Flow Control Over A

Dimpled Surface

UIS 3931 Independent Study Module

Dilip Joy Thekkoodan

U067756J

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

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)

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)

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,

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

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.

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.

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

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)

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.

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

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)

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

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.

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)

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

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)

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).

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

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 =

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).

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.

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.

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

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

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.

%

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 %