flow control over a dimpled surface3 b. a water tunnel with a test section to insert the...
TRANSCRIPT
![Page 1: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/1.jpg)
Flow Control Over A
Dimpled Surface
UIS 3931 Independent Study Module
Dilip Joy Thekkoodan
U067756J
![Page 2: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/2.jpg)
i
Table of Contents
List of Figures ........................................................................................................................ ii
List of Tables & Graphs ...................................................................................................... iiiii
Introduction ............................................................................................................................ 1
Objectives .............................................................................................................................. 2
Apparatus/Equipment Required ............................................................................................. 2
Experimental Setup ................................................................................................................ 3
Experimental Procedure ......................................................................................................... 6
Data Tables & Graphs ............................................................................................................ 7
Pictures ................................................................................................................................. 12
Observations ........................................................................................................................ 15
Future Work ......................................................................................................................... 18
Conclusions .......................................................................................................................... 19
References ............................................................................................................................ 20
Appendix .............................................................................................................................. 21
![Page 3: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/3.jpg)
ii
List of Figures
1. Circular dimple (top view)
2. Water-tunnel arrangement
3. Side view of dimple
4. Fully developed flow over dimple (visualization with all 13 dye release holes)
5. Salient features of the flow over dimple (5 images)
6. Dominant vortices seen at d = 10mm (2 images)
7. Turbulent flow over dimple
8. Dye concentration point in dimple
9. Fully developed flow for d = 3mm
10. Fully developed flow for d = 5mm
11. Fully developed flow for d = 7.5mm
12. Flow features for d = 10mm (4 images)
13. Exploded view of dimple-mount
14. Sectional view of assembled dimple mount
15. Zoomed-in view of dye reservoir inlet and outlet (2 images)
![Page 4: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/4.jpg)
iii
List of Tables & Graphs
Tables
1. Dimple depth variation with angle of rotation of piston-screw
2. Error in dimple depth measurement (using equation 3)
3. Effect of water column on dimple depth variation
4. Flow parameters
5. Intermittency factor
6. Error in dimple depth measurement (using equation 4)
7. Dimple depth-to-diameter ratios
Graphs
1. Plot of dimple depth v/s angle of rotation of piston-screw
2. Intermittency factor variation with flow velocity (for all depths)
![Page 5: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/5.jpg)
1
Introduction
One of the thrust areas of modern-day aerospace research is the reduction of drag. With
the number of flights and flight operators increasing, it is paramount to reduce the drag
force on aeroplanes and thereby improve the aircraft performance. Even a small decrease in
the net drag force could mean a drastic reduction in overall flight operating costs.
Some of the methods that are employed in modern-day aircrafts include control of
separation by suction of retarded boundary layer, energizing the boundary layer by
injection from a blower or by using a slot in the wing to accelerate the retarded boundary
layer. These methods delay or prevent boundary layer separation from the body, thereby
reducing the wake region resulting in a net pressure drag.
Another way to reduce the net drag force is by disturbing the flow. By doing this the
boundary layer becomes turbulent and therefore more resistant to separation, again
resulting in a net reduction in drag. This method is employed to reduce the drag on golf
balls (by introducing dimples on its surface). It must be noted, however, that spheres are
bluff bodies with a significant cross-sectional area, and the effect of disturbing the flow is a
net decrease in the already large pressure drag.
Drag reduction by using dimples on flat surfaces (or streamlined) is not yet clearly
understood and is a topic of current interest. This is different from the golf-ball case as here
the pressure drag is already small, and the substantial component of the drag is due to skin-
friction. Therefore, the mechanism of drag reduction, if any, must be related to altering the
pressure distribution over the surface. A recent study by Lienhart et al. (2008) showed that
a regular arrangement of circular dimples does not lead to drag reduction. Similarly,
![Page 6: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/6.jpg)
2
Zhdanov and Papenfuss (2003) studied the effect of both flat plates and circular-dimple
arrays (d/D~0.1) and concluded that circular-dimples do not produce any appreciable
reduction in drag.
While the above mentioned studies indicate negligible drag reduction properties for
circular dimples, it was considered worthwhile to investigate whether the shape of the
dimple would have any positive effect to this end. This project aims to study the effect of
the shape of a dimple on the drag force produced. The shapes that are to be tested include a
circle, an equilateral triangle and an isosceles triangle – all having the same cross sectional
area.
Objectives
There are three parts to this project:
1. To obtaining flow visualization of the fluid flow over a circular dimple (for different
d/D ratios) and study the characteristics of the flow
2. To obtain the flow visualization of the flow over the two triangular dimples (for
different depths) and compare this with the circular dimple case
3. To make measurements to estimate the drag force for each case and compare the results
This report discusses the findings from the flow visualization experiments done with the
circular dimple.
Apparatus/Equipment Required
a. For dimple mount – a plug that can be fit into a water tunnel, a brass disk (diameter =
89.85 mm), white rubber sheet (1mm thickness), water-proof white paper
![Page 7: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/7.jpg)
3
b. A water tunnel with a test section to insert the dimple-mount
c. Red colour dye, dye reservoir, 5mm hose
d. For the video recording system – Monitor, Video Cassette Recorder, blank video
cassette, video camera with adapter, lens of appropriate focal length & zoom, data
cables, camera stand
e. Laboratory equipment like spanners and screw drivers of different sizes, nuts and bolts
of different sizes, superglue, silicone glue, glycerin, cleaning oil and Vernier Caliper
Experimental Setup
The following steps were followed to set up the dimple mount:
a. A brass disk of 89.85 mm diameter that perfectly fits inside the plug is taken and a 50
mm diameter circular hole is made inside it such that the two circles are concentric.
b. A 45-degree campher is made on the edge of the inner circle.
c. Both the surfaces of the disk are cleaned thoroughly, and a thin 1 mm white rubber
sheet is fixed on the top surface using superglue. This is left to dry for a few hours.
d. The rubber sheet is cut along the boundary of the disk and the edges are scraped of any
excess rubber so that now a layer of circular rubber sheet of the exact outer-diameter as
the disk is stuck on the disk.
e. A rectangular grid with 5 mm spacing is drawn on the top side of the rubber sheet.
f. Next, along the edges of the bottom surface of the disk, silicone glue is applied and
fixed onto the plug. This is then left in an inverted position so that the surface of the
rubber layer is at the same level as the plug surface. This is left to dry for a day.
![Page 8: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/8.jpg)
4
g. The gap between the piston and the now affixed disk on the plug is filled with glycerin
and the any air bubbles present are removed and the two holes on the piston closed with
appropriate screws.
h. The thin-metal bar to hold the piston screw is place is fixed and screwed onto the plug
and the 2 hexagonal nuts of the piston-screw are affixed.
i. The top surface of the plug is cleaned and a clean white sheet of water-proof paper is
stuck on it and the edges are trimmed for a perfect fit. Holes are made at those places
where the dye exits the plug to produce the visualization.
j. Next, a dye reservoir is setup and a hose used to fix the reservoir to the inlet of the dye
reservoir in the plug. A flow regulator is fixed onto the hose which will be used to
control the dye flow. The dye will be released by a gravity-feed system.
k. A sealing gasket tape is stuck onto the section of the plug that would be in contact with
the water tunnel wall. The dimple-mount (plug) is then mounted onto the bottom wall
of the tunnel and fixed in place with the help of screws.
l. The gap between the plug and the tunnel base is sealed with an annulus-shaped white
water-proof paper. The tunnel can now be run to obtain visualizations.
There are 7 dye releasing holes that are opened to obtain the dye visualization (although in
total there are 13 available as shown in fig 4). These are positioned in a circular fashion
around the dimple with one that is in line along the centre line of the dimple (centre of a
diameter that is perpendicular to the flow direction), and three that are symmetrically
position on either side of this central dye hole. These are labeled in the fig 1.
![Page 9: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/9.jpg)
5
Fig 1: Circular dimple showing all the holes and the water flow direction (top view)
Fig 2 Fig 3
Figures: (fig 2) the water tunnel arrangement showing the
position of various parts, (fig 3) side view of the dimple and
(fig 4) the fully developed flow structure with all 13 holes
opened.
Hole 1
Hole 2b
Hole 2a
Hole 3a
Hole 4a
Hole 3b
Hole 4b
Dimple
Flow
Direction
Video Camera (mounted)
Water Tunnel
Fig 4
Side a
Side b
Dimple
![Page 10: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/10.jpg)
6
Experimental Procedure
The experiments are run as follows:
1. Firstly, the water tunnel is filled with water up to a height of about 40.2 cm
2. Next, a video camera is mounted above the water tunnel positioned directly above the
dimple and the image is brought to focus by adjusting the lens. The camera output is to
be captured and recorded on a video cassette using a Video-Cassette-Recorder (VCR)
system
3. The dye flow is first set by adjusting the valve regulator that is fixed to the hose. This is
done by releasing the dye and then adjusting the regulator so that the dye appears as a
smooth filament. After this is set the regulator is not disturbed and the dye is released or
stopped by either opening or closing (completely) the release valve near the reservoir.
4. The dimple height is set to 5mm and the tunnel is run with the velocities set at:
0.117m/s, 0.147 m/s, 0.178 m/s, 0.205 m/s and 0.235 m/s. The dimple depth is set by
rotating the piton-screw of the dimple-mount using the calibration data (given in the
section: Data Tables & Graphs)
5. Step 3 is then repeated by setting the dimple depth to 7.5 mm, 10 mm and 3mm.
To obtain 3 mm dimple-depth, the height of the water in the tunnel is reduced to 27.7 cm
and the angle of rotation is set to 0º. This is done because when the tunnel is filled up to
maximum height (40.2 cm), there is a minimum depth of about 4.8 mm. Therefore, to
achieve the 3 mm depth, the water height is reduced. Due to the change in the cross-section
that follows this, the tunnel setting is adjusted so that visualizations are obtained at the
same velocities (i.e.; 0.117m/s, 0.147 m/s, 0.178 m/s, 0.205 m/s, 0.235 m/s and 0.294m/s)
![Page 11: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/11.jpg)
7
Data Tables & Graphs
Table 1: Dimple Depth Variation with Angle of Rotation of Piston-Screw
Angle
(degrees)
Depth Measured (δ) (in mm)
R1 R2 R3 R4 R5 R6 R7 Average
0 0 0 0 0 0 0 0 0
60 0.88 0.96 1.09 0.94 0.73 0.84 1.11 0.94
120 1.74 1.78 1.99 1.92 1.9 1.74 2.17 1.89
180 2.52 2.64 2.96 2.61 2.74 2.51 2.92 2.7
240 3.37 3.5 3.87 3.6 3.28 3.33 3.89 3.55
300 4.28 4.29 4.58 4.37 4.59 4.21 4.76 4.44
360 4.88 5.11 5.34 5.22 5.26 5.08 5.52 5.2
420 5.66 5.89 6.2 6.02 6 5.9 6.19 5.98
480 6.6 6.65 6.77 6.72 6.62 6.64 7.01 6.72
540 7.29 7.13 7.19 7.54 7.26 7.43 7.68 7.36
Table 2: Percentage Deviation of (δ/L) From the Average Value
Angle
(degrees)
(∆(δ) / L) %
(δ /L) 1 (δ /L) 2 (δ /L) 3 (δ /L) 4 (δ /L) 5 (δ /L) 6 (δ/L) 7
0 0 0 0 0 0 0 0
60 0.99 0.16 2.04 0.13 3.16 1.57 2.33
120 1.34 1.05 0.46 0.04 0.18 1.34 1.76
180 1.27 0.67 0.94 0.82 0.17 1.32 0.74
240 1.17 0.67 0.74 0.29 1.52 1.32 0.82
300 1.09 1.06 0.18 0.82 0.14 1.31 0.38
360 1.54 0.94 0.34 0.65 0.55 1.02 0.13
420 1.54 1.02 0.31 0.72 0.77 0.99 0.34
480 1.16 1.05 0.81 0.91 1.12 1.07 0.33
540 1.13 1.43 1.31 0.67 1.18 0.87 0.41
Note: δ stands for the depth at any any angle θ, L the maximum depth corresponding to
540º. The maximum % deviation values are typed in boldface. The deviation values all fall
within the 5% mark.
![Page 12: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/12.jpg)
8
Graph 1: Dimple Depth v/s Angle of Rotation
Plot of dimple depth v/s angle of rotation showing close agreement of depth measurements during 7
different trials.
Table 3: Effect of Water Column on Dimple Depth Variation
Angle Of Rotation
(in degrees)
Depth (outside tunnel)
(average depth value
from Table 1)
(in mm)
Depth (with tunnel
full)
(in mm)
Difference in depth
caused by water
column
(in mm)
0 0 4.5 - 4.50
60 0.94 4.5 - 3.56
120 1.89 4.5 - 2.61
180 2.70 4.80 2.10
240 3.55 5.71 2.16
300 4.44 6.58 2.14
360 5.20 7.32 2.12
420 5.98 8.19 2.21
480 6.72 8.79 2.07
540 7.36 9.37 2.01
Due to the presence of the water tunnel there is an initial depth of 4.5mm for the first two
rotations (of 60º each). After this the increase in depth per 60º rotation for both cases is
roughly the same. This can be seen by the fact the difference in the depth values (column 4)
obtained from the two cases, for angles 180º through 540º, is approximately 2.1mm.
0
1
2
3
4
5
6
7
8
9
0 100 200 300 400 500 600
Dim
ple
Dep
th (
in m
m)
Angle Of Rotation (in degrees)
Depth v/s Angle Of Rotation
R1
R2
R3
R4
R5
R6
R7
![Page 13: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/13.jpg)
9
Table 4: Flow Parameters
Sl.
No
Tunnel Setting
(flow rate in m3/hr)
for d=5, 7.5, 10 mm
(cross-section 1)
Tunnel Setting
(flow rate in m3/hr)
for d=3 mm
(cross-section 2)
Flow Velocity
(m/s)
Reynolds
Number
(Re)
1 70 48 0.117 5826.65
2 87.5 60.5 0.147 7320.66
3 105.5 73 0.178 8864.47
4 122.5 84 0.205 10209.08
5 140.5 96.5 0.235 11703.09
6 175.5 121 0.294 14641.32
Reynolds Number: �� = ρ��
µ (1)
where;
ρ = density of fluid = 998 kg/m3
u = fluid flow velocity
d = dimple diameter = 0.05 m
µ = fluid dynamic viscosity = 1.002 · 10-3
Ns/m2
(ρ, µ values taken at temperature of 20ºC)
Water-tunnel cross-section:
Cross-section 1 = 40.2 cm x 41.2 cm (height x width)
Cross-section 2 = 27.7 cm x 41.2 cm (height x width)
![Page 14: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/14.jpg)
10
Table 5: Intermittency Factor (Turbulence Measure)
Intermittency Factor (γ)
Velocity
(in m/s) →
0.117
0.147
0.178
0.205
0.235
0.294
Depth
(mm) ↓
3 0 0 0 0 0 0.15-0.25
5 0 0 0 0 0.10-0.20 0.80-0.90
7.5 0 0 0 0.05-0.15 0.40-0.50 0.80-0.90
10 0 0 0.10-0.20 0.25-0.35 0.40-0.50 0.85-0.95
The intermittency factor is the ratio of the fraction of the time (t’) a given flow is turbulent
to the total time (T) the flow is observed.
� = �’/� (2)
t’ is measured by clocking the time during which the flow is unstable out of a visualization
video that is T seconds long.
Graph 2: Intermittency Factor Variation with Flow Velocity
A note on dimple depth measurement:
To measure dimple depth, first the piston-screw was set to a point where the depth was
0. One of the edges of this hexagonal screw was marked with a permanent marker and a
0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Inte
rmit
tency
Fac
tor
(γ)
Flow Velocity (m/s)
Intermittency Factor v/s Flow Velocity
3
5
7.5
10
![Page 15: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/15.jpg)
11
corresponding line was drawn on the metal bar holding the piston-screw. These two
markings formed the reference or starting point. In each rotation, the screw was rotated by
60º so that the next edge would now be in line with reference line drawn on the metal bar.
The process is repeated for the other rotation angle values.
Dimple depth was measured in the following two ways:
1. By clamping it and changing the angle of rotation of the piston-screw
2. By mounting the dimple-mount in the tunnel, filling water up to maximum height and
repeating the measurement. This is to investigate the effect of the water column of
depth.
The “error” in the readings obtained was estimated as follows:
a. The deviation of the measured value of depth (δ, at any angle) from the average value
of depth was calculated (∆(δ))
b. Next, the following was estimated: (L stands for maximum average depth)
%Error = ������������ℎ − �������ℎ
�����������ℎ∗ 100(3)
This gives an indication of how much the deviation ∆(δ) is with respect to the average
maximum depth. The “error” measured in this way was found to be within 5% which is
acceptable for experimental purposes.
![Page 16: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/16.jpg)
12
Pictures
Salient Features (figs 5-8)
Fig 5(a) Fig 5(b)
Fig 5(c) Fig 5(d)
Fig 5: (a) Dye enters the flow, (b) dye curving into
dimple, (c) vortices forming within dimple, (d) dye
ejection and (e) vortex pair visible
Symmetric
vortices
Dye
ejection
Dye ‘curving’
into the dimple
Fig 5(e)
![Page 17: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/17.jpg)
13
Fig 6(a) Fig 6(b)
Figure 6: (a) Dominant clockwise vortex and (b) dominant counter-clockwise vortex seen for d =
10mm at u = 0.117 m/s
Fig 7 Fig 8
Figures: (fig 7) Turbulent flow observed at Re = 14641.32 (u = 0.294 m/s) for d = 5mm and (fig 8)
remnants of the single dominant vortex observed at Re = 5826.65 (u = 0.117 m/s) for d = 10mm
nearly 30 seconds after the dye flow was stopped showing a region of dye concentration
Dominant
counter-
clockwise
vortex
Point of dye
concentration
Dominant
clockwise
vortex
![Page 18: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/18.jpg)
14
Flow Images For All Depths (figs 9-12)
Fig 9 Fig 10
Figures: General flow pattern for d = 3mm (fig 9), d =
5mm (fig 10) and d = 7.5mm (fig 11)
Fig 11
Fig 12(a) Fig 12(b) Fig 12(c)
Fig 12: Flow features for d = 10mm at velocities (a) 0.147 m/s,
(b) 0.178 m/s, (c) 0.205 m/s showing flow separation and (d)
0.294 m/s showing turbulence
Fig 12(d)Fig 12(d)
![Page 19: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/19.jpg)
15
Observations
General Flow Characteristics
When the experiments are run, the dye motion is followed and the following features are
noted in the flow:
Phase 1: The dye comes out of the reservoir through the 7 holes. The dye released from
holes 1, 2a and 2b are in line to flow above the dimple. However, the presence of the
dimple causes the dye ejecting from the other holes (3a, 3b, 4a and 4b) to be slightly pulled
towards the dimple. For the case of d = 3mm, this feature is not noticeable. See fig 5(a).
Phase 2: The dye from hole 1 first flows above the dimple and then branches into two- the
first branch flows into the dimple while the other flows downstream. The dye flowing from
the holes 2a and 2b curve into the dimple as they approach it. See fig 5(b).
Phase 3: The dye from the three central holes fills up the dimple. For depths of 5mm and
7.5 mm, symmetric vortices are observed inside the dimple - counter-clockwise on top, and
clockwise on the bottom. This orientation follows the way the dye enters the dimple. For
the dye from the hole 2a, it curves into the dimple in a counter-clockwise fashion.
Therefore, the vortex that is formed in the top section is counter-clockwise.
See fig 5(c) and 5(e).
For the 10mm case, a single dominant vortex was seen to form within the dimple (see fig 6).
Phase 4: On a periodic basis, a rush of dye gets ejected from the dimple. This ejection can
be clearly seen after the dimple gets filled with dye for the first time. This continues as long
as the dye is inserted into the flow. For the case of d = 10mm, as a single counter-clockwise
vortex is formed, the dye ejection occurred at side b. See fig 5(d).
![Page 20: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/20.jpg)
16
Features at d = 3 mm
The above described features are not clearly discernable when the dimple depth is 3mm.
For instance, phase 2 does not occur in this case while it does for all other cases. The
curving in occurs much later or doesn’t occur at all. Rather they follow the general flow
downstream and occasionally a small branch flows into the dimple. The central dye line
breaks periodically to move into the dimple. But the amount that breaks away is minimal as
the dimple never gets completely filled up with the dye, as is observed in other cases.
Consequently, phase 3 and phase 4 can’t be clearly seen either.
It can be concluded that the affect of this dimple depth to the flow is minimal. The flow
in this case is close to that without a dimple.
A Note on Flow Instability
As a general feature, it is observed that for a given dimple depth, as the flow velocity is
increased, the flow becomes increasingly unstable with intermittent flow separation. This is
first observed near the dye outlets - a swirl like motion (eddy) causing the developed flow
structure (if any) to be disturbed and cleared away in the process. Sometimes, this is
preceded by a wavering of one of the dye streak-lines. Fig 7 shows an instance of this
instability.
Lim (2000) warns that such disturbances are caused by the interaction of the dye with
the moving fluid and suggests that a proper adjusting of the dye releasing velocity can
solve the problem. To achieve this, the dye release-rate was set by using the valve regulator
and then left undisturbed. Further to this, the dye was released or stopped using only the
main valve opening near the dye reservoir. Also, after each dye visualization video was
captured and the dye cleared from the dimple, the flow was allowed 15 minutes to stabilize
![Page 21: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/21.jpg)
17
(30 minutes during the initial stages when this instability was first seen) before the next
visualization was done.
As a second method to check if this instability is due to improper dye delivery, the
following was done (for d =7.5, 10 mm):
a. First, the tunnel was set to the test velocity and the dye was allowed to fill up the
dimple.
b. Next, the dye was stopped so that no more dye was released from the holes and the
flow was observed to see if the instability was inherent. If the instability is caused by
the dye release alone, then when the dye is stopped, any dye that is in the dimple would
move downstream only by the ejection phase (phase 4).
c. However, it was observed that even when the dye was not being released, occasional
instability cleared away the dye that was present in the dimple. This suggests that the
instability is inherent in the flow at higher velocities.
Even after these steps were taken the instability was observed for higher flow velocities,
suggesting that this is probably the transitional stage from laminar to turbulent flow.
Consequently, after all the visualizations were obtained the intermittency factor (γ) was
estimated by measuring the fraction of total time this instability appeared in the flow. The
results are tabulated in table 5 and the variation of intermittency factor (γ) with dimple
depth (d) plotted in graph 2.
A pattern can be seen by inspecting the table – instability tends to occur at lower
velocities as the depth is increased. As an illustration, the instability first occurs at u =
![Page 22: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/22.jpg)
18
0.294 m/s for d = 3mm while the same can be observed at a velocity u = 0.178 m/s for d =
10mm. The table has been filled with approximate values obtained by using a stop-watch
and therefore is not precise. This is just meant to give an rough idea of the pattern observed.
Dye Concentration Points
Another interesting observation is that after the dye flow has been stopped, and the
dimple starts to clear the dye in short bursts (phase 4), the last remaining region with the
dye is seen to be the centre of the vortices. The dye from these points takes a long time to
clear out indicating the presence of a point (or region) across which the flow is much
slower than the external flow. A zoomed-in view of this revealed that this region seems to
rotate as if it is a single rigid body. This has been identified as a feature of a tornado-like
vortex interacting with a solid boundary (Nikulin: 1980)
For the case of d = 10mm (as shown in fig 8), this point retained the dye a good 30
seconds after the dye flow was stopped. During some trial runs the dye was observed to
stay for much longer periods. The dye from these points is cleared away earlier if flow
instability is present. Consequently, at higher flow velocities this phenomenon cannot be
observed.
Future Work
To better understand the flow characteristics of the fluid as it passes over (and partially
into) the dimple, it would be worthwhile to observe the flow from the side. The
visualizations obtained in this project were obtained by looking at the top view of the flow,
and as such do not clearly reveal the finer details of fluid entry into dimple (phase 2) or the
fluid ejection from dimple (phase 4).
![Page 23: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/23.jpg)
19
After this is done, the flow over the triangular dimple can be carried out and
comparisons made. Finally, flow measurements can be done to estimate the drag force for
each case.
Conclusions
The following conclusions can be drawn about the flow:
1. For a given dimple depth, as the flow velocity is increased, flow instability is
approached.
2. For a given flow velocity, as the dimple depth is varied, flow stability increases.
Consequently, flow instability occurs earliest for d = 10mm (at u = 0.178 m/s)
3. The different phases of the fluid flow is observed, by following the dye, and identified
by their prominent features.
4. While symmetric vortices are observed within the dimple for most cases (d = 3, 5, 7.5
mm), when d = 10mm a single dominant vortex is observed. The dominant vortex is
observed to be counterclockwise in most cases rather than an equal occurrence of both
orientations. This may be the result of an asymmetric deformation of the rubber sheet
during the process of increasing the depth.
![Page 24: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/24.jpg)
20
References
Bradshaw, P. & Pankhurst, R.C., 1964, "The Design of Low Speed Wind Tunnels,"
Progress in Aerospace Sciences, 5, pp. 1-69.
Lienhart, H., Breuer, M., Koksoy, C., 2008, "Drag reduction by dimples? – A
complementary experimental/numerical investigation," International Journal of Heat and
Fluid Flow, 29, pp. 783-791.
Lim, T.T., 2000, "Dye And Smoke Visualization," Flow Visualization, Lim, T.T. and
Smits, A.J., eds., Imperial College Press, London, pp. 43-72.
Nikulin, V.V., 1980, "Interaction of a tornado-like vortex with solid boundaries,"
Journal of Applied Mechanics and Technical Physics, 21, pp. 62-69.
White, F.M., 2003, Fluid Mechanics 5th
edition, McGraw-Hill, Boston
Zhdanov, V.L., Papenfuss, H.D., 2003, "Bluff body drag control by boundary layer
disturbances," Experiments in Fluids, 34, pp. 460-466.
![Page 25: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/25.jpg)
21
Appendix
Dimple Mount Diagram
Fig 13: Exploded view of the various parts of the dimple-mount
White rubber
sheet
Brass disk
Plug
Dye
reservoir
inlet
Metal bar
to position
the piston Piston
Dye
release
holes
Dye
reservoir
in the
plug
Reservoir
inlet
tubes
![Page 26: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/26.jpg)
22
Sectional View of Assembled Dimple-Mount
Fig 14: Sectional view of
assembled dimple-mount
Fig 15(a) Fig 15(b)
Figure 15: (a) Zoomed-in view showing the dye-reservoir inlet, and (b) one dye-release
hole
Reservoir
inlet tube
Dye
reservoir
Dye
release
hole
Dye
reservoir
Glycerin
to be filled
in this
space
![Page 27: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/27.jpg)
23
A Note on Error Estimation for Dimple Depth Measurement
The “error” in the readings was defined as:
%Δ(δ)%
= ������������ℎ − �������ℎ
��&'(�(�����������ℎ∗ 100
This gives an indication of how much the deviation ∆(δ) is with respect to the average
maximum depth. The “error” measured in this way was found to be within 5% which is
acceptable for experimental purposes.
However, the traditional definition of “error” is:
%Error = ������������ℎ − �������ℎ
�����������ℎ∗ 100(3)
This was not used due the following reason:
a. All the measurements are off from the average value by a maximum of +/- 0.3 mm (~ a
constant K). This constant value indicates that the error is due to a human error in
deciding when the Vernier Calliper scale has touched the dimple surface
b. Therefore;
)��*� =+
�����������ℎ∗ 100(4)
Consequently, as the depth measured increases, the error value obtained decreases for a
given deviation K, as the error is inversely proportional to the average depth. Therefore,
the error value does not seem to make sense.
c. The above problem does not occur while measuringΔ-δ.
%
![Page 28: Flow Control Over A Dimpled Surface3 b. A water tunnel with a test section to insert the dimple-mount c. Red colour dye, dye reservoir, 5mm hose d. For the video recording system –](https://reader033.vdocuments.us/reader033/viewer/2022060807/608c4168286d756b0d1e2559/html5/thumbnails/28.jpg)
24
Table 6: Percentage Error Calculated Using Equation (4)
Angle
(degrees)
Error (%)
Err (R1) Err (R2) Err (R3) Err (R4) Err (R5) Err (R6) Err (R7)
0 0 0 0 0 0 0 0
60 -6.38 2.13 15.96 0 -22.34 -10.64 18.09
120 -7.94 -5.82 5.29 1.59 0.53 -7.94 14.81
180 -6.67 -2.22 9.63 -3.33 1.48 -7.04 8.15
240 -5.07 -1.41 9.01 1.41 -7.61 -6.2 9.58
300 -3.6 -3.38 3.15 -1.58 3.38 -5.18 7.21
360 -6.15 -1.73 2.69 0.38 1.15 -2.31 6.15
420 -5.35 -1.51 3.68 0.67 0.33 -1.34 3.51
480 -1.79 -1.04 0.74 0 -1.49 -1.19 4.32
540 -0.95 -3.13 -2.31 2.45 -1.36 0.95 4.35
As can be seen from the above table, the highest error values are generally at the top of the
table and the lower error values are at the bottom.
Dimple Depth Ratios
Table 7: Dimple depth-to-diameter ratios used
Dimple depth
(d)
in mm
Depth to diameter ratio
(d/D)%
(D = 50 mm)
3 6 %
5 10 %
7.5 15 %
10 20 %