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51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
07 - 10 January 2013, Grapevine (Dallas/Ft. Worth Region), Texas
AIAA 2013-0247
Development of a Digital Image Projection Technique to
Measure Wind-Driven Water Film Flows
Downloaded by Hui Hu on January 11, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2013-247
Kai Zhang1, Song Zhang2, Alric Rothmayer3 and Hui Hu4 ()
Iowa State University, Ames, Iowa, 50011
Digital fringe projection (DFP) profilometry has been widely used to generate threedimensional (3D) surface information. In this work, a novel 3D shape measurement system
based on DFP technique is proposed for accurate and quick thin film/rivulet flow
measurement. The key concept of the technique is making use of digital image correlation
(DIC) algorithm to direct calculate the projected grid points’ displacements. In comparison
to fourier transformation based DFP system, it gives more accurate measurement result
without rigid image quality requirement. This technique was applied to characterization of
wind-driven thin film/rivulet flows that were formed in an open circuit wind tunnel. The film
thickness and surface wave frequency had been evaluated for variety of wind speeds and
flow rates. The results show that this technique successfully revealed the dynamic motion
features of thin film flows.
I. Introduction
F
ree surface flows are of interest in fundamental fluid dynamics research as well as in various practical
applications. For example, Liu et al. (1995) performed experimental investigation to explore the three
dimensional instabilities of film flows. Savelsberg et al. (2006) studied the interaction effect on free surface
deformation of the turbulence channel flow. Kouyi et al. (2003) conducted experimental measurement on the free
surface of a storm overflow of a sanitation system. Pautsch and Shedd (2006) optimized the spray cooling system
design by measuring the thickness distribution of FC-72 liquid film. Many experimental techniques have been
applied to measure the thickness distribution of liquid free surfaces. Photo luminescent techniques have been
successfully applied in measuring the free surface thickness. Liu et al. (1993) used fluorescent imaging method to
investigate the three dimensional instabilities of gravity-driven film flows. Johnson et al. (1997, 1999) also
developed a fluorescent imaging system for detecting the dynamic moving conduct line of film flow over an inclined
plate. Later, laser induced fluorescence intensity method was used to measure wavy films (Lel et al. 2005, Schagen
et al. 2007), and heated liquid film (Chinnov et al. 2007). Density-based techniques have been a useful tool to map
the free surface deformation. Zhang et al. (1996) developed a color encoding system to measure free surface
vibration by mapping the free surface slope. Scheid et al. (2000) reported a reflectance schlieren method to profile
the local heated vertical falling film flow. Moisy et al. (2009) raised a free-surface synthetic schlieren method (FSSS) and applied this method to reconstruct the wave pattern generated by the impacting water droplet. Besides
optical methods, ultrasonic technique (Li et al.2010) and electrical-based method (Burns et al. 2003) are also found
in the literature.
Recently, digital fringe projection (DFP) technique with the advantages of high-resolution, whole-field 3D
reconstruction of objects in a non-contact manner at video frame rates (Gorthi and Rastogi, 2010), has been
increasing used in free surface thickness measurements. Its applications include vertex shape reconstruction at a free
surface (Zhang and Su 2002), free surface measurement of sanitation system storm overflow ( kouyi et al. 2003),
evaluation of surge’s free surface variation of dam-break (Cochard and Ancey 2008) and water-wave trapped
modes investigation ( Cobelli et al.2011). All of those investigations used fourier transform profilometry (FTP)
system to reconstruct free water surface shape. This method requires precise projected sinusoidal fringe pattern,
1
Graduate Research Associate, Department of Aerospace Engineering
Assistant Professor, Department of Mechanical Engineering.
3
Professor, Department of Aerospace Engineering, AIAA Associate Fellow.
4
Associate Professor, Department of Aerospace Engineering, AIAA Associate Fellow, Email: [email protected]
1
American Institute of Aeronautics and Astronautics
2
Copyright © 2013 by Kai Zhang, Song Zhang, Alric Rothmayer and Hui Hu . Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
Downloaded by Hui Hu on January 11, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2013-247
which is very hard if not impossible to achieve on the liquid surface. On the other side, the two-dimensional phase
unwrapping integral calculation is sensitive to integral path and tends to accumulate errors.
In this paper, we present a novel digital image projection based technique for measuring free surface deformation
of wind-driven thin water film. The image cross-correlation based digital fringe projection system will be described
in this presentation. In contrast to directly projecting focusing sinusoidal patterns to 3D objects surface, cross line
grid is used to reconstruct the 3D shape. The grid points’ displacements between zero height reference image and
deformed liquid surface image are calculated by doing cross-correlation between the two images. The relationship of
grid displacement and object height is mapped by system calibration. In order to demonstrate the advantages of the
cross correlation DFP measurement system, both the new technique and FTP based DFP measurement technique are
used to reconstruct a sphere head shape object with known profile. The results show the novel system is more
accurate and insensitive to image quality.
The other particular interest for the present paper is the water-air interface reconstruction of wind-driven thin
water film flows. Although there are some theoretical and numerical investigations on the shear stress driven water
film flows ( Boomkamp et al.1997, Rothmayer et al.2002, Wang and Rothmayer 2009, Marshall and Ettema 2004),
the experimental investigations on wind-driven thin film flows are seldom found (Marshall and Ettema 2004, Shaikh
and Siddiqui 2010). In this paper, the cross correlation based DFP measurement system was applied to free surface
measurement of thin water film flows, which were generated by a small wind tunnel with different airflow velocities
and different water flow rates. The thin film deformation process and traveling wave frequency were quantitatively
studied.
This paper is organized in six sections as follows. Section 2 describes the principles of cross correlation based
DFP technique. Section 3 compares the measurement accuracy of our novel technique with FTP based DFP method.
Section 4 illustrates the complete experiment set up for wind-driven thin water film flow thickness measurement.
Section 5 shows the thin water film flows measurement results, such as film flow instantaneous and average
thickness, traveling wave frequency and wave deformation process. Finally, section 6 presents conclusions.
II. Description of the principles of the measurement method
2.1. Cross correlation based DFP measurement system
The basic principle of digital fringe projection technique is very simple. A typical DFP system contains a
projection unit, image capture unit and data processing unit. The projector projects a known pattern to the test
object. Due to the 3D geometry of the object, the projected image will distort. By proper processing algorithm to
compare the distorted image pattern with the reference image, the three dimensional profile of the object can be
reconstructed.
Modern projectors provide a great flexibility in projecting any kind of fringe patterns. This feature permits
researchers to design various kind of light patterns and associated processing algorithms for 3D shape profile
reconstruction (Gorthi and Rastogi, 2010). Our new cross correlation based system measurement techniques can be
seen as a development of novel projection pattern and corresponding novel processing algorithm. In addition, the
new technique is applied to a novel field of wind-driven thin film flow free surface deformation measurement
problems.
Figure1 shows the layout for the cross correlation digital fringe projection system. Computer generated cross line
grid is projected to the measurement 3D object. A CCD camera, which is synchronized with projector through a
delay generator, is used to capture the projected images. Substrate image without measurement object will also be
recorded as a reference image. Due to the 3D shape of the object, the projected grid will distort and grid points on
the 3D object surface will translate a distance. Correlation calculation between measurement images and the
reference image will be performed to obtain the distorted grid points’ displacements field. The linear converting
relationship between distorted displacements field and 3D object height can be mapped by calibration process. After
that, the geometry of the 3D object is reconstructed. The details of correlation algorithms and image processing
procedure are explained in section 2.2. Section 2.3 illustrates the principles of displacement to height coefficient
map and system calibration process.
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Fig.1: Schematic diagram of cross correlation based measurement system
2.2. Principle of digital image correlation method
Digital image correlation (DIC) algorithms are widely used in particle image velocimetry (PIV) (Adrian 1991,
Raffel et al. 1998). This method is searching for the peak correlation coefficient location of two-image sequence.
The spatial correlation algorithm developed by Gendrith and Koochesfahani (1996) is particularly suitable for digital
projection measurement technique. Cross line grids can be easily obtained by the digital projector and the algorithm
has been proven to be sub-pixel accuracy and has been successfully applied in the molecular tagging velocimetry
(MTV) technique. Instead of implementing three dimensional geometry reconstruction by converting phase
difference to height (traditional DFP method), the relationship of cross line center’s displacement to height can be
built based on the optical principal of DFP technique (discussed in section 2.3).
Figure2 shows the sketch of correlation algorithm. A zero height flat plate is taken as a reference plane. The
small red window ( I r ) refers to the interrogation window located in the grid centers of reference image (image of
reference plane). Correspondingly, the small blue window ( I ) refers to the interrogation window in the target image
(distorted grid image due to presenting the 3D object). The big rectangular region is the searching windows on the
target image. The displacements field can be obtained by doing spatial correlation calculation between the
interrogation windows of target image and reference image within the searching window. The peak correlation
coefficient R ( m, n ) location defines the displacement vector ( ∆x , ∆y ) . We describe the normalized correlation
coefficient with following formula:
∑∑ I
R(m, n) =
i
∑∑ ( I
i
r
(i, j ) I (i + r , j + s )
j
r
(i, j ) − I r )2 ( I (i + r , j + s ) − I )2
(1)
j
Where I and I r represent the interrogation window intensity of reference image and target image respectively,
I r and I are the corresponding mean intensity values of I r and I . ( r , s ) is the searching vector.
According to Gendrith and Koochesfahani (1996), the sub-pixel accuracy can be achieved by nth polynomial
fitting of the correlation coefficient. In this work, we used 4th polynomial fitting with 5 × 5 pixels fitting region. The
fitting function F (i , j ) can be expressed as:
4
F (i, j ) = ∑ (cn,0 i n j 0 + cn ,1i n −1 j1 + ... + cn , n i 0 j n )
(2)
n =0
Where (i , j ) denotes the local coordinate system. Its origin locates at the same point of the reference image cross
line center. cn ,0 , cn ,1 ...cn , n denotes fit coefficients.
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Fig. 2: Sketch of correlation algorithm.
(a)
(b)
(c)
Fig. 3: Sample experimental cross-correlation base DFP images. (a) Reference image. (b) Cross line centers
detection image. (c) Calculated grid points displacements field and distorted grid image.
Typical reference image and deformed grid image are shown in Fig. 3. Reference image is generated by
projecting cross line grid to the substrate (Fig. 3(a)). Image identification algorithm is applied to recognize the cross
line centers in the reference image (Fig. 3(b)). Those center points form the calculation grid used in the data
processing. The reference interrogation windows are centered at grid points. Spatial correlation calculation is then
performed to get the distorted displacements of the grid. The displacements of the grid deformation are shown in
Fig. 3(c).
2.3. Displacement to height conversion map
The converting coefficients map of grid points’ displacements to 3D object height can be determined by
calibrating the DFP system. Figure4 illustrates the schematic of the displacement to height conversion calibration set
up. To conduct the calibration, the camera and the projector are located at same height L and separated by a distance
d. Point D denotes the pupil center of the camera and point E denotes the pupil center of the projector. A reference
plane is used as a zero height plane. The projector projects a grid point C on the measurement object surface.
Supposing that there is no 3D object in the test plane, from projector’s perspective, grid point C should be projected
to grid point B on the reference plane. From the camera’s view, point A is the same pixel as point C in the reference
image. The grid deformation displacement between point A and point B can be expressed as:
∆ = AB = Pr ( A) − Pr ( B ) = P (C ) − Pr ( B )
(4)
Where ∆ denotes deformation grid displacement, P denotes grid points location and subscript r denotes the
reference image. Because point A is the same pixel as point C on the CCD sensor, AB = P(C ) − Pr ( B) can be
obtained by spatially correlating the reference image and object image.
Owing to the triangle ACB is similar to triangle DCE, the relationship between object height h and deformed
grid displacement AB can be represented:
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ABL
(5)
AB + d
Where subscript i, j denotes pixel location of the object on the camera captured image. The maximum height of
measurement project is much smaller than the distance between camera and projector d and projector height L, the
equation can be simplified as:
h(i, j ) =
Downloaded by Hui Hu on January 11, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2013-247
h (i , j ) =
L
AB = K (i, j ) AB
d
(6)
Fig.4: Sketch of optical configuration of DFP system
Equation (6) represents a linear relationship between deformation displacement AB and object height h.
However, for our measurement system the Y direction displacement approaches zero as ∆Y → 0 . Thus X direction
displacement is used to map the coefficients:
h (i , j ) = K ( i , j ) ∆ X ( i , j )
(7)
To accurately calibration the DFP system, 8-10 different heights of flat plate DFP images need to be recorded. A
vertical translation stage with micrometer is used to precisely adjust the vertical location of the test plate. The lowest
plate location is selected as the zero height location and its DFP image is taken as reference image. Other images are
spatial correlated with the reference image to obtain the grid displacements. Then the linear displacement to height
coefficients map is then determined by least square method.
III. Technique verification and comparison with FTP based DFP method
Currently, most of the free surface measurements using DFP system are based on fourier transform profilometry
method. The measurement accuracy of that method relies on the quality of the experiment image. It presumes a
perfect sinusoidal image intensity profile which is impossible to achieve in liquid surfaces. On the other hand, twodimensional unwrapping process is a integration calculation. It is not only highly sensitive to the integration path but
also the integration itself is inclining to accumulate measurement errors.
In this section, we will compare those two methods and demonstrate that the cross correlation DFP system is
advantageous for accurate 3D shape reconstruction. The sinusoidal fringe patterns, which are used in FTP based
DFP system, are gotten by defocused binary patterns (DBP). Fourier transform method was used to obtain the
wrapped phase map. For details of the data processing method, including phase separation algorithm, high order and
fundamental frequency noise reduction, refer to our previous paper (Wang et al. 2011).
During the experiment, Dell DLP projector (M109S) was used to project the defocused binary fringe patterns
and grid cross line patterns to a sphere head shape model with known profile. A CCD camera (DMKBU2104) with a
Pentax C1614-M lens (F/1.4, f=16mm) was used for DFP image acquisition. A digital pulse/delay generator
(Standard research system, Model DG535) was employed to synchronize the CCD camera and the projector by
VGA Vertical sync signal. The camera has a maximum frame rate of 60frames/s with a resolution of 640×480. The
camera exposure time was set at 1ms. The projector has a resolution of 858×600. A droplet like sphere head shape
was used to verify the system, The sphere head has a base circle radius of 10mm and 4mm height. This model was
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Downloaded by Hui Hu on January 11, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2013-247
3D printed by rapid prototyping machine with typical accuracy of 20µm. To improve the diffuse reflectivity of the
surface, the test model was coated with flat white paint.
Calibrations were performed to determine the phase to height coefficients map K1 (i, j ) for FTP based DFP
system and displacement to height coefficients map K 2 (i, j ) for cross correlation based DFP system. The results are
shown in Fig. 5. As seen from the figure, the phase to height conversion coefficients K1 (i, j ) are varied with each
fringe, whereas the displacement to height conversion coefficients K 2 (i, j ) are varied along camera-projector
connection direction (X direction in Fig. 4). In Fig. 5 ( xi , yj ) represents the image coordinate system.
(a)
(b)
Fig.5: Phase to height and displacement to height coefficient map. (a). Coefficient map for FTP-based system;
(b). Coefficient map for cross correlation based system
Table1shows the average measurement errors and standard deviation of the two techniques. Note that the
average measurement error was calculated from absolute differences between measurement height distribution and
design shape of the sphere head model. In addition, we only accounted for the measurement points on the sphere
head object surface and the manufacturing errors of the test model were not taken into account during this work. The
average measurement error of FTP-based DFP system is 0.12mm, its corresponding standard deviation is 0.08mm.
The average measurement error of cross correlation DFP system is only 0.04mm, its corresponding standard
deviation is 0.04mm. It is seen that the cross-correlation based DFP test system is much more accurate than the FTPbased measurement system. The measurement errors are halved by novel DFP system.
Table1. Measure error of two DFP systems
Mean error (mm)
Standard deviation of errors (mm)
FTP based DFP
0.12
0.08
Cross-correlation based DFP
0.04
0.04
Figure 6 shows the measurement height distribution of sphere head model by FTP-based DFP system. Figure
6(a) displays that sphere head shape was not precisely reconstructed. Distinct uneven fringe shape roughness can be
seen in the 3D reconstructed surface. Figure 6(b) shows the measurement errors distribution of FTP-based DFP
system. As shown in Fig. 6(b), the measurement errors are also varied by individual fringes. The measurement error
is range from -0.5mm to 0.5mm. Those measurement errors are mainly caused by the discrepancy between the
faultless sinusoidal intensity pattern and the experimental image pattern intensity profile. This inconsistency may
come from many sources including projector interpolation blur, non-uniform reflectivity of object plane, camera
lens distortion etc.
Figure 7 shows the measurement results for cross correlation based method. As shown in Fig. 7(a), the
reconstructed 3D object shape is much smoother. Only some tiny distortions on the boundary of the test object are
observed. Fig. 7(b) presents that the measurement error of our novel system is generally in the range -0.1mm0.15mm. Some relative high error scatters appear in the edge of the sphere head shape. Due to the nature of
correlation calculation, a single measurement point is ensemble-average of an interrogation window (current work
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7×7 pixels). For those boundary points whose interrogation windows are partly on the substrate and partly on the 3D
object surface, measurement errors can not be avoided. Because of the same reason, cross correlation DFP technique
significantly decreases measurement spatial resolution compared with FTP system. The measurement results
indicate that at a cost of decreasing spatial resolution, the new technique can conduct high accuracy measurement
without rigid picture quality restrictions.
Measurement
Height (mm)
Measurement
Error (mm)
0 0.5 1 1.5 2 2.5 3 3.5 4
60
0.1 0.2 0.3 0.4 0.5
40
4
2
0
60
20
80
mm
60
80
m
40
Y,
80
mm
X,
Y,
m
m
40
X,
m
Downloaded by Hui Hu on January 11, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2013-247
20
H,mm
H,mm
40
4
2
0
-0.5 -0.4 -0.3 -0.2 -0.1 0
60
100
80
100
(a)
(b)
Fig.6: Measurement results of FTP-based system. (a) 3D shape reconstruction for R10mm, H4mm sphere
head model; (b) Measurement errors distribution for R10mm, H4mm sphere head model.
(b)
(a)
Fig.7: Measurement results of cross correlation system. (a) 3D shape reconstruction for R10mm, H4mm
sphere head model; (b) Measurement errors distribution for R10mm, H4mm sphere head model.
IV. Experiment Setup and Procedure
Figure8 illustrates the schematic of the experiment setup for wind-driven thin water film flows thickness
measurement test. The DFP system set up is generally the same as the verification experiment. Camera speed is set
to 30FPS with 2ms exposure time. The field of view of CCD camera is approximately 9cm×11cm. The projected
grid size on the captured image is 7×7 pixels. It is also the interrogation window size for cross correlation
calculation. A micro digital gear pump (Cole-parmer 75211-30) and a small water tank were used to produce two
steady water flow rate of 16.7ml/min/cm and 33.3ml/min/cm. In order to generate uniform film flow, an array of
holes was drilled in the substrate that is coated with flat white paint. The dimension of water outlet holes array is
total array width D=6cm, hole distance 5mm and hole diameter 2mm (Fig. 9). The dimension of substrate is
25cm×15cm. It should be note that, during the experiment, water may run back due to the surface tension force
under low wind speed conditions. A wedge edge plane may solve the problem in the future work.
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The experiment was conducted in an open circuit low-speed wind tunnel. The wind tunnel has a plexiglas test
section with dimension of 20×14×30cm (W×H×L). Three difference wind speeds 10m/s, 15m/s and 20m/s were
used to investigate the different behaviors of the thin film flow. Flat white latex paint was added into water for
enhancing the diffusive reflection on the liquid surface. Note that latex paint affects the surface tension of the water,
as a result the film behavior in this work is different with pure water film flows. Some other coloring pigments may
be used in the future work to avoid film flow contamination (Przadka et al. 2012). The other limitation of current
experiment is that we did not investigate the errors caused by the diffusion effect of projector light ray enter into the
water.
Fig.8: Experiment set up for wind-driven thin water film flows test
The test procedure for film flows measurement is: first let the water overflow the substrate under test flow rate
condition. Then adjust the wind speed to 20m/s to generate uniform thin water film flow. Further reduce the wind
speed to 15m/s and 10m/s. For each case, 600 images (20s) were collected after the flow is steady. Each image is
carried out cross correlation calculation with reference image and the obtained results were interpolated to regular
grid points. The measurement results are normalized by the width of the water outlet holes array width D=6cm. L
denotes the distance that is away from the water holes array. W denotes the distance that is away from the centerline
of the test plane along flow direction (Fig. 9).
Figure 9. Schematic diagram of water outlet holes array and coordinate
V. Measurement Results and Discussions
Figure10 shows the instantaneous and ensemble-average thin water film flow thickness distribution as the air
velocity range from V=10m/s-20m/s at flow rate Q=16.7ml/min/cm. As displayed in Fig. 10(A), the instantaneous
film shape is almost the same with the ensemble-averaged one under wind speed V=10m/s. The water-air interface
behaves like a calm water surface. It demonstrates that the surface tension is the dominant force and resists the
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water-air interface displacement under low wind speed conditions (V<10m/s). Water surface raise was observed
near the end of the measurement field (more clearly in Fig. 12). It is because the surface tension at the vertical edge
of the substrate end will block the film flow. As the flow speed increase to V=15m/s, water traveling waves were
generated due to the disturbance of air shear stress force. We found that quasi-regular waves would emerge near the
water outlet holes and gradually attenuate as they traveled downstream. We did spectrum analysis for this case and
got some interesting results, which will discuss later. The average thickness distribution for this case is generally the
same with other flow speeds and flow rate cases except the V=10m/s, Q=16.7ml/min/cm one. The thickness
distribution is a generally symmetric distribution with respect to the centerline and decreases along flow direction.
Figure10(C) shows that water waves break into several segments at the very beginning of the thin film flow when
the airflow velocity reaches 20m/s. Those waves further breakup and evolve to small pieces as they flow
downstream. This implies the air shear stress force most dominates the flow. The ensemble-average thickness
distribution exhibits a perfect thin film shape like a flat plate.
H,mm: 0 0.2 0.4 0.6 0.8 1 1.2 1.4
0.5
0.5
0
-0.6
1
-0.4
0.5
H,mm
H,mm
D
L/
0.5
0
-0.6
1
-0.4
-0.2
D
L/
-0.2
W/D0
0.2
W/D0
1.5
0.4
0.2
1.5
0.4
0.6
0.6
a. Instantaneous measurement result
b. Ensemble-average measurement result
A. V=10m/s
H,mm: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
H,mm: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.5
0.5
0
-0.6
1
-0.4
D
L/
0.5
H,mm
H,mm
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H,mm: 0 0.2 0.4 0.6 0.8 1 1.2 1.4
0.5
0
-0.6
W/D0
D
L/
1
-0.4
-0.2
-0.2
0.2
W/D0
1.5
0.4
0.2
1.5
0.4
0.6
0.6
a. Instantaneous measurement result
b. Ensemble-average measurement result
B. V=15m/s
H,mm:
0
H,mm:
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
H,mm
1
-0.4
D
L/
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0.5
H,mm
0.5
0.5
0
-0.6
0
0.5
0
-0.6
1
-0.4
D
L/
-0.2
-0.2
W/D0
0.2
1.5
0.4
W/D0
0.2
1.5
0.4
0.6
0.6
a. Instantaneous measurement result
b. Ensemble-average measurement result
C. V=20m/s
Fig.10: DFP measurement results of different wind speeds at flow rate Q=16.7ml/min/cm.
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Figure11 shows the film thickness distribution under the flow rate Q=33.3ml/min/cm. Compare with cases of
flow rate Q=16.7ml/min/cm, the disturbances caused by overflow of water outlet holes are much more severe.
Because of larger flow rate and uneven flow rate of each hole, the water-air interfaces display an irregular surge
shape at the range close to water outlet holes (L/D<0.5). For wind speed V=10m/s case, in the range L/D>0.75, the
thin water film behaves as a generally flat surface shape which indicates the surface tension the other time
dominates the motion and tends to stabilize the water-air interface (Fig. 11(A)). For wind speed V=15m/s and 20m/s
cases, in the range L/D>0.75, the displayed instantaneous water-air interfacial waves style are roughly the same with
the Q=16.7ml/min/cm ones. The flow rates of individual holes are different, as a result, the ensemble-averaged
results show the film thicknesses are no longer uniform along the water holes’ array direction. However, the
ensemble-averaged film thicknesses are still platform like shape. Both the instantaneous and ensemble-averaged
results indicate that the flows are somewhat regulated by the combined effects of water surface tension, gravity force
and air shear stress force.
H,mm: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.5
0
-0.6
1
-0.4
D
L/
0.5
H,mm
0.5
H,mm
0.5
0
-0.6
1
-0.4
D
L/
-0.2
-0.2
W/D0
0.2
W/D0
1.5
0.4
0.2
1.5
0.4
0.6
0.6
a. Instantaneous measurement result
b. Ensemble-average measurement result
A. V=10m/s
H,mm: 0 0.1 0.2 0.3 0.4 0.5 0.6
H,mm: 0 0.1 0.2 0.3 0.4 0.5 0.6
0.5
0.5
0
-0.6
D
L/
1
-0.4
0.5
H,mm
H,mm
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H,mm: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.5
0
-0.6
1
-0.4
-0.2
W/D0
D
L/
-0.2
0.2
W/D0
1.5
0.4
0.2
1.5
0.4
0.6
0.6
a. Instantaneous measurement result
b. Ensemble-average measurement result
B. V=15m/s
H,mm:
0
H,mm:
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
H,mm
1
-0.4
D
L/
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0.5
H,mm
0.5
0.5
0
-0.6
0
0.5
0
-0.6
1
-0.4
D
L/
-0.2
-0.2
W/D0
0.2
1.5
0.4
W/D0
0.2
1.5
0.4
0.6
0.6
a. Instantaneous measurement result
b. Ensemble-average measurement result
C. V=20m/s
Fig.11: DFP measurement results of different wind speeds at flow rate Q=33.3ml/min/cm
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16.7ml/min/cm_10m/s
16.7ml/min/cm_15m/s
16.7ml/min/cm_20m/s
33.3ml/min/cm_10m/s
33.3ml/min/cm_15m/s
33.3ml/min/cm_20m/s
1.5
1.0
H, mm
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Figure12 shows the ensemble-average film thickness profiles at the centerline of film flow under different wind
speeds and different flow rates. Seen from the figure, the profiles of the thin water film generally first raise and then
decrease to a steady height except for case Q=16.7ml/min/cm, V=10m/s. The gradient of the curves are slightly
different with wind speeds and flow rates. Seen from Fig. 10(B), the water-air interfacial waves’ amplitude of case
Q=16.7ml/min/cm, V=15m/s are much higher, which leads to a gradually decreases to stable thickness profile. The
film flows thicknesses of larger flow rate are much higher than the lower flow rate ones at the range close to water
outlet hole. However, they will reach stability at downstream range. Steady thin film thicknesses vary from 0.050.35mm and decreases with increasing wind speeds and water flow rates. Those ensemble-average film thickness
profiles can be considered as a reference of two dimensional undisturbed film flow water-air interfaces.
Spectrum analysis is performed to reveal the water waves evolution for case V=15m/s and Q=16.7ml/min/cm.
Three points (L/D=0.25, W/D=0), (L/D=0.75, W/D=0) and (L/D=1.25, W/D=0) were chosen to do fourier transform
calculation. As mentioned above, our camera speed was set to 30FPS and 600 images (20s) were captured for each
case. The theoretical maximum identifiable frequency is 15Hz with a resolution of 0.05Hz. Interpolation calculation
was used to get film thickness at those three points. As shown in the Fig. 13(A), the dominant frequency at point
(L/D=0.25, W/D=0) is 7Hz which indicates the frequency of water-air interfacial waves is 7Hz. If there are no
damping effects, the wave frequency will preserve as they propagate to downstream. However, the dominant
frequency at point (L/D=0.75, W/D=0) is 3.5Hz (Fig. 13(B)) and there is no obvious dominant frequency at point
(L/D=1.25, W/D=0) (Fig. 13(C)). We examined the animation of our measurement result and found that the water
wave amplitude will attenuate as it travels downstream. Only one out of two interfacial waves can reach point
(L/D=0.75, W/D=0) without significant reduction of wave amplitude. The waves that can reach point (L/D=1.25,
W/D=0) is random, which induces several low frequency signals in the Fig. 13(C).
0.5
0.0
0.0
0.6
1.2
1.8
L/D
Fig.12: Ensemble-averaged thin water film thickness profiles at film center line W/D=0.
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0.7
0.6
H, mm
0.5
0.4
0.3
0.2
0.1
5
6
7
8
9
10
Time, S
b. Frequency spectrum
A. L/D=0.25D, W/D=0
0.6
H, mm
0.5
0.4
0.3
0.2
0.1
5
6
7
8
9
10
Time, S
a. Time history of film thickness
b. Frequency spectrum
B. L/D=0.75D, W/D=0
0.6
0.5
0.4
H, mm
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a. Time history of film thickness
0.3
0.2
0.1
0.0
5
6
7
8
9
10
Time, S
a. Time history of film thickness
b. Frequency spectrum
C. L/D=1.25D, W/D=0
Fig.13: Time history of film flow thickness and wave frequency analysis.
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VI. Conclusions
A novel cross correlation based DFP measurement system was developed to provide high accuracy measurement
on wind-driven thin film flows. The new measurement method inherits most of the ordinary DFP technique merits
such as simple set up, low cost, whole field and non-contact measurement at video speed. Compared with FTP based
DFP measurement system, the new technique was proved to be much more precise with a lower image quality
requirement. Both of those two methods were used to reconstruct a sphere head model. The average measurement
error of cross correlation based DFP system is 0.04mm with a standard deviation of 0.04mm. The average
measurement error of FTP-based DFP method is 0.12mm, with a standard deviation of 0.08mm.
Wind-driven thin water film flows were measured using this technique to demonstrate system’s applicability.
Both instantaneous and ensemble-average thin film thickness distributions were successfully reconstructed. The
dynamic motion of film flow was revealed. For wind speed 10m/s cases, the results show that the water surface
tension dominates the flow and makes the water-air interface shape like a flat plane. As the wind speed increases to
15m/s and 20m/s, water-air interfacial waves were observed. Those interfacial waves were generated at the range
near the water outlet holes and they would attenuate and broke in to small pieces as they traveled downstream. The
case of wind speed 15m/s and flow rate 16.67ml/min/cm was selected to do spectrum analysis for revealing the
frequencies and transient features of those water waves. The results show that at the position L/D=0.25, the
dominant wave frequency is 7Hz, which is quite obvious. At location L/D=0.75, the dominant frequency is reduce to
3.5Hz. There is no noticeable dominant frequency at location L/D=1.25. The ensemble-average thin film profiles at
the centerline of film flows were also plotted. The outcomes of wind-driven thin film flows measurement
demonstrates that cross correlation based DFP technique is a useful tool for unsteady water-air interface behaviors’
investigation.
Acknowledgments
The research work was partially supported by National Aeronautical and Space Administration (NASA) - Grant
number NNX12AC21A with Mr. Mark Potapczuk as the technical officer. The support of National Science
Foundation (NSF) under award number of CBET-1064196 with Dr. Sumanta Acharya as the program manager is
also gratefully acknowledged.
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