Environmental Engineering Reference
In-Depth Information
due to preprocessing. We have used a Fujifilm digital camera Finepix HS50 EXR,
with a maximal resolution of 4,608
×
3,456 pixels, capable of recording images with
16 bits per color, which are after converted to a readable format. As in the synthetic
Schlieren method, PFT require a comparison of digital images. In a first step, we take
a snapshot of the fringe pattern when liquid surface is at rest. The second step consists
in taking an image of the fringe pattern when the wave is present. Information of h
is contained in the phase difference between two images. There are several possible
configurations to arrange the camera and the video projector. In our experiments,
axis of the camera and video projector are parallel. The relation between h and the
phase difference
ʔˆ
is (Cobelli et al. 2009 ; Maurel et al. 2009 ):
ʔˆ
L
h
=
D ,
(12)
2
p
ʔˆ
where L is the distance of camera to liquid surface, D is the distance between lenses
of camera and video projector and p is the wavelength of the fringe pattern. In an
ideal case only two images are required to reconstruct the waveform. In reality we
need to subtract undesirable factors, then corrections must be incorporated. Let us
project on the liquid surface an image in which all pixels have the same intensity
level. When this pattern is recorded with the digital camera, intensity is not constant.
This is due, among other things, to the fact that when light reaches the liquid surface
three phenomena take place, that is, reflection, transmission and absorption. The
amount of energy carried by the reflected light is dependent on the incidence angle.
In order to remove this source of undesirable effects we need also to record this kind
of images and include them in the process for determining phase difference.
3.1 Experimental Setup
Experiments were carried out in a basin made in plexiglass whose dimensions are
120 cm
15 cm. Waves were produced with a parabolic wave maker whose
parameter a is2(seeEq. 4 ) and has 42 cm wide. The wave maker is connected to a
mechanical vibrator which produces a sinusoidal motion of frequencies lying in the
range 4-10Hz, corresponding towavelengths between 2.4 and 10 cm. The water level
is set to 10 cm for both synthetic Schlieren and FTP experiments. The deep water
approximation is well fulfilled because in all cases tanh
×
50 cm
×
(
kH
)>
0
.
999. Images for
synthetic Schlierenmethod cover an area of 20 cm
11.2 cm, theywere recordedwith
a full HD digital camera. In each realization a film of 50 frames/s was taken during
50 s. Each film includes frames for both unperturbed and wavy surfaces. Individual
images are extracted from the film through the use of the free software ffmpeg.
Digital processing was performed with DPIVsoft software (Meunier and Leweke
2003 ), which allows to obtain the free surface gradient. Finally the reconstruction
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