droplet characterization in the wake of steam turbine cascades (1)

7/25/2019 Droplet Characterization in the Wake of Steam Turbine Cascades (1)

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University of Tennessee, Knoxville

Trace: Tennessee Research and CreativeExchange

Masters eses Graduate School

5-2012

Droplet Characterization in the Wake of SteamTurbine Cascades

Adam Charles [email protected]

is esis is brought to you for free and open access by the Graduate School at Trace: Tennessee Research and Creative Exchange. It has been

accepted for inclusion in Masters eses by an authorized administrator of Trace: Tennessee Research and Creative Exchange. For more information,

please contact [email protected].

Recommended CitationPlondke, Adam Charles, "Droplet Characterization in the Wake of Steam Turbine Cascades. " Master's esis, University of Tennessee,2012.hp://trace.tennessee.edu/utk_gradthes/1195
http://trace.tennessee.edu/http://trace.tennessee.edu/http://trace.tennessee.edu/utk_gradtheshttp://trace.tennessee.edu/utk-gradmailto:[email protected]:[email protected]://trace.tennessee.edu/utk-gradhttp://trace.tennessee.edu/utk_gradtheshttp://trace.tennessee.edu/http://trace.tennessee.edu/


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To the Graduate Council:

I am submiing herewith a thesis wrien by Adam Charles Plondke entitled "Droplet Characterizationin the Wake of Steam Turbine Cascades." I have examined the nal electronic copy of this thesis for formand content and recommend that it be accepted in partial fulllment of the requirements for the degree

of Master of Science, with a major in Aerospace Engineering.Ahmad D. Vakili, Major Professor

We have read this thesis and recommend its acceptance:

U. Peter Solies, Basil N. Antar

Accepted for the Council:Carolyn R. Hodges

Vice Provost and Dean of the Graduate School

(Original signatures are on le with ocial student records.)


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Droplet Characterization in the Wake of

Steam Turbine Cascades

A Thesis Presented for

The Master of Science

Degree

The University of Tennessee Space Institute

Adam Charles Plondke

May 2012


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c by Adam Charles Plondke, 2012

All Rights Reserved.

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Acknowledgements

This thesis would not have been possible without the help and support of many. I am eternally

grateful to you all.

It has been an honor to work with my advisor, Dr. Ahmad Vakili. His encouragement, guidance,

patience, and wisdom were essential to the success of my education at UTSI.

Thank you to my thesis committee members, Dr. Basil Antar and Dr. Peter Solies. Without their

advice and support, the publication of this paper would not have been possible.

Thank you for the assistance of Mr. Chris Armstrong, Mr. Joel Davenport and the UTSI Shop

during the experimental phase of this effort.

Thank you to Mr. Christopher Hilgert for his research assistance.

Thank you to Capt Sarah Summers, USAF for her help in proofreading and editing of this

paper.

Last, but certainly not least, I am grateful for the love and support of my wife, Mary Anne, and our

two children, Rachel and Joseph. Without you, none of this would be possible. Thank you.

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Abstract

In low-pressure steam turbines, water droplet formation on the surfaces of stationary stator blades

can lead to erosion on downstream turbine blades and other equipment. One property that affects

the size of the droplets that are formed is the adhesive forces between the water and the surface

of the stator blade. The adhesive forces hold the droplets to the surface where they may combine,

forming increasingly larger droplets. Eventually, the aerodynamic forces will tear the droplets off

the surface, carrying them downstream.

To study the effect of stator surface properties on the droplet size distribution, four cascades of

stator blades were tested with a low-speed, cold-flow steam turbine simulator. A non-intrusive

optical system was used to detect and measure the droplets.

Of the four cascades tested, the baseline cascade that showed obvious surface roughness had the

largest average droplet size. The cascade that had been sandblasted smooth formed smaller average

droplets than the baseline cascade but larger average droplets than the cascade that was coated

with a proprietary, glass-like coating. This coating was designed to minimize the surface tension

between the surface and the water droplet. The fourth cascade was coated in a superhydrophobic

granular coating. This coating appeared to work so well to reduce the droplet size that no droplets

could be detected by the imaging system. This untested cascade could not be considered in the

quantitative analysis.

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Contents

List of Tables viii

List of Figures ix

List of Symbols and Abbreviations xi

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 General Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory and Literature Review 4

2.1 Droplet Formation and Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Hydrophobicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1 Digital Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.3 Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.4 Gaussian Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.5 Structure Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.6 Canny Edge Detection Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Experimental Approach 13

3.1 Test Facility and Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

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3.1.1 Test Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.2 Cascades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.3 Atomizer Nozzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1.4 Digital Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.5 Pressure Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.6 Data Acquisition Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Test Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.1 Droplet Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.2 Velocity Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4 Calibration and Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4.1 Spatial Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4.2 Data Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Results and Analysis 37

4.1 Test Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2 Statistical Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2.1 Equivalent Diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2.2 Relative Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2.3 Weber Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.3 Droplet Size Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3.1 Mach Number Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3.2 Water Spray Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.3.3 Overall Droplet Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.3.4 Weber Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.4 Spatial Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.5 Estimation of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5 Conclusions and Recommendations 56

5.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.2 Untested Cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

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5.3 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Bibliography 60

Vita 63

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List of Tables

3.1 Test conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1 Cascade exit velocity at droplet test conditions . . . . . . . . . . . . . . . . . . . . . 37

4.2 Corrected air and water flow rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3 Baselilne cascade droplet summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.4 Sandblasted cascade droplet summary . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.5 Glass-coated cascade droplet summary . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.6 Droplet weber number summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.7 Reference object measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

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List of Figures

2.1 Schematic of surface-water flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Schematic of typical light condensation flow . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Sketch of hydrophobic and hydrophilic droplets showing contact angle . . . . . . . . 7

3.1 UTSI cold-flow steam turbine simulator . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Nozzle and cascade section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Water spray nozzles installed in test rig . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4 Detailed view of water spray nozzles . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.5 Spray nozzle control panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.6 Schematic of test rig and instrumentation, side view . . . . . . . . . . . . . . . . . . 17

3.7 Schematic of test rig and instrumentation, top view . . . . . . . . . . . . . . . . . . . 18

3.8 Baseline cascade installed in test rig . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.9 Baseline cascade surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.10 Sandblasted cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.11 Glass coated cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.12 Untested superhydrophobic cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.13 Close up image of water atomizer nozzle . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.14 Image processing algorithm flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.15 Region of interest immediately downstream of center blade trailing edge . . . . . . . 28

3.16 Cropped center blade region of interest for droplet analysis . . . . . . . . . . . . . . 28

3.17 Example subsection region for demonstration and discussion . . . . . . . . . . . . . . 29

3.18 Typical image subsection for demonstration and discussion . . . . . . . . . . . . . . 29

3.19 Typical image subsection converted to grayscale . . . . . . . . . . . . . . . . . . . . . 30

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3.20 Result of Canny edge detection for the typical subsection image . . . . . . . . . . . . 30

3.21 Smallest eigenvalue of the structure tensor for typical subsection image . . . . . . . . 31

3.22 Image thresholding results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.23 Edge detection method and structure tensor methods combined . . . . . . . . . . . . 33

3.24 Outline of detected droplets for typical subsection image . . . . . . . . . . . . . . . . 33

3.25 Droplets identified in typical subsection image . . . . . . . . . . . . . . . . . . . . . . 34

3.26 Reference objects used for verification and estimation of error . . . . . . . . . . . . . 36

4.1 Flow Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Baseline cascade drop size at Mach number . . . . . . . . . . . . . . . . . . . . . . . 42

4.3 Sandblasted cascade drop size at Mach number . . . . . . . . . . . . . . . . . . . . . 43

4.4 Glass-coated cascade drop size at Mach number . . . . . . . . . . . . . . . . . . . . . 44

4.5 Baseline cascade spray comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.6 Sandblasted cascade spray comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.7 Glass-coated cascade spray comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.8 Baseline cascade overall droplet size . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.9 Sandblasted cascade overall droplet size . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.10 Glass-coated cascade overall droplet size . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.11 Histogram droplet size comparison of all three cascades . . . . . . . . . . . . . . . . 50

4.12 Weber number distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.13 Horizontal spatial frequency response . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.14 Vertical spatial frequency response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.1 Superhydrophobic granular-coating cascade close-up view . . . . . . . . . . . . . . . 58

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List of Symbols and Abbreviations

The dummy variable used for integration in the convolution function

Spatial frequency, line pairs per millimeter on the imaging sensor.

Surface tension of water in air, Newtons per meter

Direction of the image gradient vector

Freestream flow density, kilograms per cubic meter

Standard deviation of droplet equivalent diameter, millimeters

The convolution function

A Droplet projected area, square millimeters

B Bias of the data acquisition system, millimeters

da Droplet equivalent diameter, millimeters

Fi Indicated water flow rate, gallons per hour

fi Relative frequency of equivalent diameter rangei

I The digital image. A two-dimensional representation of a light intensity function.

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Ix The change in the grayscale value of the imageIin the horizontal direction

Iy The change in the grayscale value of the imageIin the vertical

K Kernal of the Gaussian filter

M Mach number

Ni Number of droplets detected in equivalent diameter rangei

Pi Indicated air gage pressure, pounds per square inch

Qc Corrected air flow rate, cubic feet per hour

Qi Indicated air flow rate, cubic feet per hour

sh Sobel operator image mask in the horizontal direction

sv Sobel operator image mask in the vertical direction

Sw Image Structure tensor

Ti Air temperature, degrees Fahrenheit

U Uncertainty, millimeters

V Flow velocity, meters per second

We Weber number

x The horizontal spatial dimension

y The vertical spatial dimension

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ASP-C Advanced Photo Sensor type-C. Format of camera sensor used for droplet photographs.

CMOS Complementary Metal Oxide Semiconductor. Type of imaging sensor used in the camera.

SFR Spatial Frequency Response

UTSI University of Tennessee Space Institute

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Chapter 1

Introduction

1.1 Background

The use of steam to perform mechanical work was described in the first century, A.D. by the Greek

mathematician Hero of Alexandra. His device, known as the Aeolipile, is the first known steam

turbinea device that uses steam to generate rotary motion. According to Hero of Alexandras

description and drawings, the Aeolipilewas a hollow sphere mounted to rotate about two hollow

tubes attached to a boiler. Steam was generated in the boiler and was forced, by pressure, up the

tubes to the sphere. The steam was then expelled out two canted nozzles that caused the spin on

the sphere. It is believed that the device was only used only for demonstrations; it is unlikely that

Hero of Alexandra was able to harness any of the rotational energy to perform work [1].

Centuries later, in 1884, the first modern steam turbine was built by Charles Parsons to generate

electrical energy. His critical breakthrough in steam turbine design was to use a series of stages

inside the turbine [2]. The pressure drop was spread out over the multiple turbine stages. The use of

multiple stages for the expansion of steam inside the turbine results in the increased thermodynamic

efficiency while minimizing the centrifugal forces caused by blade over-speed [3]. The design has

been the subject of continuous improvement in the years since. As of the year 2000, approximately

90% of worldwide electricity was generated using turbines of Parsons basic design [3].

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Under normal operating conditions in steam turbines, moisture in the flow can condense on the

upper and lower surfaces of compressor blades and stator vanes. This condensate will begin to form

a droplet on the trailing edge of the airfoil. As the droplet increases in size, it will shed off the

trailing edge and be carried along by the ambient flow. These droplets will then impact downstream

surfaces inside the machinery such as the leading edge of an airfoil blade or other turbine part.

Over thousands of hours of otherwise normal operation, these repeated impacts erode the precision

machined surfaces of the impact area, altering the profile and aerodynamic properties of the affected

hardware.

Erosion due to liquid droplet formation inside steam turbines is commonly found in all common

types of electricity-producing units. This erosion can lead to major problems with the equipment.

In power-producing steam turbines, up to 15% of the megawatt generating capacity can be lost

due to erosion and buildup of blade deposits from the condensate [4]. The size of the droplet is one

parameter that determines the overall thermal efficiency of the turbine. An increase in droplet size

leads to increased energy losses due to the acceleration of the fluid and increased frictional losses

in the boundary layer where the droplets are present. Increased droplet size also leads to increased

erosion and blade damage [5].

1.2 Objective

The objective of this study was to perform a comparative analysis of the sizes of the fluid droplets

shed from airfoils in a cascade with various surface coatings or treatments in simulated steam turbine

conditions. The intent is to show that the droplet size can be minimized by modifying the surface

properties of the surface of the cascade. Smaller droplets in the flow of steam turbines are desired to

minimize internal damage. Chapter 2 explains the theory and reviews the literature behind droplet

formation, hydrophobicity and image processing. Chapter 3 discusses the experimental approach,

setup and procedure, while Chapter 4 presents the results of the data obtained. Finally, Chapter

5 discusses conclusions and suggest recommendations for further investigation.

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1.3 General Approach

Data were obtained with the University of Tennessee Space Institute (UTSI) cold-flow steam turbine

cascade flow simulator. The cold-flow simulator does not replicate actual steam turbine operating

conditions. It instead uses low-speed airflow and a fine water mist to provide conditions sufficient

for a comparative analysis of droplet size between cascade sections. An impeller and water atomizer

spray nozzles were used to generate the flow conditions. To capture droplet size data over a wide

variety of flow conditions, flow velocity was varied from 14 .3 to 51.5 m/s (Mach 0.041 to 0.147).

Two spray conditions were set at each flow velocity. A sequence of digital images were taken of

each cascade under these test conditions. These digital images were processed using the image

processing software known as ImageJ to measure the droplets shed from the center trailing edge

of the cascade. The resulting droplet size distributions for the various cascade configurations were

analyzed and compared to form the conclusions.

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Chapter 2

Theory and Literature Review

2.1 Droplet Formation and Erosion

When heavy condensation occurs in the wet-steam environment of low-pressure steam turbines,

four distinct regions of surface-water flow form on the surfaces of the stationary stator blades as

seen in Figure 2.1.

First, the formation region is typically located along the leading edge of the stator blades and is

characterized by droplet impacts on the surface. The water that these droplets contain is either

ejected back into the airflow, or is absorbed into the thin film of water on the surface of the

blade.

Second, the thin film region is located downstream from the formation region. Here, the water is

spread out in a thin film across the surface and is driven in a thin film laminar flow downstream

by aerodynamic forces. Some surface waves may also be present in this region.

Third, the rivulet region forms downstream of the thin-film region where the aerodynamic forces

and surface tension effects have combined to break the thin-film into separate, constant streams of

water, known as rivulets, that continue to be driven by the aerodynamic forces towards the trailing

edge [6].

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(a) Top view

(b) Side viewFigure 2.1: Schematic of surface-water flow showing the four basic regions: (1)

impact region, (2) thin film region, (3) rivulet region, and (4) dropletregion.

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Finally, in the droplet region the surface tension forces break up the rivulets into individual droplets.

These droplets travel towards the trailing edge where they collect and coalesce into larger globules.

As these globules increase in size, the aerodynamic forces acting to tear the droplet away from the

trailing edge also increases. When the increasing aerodynamic forces exceeds the adhesive forces

of surface tension holding the fluid to the trailing edge, the droplet will separate from the surface

[7, 8, 9].

In light condensation situation, there may not be enough water present on the surface to show the

four distinct surface flow regions. Here, small individual droplets form on the surface and, due to

aerodynamic forces, are forced along the direction of the flow while being held back by adhesive

forces. As the droplets travel, they will merge with other droplets and grow. The larger droplets

will be exposed to higher aerodynamic forces and may even form rivulets or a thin film. This

behavior is the type of condensation most seen when testing for this effort. Figure 2.2 shows a

schematic describing light condensation.

Figure 2.2: Schematic of typical light condensation flow. This type ofcondensation was the most prevalent during testing.

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The fluid droplets are carried downstream by the momentum of the air flow and will impact surfaces

present there. Over the operational lifetime of the turbine, these impacts can erode the surfaces

of equipment in the impact zone. Some of the most severe erosion occurs on the leading edges

of downstream rotating blades. The tip velocities of the rotating sections can approach sonic

velocities increasing the severity of the impact and erosion from the fluid droplet. In low-pressure

steam turbines, erosion is governed by the stator surface properties, rotor blade material, the size

of the droplets in the flow, and the relative velocity between the droplets and the impacted surface

[10].

2.2 Hydrophobicity

Hydrophobicity is the property of a surface or body to repel water. The contact angle, , between

the surface and the liquid water droplet increases with the hydrophobicity of the surface. A water

droplet on a hydrophobic surface will have a high contact angle and the surface will have a small

wetted area. The interfacial tension between the fluid droplet and the hydrophobic surface acts

upon the wetted area of the droplet. The forces adhering the droplet to the surface are minimized

as the wetted area is minimized. Examples of hydrophobic and hydrophilic droplets showing the

contact angle is shown in Figure 2.3

(a) Hydrophobic (b) Hydrophilic

Figure 2.3: Sketch of a hydrophobic and hydrophilic droplets on a surface showingcontact angle

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Inside a wet-steam environment such as inside a low-pressure steam turbine, the momentum of the

flow acts to push the droplet along the surface while the adhesive forces between the fluid droplet

and the surface act to hold the droplet in place. On a hydrophobic surface, a fluid droplet has

minimal adhesive forces holding it to the surface due to the minimal wetted area for surface tension

to act upon. With the adhesive forces minimized, the fluid will transition through the thin-film

and rivulet regions and will quickly break up into individual droplets as the fluid moves across the

surface. The minimized adhesion forces experienced by the fluid will also cause the fluid coalescing

at the trailing edge to tear away at a generally smaller size than the fluid collecting along the

trailing edge of a hydrophilic surface with the higher associated adhesive forces. On a hydrophilic

surface, the fluid layer tends to stay attached on the surface longer and the fluid will grow into

larger droplets before separating from the surface.

2.3 Image Processing

2.3.1 Digital Images

Digital images were captured using a Canon 15.1 Mega-pixel digital single lens reflex camera.

Droplet data photographs were obtained with a 27 mm focal length lens and stored on a memory

card for transfer to the image processing software.

The digital images considered here are the two-dimensional representation of a light intensity

function I(x, y) for the spatial coordinates x and y. The value of I(x, y) is the brightness of

the image at the given point along the grid.

For the digital images used here, the light intensity function is displayed at discrete points along

a 4,752 by 3,168 grid. The elements of this grid are known as pixels. For each pixel, a value

between 0 (black) and 255 (white) is assigned. When these 8-bit grayscale values are arranged in

the matrix, the image can be displayed where each element in the matrix represents the brightness

of one individual point in the image.

For the digital images used here, the light intensity function is displayed as an 8-bit 4,752 x 3,168-

pixel grayscale image. For each one of the 15,054,336 pixels a value between 0 (black) to 255 (white)

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is assigned. When these 8-bit grayscale values are arranged in a 4,752 x 3,168 matrix, the image can

be displayed where each element in the matrix represents one individual point in the image.

2.3.2 Convolution

The convolution of two functions f(x) and g(x) is given by Equation 2.1.

f(x) g(x) =

+

f()g(x ) d (2.1)

In Equation 2.1, is a dummy variable used for the integration. Many image processing methods

make use of this operation. Unlike matrix multiplication, the convolution operation can be

performed with matrices of different sizes.

2.3.3 Gradient

The gradient of the image I(x, y) is defined by the vector given in Equation 2.2.

[I(x, y)] =

Ix

Iy

=

Ix

Iy

(2.2)

It is common in image analysis to use the magnitude of the gradient vector given in Equation 2.3,

and the direction of the gradient vector given in Equation 2.4.

|[I(x, y)]| = [I2x+ I2y ] |Ix| + |Iy| (2.3)

(x, y) = arctan

IyIx

(2.4)

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2.3.4 Gaussian Smoothing

All images contain a certain amount of noise in the data. To minimize the apparent noise in the

image and reduce errors in later computation, an image can be smoothed using a Gaussian filter.

The kernel of the Gaussian filter used for image processing with a standard deviation of = 1.4 is

shown in Equation 2.5.

K= 1

159

2 4 5 4 2

4 9 12 9 4

5 12 14 12 5

4 9 12 9 4

2 4 5 4 2

(2.5)

2.3.5 Structure Tensor

The structure tensor is a tool used to segment areas of interest in images. For the image I(x, y),

the structure tensor is defined by Equation 2.6.

Sw = K IIT

=

K I2x K IyIx

K IxIy K I2y

(2.6)

The eigenvalues ofSw are then calculated. The structure tensor is positive-semidefinite and thus

the eigenvalues will always be real numbers greater than or equal to zero. The largest eigenvalue

is thrown out, and the smaller eigenvalue for every pixel in the image I(x, y) is displayed as the

greyscale value in a new image.

2.3.6 Canny Edge Detection Algorithm

The Canny edge detection system is one of the standard edge detection methods used in research

and was developed by J. Canny in Reference 11.

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After smoothing the image using the Gaussian blur discussed in Section 2.3.4, the Canny edge

detection algorithm finds the locations in the image where the grayscale value experiences a

discontinuity. These discontinuities are found using the gradients of the image discussed in Section

2.3.3. For this algorithm, the gradient is calculated using three convolution masks known as the

Sobel operator. Equation 2.7 shows the Sobel operator mask for edges in the vertical direction.

Equation 2.8 shows the Sobel operator mask for edges in the horizontal direction.

sv =

1 0 1

2 0 2

1 0 3

(2.7)

sh =

1 2 1

0 0 0

1 2 1

(2.8)

When these masks are convolved with the image I(x, y), generates the gradient at all the points

in the image. These gradient magnitudes locate the edges clearly, but the indicated edges are

relatively wide. The gradient alone does not accurately show the exact location of the edge.

To develop a more precise edge from the image of the gradient magnitude, the next phase of the

Canny algorithm suppresses all non-maximal values in the gradient magnitudes. To accomplish

this, a three-step process is undertaken for each pixel in the gradient image. First, the gradient

directiongiven in Equation 2.4 is rounded to the nearest 45 corresponding to an 8-pixel connected

neighborhood. Next, the magnitude the current pixel in the gradient image is compared to its

neighboring pixels along the rounded angle. Finally, if the current pixel represents the local

maximum along the rounded angle, then that pixel will be preserved. If the current pixel does

not represent the local maximum (i.e. a neighboring pixel along the rounded angle is of greatervalue) then the current pixel is suppressed in the output image.

The final phase of the Canny algorithm is to eliminate false edges by thresholding the image with

hysteresis. Gradient magnitudes that are large tend to correspond with an actual edge. Smaller

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gradient magnitudes are more likely to be a false edge. The weak edges formed by the smaller

gradient magnitudes are kept only if they connect to a strong edge with a large magnitude.

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Chapter 3

Experimental Approach

3.1 Test Facility and Instrumentation

3.1.1 Test Rig

A UTSI open circuit, continuous cold-flow steam turbine simulator was designed and modified to

support cascade testing. This test rig was used for data collection and is shown in Figure 3.1.

Airflow to the cascades was supplied by a variable geometry impeller driven by a 60 horsepower,

variable speed motor controlled by a Dura Pulse model G53-4075 electrical controller and power

supply. Downstream of the impeller, the flow was conditioned with a screen and honeycomb

flow straighteners. Downstream of the flow straighteners, three air-assisted spray water nozzles

introduced the water spray to the air flow to simulate the condensing steam present in a saturated

steam turbine environment. The spray nozzles and flow conditioners can be seen in Figure 3.3.

Three nozzles were located along the horizontal centerline of the tunnel, one spray nozzle at the

centerline and one spray nozzle 10 inches to either side. Downstream of the water spray nozzles,

ducting directed the air into the cascade. A schematic of the entire test rig and instrumentation

are shown in Figures 3.6 and 3.7.

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Figure 3.1: UTSI cold-flow steam turbine simulator. Airflow shown from left toright.

Figure 3.2: Nozzle and cascade section. Airflow shown from left to right.

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Figure 3.3: Water spray nozzles installed in test rig. Cascade removed, viewlooking upstream

Figure 3.4: Detailed view of water spray nozzles. Pressurized air entered fromabove, pressurized water supplied from below

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Figure 3.5: Spray nozzle control panel. Air flow meters are on the top, water flowmeters on the bottom. Directions refer to the relative location of thespray nozzles when looking upstream.

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Figure 3.6: Schematic of test rig and instrumentation, side view. Airflow shown from right to left.

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Figure 3.7: Schematic of test rig and instrumentation, top view. Airflow shown from right to left.

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3.1.2 Cascades

Droplet images were obtained from three cascades, each with a different surface treatment to vary

the surface roughness and thus affect the droplet size. A fourth cascade was used, but no droplet

data could be obtained.

All cascades were taken from the same low-pressure steam turbine stage. Each section had five

blades comprising approximately 35 degrees of the circular steam turbine stage. The inner radius of

the cascade was approximately 28.5 inches while the outer radius was approximately 45.75 inches.

The length of each trailing edge in the cascade was 17.25 inches.

Baseline (untreated) Cascade

The first cascade was taken, as-is, from a functional steam turbine from an industry environment

without any additional treatments or modifications. The blade surface on this cascade had visible

signs of wear and build-up of deposits and surface roughness. This cascade served as the baseline

cascade for comparative purposes. The baseline cascade is shown installed in the test rig in Figure

3.8, and the blade surface wear and surface roughness can be seen in Figures 3.9a and 3.9b.

Figure 3.8: Baseline cascade installed in test rig

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(a) Close-up view of center blade, looking up (b) Close-up view of center blade, lookingacross surface

Figure 3.9: Baseline cascade surface roughness

Sandblasted Cascade

The second cascade tested was a section of the same used steam turbine section as the Baseline

cascade and was originally in the same condition. Before testing, this cascade was sandblasted to

eliminate the signs of built up deposits and surface roughness seen on the Baseline cascade. The

Sandblasted cascade had a smoother, more even surface texture when compared to the Baseline

cascade. This cascade is shown in Figure 3.10.

Figure 3.10: Sandblasted cascade installed in test rig

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Glass Coated Cascade

The third cascade was coated in a proprietary dark, glossy, glass-like coating to reduce the surface

drag of the water droplets. This cascade is presented in Figure 3.11.

Figure 3.11: Glass coated cascade installed in test rig

Untested Cascade

A fourth cascade had a superhydrophobic granular coating applied to the blade surface. However,

no data could be obtained and further work with this cascade was abandoned. This cascade is

shown installed in the test rig in Figure 3.12, and is further discussed in Section 5.2.

Figure 3.12: Cascade with superhydrophobic granular coating (untested cascade)installed in test rig

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3.1.3 Atomizer Nozzles

Three Spraying Systems Co. model 1/4-J-SS+SU16-SS nozzles with air cap 67-6-20-70 deg

supplied the atomized water spray into the flow upstream of the cascade (see Figures 3.3 and 3.4).

Pressurized air was supplied to each of the three nozzles through a Dwyer Visi-Float model VFB

flowmeter and pressure gage. A valve needle in each flow meter allowed for individual air control

for each spray nozzle. Water was supplied to each of the nozzles through a Dwyer Rate-Master

model RMB flowmeter. A valve needle in each flowmeter allowed for individual water control for

each spray nozzle. A close up image of the spray nozzle is presented in Figure 3.13.

Figure 3.13: Close up image of water atomizer nozzle

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3.1.4 Digital Imaging

All images were obtained with a Canon EOS Digital Rebel T1i digital single lens reflex camera with

a EF-S 1855mm f/3.55.6 IS zoom lens. The camera used an APS-C format CMOS sensor with

15.1 million pixels. During the acquisition of droplet data, the photographs were taken with the

focal length fixed at 27 mm with a shutter speed of 1/2000sec with an aperture of f/4. To minimize

the noise in the captured images, the photographs were obtained using a digital-film speed of

ISO 100, and stored using the Canon-proprietary *.cs2 image filetype. This so-called RAW file

format stored the minimally-processed data from the camera in an image file without any loss of

data or introduced unwanted noise from a compressed filetype such as JPEG. The camera lens was

positioned on a tripod approximately 35 inches from the trailing edge of the center blade of the

cascade, with the trailing edge of the middle blade centered in the image. Images were stored in anon-camera flash memory device and were transferred to a personal computer for additional image

processing. High-intensity work lights were positioned approximately 80 degrees to the left and

right of the cascades, facing in, for optimal illumination of the droplets.

3.1.5 Pressure Measurements

Pressures immediately downstream and above the center blade of the cascade were measured with

a Setra model 264 pressure transducer [12, 13] and a Dwyer 160-24 pitot stainless steel pitot tube

sensor [14]. The pressure transducer signal output was reduced to mean flowfield velocity and Mach

number using Labview 8.2 [15].

3.1.6 Data Acquisition Software

The digital image data were processed using the software ImageJ. This software was developed by

the National Institutes of Health as an open-sourced, public domain, image processing program

[16, 17]. In addition, the macro package FeatureJ was used to implement the edge detection and

structure tensor calculations [18].

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3.2 Test Procedure

3.2.1 Droplet Images

Digital photographs of the flow were obtained for all three tested cascade sections at five velocity

settings and for two spray settings at each velocity. The flow velocity was controlled by varying

the electrical input frequency to the impeller motor. The two spray settings were determined by

adjusting the valves in each of the three water and three air flow meters. The High Air spray

setting was used for large air and low water flow rates through the spray nozzles and the Low Air

spray setting was used for smaller air and higher water flow rates through the spray nozzles. The

two spray settings produced different spray geometries and atomized water droplet size from the

spray nozzles. The High Air setting produced a finer water mist than the Low Air setting. The

test conditions are given in Table 3.1 where Qi and Fi are the air flow rate and water flow rate,

respectively.

Table 3.1: Test conditions used for all cascades. Directions referto relative locations of the spray nozzles when lookingupstream.

Input Hz Spray Setting Qi

ft3

hr Fi

galhr

L1 CL2 R3 L CL R

10 Low 30 30 30 3 3 3High 60 62 60 1 1 1

15 Low 30 30 30 3 3 3High 60 60 60 1 1 1

20 Low 30 30 30 3 3 3High 65 65 60 1 1 1

25 Low 30 30 30 3 3 3High 55 60 55 1 1 1

35 Low 30 30 30 3 3 2

High 50 50 50 1 1 1

1 Left2 Centerline3 Right

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Once a cascade section was installed in the test rig and the camera and other instrumentation was

setup and configured, the motor controller and electrical supply was switched on.

When the motor reached the operating speed, the spray was activated by opening the valves on the

flow meters and adjusted until the desired flow rate of water and air was achieved for the Low Air

spray setting. The flow conditions were allowed to settle for approximately three to five minutes.

Thirty digital photographs were taken with sufficient time between exposures to ensure any given

droplet was not captured on multiple images; approximately thirty seconds between exposures. A

remote shutter release was used to ensure the camera and tripod were not disturbed during the

data acquisition process.

When the final digital photograph was obtained at the Low Air spray setting, the flow meter valves

were adjusted to the High Air spray setting. After approximately three to five minutes to allow test

conditions to settle, thirty additional digital photographs were taken at the new spray setting.

After the final digital photograph was taken at the High Air spray setting, the spray was reset

to the Low Air setting and the rig airflow velocity was increased to the next test condition.

The flow conditions were allowed to settle and the process of obtaining digital photographs was

repeated.

When all digital photographs were obtained for both spray settings at all airflow velocities, thetunnel flow was stopped and the cascade section was removed from the test rig and a different

cascade section was installed. This process was repeated until all three cascade sections were tested

and all digital photographs were obtained.

3.2.2 Velocity Measurements

Separately from obtaining the droplet digital photographs, the velocity of the flow exiting the

cascade was measured using the pitot probe and pressure transducer. The probe was mounted

immediately downstream of the center of the cascade, parallel with the flow, at the mid-span

point. A steady-state velocity of the flow was recorded for the motor speeds varying from zero to

40 Hz. No water or air flow through the spray nozzles were active during the determination of flow

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velocity. These measurements were used as a reference for droplet size comparison and further data

reduction. The results are presented in Section 4.1.

3.3 Data Processing

The captured raw images were transferred to a personal computer for further image processing.

The flowchart describing the image processing algorithm used to detect and calculate droplet sizes

is shown in Figure 3.14. An example image is shown in Figure 3.15. This example image will be

used below to illustrate the image processing steps taken.

First, the image was cropped so that only the region of interestthe area in space immediately

below the middle bladeis shown. By not further processing the areas of the image outside the

primary region of interest, the amount of time needed to complete the algorithm is greatly reduced.

An example of the cropped image is shown in Figure 3.16.

For clarity and to show detail, only a small section of the image will be shown for discussion here.

Figure 3.17 highlights this section and is shown cropped in Figure 3.18.

After removing the portions of the image outside the region of interest, the color images were

converted to an 8-bit grayscale image. Each pixel in the resulting image only has a magnitude fromblack (0) to white (255). An example of this grayscale image is shown in Figure 3.19.

The droplets present in the image were then detected and segmented from the background of the

picture using two separate processes.

The first segmentation process used the Canny edge detection algorithm described in Section 2.3.6.

This method defines the edge of the fluid droplets in the image, but also detects additional edges

of objects and features not desired to be counted as valid droplets (e.g. the trailing edge of the

blade, marks and lines on the surface of the blade). The result of this process is an 8-bit grayscale

image. An example is presented in Figure 3.20.

The second segmentation process used the structure tensor method described in Section 2.3. This

texturebased segmentation method detects the droplets without any extraneous objects. However

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INPUT:CapturedImage onCamera

CropImage

Convertto 8bit

grayscale

EdgeDetection

Thresholdto Binary

Image

SmallestStructure

Eigenvalue

Thresholdto Binary

Image

AND

FinalSegmented

Image

ScanImage to

DetectDroplet

ParticleFound?

TraceBorder ofDetectedDroplet

Take andRecordDroplet

Measure-ments

MakeDropletInvisible

DONE! AllDropletsDetected

OUTPUT:Droplet

Measure-ments

yes no

Figure 3.14: Image processing algorithm flowchart

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Figure 3.15: Region of interest immediately downstream of center blade trailingedge

Figure 3.16: Cropped center blade region of interest for droplet analysis

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Figure 3.17: Example subsection region for demonstration and discussion

Figure 3.18: Typical image subsection for demonstration and discussion

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Figure 3.19: Typical image subsection converted to grayscale

Figure 3.20: Result of Canny edge detection for the typical subsection image

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this method can be imprecise when defining the perimeter of the droplets. If this method were

used alone, the inaccurate definition of the droplet perimeter would contribute to inaccurate droplet

measurements and overall error. The result of the structure tensor method is an 8-bit grayscale

image. An example of the smallest structure tensor eigenvalue is shown in Figure 3.21.

Figure 3.21: Smallest eigenvalue of the structure tensor for typical subsectionimage

The images from the two segmentation methods were independently converted from grayscale to

binary by the determination of a gray threshold value. Any pixel whose value is less than the

threshold value is set to 0 (black), and any pixel whose value is greater than the threshold is set

to 1 (white). The intent in the determination of the threshold value is to have only those pixels

corresponding to a region of interesta droplet to be measuredto be set to 1, while all other pixels

are set to black.

The threshold value was determined by implementing the Triangle Method in Reference 19 via the

built-in algorithm packaged with ImageJ. An example of this result for both segmentation methods

are shown in Figure 3.22.

These two binary images were combined using the AND Boolean function to create a new image. A

pixel at (x, y) in the combined image is equal to one if, and only if, the pixel at the same location in

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(a) Canny edge detection method (b) Structure tensor method

Figure 3.22: Image thresholding results

the two binary images is equal to one for both the original binary images. This example is shown in

Figure 3.23. This resulting image combines the advantage of the accurate definition of the droplet

perimeters from the Canny method with the advantage of droplet detection using the structure

tensor method.

The resulting image was then analyzed using the Particle Analyzer function provided in the ImageJ

program. The image was scanned until a droplet was detected. The droplet perimeter was outlined,

measured, and made invisible. Then, the process repeated until all the droplets were measured.

Further information regarding the Particle Analyzer can be found in Reference 16. Outlines of the

droplets detected by the Particle Analyzer for the example image is shown in Figure 3.24 and the

droplets identified in the original image in Figure 3.25.

3.4 Calibration and Verification

3.4.1 Spatial Frequency Response

The Spatial Frequency Response, or SFR, of a photographic imaging system is a characterization

of the resolution of the system. The SFR is the observable contrast at a given spatial frequency,

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Figure 3.23: Edge detection method and structure tensor methods combined

Figure 3.24: Outline of detected droplets for typical subsection image

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Figure 3.25: Droplets identified in typical subsection image

, relative to the observable contrast at low frequencies and is given by the following equations.

High SFR values at high spatial frequencies indicate fine details can be resolved in the image. The

equation for SFR is given in Equation 3.1.

SF R() =C(= 0)

C() (3.1)

whereC(= 0) is the contrast at very low spatial frequencies, given in Equation 3.2.

C(= 0) =max(I(= 0)) min(I(= 0))

max(I(= 0)) min(I(= 0)) (3.2)

and C() is the contrast at spatial frequency , given by Equation 3.3.

C() =max(I()) min(I())

max(I()) min(I()) (3.3)

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Where I( = 0) and I() are the grey values at the low spatial frequency and at the spatial

frequency of, respectively.

Historically, minimum image resolution was determined by photographing a test chart containing

a series of alternating black and white lines of diminishing size. The image was visually inspected

and the smallest distinguishable pair of black and white lines were located. The resolution was

given in distinguishable line pairs per millimeter. This method introduced both human perception

and judgment in the determination of the minimum observable line pair per millimeter.

With the SFR, the distinguishable line pairs per millimeter can be quantified without human

observation and judgment. An extended SFR to high spatial frequencies corresponds to fine details

present in the subject image.

A test target consisting of alternating white and black bars of decreasing size was photographed

to determine the SFR. The spatial frequencies of this target increase logarithmically from 2 to 200

line pars per millimeter. The target was sized and positioned such that the target image was 5mm

on the imaging sensor. This ensured the SFR was calculated as line pairs per millimeter on the

sensor.

3.4.2 Data Verification

In order to verify the image data acquisition and develop an estimation of error, images of objects

of known size were taken and processed using the algorithm presented in Section 3.3. Beads of

three different sizes, U.S. one-cent coins and U.S. ten-cent coins were used as the reference objects.

These objects were measured with a vernier caliper to determine their true sizes to within 0.05

millimeters.

Thirty images were taken of the reference objects. In each image, the reference ob jects were

rearranged. An example verification image is shown in Figure 3.26.

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Figure 3.26: Reference objects used for verification and estimation of error

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Chapter 4

Results and Analysis

4.1 Test Conditions

Velocity

The Dwyer 160-24 pitot-static probe was used to determine the mean velocity of the flow at the

cascade exit. See Section 3.1.5. The exit velocity was found to be a linear function of the input

electrical frequency to the impeller motor. The cascade exit velocities for the center blade at the

mid-span location are shown in Figure 4.1. The test conditions used for obtaining droplet images

are noted in Table 4.1. These cascade exit velocities were used as a velocity reference for further

data reduction and analysis.

Table 4.1: Cascade exit velocity at droplet test conditions

Input Hz M V msec

10 0.041 14.3

15 0.063 21.920 0.084 29.625 0.106 37.235 0.147 51.5

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Figure 4.1: Flow velocity at the cascade exit as a function of compressor speed.Filled squares indicate velocities during droplet acquisition.

Water Spray

At each Mach number, the water content of the flow was varied during testing by controlling the

flow rates of air and water to each of the three spray nozzles. The flow rate of air as indicated on

the Dwyer flow rate meter has to be corrected by Equation 4.1.

Qc = Qi

530(14.7 + Pi)

14.7(490 + Ti) (4.1)

WhereQc is the corrected flow rate, Qi is the flow rate indicated on the meter, and Pi and Ti are

the indicated gage pressure in psi, and temperature in degrees Fahrenheit, respectively. The water

flow rate needed no correction [20]. The corrected flow rates are presented in Table 4.2.

The data for each cascade was obtained on separate days, but at similar atmospheric weather

conditions and inside an air-conditioned laboratory environment. It is assumed that the only

variation in the water present in the flow comes from the spray nozzles settings.

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Table 4.2: Corrected air and water flow rates. Directions refer to relativelocations of the nozzles when looking upstream.

Input Qcft3

hr Fi

1galhr

Hz M Spray Setting L2 CL3 R4 L CL R

10 0.041 High Air 52 52 52 1.0 1.0 1.0Low Air 34 34 34 2.0 2.5 2.0

15 0.063 High Air 74 71 71 1.0 1.0 1.0Low Air 62 62 62 1.5 1.5 1.5

20 0.084 High Air 81 81 75 1.0 1.0 1.0Low Air 62 62 62 1.5 1.5 1.5

25 0.106 High Air 81 81 81 1.5 1.0 1.0Low Air 64 70 64 1.5 1.5 1.5

35 0.147 High Air 70 70 70 1.5 1.5 1.5

Low Air 32 32 32 3.0 3.0 2.5

1 No correction required for the indicated water flow rate2 Left3 Centerline4 Right

4.2 Statistical Measurements

The image processing algorithm in the previous section was repeated for each digital image obtained.

The resulting droplet size data was exported to MATLAB for further statistical calculations.

4.2.1 Equivalent Diameter

One limitation of this optical approach to droplet characterization and sizing is the images produced

are strictly two-dimensional. No information regarding depth can be deduced from the image and

therefore no droplet volumes can be determined. Only the two-dimensional projected area on the

image can be considered. Nevertheless, it is expected that two-dimensional areas will be sufficient

for comparative analyses between cascades.

Because of the two-dimension constraint, several standard droplet-size descriptors cannot be used,

such as the Volume Mean Diameter, the Mass Mean Diameter, and the Sauter Mean Diameter.

These descriptors all rely on knowing the volume each droplet occupies [21].

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Instead, the data was reduced to equivalent diameter da, given by Equation 4.2. The equivalent

diameter of an irregular-shaped droplet is defined as the diameter of a circle with equal area as

the droplet in question. The droplet projected area, A, was measured by the ImageJ Particle

Analyzer.

da =

4A

(4.2)

4.2.2 Relative Frequency

For direct comparison of droplet size distributions across figures and cascades, the relative frequency

of each droplet equivalent diameter was normalized by taking the ratio of observed frequency to

the total number of drops detected for each test condition. That is, for each rangei of equivalent

diameters considered in development of the droplet size histograms, the relative frequency is given

by Equation 4.3.

fi = Ni

Ni(4.3)

Where fi is the relative frequency and Ni is the number of droplets detected in size bin i. The

denominator

Ni is the sum of the number of detected droplets in all the bins considered. This

is equivalent to the total number of droplets detected of any size for the whole image or images

considered.

4.2.3 Weber Number

To completely nondimensionalize the data for comparisons across all test conditions, the dimen-

sionless Weber Number, We, was calculated for each droplet using Equation 4.4.

We=V2da

=

997.8 kg/m3 V2 m2/s2 damm 1100

mm/m

0.0728 N/m(4.4)

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The freestream flow density, , was assumed to be a constant 997.8 kg/m3 for all testing. The

surface tension of water in air, , was also assumed to be 0.0728 N/m for all testing. This number

nondimensionalizes the data with respect to both the droplet equivalent diameter and the Mach

number of the flow.

4.3 Droplet Size Results

4.3.1 Mach Number Effects

The relative frequency of droplet equivalent diameter sizes for the three cascades at the various Mach

numbers are shown in Figures 4.2, 4.3, and 4.4 for the baseline cascade, sandblasted cascade and

glass-coated cascade, respectively. A summary of statistical measurements for the three cascades

are presented in Tables 4.3, 4.4 and 4.5.

These figures show a trend for the droplets to decrease in size as the Mach number increases. This

trend is seen with all cascades tested. One possible cause of this decrease could be the additional

aerodynamic forces that occur at the increased flow velocity. The increased forces would tear the

growing droplets away from the trailing edge of the blade earlier, before the droplet could grow

larger.

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Figure 4.2: Baseline cascade drop size relative frequency at various Mach numbers

Table 4.3: Baselilne cascade droplet summary

da mm

MachMedian Mode Mean

Standard Number ofNumber Deviation Droplets

0.041 1.7507 1.2099 1.7367 0.4039 45420.063 1.6429 1.0032 1.6560 0.4291 56730.084 1.6568 1.0906 1.7027 0.4800 9705

0.106 1.7244 0.9565 1.8332 0.6233 50590.147 1.8768 1.0906 1.9669 0.6737 6988

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Figure 4.3: Sandblasted cascade drop size relative frequency at various Machnumbers

Table 4.4: Sandblasted cascade droplet summary

da mm



0.041 1.2842 1.0088 1.3875 0.4515 87600.063 1.2910 0.9366 1.4320 0.5195 112050.084 1.3508 0.8584 1.5697 0.6362 171840.106 1.3378 0.9177 1.4972 0.5877 136080.147 1.2426 0.9734 1.4709 0.6177 14700

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Figure 4.4: Glass-coated cascade drop size relative frequency at various Machnumbers

Table 4.5: Glass-coated cascade droplet summary

da mm



0.041 1.0255 0.9795 1.0665 0.2410 93580.063 0.9605 0.8375 0.9924 0.2148 173760.084 0.9312 0.8373 0.9662 0.2084 34371

0.106 0.9605 0.8373 1.0172 0.2503 194310.147 1.0255 0.8483 1.1234 0.3623 19543

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4.3.2 Water Spray Effects

Figures 4.5, 4.6, and 4.7 show the droplet size distributions for the three tested cascades at all

Mach numbers for both the High air and Low air water spray conditions.

These figures show that the droplet size distribution are largely independent of the water mist spray.

Larger droplets were slightly more frequent at the low air setting, especially for the glass-coated

cascade.

Figure 4.5: Baseline cascade spray comparison

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Figure 4.6: Sandblasted cascade spray comparison

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Figure 4.7: Glass-coated cascade spray comparison

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4.3.3 Overall Droplet Size

Histogram plots showing the droplet size distributions for the three tested cascades at all test

conditions are shown in Figures 4.8, 4.9 and 4.10. The three plots are combined in Figure 4.11.

The baseline cascade with the roughest surface has the largest average droplet size. The droplet

sizes decrease with the sandblasted cascade. The smallest droplet sizes were measured with the

glass-coated cascade.

Figure 4.8: Baseline cascade overall droplet size

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Figure 4.9: Sandblasted cascade overall droplet size

Figure 4.10: Glass-coated cascade overall droplet size

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Figure 4.11: Histogram droplet size comparison of all three cascades

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4.3.4 Weber Number

The Weber number We was calculated to nondimensionalize droplet size and test conditions for

comparison of all droplets at all test conditions. The results for all three cascades are shown in

Figure 4.12 and summarized in Table 4.6.

Figure 4.12: Weber number distribution for all three cascades

Table 4.6: Droplet weber number summaryWe

We x104

CascadeMedian Mode Mean

StandardNumber Deviation

Baseline 2.114 1.331 2.765 2.223Sandblasted 1.624 1.032 2.216 1.683Glass-coated 1.244 1.007 1.568 1.135

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4.4 Spatial Frequency Response

Figures 4.13 and 4.14 show the captured grayscale data and SFR in the horizontal and vertical

directions, respectively. The SFR reaches 10% at approximately 85 cycles per millimeter on the

sensor which would be equivalent to clearly resolving a black and white line pair 0.15 millimeters

across at the targeted area of the steam turbine cascade. The signal from the camera sensor for

any object smaller than 0.15 millimeters at the cascade target area would likely be too small to be

detectable, regardless of the contrast.

The Nyquist frequency for the sensor is 110 cycles/mm. SFR reaches zero well before the Nyquist

limit due to antialiasing and other filtering performed onboard the camera image processor.

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Figure 4.13: Horizontal spatial frequency response

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Figure 4.14: Vertical spatial frequency response

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4.5 Estimation of Error

The reference objects were measured using the data processing method presented in Section 3.3.

The true sizes of the objects and the sizes measured by the image processing system are shown in

Table 4.7.

Table 4.7: Reference object measurements

da mm

StandardObject True Size Mean Deviation

(Caliper) (Image Processing)

Ten-cent coin 17.90 17.85 0.18

One-cent coin 19.10 19.08 0.25Large Bead 12.50 12.80 0.12Medium Bead 6.30 6.90 0.10

Small Bead 4.10 4.56 0.13

An estimation of the error in the measurement of droplet equivalent diameter was calculated using

the reference objects as a standard for measurement. The uncertainty, U, was determined using

Equation 4.5.

U=

B2 + (2)2 (4.5)

.

The total uncertainty in the measurement of da is estimated at U = 0.41 millimeters. This

represents a 95% confidence level.

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Chapter 5

Conclusions and Recommendations

5.1 Summary and Conclusions

This effort used an image processing method to study the size characteristics of droplets shed in

the wake of steam turbine cascades. Four cascades were investigated: (1) a baseline cascade taken

from a working industrial environment that showed signs of wear, (2) a cascade where the surfaces

were sandblasted smooth to remove the imperfections and surface roughness seen in the baseline

cascade, (3) a proprietary dark, glass-like coating, and (4) a superhydrophobic granular coating.The three cascade treatments were to change the blade surface-water boundary surface tension and

thus minimize the droplet size when compared with the baseline cascade. Digital images of the

cascades under various test conditions were processed to detect and size the droplets.

The image processing used a combination of an image structure tensor to detect a droplet and

canny edge detection to define the border of the droplet. With the droplets identified in a given

image and the borders clearly defined, the droplet size could be determined.

As seen in Figures 4.2, 4.3, and 4.4 and summarized in Tables 4.3, 4.4, 4.5, droplets with a smaller

equivalent diameter tended to be slightly more frequent at higher Mach numbers.

Figures 4.5, 4.6, and 4.7 show that the distributions of droplet size equivalent diameters remain

relatively constant between the two different water spray settings. Larger droplets were more

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frequent at the low air setting, and are especially prominent for the glass-coated cascade shown in

Figure 4.7.

Figure 4.11 shows the droplet size distributions at all test conditions for the three tested cascades.

With this figure, the effect of the surface coating on droplet size can be seen. The glass-coatedcascade, treated to minimize surface tension, showed a clear tendency to produce smaller droplets

than the sandblasted cascade. The sandblasted cascade also produced smaller droplets than the

baseline cascade with the roughest surface. These same conclusions can be seen in Figure 4.12.

For the cases and conditions studied here, the droplet size decreased when the surface roughness

of the cascades decreased.

5.2 Untested Cascade

In addition to the baseline, sandblasted and glass-coated cascades, a fourth cascade section with

a superhydrophobic granular coating was installed in the test rig and photographs were acquired

in the same manner. No droplets could be detected by the camera at any test condition. The

author could only observe the miniscule droplets being shed from the trailing edges when viewing

spanwise across the trailing edge. A spanwise view of the center blade trailing edge during operation

is presented in Figure 5.1.

A sample metal plate with the same superhydrophobic granular coated was tested in a droplet

angle goinometer. The contact angle was measured to be in excess of 120 degrees.

The superhydrophobic granular coating did not adhere sufficiently to the surface of the blades. An

accidental touch of the surface by the author was discovered to remove the coating and destroy

the superhydrophobic properties. Due to the concern of the impact of coating durability on

data repeatability and also the difficulty of capturing the droplets on an image, work on this

cascade was abandoned and could not be considered in the droplet size comparative analysis. Thissuperhydrophobic coating worked so well to reduce the droplet size that even the largest droplets

shed from the cascade were well below the capabilities of the data acquisition system to detect and

measure. It is, however, the opinion of the author that this coating is simply too fragile to work in

an industry environment. Further work must be done to increase the coating durability.

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Figure 5.1: Trailing edge close-up view of superhydrophobic granular-coatedcascade.

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5.3 Recommendations

Recommendations for further research

Quantification of the surface roughness of each cascade and the surface tension at the cascade

surfacewater droplet boundary

water droplet contact and roll-off angles on the various cascade surfaces

Coating durability testing

Droplet impact analysis on surfaces downstream

Data collection at actual steam turbine conditions

Financial cost-benefit study for implementation of coated surfaces inside turbines

Long-term steam turbine implementation

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Vita

Adam Charles Plondke was born in Downers Grove, Illinois on October 30, 1981 to Dr. James C.

and Mrs. N. Jean Plondke. He spent his childhood in Knoxville, Tennessee, Appleton, Wisconsin

and Madison, Wisconsin before his family settled in Valdosta, Georgia. In 1999, while still a

Junior at Valdosta High School, he started taking undergraduate coursework at Valdosta State

University. After graduating from high school, he enrolled at the Georgia Institute of Technology

in Atlanta, GA where he graduated with a Bachelor of Science degree in Aerospace Engineering

in July 2004. During his time at Georgia Tech, he worked as a manufacturing engineer-intern in

Douglas, GA at PCC Airfoilsa division of Precision Castparts Corporationwhere he assisted

with the manufacturing of turbine blades, vanes and other precision castings for the aerospace

industry.

Upon graduating from Georgia Tech, Mr. Plondke took a position with Aerospace Testing Alliance,

the operations and support contractor for Arnold Engineering Development Center (AEDC), Arnold

Air Force Base, Tennessee as a flight systems project engineer. He currently performs weapons

integration testing in AEDCs aerodynamic four-foot transonic and sixteen-foot transonic wind

tunnels. He enrolled in the graduate program at the University of Tennessee Space Institute in

2007.

droplet characterization in the wake of steam turbine cascades (1)

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