Thermal anemometry

Thermal anemometer with a digital display and with a sensor on a telescopic rod

In thermal anemometry , a sensor element is used that is electrically heated and whose electrical resistance depends on the temperature. As a result of the flow, heat is transported into the flow medium, which changes with the flow velocity. By measuring the electrical quantities, conclusions can be drawn about the flow velocity.

The sensor elements can be designed very differently (wire, film, ...) and they are partially applied to a substrate. To operate the sensors, special electronics are required that regulate the heating current and amplify the sensor signal.
Since the sensor properties and the electronic control and amplifier systems have a significant influence on the measurement signal, the entire measurement chain is usually calibrated.

Areas of application and comparison with other measurement methods

Hot wire probes offer the possibility of determining the flow velocity with high resolution over time, as is necessary for the following examinations, for example:

unsteady effects (flow separation)
aeroacoustic effects
Boundary layer, especially envelope laminar-turbulent
Degree of turbulence measurements

As an alternative to thermal anemometry, there are essentially only two other methods for this type of measurement:

Pressure probes (e.g. Prandtl probe )
Laser Doppler anemometry

Pressure probes are a cost-effective and robust solution. Multi-hole pressure probes can also be used to determine the direction of flow. Since the pressure depends on the square of the speed, measurements below 10 m / s in air are no longer very accurate. In addition, with most probes there is the problem that the static pressure is required, which in many applications cannot be precisely determined. Typically, a frequency resolution beyond 1 kHz can hardly be achieved.

The great advantage of laser Doppler anemometry is that the flow is not disturbed by a probe. However, the costs for a measuring device are very high, the flow must be "contaminated" with particles (seeding), there must be optical accessibility and protective measures are necessary due to the very strong laser beams.

Hot wire anemometry is an interesting alternative to these measuring methods. The speed can be measured with a very high resolution in terms of time, typically up to the range of 5 to 10 kHz (even beyond this if the measuring chain is specially coordinated). When using multi-wire probes, not only the amount but also the direction can be determined. The costs are well below those of an LDA system and no special protective measures are required. However, the probes are relatively sensitive to contamination and the signal depends on the flow temperature. However, the influence of temperature can be recorded and corrected via calibration.

Furthermore, the hot wire anemometry is very well suited for the measurement of low flow velocities, as it is particularly sensitive in the lower velocity range. When operating with minimal heating power, the probes can also be used as an alternative as a very fast-reacting thermometer. Hot wire probes can be used in all speed ranges (even supersonic) depending on the calibration.

Hot wire sensor

Hot wire sensor (schematic)

In hot wire anemometry, a very thin wire is used, which typically has a diameter of 2.5-10 μm. It should be at least 200 times the diameter in order to keep edge influences low. As the material be platinum , nickel , tungsten and further different alloys are used depending on the requirements of its physical properties. The wire thickness is the determining parameter for the dynamics. The thinner the wire, the higher the frequencies it can record, but the greater its mechanical sensitivity.

The wire is stretched between two much thicker steel tips to which it is welded. These so-called prongs protrude from a ceramic body that ensures mechanical stability and electrical insulation. This combination represents the actual hot wire sensor, which is inserted into a special holder or permanently connected to such a holder. The electrical connection to the hot wire bridge is established via the holder and the cable connected to it.

The speed component of the hot wire is recorded in a plane perpendicular to the wire. The component tangential to the wire has very little influence and can be neglected in most cases.

With a one-sensor hot wire probe, if the direction of flow is known, only the amount of a one-dimensional flow can be determined. In contrast, a two-dimensional flow can be measured with “double hot wire probes” or “two-sensor hot wire probes” . With this type of probe, a so-called direction detector hot wire is attached in parallel with a short distance in the thermal wake of the front hot wire, with which the amount of the flow velocity is determined. It must be taken into account that with this type of sensor, no backflows and only measurements are useful if effects of the front wire can still be demonstrated in the signal of the sensor in thermal wake. Three or four-sensor hot wire probes are used to determine a three-dimensional speed vector. With these probe types, three sensors form a measuring cube from which the components of the velocity vector are derived. With the four-sensor hot wire probe, based on the principle of the “double hot wire probe”, one of the three speed-determining sensors is fitted with an additional sensor in the thermal wake, which also allows the detection of backflows. ${\ displaystyle u = f (x, z)}$ ${\ displaystyle u = f (x, y, z)}$

Different control loops

combined air speed and air temperature sensor

A special electronic control and amplification is necessary for the operation of hot wire sensors. In the following, the two most important operating modes will be discussed:

Constant-Current Anemometry (CCA)

The CCA represents the simplest principle, as it can do without a complex regulation. The sensor is heated with a constant current. The flow changes the resistance and thus the voltage drop across the sensor, which represents the measurement signal. The disadvantages of this simple system are the lack of temperature compensation and poor frequency resolution. In addition, the principle is unsuitable for long-term measurements, as the wire ages quickly due to temperature fluctuations.

Constant-Temperature Anemometry (CTA)

With the CTA methods, very fast control loops try to keep the sensor at an average constant temperature. The electronic implementation is therefore correspondingly complex and must be adapted to the individual sensor including its cabling. Since the sensor temperature can be determined, a theoretical correction of the temperature influence is possible. This operating mode also has a wide frequency range.

Formula for the conversion

The first fundamental work was carried out by LV King in 1914. According to the formula named after him, the following applies to the required electrical power:

{\ displaystyle I ^ {2} \ cdot R_ {S} = (T_ {S} -T_ {F}) \ cdot (A + B \ cdot w ^ {0.5}) \,}

${\ displaystyle I}$	Current through the sensor
${\ displaystyle R_ {S}}$	ohmic resistance of the wire
${\ displaystyle T_ {S}}$	Sensor temperature (or wire temperature)
${\ displaystyle T_ {F}}$	Temperature of the fluid
${\ displaystyle A, B}$	Constants that depend on the physical boundary conditions
${\ displaystyle w}$	Flow velocity in a plane perpendicular to the wire

It is therefore dependent on the temperature difference between wire and fluid as well as the flow velocity (to be precise, the mass flow, for applications with approximately constant pressure and flow velocities well below the speed of sound, for simplicity only the velocity can be used) and the physical boundary conditions of the respective design. There are different approaches for the compensation function. The following approach has proven itself in practical application:

{\ displaystyle w = \ left (a + b {\ frac {U_ {Br} ^ {2}} {T_ {S} -T_ {F}}} \ right) ^ {e} \,}

${\ displaystyle a, b, e}$	Constants that depend on the physical boundary conditions and are determined during calibration
${\ displaystyle U_ {Br}}$	Output voltage of the measuring bridge

The sensor temperature cannot be determined directly, but must be calculated using the bridge settings. It has been shown that in order to be able to correct the temperature influence optimally, a somewhat lower sensor temperature than calculated must be used. This corrected sensor temperature must be determined using a corresponding calibration at different temperatures. If this is not possible, a correction can be made based on empirical values, which causes a somewhat larger temperature error. ${\ displaystyle T_ {S}}$

calibration

Calibration of a hot wire anemometer

The calibration is typically carried out in small probe wind tunnels. The speed is determined using the dynamic pressure or the pressure in the antechamber of the wind tunnel nozzle. Because of the quadratic relationship between pressure and speed, the greatest uncertainties arise for low speeds. Influencing variables are:

amplifier
Pressure sensor
atmospheric pressure
temperature
A / D conversion

Typically, the uncertainty is determined by the pressure measurement at low speeds and by the temperature measurement at high speeds.

Accuracy of the measurement process

The ambient temperature not only has an influence on the calibration, but also later on the hot wire signal. The resulting error depends on the temperature difference between the sensor and the fluid. This error can typically be reduced to around 1% through an optimized calibration at different temperatures and the possible correction of the sensor temperature.

The resistance of the sensor line is a fixed value in the sensor system. If the resistance changes (e.g. due to plugging in and unplugging or using a different cable), this leads to a measurement error.

The flow of heat is usually inhibited by soiling , which indicates that the speed is too low. In this case, the wire must be cleaned and recalibrated.

Acoustics

In the form of a differential hot wire anemometer, i.e. H. two heating wires lying close together are used, e.g. B. made of platinum , not only temporally stationary currents (wind), but also sound velocities can be measured.

literature

L. S. King: On the Convection Heat Transfer from Small Cylinders in a Stream of Fluids. Determination of Convection Constants of Small Platinum Wires with Application to Hot-Wire Anemometry . In: Phil. Trans. Roy. Soc. London , 214A, 1914, pp. 373-432.
C. Tropea, N. Damaschke, H. Nobach: Flow measurement technology lecture 4, hot wire / hot film measurement technology . (PDF) Technical University of Darmstadt
H. H. Bruun: Hot-wire Anemometry: Principles and Signal Analysis . Oxford University Press, 1995, ISBN 0-19-856342-6 (English).

Individual evidence

^ David Havelock, Sonoko Kuwano: Handbook of Signal Processing in Acoustics . Springer, 2009, ISBN 978-0-387-77698-9 , p. 1284.
↑ Michael Möser: Pocket book of technical acoustics . Gabler Wissenschaftsverlage, 2003, ISBN 978-3-540-41242-7 , p. 28.

[HavelockKuwano2009-1] David Havelock, Sonoko Kuwano: Handbook of Signal Processing in Acoustics . Springer, 2009, ISBN 978-0-387-77698-9 , p. 1284.

[moeser2003-2] Michael Möser: Pocket book of technical acoustics . Gabler Wissenschaftsverlage, 2003, ISBN 978-3-540-41242-7 , p. 28.