the flow. The local temperature rise and the energy added are used to compute mass flow.

Both types are available on the market. The high sensitivity of some designs has led to their extensive use in research applications. This sensitivity also means that the measured value can be affected by fluid properties, such as thermal conductivity and specific heat capacity, or by gas composition (in the case of mixtures) and installation conditions.

The thermal principle is widely used in various applications due to its precise mass flow measurement capabilities.

Thermal dispersion type flowmeters can operate according to one of the following methods: 1) constant power and 2) constant temperature differential.

Using the constant power method, the electronics maintain a constant electrical current through the so-called „velocity sensor“ (a heated sensor element, usually in the form of a resistive temperature detector (RTD)). Using a separate RTD, the fluid temperature is measured. With changes in the flow rate, the temperature differential (difference in measured temperatures between the velocity sensor and the fluid temperature sensor) changes.

With the constant temperature differential method, the electronics maintain a constant temperature difference between the velocity sensor and the fluid temperature sensor. As the flow changes, the power supplied to the heated velocity sensor must be adjusted to maintain the constant temperature difference. Regardless of the method used, the measured changes (in either supplied power or differential temperature) are directly proportional to changes in the flow rate. For both designs, the relationship between flow rate and heat transfer from the velocity sensor are described by King‘s equation (or a derivation thereof):

Q_L: Heat flow of the velocity sensor
ΔT: Temperature difference between velocity sensor and fluid
K: Thermal conductivity of the fluid
c_v: Specific heat capacity of the fluid at constant volume
ρ: Fluid density
v: Flow velocity
d: Diameter of the heated velocity sensor

The form of this equation shows the sensitivity to the fluid properties and the importance of the second term as flow rate increases. The equation is non-linear, but fortunately linearization is easy to apply through digital signal processing techniques. Some designs use single heated wire (anemometers are the classic type here) whilst others use two thermistors in reference and sensing mode. Figure 1 shows the tips of such a thermal probe. Fluid flows over the fluid sensor (a), the unheated element, and the velocity sensor (b), the heated element, to measure the rate of heat flow.

Figure 2 illustrates the “calorimetric” measuring principle, found in several commercial designs of thermal flowmeters. Heat is generated inside the flowmeter and applied to the flow. Two sensing elements are positioned within it to measure the variation in temperature between different points. Sometimes, two heaters and three temperature sensors are employed to give a fuller picture of the thermal profile. When no flow occurs, all the temperature sensors indicate the same temperature.

When flow occurs, the sensors become heated or cooled relative to each other and a temperature difference ∆T appears, which is directly related to flow. These meter types are characterized by the equation:

Q_m: Mass flow rate
H: Heat input
A: Constants
c_p: Specific heat at constant pressure
ΔT: Measured temperature difference

Applying heat (H) at zero flow creates an undistorted thermal profile (a), which moves to the right under flowing conditions (b).

The equation above is less dependent on the fluid properties, although the constant “A” encompasses the conductivity as well as the viscosity.

For both measuring methods (“thermal dispersion” as well as “calorimetric”), designs with single or multiple point sensors have been developed, in either full-bore or by-pass line types. This enables an enormous flow range to be covered, from the low flow of clean gases in medical usage up to large volumes of flare gas in discharge stacks.

Commercially, the two previously described principles are applied to sensors installed in the main line and those installed in the bypass loop. There is considerable overlap between the two operating principles and the two basic commercial designs, especially when flow rate and pipe dimensions are considered. Other factors that may influence the final design choice depend critically on the application and the nature of the fluid being measured.

The simplest type of thermal dispersion meter is the hot wire anemometer. The velocity sensor is a fine wire made from tungsten, platinum or nickel. Both constant power and constant temperature differential types are commercially found. The wire is 0.02 mm in diameter (typically), mounted between supports. The small size means minimal disturbance to the flow, so that sensitivity and performance are maintained. Sensors may be single or multiple in any orientation (Fig. 3). The more complex designs are frequently used in research applications.

Bypass types (or CTMF = Capillary Thermal Mass Flowmeters, as they are commonly known) are actually a subtype of the calorimetric branch of flowmeters. Often, in conjunction with the capillary bypass, they employ a laminar flow element. The capillary tube is connected to the inlet and outlet of the laminar thermal mass flow element, so that a small amount of the main flow is diverted and sampled (Fig. 4). The design ensures a fixed ratio of the total gas flow rate through the capillary for measurement. The heater and temperature sensors are usually placed on the capillary tube rather than the main conduit. Designs do exist, though, without the capillary and laminar flow element, where the sensors are located directly on the main conduit (pipe). There may be one or two heaters and up to three temperature sensors arranged in a variety of ways along the capillary.

Generally, the CTMF meter is supplied with screw threaded fittings, although flange fittings can be provided. This meter design is often combined with a mass flow measurement controller downstream of the sensing sensor. This configuration is termed a mass flow controller (MFC). Typically, the electronic interface is located within the same unit as the bypass loop.

For larger pipes, insertion meters are commonly used. However, some designs can be used for pipe diameters smaller than DN 50/2". The sensors are positioned at the end of a probe that is inserted into the flowing gas stream. Total mass flow rate is determined from the measured point flow rate, cross-sectional area and temperature compensation for the flow profile.

Some degree of physical protection of the sensors is usually included. Many mounting arrangements are available that include flanged fittings, packing glands, sanitary and ultrahigh purity fittings. The location of the sensors within the cross section of the pipe is crucial for optimum performance. If the manufacturers’ recommended installation cannot be achieved, then a correction will be necessary.

With certain insertion meter designs, it is possible to adjust the sensor location within the pipe in order to easily obtain the optimum measurement position. The installation of the insertion type meter into an existing pipe is usually achieved via an adapter welded to the external surface of the pipe. The insertion meter is installed in the pipe through this adapter. The fitting connection of the adapter must match that on the insertion probe.

In some applications, multiple insertion designs are employed. One common usage being, for instance, monitoring of flare stack or dirty process gas. Some designs may look very similar to the multi-port Pitot tubes, with thermal probes replacing the pressure ports. Such rugged designs will require periodic retraction and cleaning but have proven themselves to be acceptable methods for these difficult applications.

Inline thermal mass flowmeters (ITMF) comprise three elements: the body, the sensing element and the electronics, which may be remote from the primary sensor. As with most modern instruments, signal conditioning allows many flow and alarm function outputs in any desired format. The body is available with a wide range of process connections to suit the application (ANSI, DIN, NPT thread or hygienic). Figure 5 shows the schematic arrangement of an inline and an insertion meter.

As a class, thermal mass meters have good generic characteristics, with advantages and disadvantages. A general performance range for these devices could be said to extend from ±1% o.r. to ±3% o.r. ±0.3% o.f.s. Typical turndowns are 100:1 and higher. Repeatability is usually around ±0.5% o.r. or better. Designs are available for flow rates from 2 to 10.000 kg/h (4.4 to 22.000 lb/h) and higher.