Experiments in Fluids 25 (1998) 69—76 Springer-Verlag 1998
Taylor length scale measurement by laser Doppler velocimetry
H. Belmabrouk, M. Michard
A new method for making direct measurements of
the spatial velocity correlation coefﬁcient, based on two-point
laser Doppler velocimetry (LDV), has been developed. In this
paper, the effects of control parameters on the correlation
coefﬁcient are being investigated. The main sources of experi-
mental error have been identiﬁed and analysed. It appears that
the probe volume length has a key effect on the accuracy of
Taylor micro-scale measurement. A data processing procedure
has been established and validated for the determination
of this scale. The procedure shows that the portion of the
correlation curve used to determine Taylor scale is a function
of the integral scale to Taylor micro-scale ratio.
In most cases, properly description and modelling of one-
phase or reacting turbulent ﬂows require to evaluate, not only
the mean velocity and the root-mean square (rms) of the
ﬂuctuating velocity, but also turbulence scales. These are
derived from the correlation between adjacent ﬂuctuations (i.e.
near to each other in time or space). Two kinds of scales are
often considered: Lagrangian scales which are obtained by
tracking ﬂuid particles, and Eulerian time and length scales.
Time scales are obtained from the correlation between two
ﬂuctuations located at the same position but separated by
a variable time, while Eulerian length scales are deduced from
the correlation between two ﬂuctuations occurring at the same
Laboratoire de Transferts de Chaleur et de Masse
ENIM, 5000 Monastir
Laboratoire de Me´ canique des Fluides et d’Acoustique
Ecole Centrale de Lyon
CNRS UMR 5509
BP 163, F-69131 Ecully
Correspondence to: H. Belmabrouk
The authors would like to thank Prof. M. Lance for useful discussions
and Nathalie Grosjean for technical assistance. Thanks are also due to
the Groupement Scientiﬁque Moteur for ﬁnancial support.
time, but located at two different positions. The present study
focuses on Eulerian length scales only.
Although turbulent ﬂows are characterized by a wide range
of eddy sizes being present at the same time, only three typical
length scales are generally used to describe the structure of the
turbulent ﬁeld: the integral, Taylor and Kolmogorov scales.
The integral scale L, provides a rough estimate of the size of
large eddies and is related to transport phenomena. The Taylor
scale , characterizes smaller eddies and is related to the
dissipation rate (the ﬂow being considered as locally isotropic).
The Kolmogorov scale is the smallest turbulence scale; the
viscous dissipation of the turbulent kinetic energy occurs
mainly at scales comparable to the Kolmogorov scale. The
small scales, Taylor and Kolmogorov, are connected to mixing
Turbulence scales are commonly deduced from one-point
hot-wire anemometry measurements using Taylor’s hypothesis
(see e.g. Comte-Bellot and Corrsin 1971). However, this
technique is useful for nearly one-dimensional and weakly
turbulent ﬂows only; it is inadequate to the case of so-called
‘real’ ﬂows, exhibiting areas of recirculating ﬂows. Several
non-intrusive two-point methods have been proposed in the
literature for overcoming this difﬁculty.
Schafer (1983) added a spherical mirror to the conventional
LDV set-up, in order to generate and displace a second
(mobile) probe volume. The two laser beams which create
the ﬁxed probe volume are reﬂected by the mirror and are
re-focused, thus creating the second probe volume. This
technique has proved suitable for integral scale measurement.
However, for small separations between the ﬁxed and moving
probe volumes, the two processed signals are not uncoupled.
Indeed, each photodetector may process scattered light emitted
from both probe volumes as both are ﬁtted with identical
Chehroudi and Simpson (1985) used a scanning laser
Doppler anemometer to investigate a boundary layer. The
technique consists of rapidly moving the probe volume, so that
relative velocity is increased and turbulence may be considered
as frozen. It was then adapted by Glover et al. (1988) to
a motored internal combustion engine operating at 1200 r.p.m.
However, due to insufﬁcient spatial resolution, these authors
were unable to calculate an accurate estimate of the Taylor
Fraser and Bracco (1989) generated a single elongated probe
volume by means of a long focal length lens ( f:597 mm) and
a small separation of the incident beams (D:14 mm). Two
optical ﬁbres separated by a variable distance were used to