Hot-wire Anemometry P M V Subbarao Professor Mechanical Engineering Department True Measurement of High frequency Velocity Variations…..

Theory of operation Fundamentally, a hot wire makes use of the principle of convective heat transfer from a heated surface being dependent upon the flow conditions passing over it. The maximum temperature of the sensor is maintained at a nominally constant value of 1.7 times the fluid temperature. For a given sensor geometry, the steady state temperature distribution is a function of the cooling velocity.

Wire Temperature Distribution

Thermal model of sensor A hot-wire uses a 1 mm active region of 5 µm tungsten filament with 50 µm copper plated support stubs. The unplated tungsten is referred to as the ‘active’ portion of the sensor. The x-coordinate for the sensor is shown from the centre of the wire.

Heat balance for an incremental element

This can be simplified to give the general hot wire equation: if radiation is neglected. The constants are given by:

Time Constant of Hot-wire R wire

Frequency of Hot-wire Anemometer

Schematic of Constant Current Anemometer

Schematic of Constant Temperature Anemometer

CTA The constant temperature anemometer uses a feedback amplifier to maintain the average wire temperature and wire resistance constant {i.e., dT w / dt = 0}, within the capability of the amplifier. The practical upper frequency limit for a CTA is the frequency at which the feedback amplifier becomes unstable. A third anemometer, presently under development, is the constant voltage anemometer. This anemometer is based on the alterations of an operational amplifier circuit and does not have a bridge circuit.

Frequency Response of CTA

Steady state solution The general steady state solution to Equation, assuming that   , is found by applying the boundary condition and defining the mean wire temperature: The non-dimensional steady state wire temperature distribution is then:

A heat balance can then be performed over the whole wire, assuming that the flow conditions are uniform over the wire: The two heat transfer components can be found from the flow conditions and the wire temperature distribution:

where the corrected heat transfer coefficient is given by: to give a steady state heat transfer equation:

giving the steady state calibration equation: If the Biot number is larger than approximately 3, as is usually the case, in terms of Nusselt number this approximates to

PROBE PRE-CALIBRATION PROCEDURE Once a probe is constructed and mode of operation is selected, the following procedure should ensure accurate and reliable measurements. First, the probe should be operated at the maximum q ¥ and T w that will be used during the proposed test. This is done to pre-stress and pre-heat the wire to ensure that no additional strain will be imposed on the wire during the test that could alter its resistance. For supersonic and high subsonic flows, the wires should also be checked for strain gaging, that is, stresses generated in the wire due to its vibration. During this pre-testing many wires will fail due to faulty wires or manufacturing techniques. But it is better that the wires fail in pre-testing rather than during an actual test.

In practice, hot-wires are calibrated in the form of u= f (E). rather than the more conventional form of E =f (u). The constant T o and  version of King's law for a CTA is When expressed as u = f (E) = gives:

VELOCITY CALIBRATION, CURVE FITTING Calibration establishes a relation between the CTA output and the flow velocity. It is performed by exposing the probe to a set of known velocities, U, and then record the voltages, E. A curve fit through the points (E,U) represents the transfer function to be used when converting data records from voltages into velocities. Calibration may either be carried out in a dedicated probe calibrator, which normally is a free jet, or in a wind-tunnel with for example a pitot-static tube as the velocity reference. It is important to keep track of the temperature during calibration. If it varies from calibration to measurement, it may be necessary to correct the CTA data records for temperature variations.

Polynomial curve fitting: Plot U as function of E corr Create a polynomial trend line in 4th order:

Measurement of Multi-dimensional Flow

X-probe calibration procedure

DIRECTIONAL CALIBRATION Directional calibration of multi-sensor probes provides the individual directional sensitivity coefficients (yaw factor k and pitch-factor h) for the sensors, which are used to decompose calibration velocities into velocity components. X-array probes The yaw coefficients, k 1 and k 2, are used in order to decompose the calibration velocities U cal1 and U cal2 from an X-probe into the U and V components. Directional calibration of X-probes requires a rotation unit, where the probe can be rotated on an axis through the crossing point of the wires perpendicular to the wire plane. Calculation of the yaw coefficients requires that a probe coordinate system is defined with respect to the wires, and that the probe has been calibrated against velocity.

X-Probe

X-probe decomposition into velocity components U and V Calculate the calibration velocities U cal1 and U cal2 using the linearisation functions for sensor 1 and 2. Decomposition with yaw coefficients k 1 and k 2 : Calculate the velocities U 1 and U 2 in the wire-coordinate system (1,2) defined by the sensors using the two equations:

which gives: Calculate the velocities U and V in the probe coordinate system (X,Y) from:

Tri-axial probes The directional sensitivity of tri-axial probes is characterised by both a yaw and a pitch coefficient, k and h, for each sensor. Calibration of tri-axial probes requires a holder, where the probe axis (X-direction) can be tilted with respect to the flow and thereafter rotated 360° around its axis. Proper evaluation of the coefficient requires that a probe coordinate system is defined with respect to the sensor- orientation. Directional calibration is made on the basis of a velocity calibration.

Tri-axial probe calibration procedure

Tri-axial probe decomposition into velocity components U, V and W In a 3-D flows measured with a Tri-axial probe the calibration velocities are used together with the yaw and pitch coefficients k 2 and h 2 to calculate the three velocity components U, V and W in the probe coordinate system (X,Y,Z). The yaw and pitch coefficients for the three sensors may be the manufacturer’s default values, or if higher accuracy is required they are determined by directional calibration of the individual sensors.

Calculate the calibration velocities U cal1, U cal2 and U cal3 using the linearisation functions for sensor 1, 2 and 3. Calculate the velocities U 1, U 2 and U 3 in the wire-coordinate system (1,2,3) defined by the sensors using the three equations:

With the k 2 = and, h 2 =1.04 default values for a tri-axial wire probe, the velocities U 1, U 2 and U 3 in the wire coordinate system becomes: Calculate the U, V and W in the probe coordinate system:

Time averaged Navier Stokes Equation For all the Three Momentum Equations, turbulent stress tensor:

2.Eddy Viscosity models For 2-D incompressible boundary layer equation Momentum Equation, or

(b) ONE-EQUATION MODELS Turbulence Kinetic Energy Mean Strain Rate

(c) TWO-EQUATION MODELS Turbulence K.E. Dissipation Rate

Measurement of Turbulence

Two simultaneous velocity time series provide cross-moments (basis for Reynolds shear stresses) and higher order cross moments (lateral transport quantities), when they are acquired at the same point. If they are acquired at different points they provide spatial correlations, which carries information about typical length scales in the flow. Reynolds shear stresses:

Lateral transport quantities:

Sensor type selection Wire sensors: Miniature wires: First choice for applications in air flows with turbulence intensities up to 5-10%. They have the highest frequency response. They can be repaired and are the most affordable sensor type. Gold-plated wires: For applications in air flows with turbulence intensities up to 20-25%. Frequency response is inferior to miniature wires. They can be repaired. Fibre-film sensors: Thin-quartz coating: For applications in air. Frequency response is inferior to wires. They are more rugged than wire sensors and can be used in less clean air. They can be repaired.

Heavy-quartz coating: For applications in water. They can be repaired. Film- sensors: Thin-quartz coating: For applications in air at moderate-to- low fluctuation frequencies. They are the most rugged CTA probe type and can be used in less clean air than fibre-sensors. They normally cannot be repaired. Heavy-quartz coating: For applications in water. They are more rugged than fibre- sensors. They cannot normally be repaired.