Measurement Principles of CTA


CTA is a measurement technique well suited for the study of fine structures in turbulent flows.

The working principle is based on the cooling effect of a flow on a heated body. The CTA measures velocity at a point and provides continuous velocity time series, which can be processed into amplitude and time-domain statistics. Examples are mean velocity, turbulence intensity, higher order moments, auto-correlations, and power spectra.

image of constant temperature anemometry overview

Heat transfer from cylinders

Convective heat transfer Q from a wire is a function of the velocity U, the wire over-temperature Tw -T0 and the physical properties (k,r,m) of the fluid. The basic relation between Q and U for a wire placed normal to the flow was suggested by L.V. King (1914). In its simplest form it reads:

image of convective heat transfer equation

where Aw is the wire surface area and h the heat transfer coefficient, which are merged into the calibration constants A and B.

image of cta wire diagram

CTA principles

The wire, Rw, is connected to one arm of a Wheatstone bridge and heated by an electrical current.

A servo amplifier keeps the bridge in balance by controlling the current to the sensor so that the resistance – and hence temperature – is kept constant, independent of the cooling imposed by the fluid. The bridge voltage, E, represents the heat transfer and is thus a direct measure of the velocity. The combination of the sensor’s low thermal inertia and the high gain of the servo loop amplifier gives a very fast response to fluctuations in the flow.


CTA probes normally have tungsten wire sensors, 1 mm long and 5 µm in diameter, mounted on two needle-shaped prongs. They are available with 1, 2, and 3 wires. Film probes with thin-film sensors are recommended for liquid flows.

image of CTA probes
image of system bandwidth graph

Frequency response

The system bandwidth, fc, is defined as the frequency at which the signal amplitude is damped by -3 dB. It increases with decreasing wire time constant, with increasing servo loop gain, and with flow velocity. The bandwidth for a CTA with a 5 mm wire probe is around 100 kHz at 30 m/s. The system is optimised by applying a square-wave voltage to the bridge top and adjusting the servo-loop gain.

image of voltage graph

Velocity sensitivity

The relation between bridge voltage and velocity may be described as an exponential function or as a polynomial:

image of bridge voltage and velocity equation

The relative velocity sensitivity, 1/U · dE/dU, is almost constant over a wide velocity range. Calibration in a known flow forms the basis for the curve fit used to convert probe voltages into velocities (linearization).

Directional sensitivity

As a wire is sensitive to both flow velocity and direction, orthogonally arranged wires give information about both. The effective cooling velocity for a wire in a three-dimensional flow can be expressed as:

image of cooling velocity equation

For 2- and 3-wire probes, the effective cooling velocity equations can be solved to provide the velocity components. The pitch and yaw factors k and h are determined by a directional calibration.

image of 2-wire probe diagram

Temperature sensitivity

The bridge voltage depends on both velocity and temperature. A 1 K change gives an error of approximately 2% in velocity. The voltage may be corrected before linearization, using the ratio between the over-temperatures during calibration and measurement:

iamge of voltage equation
image of voltage table

Data conversion and reduction

Bridge voltages are acquired via fast A/D boards (up to 1 MHz or more) after proper low-pass filtering. They are converted into engineering units in three steps:

  • Temperature correction
  • Linearization
  • Decomposition into velocity components

The converted data are then reduced into flow statistics.

Discuss your CTA testing needs with an expert

Contact one of our knowledgeable global distributors to learn more about solutions from Dantec Dynamics