Experiments in Fluids 28 (2000) 58 }63 Springer-Verlag 2000
Measurements and treatment of LDA signals, comparison with hot-wire signals
A. Ramond, P. Millan
Abstract An experimental investigation was carried out in the
wind tunnel F2 of the ONERA Fauga centre for the measure-
ment of the characteristics of a turbulent wake behind a wing.
As these measurements require the calculation of time and
space correlations, two different types of acquisition means are
used : a pair of crossed hot wires and a one-dimensional
laser-Doppler anemometer. The non-intrusive characteristics
of laser anemometry allow the measurement of ﬂuid velocity
upstream of a hot wire probe without disrupting the ﬂow. It is
well known that LDA generates individual realisations of
randomly sampled velocity data because the random arrival of
seeding particles in the measurement volume is nonperiodic.
A detailed study of this random sampling quantiﬁes the
deviations from the theoretical lows, shows the limiting factors
of this sampling, and gives a characterisation of the particles
arrival law. The simultaneous acquisition of the two velocity
signals at very close points allows a good comparison between
the signals. A statistical analysis of the two signals enables us to
precisely measure the error value of the velocity estimation
made by the anemometer.
The spectrum analysis of the laser signal coupled with one of
the hot wire signals requires resampling the signal at constant
steps. Two different methods of interpolation are analysed: the
sample and hold interpolation method and the linear interpo-
lation method. The inﬂuence of these interpolation methods on
the spectrum of LDA signals is studied. Different estimators are
then calculated to evaluate the convection velocities and the
coherence length of the turbulence.
The characterisation of turbulent ﬂows and turbulence model
formulation require the knowledge not only of time-averaged
mean turbulence quantities, but also of time and space
coherency within turbulent ﬂows. Two parameters often
measured in this context are the temporal autocorrelation
function and the two-point spatial correlation function.
From these functions micro- and integral time and space
scales can be determined. Since the correlation function is the
A. Ramond, D. Millan
ONERA/DMAE, 2 av Edouard Belin BP 4025, F-31055
Toulouse Cedex, France
Correspondence to: A. Ramond
Fourier transform of the one-dimensional power spectrum, its
knowledge gives a good characterisation of the ﬂow ﬁeld.
Most measured correlation functions reported in the litera-
ture are obtained by using hot-wire anemometry. Many
measurements using this kind of system have been realised in
different ﬂows, nevertheless probes have to be inserted into the
ﬂow-ﬁeld, thereby disturbing the ﬂow. The capability of laser
anemometry of measuring instantaneous velocities non-intru-
sively makes it advantageous. In spite of the experimental
difﬁculties, spatial correlation functions were measured by
a number of researchers. Fraser et al. (1986) and Absil et al.
(1990) have reported two-point correlations using a technique
in which light was collected from two distinct locations within
a single elongated measurement volume. A disadvantage of this
method is that it can be used only on lateral correlation
functions. In a more general approach, to measure two-point
correlations, two distinct measurement volumes are used.
Morton and Clark (1971) and Benedict and Gould (1993) have
reported on two-point correlations using two separate single-
component LDA systems. With their system, they have tested
the validity of Taylor’s hypothesis with the measurement of
Tummers et al. (1994) used a two-component LDA together
with a single-component LDA to measure longitudinal two-
point correlations of the streamwise velocity and studied the
effects of noise and spatial resolution. In the present investi-
gation, a single-component LDA was used together with
a two-component hot wire system. The capability of laser
anemometry for measuring velocities non-intrusively elimin-
ates wake problems. The comparison of the two kinds of
signals is realised with different estimators. Phenomena more
speciﬁc to laser anemometry are analysed.
All experiments are performed in the F2 wind-tunnel at the
ONERA Fauga Mauzac centre. This wind tunnel is of the
closed-circuit type, working at ambient pressure. It has
a settling chamber and a contraction which guarantee a free
stream turbulent level less than 0.06%. This wind tunnel is out
ﬁtted with a three-component laser Doppler anemometer,
which enables the measurement of velocities in three direc-
tions. In the present investigation, only single-component
measurements in the streamwise direction were performed.
Two other measurements are realised by two hot wire probes.
All the measurements are made in the wake of a wing (Fig. 1)
the three points of measurement are aligned, and the distance
between the two hot wire probes is ﬁxed (4.2 mm) while that