The significance of coherent flow structures for the turbulent mixing ...

M
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6 Investigation of the xz-plane
pare [111]. This is shown in the lower right graph. It is not surprising that the maxima do
not coincide as the high momentum flow structure originates statistically from ÄHÅ locations
where » ÅFEHGJI Ä4Å while low-momentum flow structures have their origin in the near-wall
region on average, where » Å E Ä Å holds (see upper right figure). However, the reason
that the maximum of K 6 ' , with 6 Æ , is further away from the wall with respect to K 6 ' ,
with 6 £ , is not evident. To examine the physical process associated with this experimental
result, the statistical properties of a fully developed turbulent boundary layer flow along
a flat plate is investigated in stream-wise span-wise planes located at Ä Å ;
by using the multiplane stereo PIV technique described in chapter 4. First of all, the joint
probability density function of the velocity fluctuations is analysed to determine the basic statistical
properties of the coherent velocity structures like their occurrence, intensity and main
flow direction relative to the wall. Thereafter various spatial correlation, cross-correlation and
conditional-correlation functions are presented in order to compare the mean size and shape
of the dominant flow structures being present in the near-wall region of the flow. The dynamic
of the dominant structures is investigated by means of spatio-temporal correlation and
cross-correlation functions measured in spatially separated planes. Finally, characteristic flow
fields are considered to illuminate the relation between the instantaneous flow structures with
respect to the averaged ones and to estimate the contribution of the identified coherent flow
structures to the production of turbulence and transport of Reynolds stresses.
6.1 Experimental set-up
þ¡
Ó and ,
The experimental investigation was performed 18 m behind the leading edge of the flat plate
in the temperature stabilised closed-circuit wind-tunnel shown in figure 1.4 on page 8. The
multiplane stereo PIV-equipment applied for the investigation consists of the same BMI four
pulsed Nd:YAG laser system as outlined in section 5.2, but in contrast to the configuration
described on page 72, here the system was arranged in such a way that the differently polarised
light pulses leave the laser housing at different output ports. This allows to cover a wider
range of light-sheet spacings (up to a few cm) and an independent positioning of both beampairs,
as pointed out in section 4.2. Behind each port one optical bench was installed with
three appropriate lenses and a L98ŒÓ -retardation plate which allows to rotate the direction of the
polarisation vector continuously. By using long focal length lenses, the laser beams could be
formed into sheets of about * Á mm thickness at the measurement position, corresponding to
. It should be noted that the main problem associated with the generation of a light-
ÅN; Ä
sheet running parallel to a flat surface is the loss of energy with decreasing wall distance, due to
the darkening of the light-sheet by the wall. This difficulty can be solved either by using more
optical elements, as described in section 4.8, or by using long focal length lenses (in the meter
range) as applied here. The positions of the light-sheets could be smoothly adjusted in vertical
direction by moving properly coated mirrors, mounted on a micrometer translation stage. The
determination of the distance of the light-sheets from the wall was achieved by illuminating
a square metal block, placed on the flat plate and covered with light-sensitive paper. The
recording system utilised for this investigation is similar to the unit described in section 5.2
apart from the lenses, which where replaced by mm Carl Zeiss lenses because of the short
observation distance þ¡ (see table 6.1), and the required polarising beam splitter-cubes and
OP
mirrors in front of the lenses according to section 4.1. The arrangement was installed below
the wind-tunnel, as shown in figure 6.2, at positions summarised in table 6.1. The positions of
98