EXPERIMENTAL I A -K G CONTINUOUS H -D G · Experimental Investigation of Air-Knife Geometry in...

EXPERIMENTAL INVESTIGATION OF AIR-KNIFE GEOMETRY IN CONTINUOUS HOT-DIP GALVANIZING

Experimental Investigation of Air-Knife Geometry in Continuous Hot-Dip Galvanizing

By

SEPIDEH ALIBEIGI, B.A.Sc.

A Thesis

Submitted to the School of Graduate Studies

In Partial Fulfillment of the Requirements

For the Degree

Master of Applied Science

McMaster University

© Copyright by Sepideh Alibeigi, November 2013

ii

Master of Applied Science (2013) McMaster University

(Mechanical Engineering) Hamilton, Ontario

TITILE: Experimental Investigation of Air-Knife Geometry in Continuous Hot-Dip Galvanizing

AUTHOR: Sepideh Alibeigi, B.Sc. (Azad University, Iran)

SUPERVISORS: Dr. Joseph R. McDermid, Dr. Samir Ziada

NUMBER OF PAGES: xvii, 115

iii

Abstract

This thesis investigates the wall pressure distributions of the single-slot impinging

jet and multiple-slot impinging jet as a function of various parameters and compares the

results obtained with the computational study of Tamadonfar [2010]. The process of gas

wiping is used in many industrial applications such as tempering of the plate glass, the

chemical mixing process, and turbine blade cooling. One of the most important industrial

applications of gas jet wiping is the production of galvanized steel strip in a continuous

hot-dip galvanizing line. In this process, an impinging jet is used to remove the excess

zinc alloy from the steel strip and control the final coating weight by applying wall

pressure and shear stress on the moving substrate emerging from the bath of molten zinc.

Changing the various operating parameters such as jet Reynolds number (Re), the jet to

strip distance (z), the jet slot width (d), and jet inclination angles (α) allows manufacturers

manipulate the final coating weight on the substrate. Production of high quality sheet

steels, which have a very thin coating weight and high uniformity quality, is one of the

goals of the automotive industry. In order to obtain thinner and more uniform coating

weight, a new model of impinging jet which is comprised of one main jet with two

auxiliary jets, one on each side of the main jet, called a multiple-slot impinging jet, is of

considerable interest.

For the current study, a multiple-slot impinging jet was designed and

manufactured and measurements were performed for both the single-slot impinging jets,

the current model used in continuous hot-dip galvanizing lines, and the multiple-slot

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impinging jet subjected to a wide range of gas wiping parameters which include the main

jet Reynolds number (Rem), the auxiliary jet Reynolds number (Rea), and the plate-to-

nozzle ratio (z/d). A comparison between the measured results obtained for the two

impinging jet configurations and the numerical results by Tamadonfar [2010] has been

provided. The similarities and differences between the experimental and numerical results

are presented and discussed.

v

Acknowledgments

I would like to take this opportunity to express my sincere appreciation to Dr.

Joseph R. McDermid and Dr. Samir Ziada for their guidance and unconditional support

throughout my graduate studies.

I am also very grateful to Dr. Frank Goodwin, Executive Vice President of

Technology and Market Development at the International Lead-Zinc Research

Organization. The work done in this research would have not been made possible without

his financial support.

I would also like to acknowledge the Mechanical Engineering Department

Machine Shop technicians Ron Lodewyks, Michael Lee, Joe Verhaeghe, Jim McLaren,

and Mark MacKenzie for their assistance for the fabrication and development of the

devices and setups.

Finally, I deeply thank my parents and my sister Samaneh, for their love, supports

and patience that made this journey so much easier for me.

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Table on Contents

Abstract .......................................................................................................................... iii

Acknowledgments ............................................................................................................ v

Table on Contents ........................................................................................................... vi

List of Figures .............................................................................................................. viii

List of Tables ................................................................................................................ xiv

Nomenclature ................................................................................................................ xv

Chapter 1: Introduction ................................................................................................ 1

1.1 Thesis Statement .......................................................................................................... 1 1.2 Motivation and Objectives ........................................................................................... 2 1.3 Thesis Organization ..................................................................................................... 4

Chapter 2: Literature Review ....................................................................................... 6

2.1 Continuous Hot-Dip Galvanizing ................................................................................. 6 2.2 Impinging Jets ............................................................................................................. 8 2.3 Coating Weight Model ............................................................................................... 16 2.4 Multiple-Slot Impinging Jet ....................................................................................... 24

Chapter 3: Experimental Setup .................................................................................. 30

3.1 Single-Slot Impinging Jet ........................................................................................... 30 3.2 Multiple-Slot Impinging Jet ....................................................................................... 34 3.3 Pressure Transducers ................................................................................................. 39

Chapter 4: Results and Discussion .............................................................................. 42

4.1 Single-Slot Impinging Jet ........................................................................................... 42 4.1.1 Effect of Plate-to-Nozzle Ratio (z/d) ...................................................................... 43 4.1.2 Effect of Main Jet Reynolds Number (Rem) ............................................................ 45 4.1.3 Effect of Jet Inclination Angle (α) .......................................................................... 51 4.2 Multiple-Slot Impinging Jet ....................................................................................... 56 4.2.1 Effect of Plate-to-Nozzle Ratio (z/d) ...................................................................... 57 4.2.2 Effect of Main Jet Reynolds Number (Rem) ............................................................ 60 4.2.3 Effect of Auxiliary Jet Reynolds Number (Rea) ...................................................... 61 4.3 Comparison between Multiple-Slot and Single-Slot Impinging Jet ............................. 64 4.4 Computational Results Validation .............................................................................. 69

vii

4.4.1 Single-slot Impinging Jet ....................................................................................... 69 4.4.2 Multiple-Slot Impinging Jet ................................................................................... 73 4.5 Discussion ................................................................................................................. 78 4.5.1 Effect of Plate-to-Nozzle Ratio (z/d) ...................................................................... 78 4.5.2 Reynolds Number Effect (Re) ................................................................................ 82 4.5.3 Jet Inclination Effect (α)......................................................................................... 84

Chapter 5: Conclusions and Future Work ................................................................. 85

5.1 Conclusions ............................................................................................................... 85 5.2 Future Work .............................................................................................................. 87

Appendix A: Dimensions of Impinging Jets ............................................................... 92

A.i Single-Slot Impinging Jet ........................................................................................... 92 A.ii Multiple-Slot Impinging Jet ....................................................................................... 97

Appendix B: Wall Pressure Profiles ......................................................................... 105

B.i Single-Slot Impinging Jet ..........................................................................................105 B.ii Multiple-Slot Impinging Jet ......................................................................................109

Appendix C: Uncertainty Analysis ........................................................................... 112

C.i Flow Velocity Uncertainty ........................................................................................112 C.ii Experimental Setup Uncertainty ................................................................................115

viii

List of Figures

Figure 1-1: a) Schematic of single-slot impinging jet b) Schematic of multiple-slot impinging jet. ................................................................................................................. 1

Figure 1-2: Schematic of gas wiping process [Ahn & Chung, 2006]................................ 3

Figure 2-1: Schematic of a continuous hot dip galvanizing line [Marder, 2000]. ............. 7

Figure 2-2: Schematic of the gas jet wiping process in the continuous hot-dip galvanizing line [Gosset & Buchlin, 2007 and Elsaadawy et al. 2007]. .............................................. 8

Figure 2-3: Visualization of an impinging jet flow field [Maurel & Solliec, 2001]. ........10

Figure 2-4: Splashing in a continuous hot-dip galvanizing line [Dubois, 2005]. .............11

Figure 2-5: Computational domain and boundary conditions [Cho et al., 2009]. .............12

Figure 2-6: Normalized coating thickness for different configurations [Myrillas et al., 2013]. ............................................................................................................................13

Figure 2-7: Schematic of a steel strip with edge overcoating [Arthurs, 2007]. ................14

Figure 2-8: Bowtie air knife profile [Arthurs, 2007]. ......................................................15

Figure 2-9: Schematic of air knives with edge baffles [Arthurs, 2007] ...........................16

Figure 2-10: Schematic of gas-jet wiping process [Kweon & Kim, 2011]. .....................16

Figure 2-11: a) Comparison of the coating weight predictions between the coating weight model of Tu and the industrial line data b) Comparison between the Elsaadawy et al. [2007] model and the measured industrial data. .............................................................20

Figure 2-12: Non-dimensional pressure profile for all z/d at Re=11000 [Tu & Wood, 1996]. ............................................................................................................................21

Figure 2-13: Comparison of Stanton and Preston tube for measuring the wall shear stress [Tu & Wood, 1996]. ......................................................................................................22

Figure 2-14: The schematic of the single-slot impinging jet [Tamadonfar, 2010]. ..........23

Figure 2-15: Non-dimensional wall pressure distribution for 2≤z/d≤12 [Tamadonfar, 2010]. ............................................................................................................................24

ix

Figure 2-16: Schematic of the simulation domain and parameters of the double air knife [Yoon & Chung, 2010]. .................................................................................................25

Figure 2-17: Proposed multiple jet [Kim et al., 2010]. ....................................................26

Figure 2-18: Schematic of multiple-slot impinging jet [Tamadonfar, 2010]. ...................28

Figure 2-19: Coating weight comparison between the single-slot and multiple-slot impinging jets as a function of z/d [Tamadonfar, 2010]. .................................................29

Figure 3-1: Single-slot impinging jet set-up. ..................................................................31

Figure 3-2: Single-slot impinging jet. .............................................................................32

Figure 3-3: a) Velmex™ traverse, b) Newport 481 A series rotary table. ........................33

Figure 3-4: Single-impinging slot set-up parameters. .....................................................33

Figure 3-5: Multiple-slot impinging jet schematic. .........................................................36

Figure 3-6: Schematic of multiple-slot impinging jet parameters. ...................................37

Figure 3-7: Non-dimensional velocity profile at the exit of the short nozzle and long nozzle single-slot impinging jets at Rem = 11000(PPlenum= 7.91 kPa), d = 1.5 mm. .........38

Figure 3-8: Non-dimensional velocity profile at the exit of the multiple-slot impinging jet nozzles...........................................................................................................................39

Figure 3-9: Schematic of pressure measurement facility. ................................................40

Figure 4-1: Schematic of the single-slot impinging jet a) short nozzle b) long nozzle. ....43

Figure 4-2: Non-dimensional wall pressure distribution at Rem=11000 for all z/d for the short nozzle single-slot impinging jet. ............................................................................44

Figure 4-3: Non-dimensional wall pressure distribution at Rem=11000 for all z/d for the long nozzle single-slot impinging jet. .............................................................................45

Figure 4-4: Non-dimensional wall pressure profile for the short nozzle and long nozzle single-slot impinging jets for different z/d at Rem=11000. ..............................................46

Figure 4-5: Non-dimensional wall pressure distribution at Rem=20000 for the short nozzle single-slot impinging jet. ...............................................................................................48

Figure 4-6: Non-dimensional wall pressure distribution at Rem =30000 for the short nozzle single-slot impinging jet. ....................................................................................48

x

Figure 4-7: Wall pressure profile distribution for different Rem and z/d for the single-slot impinging jet with short nozzle. .....................................................................................49

Figure 4-8: Maximum wall pressure gradient as a function of Rem and z/d for the short nozzle single-slot impinging jet. ....................................................................................50

Figure 4-9: Schematic of oblique single-impinging slot jet. ............................................50

Figure 4-10: Non-dimensional wall pressure distribution for different z/d at Rem=11000 for short nozzle single-slot impinging jet. ......................................................................52

Figure 4-11: Comparison of the maximum wall pressure as a function of z/d at α=0° and α=3° for short nozzle single-slot impinging jet. .............................................................52

Figure 4-12: Wall pressure gradient distribution as a function of Rem at z/d=10 for 3° tilted short nozzle single-slot impinging jet. ...................................................................53

Figure 4-13: Maximum wall pressure gradient as a function of Rem and z/d for 3° tilted short nozzle single-slot impinging jet. ............................................................................54

Figure 4-14: Comparison of maximum pressure gradient as a function of Reynolds number between α=0° and α=3° tilted for the short nozzle single-slot impinging jet..55

Figure 4-15: Geometry of the multiple-slot impinging jet...............................................57

Figure 4-16: Non-dimensional wall pressure distribution as a function of z/d at Rem=9000 and Rea=11000. .............................................................................................................59

Figure 4-17: Non-dimensional wall pressure distribution as a function of z/d at Rem=11000 and Rea=11000. ..........................................................................................59

Figure 4-18: Non-dimensional wall pressure distribution as a function ofz/d at Rem=13000 and Rea=11000 ...........................................................................................60

Figure 4-19: Experimental wall pressure distribution as a function of Rem at Rea=11000 and z/d=6.......................................................................................................................61

Figure 4-20: Experimental non-dimensional wall pressure distribution as a function of Rea with Rem=11000 at z/d=8. .............................................................................................62

Figure 4-21: Experimental non-dimensional wall pressure distribution for different Rea with Rem=11000 and z/d=4. ...........................................................................................63

Figure 4-22: Experimental maximum pressure gradient as a function of auxiliary jet Reynolds number (Rea) with Rem=11000 and z/d=4. ......................................................63

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Figure 4-23: Comparison of non-dimensional pressure distribution between the single-slot and multiple slot impinging jets for Rem=11000, Rea=11000 and z/d=10. ......................65

Figure 4-24: Comparison of maximum pressure of short nozzle single-slot and multiple-slot impinging jets for various values of z/d, Rem=11000 and Rea=11000. .....................65

Figure 4-25: Comparison of maximum pressure gradient of single and multiple-slot impinging jets for various values of z/d, Rem=11000 and Rea=11000. ............................67

Figure 4-26: Non-dimensional shear stress for single-slot and multiple-slot impinging jet at Rem=11000 and Rea=11000 [Tamadonfar, 2010]. ......................................................67

Figure 4-27: Comparison of force per unit width of single-slot and multiple-slot impinging jet as a function of z/d at Rem=11000 and Rea=11000. ..................................68

Figure 4-28: Experimental versus simulated [Tamadonfar, 2010] non-dimensional pressure profile for different z/d at Rem=11000 (short nozzle single-slot impinging jet). 71

Figure 4-29: Comparison of simulated [Tamadonfar, 2010] and experimental pressure

profile derivatives dpdx

at Rem=11000 for the short nozzle single-slot impinging jet. ..72

Figure 4-30: Experimental and simulated [Tamadonfar, 2010] maximum pressure gradient as a function of z/d for Rem=11000 for the short nozzle single-slot impinging jet. ......................................................................................................................................72

Figure 4-31: Comparison between the experimental and simulated jet exit velocity profile [Tamadonfar, 2010]. ......................................................................................................73

Figure 4-32: Simulated [Tamadonfar, 2010] and experimental non-dimensional pressure profile distribution comparison for different z/d at Rem=11000 and Rea=11000 for multiple-slot impinging jet. ............................................................................................74

Figure 4-33: Comparison of simulation [Tamadonfar, 2010] and experimental maximum pressure gradient as a function of z/d at Rem=11000 and Rea=11000 for multiple-slot impinging jet. ................................................................................................................75

Figure 4-34: Comparison of the experimental and numerical [Tamadonfar, 2010] wall pressure distribution for Rem=11000, Rea=11000 at z/d=4 for multiple-slot impinging jet. ......................................................................................................................................76

Figure 4-35: Maximum wall pressure gradient for different main jet Reynolds number at z/d=4 and Rea=11000 [Tamadonfar, 2010] for multiple-slot impinging jet. ...................77

xii

Figure 4-36: Numerical maximum wall pressure gradient as a function of Rea with Rem=11000 and z/d=4. ..................................................................................................77

Figure 4-37: Maximum wall pressure gradient for the multiple-slot impinging jet as a function of Rem for 4z/d12 at Rea=11000. ...................................................................79

Figure 4-38: Maximum wall pressure for the short nozzle single-slot impinging jet as a function of z/d for different Rem at Rea=11000. ..............................................................79

Figure 4-39: Maximum wall pressure for the multiple-slot impinging jet as a function of z/d at Rem=11000 and Rea=11000. .................................................................................80

Figure 4-40: Maximum wall pressure of short nozzle single-slot impinging jet as a function of Rem for 6z/d12. .........................................................................................82

Figure 4-41: Maximum wall pressure of multiple-slot impinging jet as a function of Rem

for 4 z/d 12 and Rea=11000. .......................................................................................83

Figure A-1: Isometric view of the single-slot impinging jet. ...........................................92

Figure A-2: Single-slot impinging jet plenum. ...............................................................93

Figure A-3: Single-slot impinging jet top cap. ................................................................94

Figure A-4: Single-slot impinging jet nozzle flange. ......................................................95

Figure A-5: Single-slot impinging jet bottom cap. ..........................................................96

Figure A-6: Isometric views of multiple-slot impinging jet. ...........................................97

Figure A-7: Top cap of the multiple-slot impinging jet...................................................98

Figure A-8: Main jet plenum of the multiple-slot impinging jet......................................99

Figure A-9: Auxiliary jet plenum of the multiple-slot impinging jet. ............................ 100

Figure A-10: Main jet nozzle flange of the multiple-slot impinging jet. ........................ 101

Figure A-11: Auxiliary jet side flange of the multiple-slot impinging jet. ..................... 102

Figure A-12: Auxiliary jet front flange of the multiple-slot impinging jet..................... 103

Figure A-13: Bottom cap of the multiple-slot impinging jet. ........................................ 104

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Figure B-1: Wall pressure distribution at U=113m/s for all z/d for the short nozzle single-slot impinging jet at α=0°............................................................................................. 105

Figure B-2: Wall pressure distribution at U=200 m/s for all z/d for the short nozzle single-slot impinging jet at α=0°............................................................................................. 106

Figure B-3: Wall pressure distribution at U=300 m/s for all z/d for the short nozzle single-slot impinging jet at α=0°............................................................................................. 106

Figure B-4: Wall pressure distribution for different z/d at U=113 m/s for short nozzle single-slot impinging jet at α=3°. ................................................................................. 107



Figure B-7: Wall pressure distribution for different z/d at Um=90 m/s and Ua=55 m/s for multiple-slot impinging jet. .......................................................................................... 109



Figure B-10: Wall pressure distribution for different Ua at Um=113 m/s and z/d=4 for multiple-slot impinging jet. .......................................................................................... 110



FIGURE C-1: CALIBRATION DIAGRAM FOR DIAPHRAGM NUMBER 32 (P=1.25 PSI OR 14 KPA). .................................................................................................................... 115

xiv

List of Tables

Table 3-1: Pressure transducer properties. ......................................................................41

Table 4-1: Shear layer thickness (δ, δ*, θ*) of computational [Tamadonfar, 2010] and experimental results at the exit of the nozzle. .................................................................70

Table C-1: Uncertainty in the geometry parameters of the experimental setup. ............ 115

xv

Nomenclature

푎 Wall distance between two jets [mm]

푑 Air-knife gap width [mm]

푔 Gravitational constant [m s⁄ ]

퐺 Non-dimensional effective gravitational acceleration

푃 Pressure along the sheet substrate [Pa]

푃 Maximum pressure on the sheet substrate [Pa]

푞 Volumetric flow rate per unit of film width [m s⁄ ]

푄 Non-dimensional withdrawal flux

푅푒 Auxiliary slot jet Reynolds number

푅푒 Main slot jet Reynolds number

푠 Distance of the main slot jet to the auxiliary slot jet [mm]

푆 Non-dimensional shear stress

푢 Fluid velocity [m s⁄ ]

xvi

푈 Mean fluid velocity [m s⁄ ]

푉 Sheet substrate velocity [m s⁄ ]

w Film thickness [m]

W Non-dimensional film thickness

푥 Cartesian coordinate [m]

푦 Cartesian coordinate [m]

푧 Impingement distance [mm]

Greek Symbols

훼 Jet angle [˚]

훿 Disturbance thickness [mm]

훿∗ Displacement thickness [mm]

휃∗ Momentum thickness [mm]

휇 Dynamic viscosity [Pa.s]

xvii

휈 Kinematic viscosity [m s⁄ ]

휌 Mass density [kg m⁄ ]

휏 Wall shear stress on the sheet substrate [Pa]

휏 Maximum wall shear stress [Pa]

Abbreviations

CGL Continuous Galvanizing Line

EOC Edge Over Coating

LES Large Eddy Simulation

LDV Laser Doppler Velocimetry

PIV Particle Image Velocimetry

RMS Root Mean Square

McMaster University-Mechanical Engineering M.A.Sc. Thesis- S. Alibeigi

1

Chapter 1: Introduction

1.1 Thesis Statement

An experimental investigation has been done on a single-slot impinging jet (a

conventional air knife design) and a multiple-slot impinging jet [Figure 1-1] to study the

effect of the process parameters and air-knife geometry on the wall pressure distribution.

In order to facilitate this project, an experimental multiple-slot impinging jet was

designed, manufactured and tested. The experimental results for both single-slot and

multiple-slot impinging jets were compared with the simulated results of Tamadonfar

[2010] for the same operating conditions.

Figure 1-1: a) Schematic of single-slot impinging jet b) schematic of multiple-slot

impinging jet.


2

1.2 Motivation and Objectives

Impinging jets have many useful properties which make them suitable for a

variety of different applications. One of these applications, which is the focus of this

project, is gas-jet wiping in the continuous hot-dip galvanizing process. In this process an

impinging jet, in the industry known as air knife, controls the Zn-alloy coating thickness

by removing excess zinc from the moving substrate immediately after dipping in the

molten zinc bath. Figure 1-2 shows a schematic of the gas-jet wiping process with a

conventional air knife configuration, consisting of a single-slot nozzle.

Zinc coating weight is one of the concerns of the automotive industry. The

minimum possible coating weight with the conventional air knife is currently

approximately 40 g/m2 whereas the automotive industry is demanding lighter coating

weights. In order to obtain lower coating weight at reasonable strip velocity, the wiping

pressure should increase significantly. However, increasing the pressure causes some

industrial difficulties such as splashing and generation of higher noise. Splashing is

characterized by the ejection of zinc droplets from the strip which can be deposited on or

around the jet nozzle or on the strip itself, resulting in defects. Full splashing happens

when the shear forces applied on the film becomes higher than the liquid surface tension.

Currently, in order to cope with splashing, the steel strip moves at lower speeds in the

hot-dip galvanizing process resulting in decrease in steel strip production. Kim et al.

[2010] proposed a multiple-slot jet air knife design model in order to solve the splashing

problem and enhance coating quality.


3

Figure 1-2: Schematic of gas wiping process [Ahn & Chung, 2006].

In addition, zinc coating quality is an important industrial issue, especially in the

automobile industry which requires sheet steels with a uniform coating and excellent

corrosion resistance. One of the coating defects in the continuous hot-dip galvanizing

process affecting final coating quality is a localized non-uniform coating known as check

mark [Yoon & Chung, 2010]. Check marks which appear on the steel strip may be caused

by flow instabilities arising from gas jet flow flapping.

Considerable numerical and experimental work has been done to study the single-

slot impinging jet in the continuous hot-dip galvanizing line, while few studies exist on

the multiple-slot jet. In the present work, the effect of different air knife geometries on

the wall pressure distribution as a function of processing parameters such as Reynolds

numbers and plate-to-nozzle spacing ratio have been studied experimentally for a single-


4

slot and multiple slot impinging jet. In addition, the computed results of Tamadonfar

[2010] were compared with the experimental results.

1.3 Thesis Organization

This thesis consists of five Chapters and two Appendices. Chapter 1 contains an

introduction of the present work, including the motivation and objectives of this study.

Chapter 2 comprises the literature survey and begins with information concerning the

continuous hot-dip galvanizing process and impinging jet applications in industry and

specifically in continuous hot-dip galvanizing lines. Chapter 2 then continues with the

introduction of the coating models used for estimating the final coating thickness on the

moving substrate. It continues with the provision of information about the new proposed

air knife model, a multiple-slot impinging jet, as well as a brief literature review on past

studies. Chapter 3 details the experimental apparatus used for the measurements and the

investigated experimental parameters. Chapter 4 presents the experimental results for

both impinging jet designs as well as comparison between the results of both

configurations and the computed results of Tamadonfar [2010]. The last section of

Chapter 4 presents the discussion of the results. Chapter 5 provides conclusions and

various suggestions for future work.

Additional sections are provided at the end of this thesis. Appendix A contains

details of the parts and dimensions for the multiple-slot and single-slot impinging jet.


5

Appendix B and appendix C provide the pressure profiles for the different studied cases

in dimensional form and the error analysis in the measurements, respectively.


6

Chapter 2: Literature Review

This chapter begins with a brief description of the continuous hot-dip galvanizing

process and introduces an impinging jet and its application in the continuous galvanizing

line for controlling the coating thickness on a steel substrate. It then presents various

coating weight models. Finally, a new air knife entailing a multiple-slot impinging jet is

introduced.

2.1 Continuous Hot-Dip Galvanizing

Continuous hot-dip galvanizing process is a very high production volume process

such that the galvanized sheet production increased by 40% to 32.5 million tons (Mt) in

2012 from 23.1 Mt in 2009. Therefore, it is a major process worthy of attention. In the

continuous hot-dip galvanizing process, sheet steel is coated with a layer of zinc to

protect it from corrosion. Figure 2-1 shows a schematic of the continuous hot-dip

galvanizing process. After the steel sheet goes through the heat treatments and surface

preparation in order to improve coating adherence, it is immersed into the 460ºC molten

zinc pot. After the steel strip exits the zinc bath, a pair of two-dimensional high speed

opposing plane gas jets, which impinge on the substrate, remove any excess molten zinc

from the substrate surface using the combined actions of gravity, wall pressure, and wall

shear stress which causes the excess zinc to run back into the bath. Next, the strip is air-

cooled by forced or natural convection to produce metallic galvanized coatings or

proceeds to a further heat treatment to produce galvannealed coatings. The gas wiping


7

jets, or air knives, utilize either nitrogen or compressed air as a working fluid and the air

knives are aligned to impinge symmetrically at the same position on both sides of the

steel strip [Marder, 2000]. Figure 2-2 shows a schematic of the gas-jet wiping process,

and approximate position of the strip, zinc pot, and the air knives.

Figure 2-1: Schematic of a continuous hot dip galvanizing line [Marder, 2000].

The main process parameters that control the coating weight are the impingement

distance (z), the jet slot width (d), and the plenum pressure (P) as shown in Figure 2-2.

The impingement distance is usually used in its non-dimensional form, known as the

impingement ratio (z/d), which basically is non-dimensionalized by the jet slot width.


8

Figure 2-2: Schematic of the gas jet wiping process in the continuous hot-dip galvanizing

line [Gosset & Buchlin, 2007 and Elsaadawy et al. 2007].

2.2 Impinging Jets

Impinging jets have many applications in industry because of their useful

properties. For example, due to their high Nusselt number near the wall region, which

leads to high rate of heat transfer, impinging jets are very useful in applications such as

the cooling of turbine blades [Li et al., 2011] or electronic systems, in the shaping and

tempering of glass plates [Lee & Viskanta, 2012 and Camci & Herr, 2002] and deicing

the aircraft systems. Considerable numerical studies have been done on impinging jets,

focusing on heat transfer such as those of Behnia [1999], Kubacki and Dick [2010] and

Zu et al. [2011]. Moreover, because of their highly turbulent mixing and high Sherwood

number, impinging jets are useful for mixing enhancements (for instance in chemical


9

processing) and material deposition processes (such as plasma spray), respectively.

Impinging jets, in addition, are well known in industry because of their high level of

shear stress at the wall regions which makes them attractive for drying in paper

production as well as for coating applications such as gas-jet wiping process in

continuous galvanizing lines. The last application is the subject of this study.

The impinging jet in continuous galvanizing lines is known as an air-knife. Its

application is to control the thickness of the liquid coating metal, mostly zinc, on the steel

sheet substrate. Impinging jets have a highly complex flow structure, so that many studies

have been done to examine impinging jet flow fields experimentally and numerically.

There are different techniques of studying the fluid flow field such as Particle Image

Velocimetry (PIV), Laser Doppler Anemometry (LDA), and Hot-Wire Anemometry.

Esirgenez et al. [2007], Fairweather et al. [2002], Durst et al. [1996], Maurel & Solliec

[2001], Loureiro & Silva Freire [2012], Brata et al. [2004], Durst [1995], and Durst et al.

[2001] used Laser Doppler Anemometry to investigate the fluid flow field. Maurel &

Solliec [2001], Hammad & Milanovic [2011], and Fairweather & Hargrave [2002] used

the PIV technique to study the flow field of impinging jets. Zhe & Modi [2001] and Durst

et al. [2001] used Hot Wire Anemometry to measure the flow field near the wall.

Maurel & Solliec [2001] studied the impinging jet flow structure experimentally.

As it can be seen in Figure 2-3 they divided impinging jet flow field into three zones as

follows:


10

Potential Core Zone. In this zone, the centerline velocity is the same as the jet

exit velocity. The length of this zone is 3<z/d<6.

Intermediate Zone. In this zone, the axial velocity profile starts decaying and the

turbulence level is rising.

Impinging Zone. As the flow reaches to the plate, the value of velocity normal

to the plate becomes zero and the flow turns. The flow builds up the higher

pressure and shear stress on the wall. In this region, the vortices stretch and

turbulence increases.

Figure 2-3: Visualization of an impinging jet flow field [Maurel & Solliec, 2001].

One of the undesirable phenomena in continuous galvanizing lines which

decrease the wiping efficiency is splashing. Splashing is characterized by ejection of


11

liquid zinc droplets of the runback film flow from the coating surface. Splashing is

initiated at the edge of the strip at some high speed lines, and spreads toward the center of

the strip. Splashing decreases the quality of the coating and can result in nozzle blockage

due to liquid zinc droplets solidify on the air-knife nozzle. Figure 2-4 shows a full

splashing in a continuous hot-dip galvanizing line. Full splashing occurs when the

applied force on the upstream film is higher than the liquid surface tension. One of the

documented cases in which full splashing occurred is for a zinc coating thickness of 20

µm produced at line speed of 160-170 m/min when the distance between the strip and air-

knife was short (z/d<6) [Dubois, 2011]. There are some experimental and numerical

studies shows that the wiping angle or the shape of the jet can delay this phenomenon,

such as Dubois et al. [2005]. They expected a 30% increase in line speed by inclining the

jet angle by up to 30˚, although an inclination angle greater than 10˚ has some physical

setup limitations.

Figure 2-4: Splashing in a continuous hot-dip galvanizing line [Dubois, 2005].


12

Cho et al. [2009] numerically studied the effect of the tilting angle of an air-knife

with constant expansion rate and strip speed on coating thickness. Figure 2-5 shows the

computational domain and boundary condition of this research. Their proposed air-knife

system with a constant expansion rate diminished the splashing problem, and saved

energy in comparison with the conventional design. They concluded that tilting the air

knife probably alleviates splashing problem. However, by increasing the jet inclination

for angles higher than five degrees, the coating thickness increased up to 11%. For jet

angles less than 5 degrees, a significant difference has not been observed. They also

studied the effect of strip velocity with a constant jet inclination of 5º. They showed that

by decreasing the strip velocity, the coating thickness reduced since when the strip

velocity increases, the momentum influx per unit area of the strip decreases.

Figure 2-5: Computational domain and boundary conditions [Cho et al., 2009].


13

Myrillas et al. [2013] experimentally studied the effect of a side jet on delaying

splashing by stabilizing the runback flow. They showed that using the side jet results in

the stronger wiping and consequently lower value of coating thickness. They put the side

jet parallel to the main jet and at the distance of 1 mm away from the main jet, once at the

top and once at the bottom of the main jet. Figure 2-6 shows the non-dimensionalized

coating thickness results for main jet with side jet at upstream, side jet at downstream,

and no side jets. It can be seen that the presence of side jet has delayed the splashing. It

can be seen also that by avoiding splashing, thinner coating thickness can be reached

because the main jet can be operated at higher pressure. They used propylene glycol as a

liquid for experiments.

Figure 2-6: Normalized coating thickness for different configurations [Myrillas et al.,

2013].


14

Another undesirable phenomenon in gas jet wiping is edge overcoating (EOC),

where the coating at the edge of the sheet is thicker than the middle of the strip [Figure 2-

7]. EOC can cause some difficulties in coiling or inadequate galvannealing at the edge of

the sheet substrate [Arthurs, 2007]. There are different techniques to overcome this

problem.

Figure 2-7: Schematic of a steel strip with edge overcoating [Arthurs, 2007].

Using bowtie profile air knifes is one of the ways of combating this problem

[Arthurs, 2007]. Figure 2-8 shows the typical dimensions of a bowtie air knife. It can be

seen that the jet width at the edge of the bowtie air knife is wider than the center, and

therefore the momentum of the flow at the edge of the strip increases. Additional

momentum at the edge of the strip results in more zinc being removed at the edge of the

sheet. Zhang et al. [2012] numerically studied the effect of an air knife with a variable

nozzle slot opening on coating, and they concluded this type of air knife provides a more

uniform coating thickness. The study of Kim et al. [2003] showed that EOC is caused by

the alternating vortices which are generated by the collision of the opposing air jets

outside of the strip. Ahn and Chung [2006] numerically studied the effect of adding a


15

small diameter cylinder at the lower lip of both air knives in order to deflect the jets

downward and prevent EOC. By this method, the collision between the two opposing

edges happened at an angle of less than 180º, and made the vortical structures at the edge

of the sheet disappear. By eliminating the vortices at the edge of the sheet, the pressure

across the surface becomes uniform. This uniformity causes the consistency of coating

weight.

Figure 2-8: Bowtie air knife profile [Arthurs, 2007].

Another method to solve the EOC problem is using edge baffle plates, which are

also used to reduce the noise level in the gas-jet wiping process [Figure 2-9]. Zhang et

al.’s [2012] numerical study showed that using wider baffle plates and shorter distance

between the baffle plates to the strip can effectively control EOC. However, Ahn and

Chung [2006] claimed that using the small diameter cylinder at lower lips of air knives is

more effective than using baffle plates.


16

Figure 2-9: Schematic of air knives with edge baffles [Arthurs, 2007]

2.3 Coating Weight Model

Many researchers have tried to predict the coating weight as a function of

operating parameters using experimental, empirical, or simulation techniques. The first

work in this field is done by Thorton and Graff [1976]. They assumed that the coating

weight was only a function of the wall pressure profile imposed on the film created by the

impinging jet. The defect in their model was in neglecting the effect of shear stress on the

coating weight.

Figure 2-10: Schematic of gas-jet wiping process [Kweon & Kim, 2011].


17

Ellen and Tu [1984] further developed the model of Thornton and Graff [1976] by

taking the wall shear stress into account. It was shown that including the wall shear stress

into the model enhanced the coating weight model accuracy. The simplified two-

dimensional Navier-Stokes equation was used to calculate the coating thickness. In order

to simplify the Navier-Stokes equation, it has been assumed that the molten zinc on the

coating layer was at steady state, and isothermal with a constant viscosity and density

(incompressible flow), and it was also assumed that the pressure across the coating layer

was constant since the velocity perpendicular to the substrate is negligible. From these

assumptions, the two-dimensional Navier-Stokes equation at the substrate wall was

reduced to:

202

d u dpgdxdy

(2-1)

Where u is the liquid film velocity, p the pressure along the substrate, g the gravitational

acceleration and μ and ρ are the viscosity and density of the coating material,

respectively. The boundary conditions for solving equation (2-1) are:

at 0 (No slip condition)

= at

u V yStripdu y wdy

(2-2)

whereτ is the shear stress imposed on the film by the impinging jet, and w is the film

thickness. By integrating equation (2-1) and applying the boundary conditions, the liquid

film velocity can be derived:


18

21 2

2y y y GWu V SWs w w w

(2-3)

In equation (2-3), W is the non-dimensional film thickness gW w

VStrip

, S is

the non-dimensional shear stress SV gStrip

, and G is the gravitational acceleration

11 dpGg dx

.

Based on the conservation of mass, the net vertical liquid mass flow rate at any

position must be equal to the final coating mass multiplied by the strip velocity.

Therefore, the liquid zinc flux can be written as follows:

21

2 30

h Sw Gwq udy V wStrip

(2-4)

Thus, the non-dimensional flux Strip Strip

q gQV V

converts to:

3 2

3 2GW SWQ W

(2-5)

The non-dimensional film thickness W corresponds to the maximum withdrawal

flux, so W can be determined by solving 0dQdW [Ellen and Tu, 1984].


19

2 42

S S GWG

(2-6)

It can be seen that the maximum non-dimensional withdrawal flux and

corresponding non-dimensional film thickness are function of the pressure gradient and

shear stress. Once the liquid film solidified, the coating thickness can be written as:

minQMaxw

gVStrip

(2-7)

Myrillas et al. [2009] used an analytical model with surface tension [Yoneda,

1993] for predicting the coating thickness. They used the maximum pressure gradient and

maximum shear stress to calculate the coating thickness on the moving substrate. The

model showed 7% difference with the experimental results.

Elsaadawy et al. [2007] further developed the coating weight model as a function

of operating parameters by combining experimental and computational methods to

improve the pressure and shear stress correlation using the k-ε turbulence model in the

FLUENT CFD code. They developed the pressure and shear stress correlation based on

the earlier work of Ellen and Tu [1984]. Figure 2-11a illustrates the comparison between

the coating weight prediction of Ellen and Tu [1984] with experimental results, and

Figure 2-11b shows the comparison between the experimental results and the developed

model of Elsaadawy et al. [2007]. By comparing these two figures, it can be seen that a

significant improvement with the new developed coating weight model has been


20

achieved. Their model is in good agreement with industrial data for coating weights of

less than 75 g/m2 (Wc<75 g/m2). Since the model neglected the inertial effects of the

entrained molten coating, which is significant when the coating thickness increased, their

model was less accurate for higher coating weight. They improved the coating weight

model by adding the convective heat transfer effect into their model.

Figure 2-11: a) Comparison of the coating weight predictions between the coating weight

model of Tu and the industrial line data b) Comparison between the Elsaadawy et al. [2007] model and the measured industrial data.

Tu and Wood [1996] measured the wall pressure and shear stress profile of an

impinging jet for wide range of Reynolds numbers, 3000Re6300, and plate-to-nozzle

ratios, 1z/d20, where the nozzle width was kept constant at 0.97 mm. They also

measured wall pressure and shear stress profiles for Re=11000, plate-to-nozzle ratios

between 1 and 12, and a nozzle width of 6.4 mm. Figure 2-12 shows the non-dimensional

pressure profile for all z/d at Re=11000. They concluded that the length of the potential


21

core is five times the jet width. They examined a range of Preston and Stanton tubes for

measuring the shear stress, and found that a 0.05 mm-high Stanton tube gave the most

accurate results [Figure 2-13]. They found that the non-dimensional shear stress profile

was dependent on the plate-to-nozzle ratio and Reynolds number.

Figure 2-12: Non-dimensional pressure profile for all z/d at Re=11000 [Tu & Wood,

1996].


22

Figure 2-13: Comparison of Stanton and Preston tube for measuring the wall shear stress

[Tu & Wood, 1996].

Tamadonfar [2010] numerically investigated the wall pressure and shear stress

profile, and consequently calculated the coating thickness as function of plate-to-nozzle

ratio for 6<z/d<12. The mesh used for this configuration was comprised of quadrilaterals

and was generated with GAMBIT. The meshed geometry is shown in Figure 2-14. He

refined the mesh in order that the solutions become mesh independent. Depending on the

plate-to-nozzle ratio, number of nodes varied between 70,000 and 130,000. The

simulations have been solved using FLUNTTM. The simulations were performed using

the standard k-ε turbulence model. The inlet condition was defined as velocity-inlet, and

the far-field boundary condition was set to atmospheric pressure. He considered the

substrate in his simulation stationary since the ratio of jet velocity to the substrate

velocity is high. He assumed the effect of the moving plate on the pressure and shear

stress is negligible. No-slip condition was defined for the substrate. Figure 2-15 shows

the non-dimensional wall pressure distribution as a function of plate-to-nozzle ratio. It


23

illustrates that the non-dimensional wall pressure profile and the maximum non-

dimensional wall pressure does not change significantly to 2≤z/d≤8. However, the non-

dimensional maximum wall pressure drops for z/d>8 because the plate is outside of the

jet potential core. Therefore, he concluded the length of the potential core is eight times

the jet width. His results showed that the non-dimensional shear stress for 2≤z/d≤12

changes from zero to its maximum value linearly, and the maximum shear stress on the

plate is in the laminar boundary layer. He also calculated the coating weight for different

plate-to-nozzle ratios. He concluded that the coating weight does not change significantly

for z/d≤8 since the plate is in the potential core of the jet whereas the coating weight

increases by going outside of the potential core (z/d≥10).

Figure 2-14: The schematic of the single-slot impinging jet [Tamadonfar, 2010].


24

Figure 2-15: Non-dimensional wall pressure distribution for 2≤z/d≤12 [Tamadonfar,

2010].

2.4 Multiple-Slot Impinging Jet

The idea of using auxiliary jets in addition to the main jet was proposed by Tu et

al. [1993, 1994]. In a patent which they filed, different configurations of impinging jets

were proposed. Two of the proposed models, a main jet with inclined auxiliary impinging

slot jet configuration and two parallel impinging slot jets, were studied computationally

by Tamadonfar [2010] and Yoon and Chung [2010].

Yoon and Chung [2010] used unsteady 3D compressible FLUENT to simulate the

flow field. They used Large Eddy Simulation (LES) to solve this flow field. In order to

figure out the optimum configuration, they performed a series of parametric studies. The


25

parameters and the calculation domain of the double jet are shown in Figure 2-16. The

angle between the main jet and the guide jet was changed between the ranges of 0˚ to 2˚.

The inclined jet operated as a guide jet in order to make the flow field of the main jet

more stable. The guide jet prevented the formation of vortices on the stagnation line and

resulted in decreasing the check-mark stain on the substrate. They concluded that the

maximum pressure of the model with two parallel jets was lower than the model with the

main jet and the inclined jet. They also suggested that the multiple-slot jet with the two

parallel jets could produce a thinner coating weight compare to the single-slot impinging

jet. However, they have not specified the coating thicknesses of the different

configurations of the double air knife. They used the maximum pressure and the RMS

value of pressure fluctuation to figure out the optimum configuration of the double air

knife. The optimum configuration is found to be when d03=0.6 mm, d04=0.2 mm, θ=1°

and P03=15 kPa.

Figure 2-16: Schematic of the simulation domain and parameters of the double air knife

[Yoon & Chung, 2010].


26

In addition, Tamadonfar [2010] used k-ε model to solve the 2D dimensional flow

fields of two configurations of multiple-slot impinging jets, one consists of two parallel

jets and the other consists of one main jet with an inclined jet. The angle between the

main jet and the inclined jet is 20˚. He showed that the maximum pressure for both

configurations is less than the single-slot impinging jet maximum pressure. The coating

weight of the multiple-slot impinging jet with one main jet and one inclined jet is lighter

than the multiple-slot jet with two parallel jets. The coating weight of the single-slot

impinging jet is less than the multiple-slot impinging jet configuration coating weight.

Figure 2-17: Proposed multiple jet [Kim et al., 2010].

Kim et al. [2010] proposed a new design of multiple-slot jet which contains one

main jet and 4 auxiliary inclined jets which had a lower velocity compared to the main jet


27

[Figure 2-17]. In this design, the gas discharging from the main and the auxiliary jets

provided the necessary force for wiping excess molten zinc from the sheet. The second

auxiliary jets are used to prevent splashing. The auxiliary jets restrain zinc droplets from

splashing by mixing the gas particles of the main jet and auxiliary jet which are in lower

speed compare to the main jet particles resulting in the lower speed of the jet wall along a

length direction of the substrate. The lower speed of the wall jet weakens the shear stress,

therefore it prevents splashing of zinc droplets.

Tamadonfar [2010] investigated the flow field characteristics of multiple-

impinging slot jet which consists of one main jet and two adjacent inclined auxiliary jets,

for various operating parameters with the goal of estimating the final coating weight.

Eventually, he compared the coating weight of single-impinging slot jet with that of the

multiple-slot impinging jet. The multiple-slot impinging jet configuration is shown in

Figure 2-18. For all the simulation cases, d=1.52 mm and s/d=13.15. He solved the

simulation for 2≤z/d≤12 at Rem=11000 and Rea=11000. He observed that the maximum

pressure gradient is sensitive to z/d ratio, and it increases with decreasing z/d ratio.

Adding auxiliary jets resulted in increasing of the pressure along the wall in comparison

with the single-slot impinging jet. Figure 2-19 shows the comparison of coating weight

for single-slot impinging jet and multiple-slot impinging jet as a function of z/d. It can be

seen that the coating weight of multiple-slot impinging jet is greater than that of the

single-slot jet case for each z/d ratio.


28

Figure 2-18: Schematic of multiple-slot impinging jet [Tamadonfar, 2010].

In addition, Tamadonfar [2010] studied the effect of auxiliary jets Reynolds

number ranging from 4000 and 13000 with Rem=11000 and z/d=4 and 10. The maximum

pressure increased with increasing the auxiliary jets Reynolds number. The results

showed that Rea does not have a significant effect on the coating weight with Rem=11000

and z/d=4, whereas the coating weight increases with increasing Rea for z/d=10 and

Rem=11000.

There are few studies on multiple-slot jets, and most of these studies are

numerical studies. In this project, the above model by Tamadonfar [2010] is examined

experimentally. The experimental results are compared with those of the conventional

model of air knife (single-slot impinging jet) and numerical results of Tamadonfar

[2010].


29

Figure 2-19: Coating weight comparison between the single-slot and multiple-slot

impinging jets as a function of z/d [Tamadonfar, 2010].


30

Chapter 3: Experimental Setup

This chapter introduces the experimental apparatus used to do the current

measurements. It starts with explaining the single-slot impinging jet set-up, and continues

with presenting the multiple impinging slot-jet. Finally, the measurement facility set-up

will be explained.

3.1 Single-Slot Impinging Jet

Measurements were performed using a high-speed planer impinging jet. A general

view of the single-slot impinging jet experimental apparatus is presented in Figure 3-1.

The planar nozzle, plenum, and plate were machined out of aluminum. The plenum was

pressurized with compressed air from a 550 kPa supply. The air supply line consists of a

5 cm regulator at the beginning with a 5cm ball valve and a 5 cm gate valve. Afterward,

air enters into a T shaped manifold with three outlets, each with a 2.5 cm globe valve,

which were used to control the pressure for each of the three nozzles of the multiple-slot

impinging jet facility.

In all tests, measurements started when the system achieved a stable operating

condition. As shown in Figure 3-1 and Figure 3-2, air entered into the plenum from the

25.4 mm diameter hole at the top of plenum and then went through the 25.4 mm diameter

flow distributor and then passed through a series of mesh screens located upstream of the

nozzle contraction in order to break up any large-scale turbulence structures. These


31

screens consist of stainless steel cloth with a density of 70 wires per inch and an open

area fraction of β=0.58 [Mehta & Bradshaw, 1979]. Air exits the nozzle at 90 to the

direction to which it entered into the plenum [Figure 3-2]. The nozzle has an elliptical

profile shape with major and minor axes of 45 mm and 30 mm, respectively. The nozzle

has a span length (L) of 100 mm. The jet thickness for this study was fixed at 1.5 mm.

The jet thickness (d) was adjusted by a feeler gauge and was double checked by using a

Vernier Caliper. The overall aspect ratio (L/d) of the nozzle was 66.67. Detailed

dimensions of the jet facility are presented in Appendix A.

Figure 3-1: Single-slot impinging jet set-up.


32

Figure 3-2: Single-slot impinging jet.

The planar jet impinged normally on a 150 mm×200 mm aluminum plate of 10

mm thickness. The plate was milled using a single fly-cutter in order to provide the

flattest surface possible. The plate was mounted on a Velmex™ 6.35cm wide A25 series

traverse with a resolution of 0.0254 mm, as shown in Figure 3-3a. In order to measure the

wall pressure profiles, the jet was kept stationary and the impingement plate was moved

manually. For adjusting the distance between the nozzle and the plate, the impinging jet

was mounted on a computer controlled traverse system consisting of a VXM-3 Velmex™

power supply with a Slo-syn stepper motor with the minimum division of 5 microns. In

order to adjust the angle of the jet, a Newport 481 A series rotary positioning stage with a


33

resolution of 0.008º was used. This rotary table was equipped with both fine and coarse

adjustments and a locking mechanism [Figure 3-3b].

Figure 3-3: a) Velmex™ traverse, b) Newport 481 A series rotary table.

Figure 3-4: Single-impinging slot set-up parameters.

Figure 3-4 shows the experimental parameters for the single-slot impinging jet.

The axes are defined as x and y, where the x-axis is parallel to the surface of the


34

impingement plate, and the y-direction is parallel to the centerline of the jet. The nozzle

width is defined as d, which was fixed to 1.5 mm in this study, and z represents the

distance from the exit of the nozzle to the plate. The effect of jet velocity was studied by

changing the plenum pressure. The results are presented as functions of non-dimensional

parameters such as Reynolds number (Re) and plate to nozzle ratio (z/d).


In order to facilitate the study of this geometry, planar nozzles and separate

plenums were constructed. All parts were manufactured using aluminum. This model

consists of three jets, one main jet and two auxiliary jets on both sides of the main jet.

The main jet was perpendicular to the impingement plate and the auxiliary jets were

inclined at 20 from the main jet centerline. Each jet has its individual plenum and valve

in order to manipulate the pressure at each plenum separately. Compressed air was used

for pressurizing the plenums. After air passed through the 5 cm regulator valve, 5 cm ball

valve and 5 cm gate valve, air entered into a T-shaped manifold with three 2.5 cm globe

valves in order to control the pressure for each nozzle. Consistent with the single-slot jet,

air entered into each plenum from a 25.4 mm diameter hole at the top of the plenum, and

after passing through the air distributor tube and mesh screens, it exited the nozzle at 90

to its inlet direction. A high grade of surface finished for the nozzles was desired in order

to minimize disturbances in the outgoing air flow. This was obtained with CNC

machining and hand-polishing. The nozzles geometries implemented in this design were


35

an elliptical profile. A CFD analysis was performed to determine the optimal design

parameters to ensure that the exiting jet velocity had the uniform "top-hat" shape velocity

profile [Youanas, 2012]. The k-ε turbulence model in the CFX ANSYS software was

used for this analysis. The main jet, which is the middle jet, had the longest nozzle length

with dimensions of the major and minor ellipse axes of 120 and 54 mm, respectively. The

major axis of the nozzle aligned with the stream-wise direction of the exiting flow. The

nozzles of the auxiliary jets had the dimensions of 37 and 23 mm for the major and minor

elliptical axes, respectively. The flat edge of the nozzle lips was 2 mm wide. The main jet

and auxiliary jet nozzle thickness were designed to be able to vary from 0.8 to 5 mm and

from 0.2 to 50 mm, respectively. The distance of the auxiliary jet exits to the main jet exit

could be varied from 0 to 45 mm. Control of each jet parameter was designed to be

independent from the parameters of the other jets. A schematic of the multiple-slot

impinging jet is shown in Figure 3-5. Detailed dimensions of the multiple-slot impinging

jet apparatus are presented in Appendix A.

Another capability of this design is that the auxiliary jets can be disassembled

from the main jet, and the main jet operates as a single-slot impinging jet. The difference

between this model of the single-slot impinging jet and the previous one is in the nozzle

dimensions. In this thesis, these two different single-slot impinging jets are referred to as

the short nozzle single-slot impinging jet [Figure 3-2] and the long nozzle single-slot

impinging jet [Figure 3-5]. The effect of these two designs on wall pressure profiles will

be presented in Chapter 4.


36

Figure 3-5: Multiple-slot impinging jet schematic.

The experimental operating parameters for the multiple-slot impinging jet are

presented in Figure 3-6. As was the case for the single-slot impinging jet, d is the main

nozzle width and z is the distance from the exit of the main jet to the impingement plate.

The width of the auxiliary jet is designated by a, and the distance of the exit of the

auxiliary jet to the exit of the main jet is s. The distance from the exit of the main jet to

the impingement plate and the distance from the exit of the auxiliary jet to the exit of the

main jet were non-dimensionalized by dividing by the main nozzle width (d). The

measurements were performed for 4≤z/d≤12 in increments of 2. The common plate-to-

nozzle ratio in industry is 8, but it is required to carry out the measurements for lower and

greater value of z/d. In this study the auxiliary slot jet width was held constant at twice of

the main slot jet width, and the auxiliary jet velocity was lower than the main jet velocity.


37

Most of the parameters values in this study were chosen based on the Tamadonfar [2010]

simulation parameters.

Figure 3-6: Schematic of multiple-slot impinging jet parameters.

A specially constructed stagnation pressure probe used by Arthurs et al. [2013]

was used to measure the jet velocity profile at the jet exit for both the single-slot

impinging jet and multiple-slot impinging jet. Figure 3-7 compares the non-dimensional

velocity profiles at the exit of the short nozzle and long nozzle single-slot impinging jets.

As it can be seen, the velocity profiles had a uniform "top-hat" shape. It can be seen that

the boundary thickness of the long-nozzle single-slot jet is greater than that of the short

nozzle single-slot jet. Long nozzle provides more time for the boundary layer of the flow

to grow.


38

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.60.0

0.2

0.4

0.6

0.8

1.0

Dim

ensi

onle

ss fl

ow v

eloc

ity (u

/U)

Dimensionless cross stream position (x/d)

Short Nozzle Long Nozzle

Figure 3-7: Non-dimensional velocity profile at the exit of the short nozzle and long

nozzle single-slot impinging jets at Rem = 11000(PPlenum= 7.91 kPa), d = 1.5 mm.

The disturbance thickness (δ), displacement thickness (δ*) and the momentum

thickness (θ*) at the outlet of the long nozzle single-slot impinging jet for the free stream

jet velocity (U) of 113 m/s were 0.35, 0.155, and 0.036 mm, respectively, where the

definitions of disturbance thickness, displacement thickness and momentum thickness are

as follow:

(3-1)

0 0

( ) ( )1 1u y u ydy dyU U

(3-2)

0 0

( ) ( ) ( ) ( )1 1u y u y u y u ydy dyU U U U

(3-3)

( ) 0.99 y for u y U


39

The dimensionless velocity profile at the exit of the multiple-slot impinging jet

nozzles for a main jet velocity of 113 m/s and auxiliary jet velocity of 55 m/s is shown in

Figure 3-8.

Figure 3-8: Non-dimensional velocity profile at the exit of the multiple-slot impinging jet

nozzles.

3.3 Pressure Transducers

In order to measure the pressures in the plenum and on the impingement plate, a

Validyne DP-15 pressure transducer was used. The pressure within the plenum was

measured at the centerline of the jet upstream of the nozzle contraction. The accuracy of

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 80.0

0.2

0.4

0.6

0.8

1.0

Dim

ensi

onle

ss fl

ow v

eloc

ity (u

/U)

Dimensionless cross-stream position (x/d)


40

pressure transducer was 0.25% of full scale output. Different pressure sensor diaphragms

were used for every Reynolds number in order to improve the measurement accuracy.

The sensors properties for each Reynolds number are listed in Table 3-1. The

impingement plate was instrumented with 0.6 mm diameter holes to measure the static

pressure profiles at the plate. The 1 mm diameter static pressure tube has been connected

to the pressure transducer. The schematic of pressure measurement system is shown in

Figure 3-9.

Figure 3-9: Schematic of pressure measurement facility.

The flow velocity (V) at the exit of the nozzle was calculated by the following formula:

12. 11

sP PV cP

(3-4)

where c is the speed of sound (343 m/s), is the ratio of specific heats of air, Ps is the

static pressure in the plenum and P is the ambient pressure. The static pressure was

measured upstream of the nozzle contraction of the nozzles.


41

Table 3-1: Pressure transducer properties.

Main Jet Reynolds Number

Jet Velocity (m/s)

Plenum Pressure

(kPa)

Pressure Transducer Sensor Properties

Sensor Number

Full scale output (kPa)

9000 90 4.97 30 8.6

11000 113 7.91 30 8.6

13000 130 10.5 32 14

20000 200 26.23 36 35

30000 300 65.44 40 86


42

Chapter 4: Results and Discussion

This chapter begins with discussing the results of two different single-slot

impinging jets. The effect of various parameters will be studied. This includes the effect

of plate-to-nozzle ratio (z/d), main jet Reynolds number (Rem), and jet inclination (∝) on

the wall pressure distribution. The chapter then continues with presenting the

experimental results for the multiple-slot impinging jet, which is composed of one main

slot jet with two adjacent inclined auxiliary slot jets, as a function of plate-to-nozzle

ratios (z/d), main jet Reynolds number (Rem), and auxiliary jet Reynolds number (Rea).

The measured results for both single-slot and multiple-slot impinging jets will then be

used to verify the computational results of Tamadonfar [2010]. Finally, the effects of

process parameters on both single-slot and multiple-slot impinging jets will be

summarized and discussed in the last section.

4.1 Single-Slot Impinging Jet

The single-slot impinging jet, which is the conventional model of air knife used in

galvanizing lines, consists of one main slot jet which discharges air onto the plate. In this

section, the effect of plate-to-nozzle ratio (z/d), main jet Reynolds number (Rem) and jet

inclination angle (∝) on the pressure profile distribution on the plate will be presented.

Figure 4-1 shows a schematic of the short and long nozzle single-slot impinging jets,

where d is the main jet slot width and z is the distance of the main jet exit to the strip. In

this study the main jet width was fixed at 1.5 mm.


43

Figure 4-1: Schematic of the single-slot impinging jet a) short nozzle b) long nozzle.

4.1.1 Effect of Plate-to-Nozzle Ratio (z/d)

The effect of plate-to-nozzle ratio (z/d) on the wall pressure distribution is

examined in this section. The non-dimensional wall pressure distributions for 6 z/d12

in increments of z/d=2 at Rem =11000 (Pplenum=7.91 kPa), which corresponds to a main

jet velocity of 113 m/s, for the short nozzle single-slot impinging jet and the long nozzle

single-slot impinging jet are shown in Figure 4-2 and Figure 4-3, respectively. The

horizontal axis is non-dimensionalized by the nozzle thickness (d) and the vertical axis is

non-dimensionalized by the dynamic pressure (0.5ρU2). It shows that the maximum non-

dimensional wall pressure is at the center line of the jet for all z/d. It can also be seen that

at z/d=6 the plate seems to be in the potential core of the jet because the dynamic

pressure at the jet exit (0.5ρU2) is fully recovered. By going outside the potential core

(i.e. for z/d≥8), the maximum pressure decreases significantly with increasing z/d.


44

Figure 4-2: Non-dimensional wall pressure distribution at Rem=11000 for all z/d for the

short nozzle single-slot impinging jet.

The non-dimensional wall pressure profiles for both the short nozzle and long

nozzle single-slot impinging jet for 6z/d12 at Rem=11000 are presented in Figure 4-4.

It can be seen that there were insignificant differences between the short nozzle and the

long nozzle wall pressure distribution at z/d=6. However, the maximum non-dimensional

pressure for the short nozzle design is higher than the long nozzle design for z/d higher

than 6. The wall pressure distribution at z/d=6 did not change much because the plate was

within the potential core of the jet, however for higher z/d the plate was outside of the

potential core. The reason that the long nozzle had a lower non-dimensional maximum

pressure than the short nozzle design is that the long nozzle design has thicker boundary

layers, as shown in Figure 3-7.

-4 -2 0 2 40.0

0.2

0.4

0.6

0.8

1.0

P/0.

5U

2

x/d

z/d=6 z/d=8 z/d=10 z/d=12


45

-4 -2 0 2 40.0

0.2

0.4

0.6

0.8

1.0

P/0

.5U

2

x/d

z/d=6 z/d=8 z/d=10 z/d=12

Figure 4-3: Non-dimensional wall pressure distribution at Rem=11000 for all z/d for the

long nozzle single-slot impinging jet.

4.1.2 Effect of Main Jet Reynolds Number (Rem)

In this section, the effect of the main jet Reynolds number on the wall pressure

distribution will be reviewed. The main jet Reynolds number at the exit of the jet was

changed by varying the plenum pressure. The exit velocity was calculated by measuring

the static pressure in the plenum using the following formula [White, 2003]:

1

2. 11

sP PU cP

(4-1)


46

where c is the speed of sound, P the ambient pressure and the specific heat ratio of air

[Table 3-1]. The pressure profiles for Rem of 11000, 20000, and 30000 for different plate-

to-nozzle ratios were investigated.

-4 -2 0 2 40.0

0.2

0.4

0.6

0.8

1.0

z/d = 6 Long Nozzle Jet z/d = 6 Short Nozzle Jet

P/0.

5U

2

x/d-4 -2 0 2 4

0.0

0.2

0.4

0.6

0.8

1.0

z/d = 8 Long nozzle Jet z/d = 8 Short Nozzle Jet

P/0.

5U

2

x/d

-4 -2 0 2 40.0

0.2

0.4

0.6

0.8

1.0

P/0

.5U

2

z/d = 10 Long Nozzle Jetz/d = 10 Short Nozzle Jet

x/d-4 -2 0 2 4

0.0

0.2

0.4

0.6

0.8

1.0z/d = 12 Long Nozzle Jetz/d = 12 Short Nozzle Jet

P/0

.5U

2

x/d Figure 4-4: Non-dimensional wall pressure profile for the short nozzle and long nozzle

single-slot impinging jets for different z/d at Rem=11000.


47

Figure 4-5 and Figure 4-6 show the non-dimensional wall pressure distribution for

Rem=20000 and Rem=30000 as a function of plate-to-nozzle ratio (z/d). The pressure is

non-dimensionalized by the jet dynamic pressure. Due to the fact that at this Reynolds

number the flow is in the compressible regions, the compressible value of the gas density

at the exit of the nozzle has used in calculations of the dynamic pressure. These figures

show that the maximum non-dimensional pressure occurred at the center line of the jet

for all z/d. It can be seen that the impingement plate was in the jet potential core at z/d=6.

As z/d increased, the maximum non-dimensional pressure decreased, indicating that the

impingement plate was no longer in the potential core. It can be seen that for Rem=30000,

the maximum pressure dropped significantly from z/d=6 to 8. Comparison of the non-

dimensional wall pressure profiles for different Reynolds numbers [Figure 4-2, Figure 4-

5, and Figure 4-6] shows the plate was within the potential core for z/d=6 for all

Reynolds numbers. Thus, it can be concluded that the length of the potential core was

independent of the Reynolds number for the Rem range explored in this study.


48

-4 -2 0 2 40.0

0.2

0.4

0.6

0.8

1.0

P/(0

.5U

2 ) noz

zle

x/d

z/d=12 z/d=10 z/d=8 z/d=6

Figure 4-5: Non-dimensional wall pressure distribution at Rem=20000 for the short

nozzle single-slot impinging jet.

-4 -2 0 2 40.0

0.2

0.4

0.6

0.8

1.0

P/(0

.5U

2 )N

ozzl

e

x/d

z/d=6 z/d=8 z/d=10 z/d=12

Figure 4-6: Non-dimensional wall pressure distribution at Rem =30000 for the short



49

Figure 4-7 compares the wall pressure distribution at different z/d as a function of

the main jet Reynolds number. It shows that the maximum wall pressure increased

significantly by increasing the main jet Reynolds number for all plate-to-nozzle ratios

(z/d).

The effect of main jet Reynolds number on the maximum wall pressure gradient

for different plate-to-nozzle ratios (z/d) is summarized in Figure 4-8. It shows that by

increasing the plenum pressure, which increases the main jet Reynolds number, the

maximum wall pressure gradient increases significantly for all z/d and decreases with

increasing z/d for all Reynolds numbers.

-4 -2 0 2 40

10000

20000

30000

40000

50000

60000z/d=6

Rem=11000 Rem=20000 Rem=30000

Pre

ssur

e (P

a)

x/d-4 -2 0 2 4

0

10000

20000

30000

40000

50000

60000z/d=8

Pres

sure

(Pa)

x/d

Rem=11000 Rem=20000 Rem=30000

-4 -2 0 2 40

10000

20000

30000

40000

50000

60000z/d=10

Pres

sure

(Pa)

x/d

Rem=11000 Rem=20000 Rem=30000

-4 -2 0 2 40

10000

20000

30000

40000

50000

60000 z/d=12

pres

sure

(Pa)

x/d

Rem=11000 Rem=20000 Rem=30000

Figure 4-7: Wall pressure profile distribution for different Rem and z/d for the single-slot

impinging jet with short nozzle.


50

6 7 8 9 10 11 120

5000

10000

15000

20000

25000

30000

|(dP/

dx) m

ax| (

Pa/m

m)

z/d

Rem=30000 Rem=20000 Rem=11000

Figure 4-8: Maximum wall pressure gradient as a function of Rem and z/d for the short


Figure 4-9: Schematic of oblique single-impinging slot jet.


51

4.1.3 Effect of Jet Inclination Angle (α)

The effect of jet inclination on the wall pressure profile was investigated for

different plate-to-nozzle ratios and Reynolds numbers. The measurements were

performed for 6z/d12 in increments of z/d=2 at a downward jet inclination angle of 3°

(α=3º). The main jet Reynolds number was changed between 11000 and 30000. Figure

4-9 shows the configuration of a single-slot impinging jet with an incident angle of α.

The non-dimensional pressure profile for the 3° tilted jet as a function of z/d for

Rem=11000 is shown in Figure 4-10. The non-dimensional maximum pressure decreased

with increasing z/d ratio. By inclining the jet, the maximum pressure did not change and

the location of the non-dimensional stagnation pressure moved further away from the

centerline of the main jet with increasing z/d ratio. The same trend was observed for

Reynolds numbers of 20000 and 30000.

Figure 4-11 compares the maximum pressure for the 3° inclined short nozzle

single-slot impinging jet with the non-inclined single-slot impinging jet as a function of

z/d for Rem=11000, 20000, and 30000, which correspond to the velocities of 113 m/s,

200, and 300 m/s, respectively. It can be observed that the maximum pressure for all

plate-to-nozzle ratios (z/d) did not change significantly at Rem=11000 and Rem=20000.

The difference between the α=0° and α=3° is slightly greater for Rem=30000. However,

this difference is less than 6%.


52

-8 -6 -4 -2 0 20.0

0.2

0.4

0.6

0.8

1.0

P/0.

5U

2

x/d

z/d=6 z/d=8 z/d=10 z/d=12

Figure 4-10: Non-dimensional wall pressure distribution for different z/d at Rem=11000

for short nozzle single-slot impinging jet.

Figure 4-11: Comparison of the maximum wall pressure as a function of z/d at α=0° and

α=3° for short nozzle single-slot impinging jet.


53

Figure 4-12 shows the wall pressure gradient distribution for different Reynolds

numbers at z/d=10. The location of the maximum pressure gradient moved to a higher x/d

ratio by increasing Reynolds number. The value of the maximum pressure gradient

increased with increasing Reynolds number.

-8 -6 -4 -2 0 2 4-15000

-10000

-5000

0

5000

10000

15000

dp/d

x (P

a/m

m)

x/d

Rem=11000 Rem=20000 Rem=30000

Figure 4-12: Wall pressure gradient distribution as a function of Rem at z/d=10 for 3°

tilted short nozzle single-slot impinging jet.

Derivatives of the wall pressure gradient were calculated and the maximum

values of the pressure gradient plotted as functions of z/d and Reynolds number in Figure

4-13. As illustrated in this figure, by increasing the plate-to-nozzle ratio, the maximum

pressure gradient decreased for all the Reynolds numbers, while the maximum pressure

gradient increased by increasing the Reynolds number for a fixed z/d.


54

6 7 8 9 10 11 120

5000

10000

15000

20000

25000

30000

35000

40000

|(dP/

dx) m

ax| (

Pa/

mm

)

z/d

Rem=11000 Rem=20000 Rem=30000

Figure 4-13: Maximum wall pressure gradient as a function of Rem and z/d for 3° tilted

short nozzle single-slot impinging jet.

Figure 4-14 compares the maximum pressure gradient of the tilted and non-tilted

single-slot impinging jet as a function of Rem for 6z/d12. It can be seen that for

Rem=11000 there was no significant difference in the maximum pressure gradient

between the tilted and non-tilted impinging jet. In addition, the maximum pressure

gradient of the tilted single-slot impinging jet is higher than the non-tilted single-slot

impinging jet for all measurement parameters except for z/d=10 at Rem=30000 which is

due to the lower maximum pressure of tilted impinging jet compare to the non-tilted

impinging jet [Figure 4-11]


55

10000 15000 20000 25000 300000

5000

10000

15000

20000

25000

30000

35000

40000 z/d=6|(d

P/d

x)m

ax| (

Pa/

mm

)

Rem

Non-tilted

10000 15000 20000 25000 30000

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000 z/d=8 Non-tilted

|(dP

/dx)

max

| (P

a/m

m)

Rem

10000 15000 20000 25000 30000

2000

4000

6000

8000

10000

12000

14000

16000z/d=10

Non-tilted

|(dP

/dx)

max

| (P

a/m

m)

Rem

10000 15000 20000 25000 30000

2000

4000

6000

8000

10000

12000 z/d=12 Non-tilted

|(dP

/dx)

max

| (P

a/m

m)

Rem

Figure 4-14: Comparison of maximum pressure gradient as a function of Reynolds

number between α=0° and α=3° tilted for the short nozzle single-slot impinging jet.


56


In this section, a proposed design for the multiple-slot impinging jet by

Tamadonfar [2010] which consists of one main jet with two inclined jets at both sides of

the main jet was studied experimentally. The main slot jet discharges air perpendicular to

the plate while the auxiliary jets discharge air at a lower velocity than the main jet at a

20 angle from the main slot jet centerline [Figure 4-15]. The effect of the plate-to-nozzle

ratio (z/d), which was changed between 4 and 12, the main jet Reynolds numbers

changing between 9000 and 13000, and the auxiliary slot jets Reynolds number, changing

between 11000 and 15000, on the pressure distribution will be discussed. The main jet

width (d), auxiliary jet width (a) and the distance between the exit of the main and

auxiliary jet (s) were fixed at d=1.5 mm, a=3 mm (double the main jet width) and s=19.7

mm, respectively. The wall pressure distribution for different plate-to-nozzle ratio (z/d),

main jet Reynolds number (Rem), and auxiliary jet Reynolds number (Rea) will be

presented.

It should be noted that, although the auxiliary jet Reynolds number was in the

same range as the main jet Reynolds number, the velocity of the auxiliary jet was lower

than the velocity of the main jet because the width of the auxiliary jet was twice that of

the main jet. The velocity of main jet was changed from 90 m/s to 130 m/s, and the

velocity of auxiliary jet was changed from 55 to 75 m/s.


57

Figure 4-15: Geometry of the multiple-slot impinging jet.


The effect of the plate to nozzle ratio on the normalized pressure distribution is

reviewed for the multiple-slot impinging jet in this section. First, the experimental results

for different plate-to-nozzle ratios (z/d) at fixed main jet and auxiliary jet Reynolds

numbers are presented. It should be noted that, because of air supply limitations and

symmetric resulted profile of the multiple-slot impinging jet [Figure 3-8], the

measurements were performed for one half of the jet only. However, both auxiliary jets

were always used.

Figure 4-16 shows the wall pressure distribution for different values of z/d at the

main jet Reynolds number of Rem=9000 and auxiliary jets Reynolds number of

Rea=11000. It can be seen that adding auxiliary jets to the main jet changed the wall

pressure profile distribution compared to the single-slot impinging jet wall pressure


58

profile. The shoulder which is seen in the pressure profile for z/d≤6 disappears for z/d=8

and higher. In addition, it shows that the stagnation pressure dropped as z/d increased.

Figure 4-17 and Figure 4-18 show the effect of z/d for the higher Rem of 11000 and 13000

for the same Rea=11000. The same trends seen in Figure 4-16 are exemplified in these

two figures. It can be seen that, while the impingement plate was in the potential core at

z/d=6 for the single-slot impinging jet, the plate was not in the main jet potential core at

z/d=6 for the multiple-slot impinging jets. At the interaction zone of the auxiliary jet and

the main jet, the auxiliary jet flow accelerated and the main jet flow decelerated because

the auxiliary jet velocity was lower than the main jet velocity. Consequently, the main jet

potential core became a little bit smaller. It can be seen that the impingement plate was at

the main jet potential core at z/d=4 for all cases studied [Figure 4-16, Figure 4-17, and

Figure 4-18]. In addition, it can be seen that at low z/d there was a secondary peak

pressure which is resulted from the presence of the auxiliary jet, while at higher z/d the

secondary pressure peak disappeared. At z/d=4 and 6, the flow field of the auxiliary jets

and the main jet have not merged, while at z/d>6the auxiliary and main jets flow fields

have been mixed.


59

0 2 4 6 8 10 12 140.0

0.2

0.4

0.6

0.8

1.0

P/(0

.5U

m2 )

Noz

zle

x/d

z/d=4 z/d=6 z/d=8 z/d=10 z/d=12

Figure 4-16: Non-dimensional wall pressure distribution as a function of z/d at Rem=9000

and Rea=11000.

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

P/(0

.5U

m2 ) N

ozzl

e

x/d

z/d=4 z/d=6 z/d=8 z/d=10 z/d=12

Figure 4-17: Non-dimensional wall pressure distribution as a function of z/d at

Rem=11000 and Rea=11000.


60

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

P/(0

.5U

m2 ) N

ozzl

e

x/d

z/d=4 z/d=6 z/d=8 z/d=10 z/d=12

Figure 4-18: Non-dimensional wall pressure distribution as a function ofz/d at

Rem=13000 and Rea=11000

4.2.2 Effect of Main Jet Reynolds Number (Rem)

The effect of main jet Reynolds number (Rem) on the wall pressure distribution is

presented in this section. Rem was varied between 9000 and 13000 while Rea was fixed at

11000. For all these cases, the main jet velocity was higher than the auxiliary jet velocity.

That is, the main jet velocity changed from 90 to 130 m/s, whereas the auxiliary jet

velocity was 55 m/s.

Figure 4-19 demonstrates the experimental wall pressure distribution at z/d=6. It

can be seen that increasing the main jet velocity did not have a significant effect on the

wall jet region (x/d>2), while the stagnation pressure increased with increasing Rem. The

same trend was seen for all z/d.


61

0 2 4 6 8 10 12 14

0

2000

4000

6000

8000

10000

12000

Pre

ssur

e (P

a)

x/d

Rem=9000 Rem=11000 Rem=13000

Figure 4-19: Experimental wall pressure distribution as a function of Rem at Rea=11000

and z/d=6.

4.2.3 Effect of Auxiliary Jet Reynolds Number (Rea)

The effect of Rea on the wall pressure distribution was investigated while keeping

Rem constant. Figure 4-20 shows the wall pressure distribution for two different Rea of

11000 and 13000 with fixed Rem=11000 for z/d=8. According to this figure, by

increasing the auxiliary jet Reynolds number, the shoulder of the pressure distribution

became more pronounced while the main jet stagnation pressure dropped.


62

0 2 4 6 8 10 12

0.0

0.2

0.4

0.6

0.8

P/(0

.5U

m2 ) N

ozzl

e

x/d

Rea=13000 Rea=11000

Figure 4-20: Experimental non-dimensional wall pressure distribution as a function of

Rea with Rem=11000 at z/d=8.

Figure 4-21 presents the non-dimensional wall pressure distributions for different

Rea with Rem=11000 and z/d=4. The pressure was non-dimensionalized by the dynamic

pressure of the main nozzle. It can be seen that the main jet stagnation pressure was

independent of Rea, since the plate was within the potential core of the jet while the

shoulder of the wall pressure distribution (2<x/d<10) increased with increasing Rea.

Figure 4-22 shows the maximum pressure gradient for 11000Rea15000 with

Rem=11000 and z/d=4. Although the maximum pressure was independent of Rea at z/d=4

[Figure 4-21], it can be seen that the maximum pressure gradient was sensitive to Rea and

decreased with increasing Rea. The same trend has been seen for higher z/d.


63

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

P/(0

.5U

m2 ) N

ozzl

e

x/d

Rea=14000 Rea=12000 Rea=10000

Figure 4-21: Experimental non-dimensional wall pressure distribution for different Rea

with Rem=11000 and z/d=4.

11000 12000 13000 14000 150003000

3100

3200

3300

3400

3500

3600

3700

|(dP/

dx) m

ax| (

Pa/

mm

)

Rea Figure 4-22: Experimental maximum pressure gradient as a function of auxiliary jet

Reynolds number (Rea) with Rem=11000 and z/d=4.


64

4.3 Comparison between Multiple-Slot and Single-Slot Impinging Jet

In this section, the effect of adding the two inclined auxiliary jets to the main jet

on the pressure profiles will be examined. Figure 4-23 compares the non-dimensional

pressure profile distribution of the multiple-slot impinging jet and the single-slot

impinging jet with Rem=11000 and Rea=11000 at z/d=10. As observed in this figure, the

non-dimensional maximum wall pressure for the main jet of the multiple-slot impinging

jet configuration was higher than that of the single-slot impinging jet. As a result of the

presence of the auxiliary jets, more momentum has been added to the flow field, and that

caused the maximum pressure of multiple-slot impinging jet to be higher than that of the

single-slot jet.

Figure 4-24 shows the main jet maximum wall pressure as a function of plate-to-

nozzle ratio for both multiple and single-slot impinging jets. It can be seen that at low z/d,

there was no significant difference in the main jet maximum wall pressure between the

single-slot and multiple-slot impinging jets. However, the maximum pressure of the

multiple-slot impinging jet became higher than that of the maximum pressure for the

single-slot impinging jet by increasing z/d.


65

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

P/(0

.5U

2 )

x/d

Single-impinging slot jet Multiple-impinging slot jet

Figure 4-23: Comparison of non-dimensional pressure distribution between the single-

slot and multiple slot impinging jets for Rem=11000, Rea=11000 and z/d=10.

6 7 8 9 10 11 12

5000

5500

6000

6500

7000

7500

8000

Pm

ax (P

a)

z/d


Figure 4-24: Comparison of maximum pressure of short nozzle single-slot and multiple-

slot impinging jets for various values of z/d, Rem=11000 and Rea=11000.


66

Although the maximum non-dimensional pressure of multiple-slot impinging jet

is higher than the single-slot impinging jet [Figure 4-24], the maximum pressure gradient

for the multiple-slot impinging jet was lower than that of the single-slot impinging jet, as

can be seen from Figure 4-25. These results matched well with the results of Kim et al.

[2010] who proposed the multiple-slot impinging jet. The auxiliary nozzles gas particles,

which have the lower speed compared to the main nozzle, collide with the main jet gas

particles and it results in the overall gas speed decrease along the length of the steel

substrate.

Based on the coating weight model of Elsaadawy [2007], the final coating weight

is a function of maximum pressure gradient and maximum shear stress. Figure 4-26

shows that at low z/d for the single-slot impinging jet and all z/d for the multiple-slot

impinging jet, the maximum shear stress does not change significantly. Thus, it is

expected that at these regions, the maximum pressure gradient has more dominant effect

on the final coating weight. However, maximum shear stress changes become more

significant for higher z/d. Since, increasing the Reynolds number results in higher values

of the maximum wall pressure gradient [Figure 4-7], this is likely to lead to thinner

coatings. However, there is still limitation due to the full splashing [Dubois, 2005] or

high noise levels generation at high Reynolds numbers which are close to the sonic

velocity. For higher z/d, the value of shear stress should be obtained in order to fully

determine the trends of coating weight changes with z/d or Rem.


67

6 7 8 9 10 11 12

1500

2000

2500

3000

3500

4000

4500

|(dP

/dx)

max

| (P

a/m

m)

z/d


Figure 4-25: Comparison of maximum pressure gradient of single and multiple-slot

impinging jets for various values of z/d, Rem=11000 and Rea=11000.

Figure 4-26: Non-dimensional shear stress for single-slot and multiple-slot impinging jet

at Rem=11000 and Rea=11000 [Tamadonfar, 2010].


68

The area under the half of pressure profiles for the single-slot and multiple-slot

impinging jets, which represents the reaction force per unit width of plate, for 6z/d12

was numerically calculated by integrating the pressure distribution curve using Trapezoid

rule [Equation (4-2)] for each z/d. The results are shown in Figure 4-27. It can be seen

that the force per unit width of plate for the single-impinging jet remained nearly constant

(the maximum difference is 3 percent) in order to balance the jet’s momentum flux.

Moreover, the value of F/dx for the multiple-slot impinging jet was greater than that of

the single-slot impinging jet, so the force that the multiple-slot impinging jets exerted on

the plate was greater than that of the single-slot impinging jet. Therefore, the use of the

multiple-slot impinging jet may stabilize the steel strip and reduce its vibration.

1 11

1( )2

b Nk k k k

kaf x dx x x f x f x

(4-2)

6 7 8 9 10 11 1226

28

30

32

34 Multiple-slot impinging jet Single-slot impinging jet

Forc

e / W

idth

(N/m

)

z/d Figure 4-27: Comparison of force per unit width of single-slot and multiple-slot

impinging jet as a function of z/d at Rem=11000 and Rea=11000.


69

4.4 Computational Results Validation

The computational results of Tamadonfar [2010] for the single-slot and multiple-

slot impinging jets configurations were compared with the present experimental results in

this section.

4.4.1 Single-slot Impinging Jet

Experimental versus simulated pressure profiles for 6z/d12 at Rem=11000 are

presented in this section. Figure 4-28 presents a comparison of the numerical non-

dimensional wall pressure profile versus the experimental data for the short nozzle single-

slot impinging jet as function of z/d. It can be seen that the value of the predicted

maximum non-dimensional pressure for z/d=6 is not significantly different from the

measured one. However, the simulated maximum non-dimensional pressure is slightly

higher than the experimental maximum non-dimensional pressure for z/d≥8. Also, it can

be seen that the experimental pressure distributions were slightly broader than the

simulated pressure profile distributions.

Figure 4-29 shows the simulated maximum pressure gradient versus the

experimental maximum pressure gradient for the short nozzle design for z/d=6 at

Rem=11000. It can be seen that the maximum pressure gradient is shifted to higher x/d

compared to the simulation results. This is due to the fact that the experimental pressure

distribution is broader than the simulated pressure distribution. Figure 4-30 compares the

simulated and calculated maximum pressure gradient as a function of plate-to-nozzle


70

ratio (z/d). It can be seen that for all plate-to-nozzle ratios, the simulated maximum

pressure gradient is higher than the experimental. These differences might be resulting

from the difference between the simulation jet exit velocity profile and the experimental

jet exit velocity profiles. Figure 4-31 shows that the simulated velocity profile has a

parabolic shape which arises from the long parallel nozzle geometry of the simulation.

The disturbance thickness (δ), displacement thickness (δ*) and the momentum thickness

(θ*) of computational result of Tamadonfar [2010] and the current measurements are

presented in Table 4-1.

Table 4-1: Shear layer thickness (δ, δ*, θ*) of computational [Tamadonfar, 2010] and experimental results at the exit of the nozzle.

Computational Experimental

disturbance thickness (δ) (mm) 0.62 0.35

displacement thickness (δ*) (mm) 0.15 0.155

momentumthickness (θ*) (mm) 0.095 0.036


71

Figure 4-28: Experimental versus simulated [Tamadonfar, 2010] non-dimensional

pressure profile for different z/d at Rem=11000 (short nozzle single-slot impinging jet).


72

-6 -4 -2 0 2 4 6-6000

-4000

-2000

0

2000

4000

6000

dP/d

x (P

a/m

m)

x (mm)

z/d = 6 Simulation z/d = 6 Experiment

Figure 4-29: Comparison of simulated [Tamadonfar, 2010] and experimental pressure

profile derivatives dpdx

at Rem=11000 for the short nozzle single-slot impinging jet.

6 7 8 9 10 11 121500

2000

2500

3000

3500

4000

4500

5000

|(dP/

dx) m

ax| (

Pa/m

m)

z/d

Experiment Simulation

Figure 4-30: Experimental and simulated [Tamadonfar, 2010] maximum pressure

gradient as a function of z/d for Rem=11000 for the short nozzle single-slot impinging jet.


73

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.60.0

0.2

0.4

0.6

0.8

1.0D

imen

sion

less

flow

vel

ocity

(u/U

)

Dimensionless cross stream position (x/d)

Simulation Short Nozzle Long Nozzle

Figure 4-31: Comparison between the experimental and simulated jet exit velocity profile

[Tamadonfar, 2010].

4.4.2 Multiple-Slot Impinging Jet

Figure 4-32 compares the experimental non-dimensional wall pressure

distribution with the numerical results of Tamadonfar [2010] as a function of z/d ratio.

The second peak pressure seen in the experimental pressure profiles at z/d6 was not

observed in the simulation results. The simulated non-dimensional pressure profiles at

x/d>4, the area affected by the presence of the auxiliary jet, were in good agreement with

the experimental results for z/d≥8. However, the simulated stagnation pressure is higher

than the experimental one. As observed in Figure 4-32, the simulated maximum non-

dimensional pressure at z/d=6 was more than one, which means that the stagnation


74

pressure was higher than the pressure inside the plenum, which does not seem reasonable.

Therefore, it can be concluded that the simulation has overestimated the maximum

pressure.

The comparison between the simulated and experimental maximum pressure

gradient as a function of z/d for a Rem=11000 and Rea=11000 is shown in Figure 4-33. It

shows that the simulated maximum pressure gradient was higher than the experimental

result, which was also seen in the single-slot impinging jet results.

Figure 4-32: Simulated [Tamadonfar, 2010] and experimental non-dimensional pressure

profile distribution comparison for different z/d at Rem=11000 and Rea=11000 for multiple-slot impinging jet.


75

6 7 8 9 10 11 12

1500

2000

2500

3000

3500

4000

|(dP/

dx) m

ax| (

Pa/

mm

)

z/d

Simulation Experiment

Figure 4-33: Comparison of simulation [Tamadonfar, 2010] and experimental maximum

pressure gradient as a function of z/d at Rem=11000 and Rea=11000 for multiple-slot impinging jet.

The comparison of wall pressure distributions between the simulation data of

Tamadonfar [2010] and the experimental results at Rem=11000, Rea=11000 and z/d=4 is

presented in Figure 4-34. The experimental stagnation pressure is significantly lower than

the simulated stagnation pressure. Since the plate was at the potential core of the main jet

z/d=4, the same pressure as the plenum pressure was expected for the stagnation

pressure. As mentioned earlier the simulation likely over-predicted the stagnation

pressure. In addition, it can be seen that no secondary peak pressure, observed at low z/d

in the experimental results, was detected for the simulation results for all z/d ratios.


76

Figure 4-35 compares the experimental and simulated maximum pressure gradient

as a function of Rem at fixed Rea and z/d. The simulated maximum pressure gradient was

significantly higher than the experimental results.

0 2 4 6 8 10 120

2000

4000

6000

8000

10000

Pre

ssur

e (P

a)

x/d


Figure 4-34: Comparison of the experimental and numerical [Tamadonfar, 2010] wall

pressure distribution for Rem=11000, Rea=11000 at z/d=4 for multiple-slot impinging jet.

The numerical maximum pressure gradient as a function of auxiliary jet Reynolds

number at Rem=11000 and z/d=4 is presented in Figure 4-36. According to this figure,

the maximum pressure gradient decreased with increasing Rea to approximately 12000

and then it increased. By comparing Figure 4-22 and Figure 4-36, it can be seen that there

is a significant difference between the values of the numerical and experimentalmax

dpdx

.

Also, the experimental max

dpdx

did not increase at Rea=14000, but continued to decrease

with increasing auxiliary jet Reynolds number.


77

9000 10000 11000 12000 130002000

2500

3000

3500

4000

4500

5000

5500

6000

6500

|(dP

/dx)

max

| (P

a/m

m)

Rem


Figure 4-35: Maximum wall pressure gradient for different main jet Reynolds number at

z/d=4 and Rea=11000 [Tamadonfar, 2010] for multiple-slot impinging jet.

4000 6000 8000 10000 12000 140003600

3800

4000

4200

4400

4600

|(dP

/dx)

max

| (P

a/m

m)

Rea Figure 4-36: Numerical maximum wall pressure gradient as a function of Rea with

Rem=11000 and z/d=4.


78

4.5 Discussion

In this section, the results of the experiments are summarized and discussed. An

experimental study has been carried out to understand the effect of various gas jet wiping

process parameters such as Reynolds number (Rem, Rea), plate-to-nozzle ratio (z/d) and

jet inclination angle (α) on the wall pressure distribution for two different air knife

configurations, which are the conventional air knife (single-slot impinging jet) and

multiple-slot impinging jet, respectively.


The effect of plate-to-nozzle ratio (z/d) on the wall pressure distribution and

maximum pressure gradient for single-slot and multiple-slot impinging jets was

investigated and compared with the numerical results of Tamadonfar [2010]. The results

showed that by increasing the plate-to-nozzle ratio (z/d), the maximum wall pressure

gradient [Figure 4-8 and Figure 4-37] and maximum wall pressure [Figure 4-38 and

Figure 4-39] decreased for both the single-slot and multiple-slot impinging jet designs.


79

9000 10000 11000 12000 13000

1000

2000

3000

4000

5000

6000

7000

8000

9000

|(dP

/dx)

max

| (P

a/m

m)

Rem

z/d=4 z/d=6 z/d=8 z/d=10 z/d=12

Figure 4-37: Maximum wall pressure gradient for the multiple-slot impinging jet as a

function of Rem for 4z/d12 at Rea=11000.

6 7 8 9 10 11 12

10000

20000

30000

40000

50000

60000 Rem = 11000 Rem = 20000 Rem = 30000

P max

(Pa)

z/d

Figure 4-38: Maximum wall pressure for the short nozzle single-slot impinging jet as a function of z/d for different Rem at Rea=11000.


80

4 6 8 10 125000

5500

6000

6500

7000

7500

8000

P max

(Pa)

z/d

Figure 4-39: Maximum wall pressure for the multiple-slot impinging jet as a function of z/d at Rem=11000 and Rea=11000.

At z/d=6, the plate was within the potential core of the single-slot impinging jet

for all Rem as the non-dimensional wall pressure was equal to one [Figure 4-3, Figure 4-5,

and Figure 4-6]. However, Figure 4-16, Figure 4-17, and Figure 4-18 showed that the

maximum wall pressure for the multiple-slot impinging jet was somewhat smaller than

the plenum pressure at z/d=6, which indicates that at this z/d ratio the impingement plate

was slightly out of the potential core of the main jet. Although, the maximum pressure of

the multiple-slot impinging jet at z/d>6 was higher than the maximum pressure of the

single-slot impinging jet [Figure 4-24], the maximum pressure gradient for the multiple-

slot impinging jet was smaller than the maximum pressure gradient of the single-slot

impinging jet for z/d>6 [Figure 4-25]. By assuming that the maximum pressure gradient

is the only process parameter in determining the final coating weight, it can be concluded


81

that the single slot impinging jet would produce a lighter coating weight. However, it

should be noted that based on the Elsaadawy [2007] coating weight model, [Equation (2-

6)], the shear stress also has effect on the final coating weight. Therefore, in order to state

the definitive effect of the multiple-slot impinging jet and single-slot impinging jet on the

coating weight, the shear stress at the wall must be measured. The simulated wall

pressure profiles of Tamadonfar [2010] are similar in shape with the experimental results

of this study and most authors such as Tu & wood [1996], Elsaadawy et al. [2007], and

Cho et al. [2009]. However, for both the single-slot and multiple-slot impinging jets the

experimental values of the maximum wall pressure and maximum wall pressure gradient

were lower than the simulation results for z/d>6. The computational results shown in

Figure 4-28 indicate that the plate is still in the potential core of the jet at z/d=8. The

instabilities in the shear layer of the main jet grow exponentially as they convect

downstream. The generated flow vortical structures impinge on the plate, and generate

pressure fluctuations at the impinging zone which travel back upstream to exit lips of the

nozzle and enhance the instabilities in the initial shear layer [Arthurs, 2012]. This

mechanism increases the velocity fluctuations of the jet column and jet spread rate. The

simulation [Tamadonfar, 2010] does not account for the shear layer instability and the

pressure perturbation in the impingement zone accurately. As a result, the value of the

potential core length of the main jet is greater than it was shown in the experimental

results.


82

4.5.2 Reynolds Number Effect (Re)

The effect of the main jet Reynolds number (Rem) on the maximum pressure and

maximum pressure gradient were examined experimentally for two models of air knife as

well as the effect of the auxiliary jet Reynolds number (Rea) for the multiple-slot jet. The

experimental results were compared to the simulation results of Tamadonfar [2010]. It

was shown that increasing the Rem at a constant z/d caused the maximum wall pressure

(Pmax) [Figure 4-40 and Figure 4-41] and maximum wall pressure gradient max

dpdx

[Figure 4-8 and Figure 4-37] to increase for both the single-slot and multiple-slot jet

designs.

10000 15000 20000 25000 300000

10000

20000

30000

40000

50000

60000

P max

(Pa)

Rem

z/d=6 z/d=8 z/d=10 z/d=12

Figure 4-40: Maximum wall pressure of short nozzle single-slot impinging jet as a

function of Rem for 6z/d12.


83

9000 10000 11000 12000 13000

3000

4000

5000

6000

7000

8000

9000

10000

11000

P max

(Pa)

Rem

z/d=4 z/d=6 z/d=8 z/d=10 z/d=12

Figure 4-41: Maximum wall pressure of multiple-slot impinging jet as a function of Rem

for 4 z/d 12 and Rea=11000.

It was also determined from Figure 4-20 and Figure 4-22 that the maximum wall

pressure (Pmax) and maximum wall pressure gradient max

dpdx

decreased by increasing

the auxiliary jet Reynolds number (Rea) when the Rem and z/d were kept constant for

z/d>6. While the plate is at the potential core of the jet (z/d<6), the maximum pressure

was not affected by Rea changes, whereas, the maximum pressure gradient decreases

since the main peak of the pressure profiles became wider [Figure 4-21 and Figure 4-22].

However, the numerical investigation of Tamadonfar [2010] on predicting the effect of

Rea on the wall pressure profile showed that increasing the Rea would cause the

maximum wall pressure to increase. Based on the numerical results it was expected

adding the auxiliary jets makes the main jet flow more confined and adds more


84

momentum into the flow and as a result increase the maximum wall pressure. Although,

the experimental results showed that adding auxiliary jet increased the flow momentum

and enhanced the maximum pressure compare to the single impinging jet, increasing the

auxiliary jet velocity at z/d>6 resulted in that auxiliary flow field cut into the main jet

flow field column and caused a drop in the maximum wall pressure.

4.5.3 Jet Inclination Effect (α)

The effect of impinging jet inclination on the gas wiping process was investigated

for the single-slot impinging jet design. The study was done for a jet inclination angle of

3° and the results were compared with the non-inclined jet. The results showed that the

maximum wall pressure gradient increased as the Rem increased and the z/d decreased, as

shown in Figure 4-13. It was also seen that the maximum pressure gradient was

independent of jet inclination for low main jet Reynolds numbers [Rem=11000]. For the

higher main jet Reynolds number of Rem=20000 and Rem=30000, the inclined jet

maximum pressure gradient was somewhat higher than that of non-inclined jet [Figure 4-

14]. However, the maximum wall pressure was not affected by an inclination angle of

3°for all tested z/d [Figure 4-11]. The simulation results of Elsaadawy et al. [2004] also

showed that the maximum wall pressure does not change significantly by changing the jet

inclination between 0° and 30° at Re=11000.


85

Chapter 5: Conclusions and Future Work

5.1 Conclusions

This thesis experimentally investigated the behaviour of two air knife geometries:

a single-slot impinging jet (conventional air knife) and a multiple-slot impinging jet

composed of one main jet and two inclined auxiliary jets discharging air at a lower

velocity in comparison with the main jet, for different continuous hot-dip galvanizing

process parameters such as main jet Reynolds number (Rem), auxiliary jet Reynolds

number (Rea), plate-to-nozzle ratio (z/d), and jet inclination angle (α). The experimental

results were then used to examine the computational study of Tamadonfar [2010].

For the single-slot impinging jet, the maximum wall pressure and the maximum

wall pressure gradient decreased with increasing z/d at constant Rem. Whereas the

maximum wall pressure and maximum wall pressure gradient increased with increasing

Rem. Comparing the results of the tilted and not-tilted (horizontal) single-slot impinging

jet showed that the maximum wall pressure did not change with an inclination angle of 3°

for the tested range of Reynolds numbers. However, the maximum pressure gradient of

the inclined impinging jet for high Reynolds numbers was higher than the maximum

pressure gradient of the non-inclined impinging jet.

Similarly, the maximum wall pressure and maximum wall pressure gradient of the

multiple-slot impinging jet decreased with increasing z/d and decreasing Rem. However,

increasing the auxiliary jet Reynolds number (Rea) resulted in a decrease in the maximum


86

wall pressure. Comparison between the single-slot and multiple-slot impinging jet

showed that the maximum wall pressure of the multiple-slot impinging main jet was

higher than that of the single-slot impinging jet. However, the maximum pressure

gradient of the multiple-slot impinging main jet was less than the maximum wall pressure

gradient of the single-slot impinging jet. In addition, the length of the main jet potential

core for the multiple-slot impinging jet was slightly less than that of the single-slot

impinging jet.

Comparison between the numerical results of Tamadonfar [2010] and the

experimental results showed that the value of the simulated maximum wall pressure for

the single-slot impinging jet was greater than the experimentally measured maximum

wall pressure except for z/d=6. Based on the numerical results, the plate at z/d=8 was still

in the potential core of the jet, so the numerical results could not successfully predict the

length of the potential core of the jet. It seems that the simulation could not accurately

simulate the instabilities in the shear layer, flapping of the jet and small pressure

perturbations at the impingement zone which combined to produce a source of the energy

dissipation. Similarly, the maximum wall pressure of the multiple-slot impinging jet

obtained from the simulations of Tamadonfar [2010] was higher than the experimental

maximum pressure. The trends of the numerical results agreed with the experimental

results at z/d≥8 for all tested Rem. The effect of the auxiliary jet on the experimentally

measured pressure profiles at high x/d for z/d≤6, which showed the presence of a

secondary pressure peak, was not observed in the numerical results. Besides, inconsistent

with the experimental results, the computational results showed that by increasing Rea the


87

maximum wall pressure increased. In the simulated flow field, the auxiliary jet flows

merged with the main jet flow field at lower z/d and formed one flow field which also

helped in increasing the main jet flow field momentum. As a result, some differences

(higher maximum pressure and not detecting the second peak pressure) have been

observed between the simulated and experimental results for the multiple-slot impinging

jet. In experimental measurements at z/d<6, the pressure field associated with the two

auxiliary jets and the main jet could still be identified on the plate.

5.2 Future Work

The use of multiple-slot jets for coating weight control in continuous galvanizing

is a new idea, and there are some numerical studies on this. On the other hand, there are

no experimental studies which focus on multiple-slot impinging jet applications in the

hot-dip galvanizing process. This study was the first which attempted to study multiple-

slot impinging jets experimentally. As a result, there are a lot of studies remaining to be

completed. In order to determine the final coating weight, the shear stresses at the wall

must be measured. A new technique should be developed to enhance the plate boundary

layer measurements at high jet velocities. There are still considerable studies which can

be done on studying the effect of the different parameters such as s/d, a, or Rea on wall

pressure and shear stress profile and consequently the final coating weight. In this work

the value of Rea for both auxiliary jets was kept the same, but in future studies the effect

of non-symmetric Rea can be examined. In addition, there was no attempt to study the

noise generation of multiple-slot impinging jet in this thesis. Therefore, studies should be


88

carried out in order to characterize the noise generation with multiple-slot impinging jet

as a function of different process parameters.

McMaster University-Mechanical Engineering M.A.Sc. Thesis-S. Alibeigi

89

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92

Appendix A: Dimensions of Impinging Jets

In this section, the dimensions of each part of the single-slot and multiple-slot

impinging jet have been presented.

A.i Single-Slot Impinging Jet

Figure A-1: Isometric view of the single-slot impinging jet.


93

Figure A-2: Single-slot impinging jet plenum.


94

Figure A-3: Single-slot impinging jet top cap.


95

Figure A-4: Single-slot impinging jet nozzle flange.


96

Figure A-5: Single-slot impinging jet bottom cap.


97

A.ii Multiple-Slot Impinging Jet

Figure A-6: Isometric views of multiple-slot impinging jet.


98

Figure A-7: Top cap of the multiple-slot impinging jet


99

Figure A-8: Main jet plenum of the multiple-slot impinging jet.


100

Figure A-9: Auxiliary jet plenum of the multiple-slot impinging jet.


101

Figure A-10: Main jet nozzle flange of the multiple-slot impinging jet.


102

Figure A-11: Auxiliary jet side flange of the multiple-slot impinging jet.


103

Figure A-12: Auxiliary jet front flange of the multiple-slot impinging jet.


104

Figure A-13: Bottom cap of the multiple-slot impinging jet.


105

Appendix B: Wall Pressure Profiles

In this section, the wall pressure profiles of single-slot impinging jet and the

multiple-slot impinging jet are presented in the dimensional scale.

B.i Single-Slot Impinging Jet

-6 -4 -2 0 2 4 60

1000

2000

3000

4000

5000

6000

7000

8000

pres

sure

(Pa)

x (mm)

z/d=6 z/d=8 z/d=10 z/d=12

Figure B-1: Wall pressure distribution at U=113m/s for all z/d for the short nozzle single-

slot impinging jet at α=0°.


106

-6 -4 -2 0 2 4 60

2000400060008000

100001200014000160001800020000220002400026000

pres

sure

(Pa)

x (mm)

z/d=12 z/d=10 z/d=8 z/d=6

Figure B-2: Wall pressure distribution at U=200 m/s for all z/d for the short nozzle single-


-8 -6 -4 -2 0 2 4 6 80

10000

20000

30000

40000

50000

60000

pres

sure

(Pa)

x (mm)

z/d=12 z/d=10 z/d=8 z/d=6

Figure B-3: Wall pressure distribution at U=300 m/s for all z/d for the short nozzle single-



107

-12 -10 -8 -6 -4 -2 0 2 40

1000

2000

3000

4000

5000

6000

7000

8000

pres

sure

(Pa)

x (mm)

z/d=12 z/d=10 z/d=8 z/d=6

Figure B-4: Wall pressure distribution for different z/d at U=113 m/s for short nozzle

single-slot impinging jet at α=3°.

-14 -12 -10 -8 -6 -4 -2 0 2 4 60

5000

10000

15000

20000

25000

pres

sure

(Pa)

x (mm)

z/d=12 z/d=10 z/d=8 z/d=6




108

-12 -10 -8 -6 -4 -2 0 2 40

10000

20000

30000

40000

50000

60000

70000

pres

sure

(Pa)

distance (mm)

z/d=12 z/d=10 z/d=8 z/d=6




109

B.ii Multiple-Slot Impinging Jet

0 2 4 6 8 10 12 14 160

1000

2000

3000

4000

5000Pr

essu

re (P

a)

x (mm)

z/d=4 z/d=6 z/d=8 z/d=10 z/d=12

Figure B-7: Wall pressure distribution for different z/d at Um=90 m/s and Ua=55 m/s for

multiple-slot impinging jet.

0 2 4 6 8 10 12 140

1000

2000

3000

4000

5000

6000

7000

8000

9000

Pres

sure

(Pa)

x (mm)

z/d=4 z/d=6 z/d=8 z/d=10 z/d=12




110

0 2 4 6 8 10 12 140

2000

4000

6000

8000

10000

12000

Pre

ssur

e (P

a)

x (mm)

z/d=4 z/d=6 z/d=8 z/d=10 z/d=12



0 2 4 6 8 10 12 14 16 180

1000

2000

3000

4000

5000

6000

7000

8000

Pre

ssur

e (P

a)

Distance (mm)

Ua=75 m/s Ua=65 m/s Ua=55 m/s

Figure B-10: Wall pressure distribution for different Ua at Um=113 m/s and z/d=4 for



111

0 2 4 6 8 10 12 14 16 18

0

1000

2000

3000

4000

5000

6000

7000 Ua=55 m/s Ua=65 m/s

Pres

sure

(Pa)

Distance (mm)



0 2 4 6 8 10 12 14 16 18

0

1000

2000

3000

4000

5000

6000

Pre

ssur

e (P

a)

Distance (mm)

Ua=55 m/s Ua=65 m/s




112

Appendix C: Uncertainty Analysis

The uncertainties associated with the present experimental results are discussed in

this section. According to Coleman and Steels [1999], for a variable (r) which is functions

of J independent measured variables (Xi):

1 2( , ,..., )Jr f X X X (C-1)

the overall uncertainty in variable (r), ( r ), can be found by using the Kline and

McClintok method given as:

2

1

J

i ii

r X

(C-2)

where ii

rX and iX is the uncertainty for each measured variable.

C.i Flow Velocity Uncertainty

The flow velocity at the exit of the nozzle was calculated by using the following

equation which is for compressible flow through an isentropic and lossless nozzle:


113

1

2. 11

sP PU cP

(C-3)

where c is the speed of sound in air, is the ratio of specific heats of air, Ps is the static

pressure in the plenum and P is the ambient pressure. Air can be assumed as an ideal gas

with =1.40. The speed of sound in air is calculated as:

c RT (C-4)

where R is the ideal gas constant [R=287.04 J/(kg.K)] and T is the ambient temperature in

Kelvin. Therefore, the equation (C-3) can be written as:

1

2 11

sP PRTUP

(C-5)

The independent variables used in equation (C-5) which affect the uncertainty in

U are: the ambient temperature (T), the ambient pressure (P∞), and the static pressure in

the nozzle plenum (Ps). Therefore, expanding equation (C-2) for the three introduced

variables, we obtain:

2 22

ss

U U U UT P PU T P P

(C-6)


114

Substituting the equation (C-5) into equation (C-6) and simplifying, equation (C-3) leads

to the following [Arthurs, 2012]:

2 2

2 22 2

22 21 1

1 12 21

2

ss

s s s s

PP P

P PU TU T

P P P P P P P PP P P P

(C-7)

The ambient temperature was measured by the thermocouple with the resolution

of 0.1 K. The maximum temperature variation during the experiment was 2T K . The

variation in the ambient pressure is estimated to be 0.1P kPa . The static pressure

within the nozzle plenum was measured using a Validyne DP-15 pressure transducer with

an accuracy of ±2.5% over the full scale. Different pressure transducer diaphragms were

used for different measurement Reynolds number [Table 3-1]. The uncertainty in the

static pressure within the plenum for the pressures of 4.97, 7.91, 10.5, 26.23, and 65.44

kPa are 0.0124, 0.02, 0.026, 0.065, and 0.164 kPa respectively. By substituting the values

in the equation (C-7), the relative uncertainty in flow velocity ( UU ) was found to be

less than 0.336%.

The diaphragms of the pressure transducer were calibrated with the special

pressure calibrator. Figure C-1 shows the calibration diagram.


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Figure C-1: Calibration Diagram for diaphragm number 30 (P=1.25 psi or 8.6 kPa).

C.ii Experimental Setup Uncertainty

In this study the geometric variables such as, the nozzle width, inclination angle,

and the impingement distance were measured by tools with known error range. Table [C-

1] presents the uncertainty in measurement of the setup geometry parameters.

Table C-1: Uncertainty in the geometry parameters of the experimental setup.

Geometry Parameter Measurement Uncertainty

z (impingement distance) ±0.0127 mm

d, a (main jet and auxiliary jet gap width) ±0.01 mm

x (measurement distance) ±0.0127 mm

s (distance of the main slot jet to the auxiliary slot jet)

±0.01 mm

EXPERIMENTAL I A -K G CONTINUOUS H -D G · Experimental Investigation of Air-Knife Geometry in...

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