A velocity dependent effective angle method for calibration
of X-probes at low velocities
Ole Martin Bakken, Per-A
Abstract A velocity dependent effective angle (VDEA)
method for the calibration of yaw response of hot-wire
X-probes at low ﬂow velocities (0.5–6 m/s) is presented.
Comparisons with a full velocity vs. yaw-angle method
sterlund 1999) in a smooth wall channel ﬂow indicate
that there is only moderate advantage in using the latter
method, which is considerably more laborious. Compari-
sons with direct numerical simulations (DNS) (Moser et al.
1999) and the more common ﬁxed effective angle method
(FEA) show that the VDEA method signiﬁcantly improves
estimates of Reynolds stresses compared to the FEA
The topic of hot-wire anemometry and calibration of
single and X-probes has been substantially covered in the
literature and the advantages and shortcomings of a lot of
different methods are well documented (e.g. Bradshaw
1971; Perry 1982; Bruun 1995). However, the treatment of
calibration procedures for the directional response of
X-probes at low ﬂow velocities (0.5–6 m/s) is sparse.
In its simplest form the probe yaw response is assumed
to be dependent on the probe geometry only. This means
that the angular sensitivity only needs to be calibrated for
at one arbitrarily chosen velocity. Using the effective angle
method of Bradshaw (1971), this leads to an angle which is
assumed to apply to all measurement situations. Because
of its simplicity this method is widely used.
Several investigators have, however, found that the yaw
response may be dependent on velocity.
Shabbir et al. (1996) proposed a method using
-factor dependent on velocity to allow for the
longitudinal cooling of the wire. Snyder and Castro (1989)
compared the conventional effective angle method of
Bradshaw with a method where the effective angle is
dependent on the mean velocity.
In the present investigation three methods for
calibrating the yaw response are compared and evaluated.
All these methods require that there is no time-averaged
binormal velocity component, normal to the wire and
normal to the planes of the prongs.
1. A yaw calibration is performed using a constant velocity
to determine an effective angle, which is then used over
the entire velocity range (Bradshaw 1971). This ﬁxed
effective angle (FEA) method is popular because of
its simple calibration procedure and its ease of imple-
mentation. Additionally, it is veriﬁed to give very similar
results to those obtained with a FULL method
(technique 3 below) for the mean velocity and Reynolds
stresses at high velocities and high turbulence intensities
(Browne et al. 1989).
2. As originally suggested by Snyder and Castro (1989), a
velocity dependent effective angle (denoted as the
VDEA method) is determined for the full range of
velocities in the experiment. This information is
assumed to be a property of the probe and is only
calibrated for once. Contrary to the method of Snyder
and Castro, who reduced the data using the velocity
dependent effective angle on a mean velocity basis,
a method is proposed where the effective angle used is
calculated on a sample-by-sample basis.
3. A full velocity vs. yaw-angle calibration method deve-
loped by O
sterlund (1999) is studied. This method is
called the FULL method.
In this paper the attention is focused on: showing the
limitations of the FEA method at low velocities; intro-
ducing a simple and time-saving VDEA method as sket-
ched above and validating it against a FULL method
sterlund 1999) and results from DNS (Moser et al. 1999).
The hot-wires were purpose made X-probes partly etched
from 2.5 lm Wollaston Pt-10% Rh wire with an active
length of about 0.5 mm. The length to diameter ratio was
close to 200, and the included angle of the two wires was
near 100°. The separation between the wires was approx-
imately 0.5 mm. Yaw calibrations were performed for
angles in the range ±35° in steps of 7°.
The in-house made constant temperature anemometers
were operated with an overheat ratio of 1.5. The ﬁlter
frequency of the low-pass ﬁlter, f
= 2.5 kHz, was ad-
justed after spectral investigation to closely match the
highest Kolmogorov frequency in the ﬂow. About 8 Â 10
Experiments in Fluids 37 (2004) 146–152
Received: 9 May 2003 / Accepted: 16 February 2004
Published online: 28 April 2004
Ó Springer-Verlag 2004
O. M. Bakken, P.-A
. Krogstad (&)
Department of Energy and Process Engineering,
Norwegian University of Science and Technology,
kolbjoern Hejes v. 2, N-7491 Trondheim, Norway
The authors are grateful to Dr. O
sterlund for making available the
source code of his calibration procedure.