ANSYS Fluent Modelling of an Underexpanded Supersonic Sootblower Jet Impinging into Recovery

Boiler Tube Geometries

by

Shahed Doroudi

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Graduate Department of Mechanical and Industrial Engineering University of Toronto

© Copyright by Shahed Doroudi 2015

ii

ANSYS Fluent Modelling of an Underexpanded Supersonic

Sootblower Jet Impinging into Recovery Boiler Tube Geometries

Shahed Doroudi

Master of Applied Science

Graduate Department of Mechanical and Industrial Engineering

University of Toronto

2015

Abstract

Sootblowers generate high pressure supersonic steam jets to control fireside deposition on heat

transfer tubes of a kraft recovery boiler. Sootblowing is energy expensive, using 3-12% of the

mill’s total steam production. This motivates research on the dynamics of sootblower jet

interaction with tubes and deposits, to optimize their use. A CFD investigation was performed

using ANSYS Fluent 15.0 to model three-dimensional steady-state impingement of a Mach 2.5

mildly underexpanded (PR 1.2) air jet onto arrays of cylindrical tubes with and without fins, at

various nozzle-to-tube centerline offsets.

A free jet and four impingement cases for each of the economizer and generating bank

geometries are compared to experimental visualizations. Pressure distributions on impinging

surfaces suggest that the fins in the economizer produce a reduced but uniform sootblowing

force. Pressure contours along the tubes (in the vertical direction) show a sharp decline one tube

diameter away from the jet mid-plane.

iii

Acknowledgments

I would like to express my heartfelt gratitude to my supervisor, Professor Markus Bussmann,

for his compassion, patience and constant guidance throughout the course of my research. You

have been the most inspirational figure in my academic career.

I would also like to thank my co-supervisor, Professor Honghi Tran, for providing me with this

research opportunity as well as the continuous support and encouragement to complete this

work. Your wisdom and experience helped me gain perspective to set my research on the right

track. Thank you for having confidence in me even when I was doubtful of myself.

I also wish to thank my co-supervisor Danny Tandra, as well as my committee members,

Professors Nasser Ashgriz and Javad Mostaghimi for their insightful comments and valuable

advice. To Professor Nasser Ashgriz, you have been a great mentor throughout my academic

career and I am indebted to you for many academic opportunities.

I would like to acknowledge members from the research program on “Increasing Energy and

Chemical Recovery Efficiency in the Kraft Pulping Process” for their financial support. This

research is jointly supported by the Natural Sciences and Engineering Research Council of

Canada (NSERC) and the following pulp and paper related companies: Abitibi-Bowater Inc.,

Andritz Inc., Babcock & Wilcox Company, Boise Inc., Carter Holt Harvey, Celulose Nipo-

Brasileira S.A., Clyde-Bergemann Inc., Daishowa-Marubeni International Ltd., Fibria,

FPInnovations, International Paper Company, Irving Pulp & Paper Limited, Klabin Company,

MeadWestvaco Corporation, Metso Power Oy, Stora Enso Research, Suzano Pulp and Paper,

Tolko Industries Ltd. and Tembec Inc. I would also like to thank the Ontario Graduate

Scholarship (OGS) for helping fund this research project.

I am grateful to Araz Sarchami and Esmaeil Safaei for their useful suggestions on modelling

using the ANSYS Workbench. Many thanks to my dear friends: Amirali, Sasan, Eric, Adam,

Shenglong, Hugo, Michael and Amirhossein for a fun and memorable graduate experience.

Last, but not least, I want to thank my family for their unconditional love throughout my life.

To my inspirational sister, Hamaseh Doroudi, thank you for babysitting me since the day I was

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born. To my selfless mother, Sogand Ijadi, you are the reason I never feel alone. To my father

and guide, Abolghasem Doroudi, I can only hope to someday be half the man you are.

v

Table of Contents

ABSTRACT ................................................................................................................................................. II

ACKNOWLEDGMENTS ........................................................................................................................... IIII

TABLE OF CONTENTS ............................................................................................................................. III

LIST OF TABLES .................................................................................................................................... VII

LIST OF FIGURES .................................................................................................................................. VIII

LIST OF APPENDICES ............................................................................................................................ XI

CHAPTER 1 INTRODUCTION ................................................................................................................... 1

PROBLEM OVERVIEW ........................................................................................................................ 2 1.1

1.1.1 Kraft Recovery Process ......................................................................................................... 4

1.1.2 Fouling ................................................................................................................................... 6

1.1.3 Sootblowing ........................................................................................................................... 7

THESIS OBJECTIVES ......................................................................................................................... 9 1.2

CHAPTER SUMMARIES .................................................................................................................... 10 1.3

CHAPTER 2 BACKGROUND ................................................................................................................... 11

POPHALI’S EXPERIMENTAL SOOTBLOWING MODEL ........................................................................... 11 2.1

2.1.1 Air versus steam .................................................................................................................. 12

2.1.2 Schlieren technique ............................................................................................................. 13

2.1.3 Tube geometries .................................................................................................................. 14

KEY CONCEPTS .............................................................................................................................. 15 2.2

2.2.1 Shock waves ........................................................................................................................ 16

2.2.2 Peak impact pressure .......................................................................................................... 17

2.2.3 Off-design jets ...................................................................................................................... 19

2.2.4 Supersonic impingement ..................................................................................................... 20

RELEVANT CFD INVESTIGATIONS .................................................................................................... 21 2.3

CHAPTER 3 THEORETICAL CONSIDERATIONS.................................................................................. 23

GOVERNING EQUATIONS ................................................................................................................. 23 3.1

K-Ε TURBULENCE MODEL ................................................................................................................ 24 3.2

ENHANCEMENTS TO THE RKE MODEL .............................................................................................. 25 3.3

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CHAPTER 4 METHODOLOGY ................................................................................................................ 27

ANSYS MODELLING CHALLENGES .................................................................................................. 27 4.1

4.1.1 Initial mesh generation ........................................................................................................ 28

4.1.2 Divergence with the Density-based Solver .......................................................................... 30

4.1.3 Pressure-based Solver shortcomings.................................................................................. 31

4.1.4 The addition of a nozzle ...................................................................................................... 34

GEOMETRY AND MESH GENERATION ............................................................................................... 35 4.2

4.2.1 Free Jet ................................................................................................................................ 35

4.2.2 Economizer .......................................................................................................................... 37

4.2.3 Generating Bank .................................................................................................................. 40

4.2.4 Offset Models ....................................................................................................................... 42

PREPROCESSING AND SOLVING ....................................................................................................... 43 4.3

4.3.1 Setup ................................................................................................................................... 43

4.3.2 Boundary Conditions ........................................................................................................... 44

4.3.3 Solving ................................................................................................................................. 45

4.3.4 Solution Initialization ............................................................................................................ 46

4.3.5 Gradient-based Mesh Adaption ........................................................................................... 47

CHAPTER 5 RESULTS AND DISCUSSION ............................................................................................ 48

FREE JET VALIDATION ..................................................................................................................... 49 5.1

FREE JET, ECONOMIZER AND GENERATING BANK: COMPARISON WITH SCHLIEREN VISUALIZATION .... 53 5.2

ECONOMIZER AND GENERATING BANK: PRESSURE DISTRIBUTION ON IMPINGING SURFACES ............. 57 5.3

EFFECT OF ECONOMIZER FINS ........................................................................................................ 58 5.4

5.4.1 PIP Distribution: Leading Tube ............................................................................................ 59

5.4.2 PIP Distribution: Leading Fin ............................................................................................... 63

5.4.3 Maximum PIP ...................................................................................................................... 64

5.4.4 Free jet vs Midway offset ..................................................................................................... 65

SECONDARY JET CHARACTERIZATION .............................................................................................. 67 5.5

MODEL LIMITATIONS ....................................................................................................................... 69 5.6

CHAPTER 6 CLOSURE ........................................................................................................................... 71

SUMMARY ...................................................................................................................................... 71 6.1

CONCLUSIONS ................................................................................................................................ 72 6.2

IMPLICATIONS ON SOOTBLOWING ..................................................................................................... 73 6.3

RECOMMENDATIONS FOR FUTURE WORK ......................................................................................... 73 6.4

References……………………………………………..………………………………………………………74

Appendix A………………………………………………………………………………...……………….….78

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List of Tables

Table 1. A summary of observations from the PIP distributions on the leading tubes. ............................ 60

Table 2. Maximum PIP values associated with each simulation. ............................................................. 65

viii

List of Figures

Figure 1. The Kraft process is the conventional chemical process of turning wood into pulp for

papermaking. ...................................................................................................................................... 4

Figure 2. The layout of a typical kraft recovery boiler [3]. ......................................................................... 5

Figure 3. A boiler tube coated by a deposition of carryover and fume particles[8]. ................................... 6

Figure 4. The distal end of a sootblower lance tube showing the supersonic nozzle outlet. ....................... 7

Figure 5. A view of a sootblower in operation as it traverses into the boiler. ............................................. 7

Figure 6. Sootblowers operating near a superheater platen [3]. .................................................................. 8

Figure 7. A schematic of Pophali’s experimental apparatus [3]. .............................................................. 11

Figure 8. Schematic of a schlieren visualization apparatus in operation [3]. ............................................ 13

Figure 9. Pophali's experimental generating bank model [3]. ................................................................... 14

Figure 10. Experimental economizer model: (a) schematic of one row of tubes; (b) experimental setup

[3]. .................................................................................................................................................... 14

Figure 11. In the presence of a supersonic flow, an oblique shock is formed at the tip of an object [14].

.......................................................................................................................................................... 16

Figure 12. A jet flow diverges as it interacts with tube curvature, forming an expansion shock wave [3].

.......................................................................................................................................................... 16

Figure 13. As a blunt body moves right to left in a supersonic wind tunnel, a nomal shock propogates

perpendicular to the impinging surface [15]. .................................................................................... 17

Figure 14. Multi-cell shock structure of a supersonic underexpanded jet (nozzle exit on the left) [16]. .. 19

Figure 15. Three key parameters of incompressible jet impingement onto a cylinder [3]. ....................... 20

Figure 16. A comparison of the computed axial velocity distribution along the centerline of a free

supersonic jet [4] and corresponding experimental data [22]. ue and D represent the nozzle exit

velocity and diameter, respectively. ................................................................................................. 21

Figure 17. Mach contours of fully-expanded (top) and underexpanded (bottom) sootblower jets [2]. .... 27

Figure 18. 3D perspective view of economizer tubes. .............................................................................. 28

Figure 19. A top view of the hybrid mesh. ................................................................................................ 29

Figure 20. Cross sectional view of the hybrid mesh showing large size variation between elements which

leads to an overall low quality mesh. ............................................................................................... 29

Figure 21. Dimensions and boundary conditions for the Economizer model from the jet exit onwards. . 30

Figure 22. Velocity (m/s) contour of a DBS simulation for the economizer model from the jet exit

onwards. ........................................................................................................................................... 31

Figure 23. Mach contours of PBS economizer simulations in order of increasing inlet Mach number .... 32

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Figure 24. Mach contours of the Mach 2.5 underexpanded jet into an economizer, as solved by the PBS

.......................................................................................................................................................... 32

Figure 25. Visual comparison of experimental schlieren image (left) to the CFD Mach field (right) ...... 33

Figure 26. Centerline total pressure distribution from the coupled PBS economizer simulation. p0 = 2.14

MPa and de = 7.4 mm ....................................................................................................................... 33

Figure 27. Side-view of the converging-diverging nozzle used by Pophali.............................................. 34

Figure 28. Mach contour of flow within the experimental nozzle with a supply pressure of 2.14 MPa ... 34

Figure 29. Computational domain for the free jet simulation. Dt = 11 mm is the economizer tube

diameter. ........................................................................................................................................... 35

Figure 30. Side view of the cylindrical quarter model free jet mesh. ....................................................... 36

Figure 31. Front view of the free jet mesh showing the radial refinement near the jet core. .................... 36

Figure 32. Computational domain of a sootblower jet impinging head-on onto an economizer fin Dt = 11

mm. ................................................................................................................................................... 37

Figure 33. Top view of the economizer geometry blocks. ........................................................................ 38

Figure 34. Symmetry plane view of the economizer mesh for the head-on case. ..................................... 38

Figure 35. Front view of the economizer mesh displays the mesh sweeping in the vertical direction, with

an inflation bias towards the symmetry plane. ................................................................................. 39

Figure 36. a) Top view of the mapped nozzle mesh; b) O-grid mesh refinement around finned tubes .... 39

Figure 37. Computation domain of a sootblower jet impinging head-on onto a generating bank cylinder.

.......................................................................................................................................................... 40

Figure 38. Top view of the generating bank geometry blocks. ................................................................. 41

Figure 39. Symmetry plane view of the generating bank mesh for the head-on case. .............................. 41

Figure 40. O-grid mesh and radial refinement around generating bank cylinders. ................................... 41

Figure 41. The following offset cases were selected for CFD modelling. ................................................ 42

Figure 42. The final mesh of the generating bank mid-platen offset case ................................................ 43

Figure 43. Boundary conditions imposed on the economizer domain. ..................................................... 44

Figure 44. A wall was created around the nozzle exit to avoid backflow into the surrounding outlet

surfaces. ............................................................................................................................................ 44

Figure 45. The Fluent mass balance report for the generating bank simulation. ...................................... 45

Figure 46. Mach contour of an initial economizer solution, as determined by FMG initialization. ......... 46

Figure 47. The effects of shock resolution on the Mach contour of the head-on economizer simulation. 47

Figure 48. Jet centerline PIP distribution: CFD vs. experimental measurement [3]. ............................... 49

Figure 49. Radial PIP distribution of the Pophali [3] experimental jet 10.8 diameters from the nozzle

exit. ................................................................................................................................................... 51

x

Figure 50. A comparison of the jet radial expansion: CFD vs. experimental results [3]. ......................... 52

Figure 51. Flow visualization of a free jet (Top to bottom: experimental, density gradient magnitude,

Mach number) .................................................................................................................................. 53

Figure 52. Visualization of flow into an economizer at various offsets (left to right: Mach number,

density gradient magnitude, experimental) ...................................................................................... 54

Figure 53. Visualization of flow into a generating bank at various offsets (left to right: Mach number,

density gradient magnitude, experimental) ...................................................................................... 55

Figure 54. The pressure distribution on the tubes and fins of the economizer. ......................................... 57

Figure 55. The pressure distribution on the tubes of the generating bank. ............................................... 57

Figure 56. PIP distribution on the top quadrant of the leading tube EC tube............................................ 59

Figure 57. PIP distributions on the top quadrant of the leading GB tube. ................................................ 60

Figure 58. PIP distribution on the top surface of the EC leading fin. ....................................................... 63

Figure 59. Position of maximum PIP for the GB and EC “slight offset” cases. ....................................... 64

Figure 60 Experimental centerline PIP distribution for a free jet, and jets midway between tubes of EC

& GB [3]. .......................................................................................................................................... 66

Figure 61. CFD centerline PIP distribution for a free jet, and jets midway between EC and GB tubes [3].

.......................................................................................................................................................... 66

Figure 62. A Mach contour plot showing the secondary jets for the "top half of first tube" case. ........... 67

Figure 63. The angular PIP distributions on the leading and secondary tubes of EC. .............................. 68

Figure 64. The angular PIP distributions on the leading and secondary tubes of GB. .............................. 69

xi

List of Appendices

Appendix A. Turbulence Correction UDF Codes ……………………………………………………….78

1

Chapter 1 Introduction

A persistent problem in kraft recovery boilers is “fouling”, the accumulation of fireside deposits

onto heat transfer surfaces. Fouling is controlled by the use of “sootblowers”, long lance tubes

with radially opposed nozzles that are periodically used to blow steam at supersonic velocities

(typically around Mach 2.5.) to erode and remove deposits. The effectiveness of a sootblower jet

is a strong function of the force it exerts on deposits, which is largely dependent on the local

geometry it impinges upon. In the superheater section of a recovery boiler, sootblower jets have

easier access to deposits due to the generous spacing between platens. Tubes in the generating

bank and economizer sections are more closely spaced, limiting jet access to interior deposits

beyond the leading tube. In either case, the interaction of a supersonic steam jet with tubes and

deposits is a complex phenomenon that requires further investigation.

For most of a decade, research at the University of Toronto has examined the dynamics of

sootblower jet interaction with tube geometries characteristic of a recovery boiler, in order to

quantify sootblower effectiveness. This research has involved both experimental and CFD

analyses. Pophali [3] performed experiments with a quarter scale sootblower model, using the

schlieren technique to visualize the flow of a supersonic air jet impinging onto recovery boiler

tube geometries. Pophali also used a pitot tube to measure static pressures within the jet core at

various nozzle-to-tube offsets. Tandra [1] investigated fully expanded jets with CFD, including

a study of the effectiveness of low pressure sootblowing. Emami [2] extended the CFD work to

off-design (over and underexpanded) jets impinging on geometries characteristic of superheater

platens in kraft recovery boilers. Tandra [1] and Emami [2] employed the CFDLib research code

(developed at the Los Alamos National Laboratory), and developed various modifications to the

k-ε turbulence model in order to accurately capture sootblower jet flow features. This modified

code was dubbed “Sootblower Jet Turbulence” (SJT) model [4].

The aforementioned CFD studies accurately predicted sootblower jet characteristics as well as

jet impingement onto solid surfaces. However, it was difficult to apply the CFDLib code to

flows in more complex geometries, such as those in the generating bank and economizer

sections of a recovery boiler. The present work creates such a model using ANSYS Fluent 15.0,

commercial CFD software capable of modelling and solving the 3D flow of a supersonic jet

2

impinging onto complex geometries. This work builds on the work of Tandra and Emami [4] by

implementing the modifications of the SJT model into the Fluent realizable k-ε turbulence

model. The two geometries considered in this work are the economizer and generating bank

within a kraft recovery boiler, also studied experimentally by Pophali [3]. The spreading rate

and centerline Peak Impact Pressure (PIP) distributions of a free jet simulation are compared to

experimental data for validation of the CFD model. Sootblower flow into the economizer and

generating bank geometries is studied by plotting and analyzing pressure distributions on tube

surfaces. The key difference between the two geometries is the presence of fins connecting the

economizer tubes. The ANSYS Fluent model is used to assess the influence of these fins on

sootblower jet/tube interaction. Furthermore, the secondary jets that form as the primary jet

deflects off the leading tube are studied by examining the pressure distributions they exerts on

an interior tube.

In what follows, section 1.1 is a review of background information on the kraft pulping process,

fouling and sootblowing. There will be a focus on the implications of sootblowing in capital and

energy expenditures. Section 1.2 presents the thesis objectives as well as a summary of the rest

of the thesis.

Problem Overview 1.1

The pulp and paper industry refers to manufacturing enterprises that use wood as raw material to

produce pulp, paper, paperboard, and other paper-related products. In 2011, the pulp and paper

industry was responsible for 25% percent of the total energy consumption in the Canadian

manufacturing sector, making it the most energy-intensive manufacturing subsector [5]. As

result, improving energy efficiency is of utmost importance to the industry.

Paper is made of pulp, a fibrous material extracted from wood. A pulp mill is the facility in

which pulp is produced, usually by means of a chemical process. The kraft process is the most

common such process, due to its versatility and the high quality of the pulp it produces. The first

step of this process is a chemical reaction between wood chips and the pulping chemicals. A

byproduct of this process is “black liquor”, a solution of the pulping chemicals as well as the

dissolved organic matter from wood. This solution is concentrated, and then burned in a kraft

3

recovery boiler to recover the inorganic chemicals, and to produce steam and power from the

combustion of the organic matter.

Fouling occurs in kraft recovery boilers because large quantities of inorganic, low-melting

temperature “fly ash” particles accumulate on heat transfer surfaces. These ash deposits have a

low thermal conductivity and restrict heat transfer between the hot flue gas and tube surfaces.

The deposits reduce overall boiler thermal efficiency and can corrode boiler tubes. In severe

cases, fouling may completely block flue gas passages requiring a costly shutdown of the boiler

to water wash the deposits.

Fouling in recovery boilers is controlled by the regular operation of sootblowers. These long

tubes traverse in between heat transfer surfaces, and produce two radially opposed supersonic

steam jets that attempt to remove deposits upon impact, to control deposit accumulation.

Anywhere from 3% to 12% of the total steam produced by a kraft recovery boiler is used for

sootblowing.

Brewster [6] describes the pulp business as “one of the most capital intensive businesses in the

world with total capital investment for a new mill being roughly four times the annual sales

revenue generated”. The recovery boiler alone represents 20% of the total investment and its

efficient operation is crucial to achieving maximum economic return from the capital

investment. A characteristic of capital intensive businesses is that the difference between net

losses and gains lies in the small final fraction of production. Brewster shows that a 5% increase

in production volume of a mill can represent a 35% increase in profits. With an annual profit as

high as $20 million dollars, an incremental change in the production of a boiler may have

substantial financial consequences. Fouling poses the greatest threat to steam generation,

especially because sootblower effectiveness is difficult to measure. This motivates research on

understanding and improving two aspects of sootblower operation. First, understanding the

pressure exerted on tube banks can help devise a strategy to maximize deposit removal. Second,

research on minimizing steam consumption while maintaining the effectiveness of sootblowers

could result in substantial financial gain for pulp mill owners.

The remainder of this section provides a more detailed overview of the kraft process, recovery

boiler fouling, and sootblowing.

4

1.1.1 Kraft Recovery Process

Figure 1. The Kraft process is the conventional chemical process of turning wood into pulp for papermaking.

The kraft process is the most widely used chemical pulping process within the pulp and paper

industry. Wood chips are treated with a solution containing a mixture of sodium hydroxide

(NaOH) and sodium sulfide (Na2S) at temperatures as high as 170 °C to create pulp for

papermaking (see figure 1). The pulp is then water washed creating a liquid solution called

“weak black liquor” consisting of the inorganic cooking chemicals of the pulping process as

well as the leftover organic material from the wood. The inorganic cooking chemicals of the

pulping process are too costly for one time use [7]. Consequently, a subsequent step in the kraft

process is to recover and reconstitute the pulping chemicals to be used again.

To start the chemical recovery process, the dilute “weak black liquor” is sent to an evaporator

where its concentration is increased to the 65-85% range to form “black liquor”. The black

liquor is then fed into a kraft recovery boiler and burnt by a furnace at the bottom (see figure 2).

Upon combustion, the inorganic portion of the black liquor forms “smelt” on the bed at the

bottom of the recovery boiler. Smelt is dissolved in water to form “green liquor”, a solution

from which sulphur and sodium are extracted to recycle the chemical agents.

5

Figure 2. The layout of a typical kraft recovery boiler [3].

In addition to the chemical recovery process, the recovery boiler generates steam and power

using the heat from the organic portion of black liquor. Unlike the inorganic compounds which

fall onto the bed to form smelt, the organic material burns and forms a hot flue gas which rises

and passes through several arrays of boiler tubes. Feedwater circulating inside the boiler tubes

extracts the thermal energy from the hot flue gas to produce high pressure steam. As shown in

figure 2, there are three types of tube banks within the top portion of a recovery boiler that form

a heat transfer circuit. Feedwater entering the economizer is heated to a temperature slightly

below the boiling temperature. In the subsequent generating bank and superheater sections, the

water becomes steam and superheated steam respectively. Note that in figure 2 the flue gases

flow from left to right, while the water flows from the rightmost tubes of the economizer into

the superheater.

6

1.1.2 Fouling

Figure 3. A boiler tube coated by a deposition of carryover and fume particles[8].

Fouling is a persistent problem in recovery boiler operation, caused by fly ash particles

entrained in the hot flue gas, that accumulate on the surface of heat transfer tubes. Fly ash

particles consist of carryover, larger particles formed during black liquor combustion, and fume

particles that condensate from inorganic volatile compounds. Figure 3 shows the accumulation

of these two deposit types on a boiler tube. Carryover particles range from 20 μm to 3 mm in

size and tend to accumulate by impaction, and form hard deposits that adhere to tube surfaces.

Fume particles are much finer at an average diameter of 0.5 μm, and form softer deposits that

can sinter into more dense deposits. Carryover deposition is dominant in the superheater section

that particles first encounter. Fume, on the other hand, only forms at the lower flue gas

temperatures downstream of the superheater, and so tends to deposit in the generating bank and

economizer sections.

7

1.1.3 Sootblowing

Figure 4. The distal end of a sootblower lance tube showing the supersonic nozzle outlet.

Sootblowing is the industry standard means of mitigating fouling within kraft recovery boilers.

As depicted in figure 4, sootblowers are steel lance tubes, typically a few meters in length and 9

cm in diameter, with two radially opposing nozzles that produce supersonic steam jets to erode

and remove deposits [2]. The two mechanisms by which sootblowers remove deposits are

“brittle breakup” and “debonding”. Brittle breakup occurs by imposing internal stresses on

deposits above their ultimate tensile strength, to induce fracture. Debonding refers to the

weakening of the adhesive force between a deposit and a tube.

Figure 5. A view of a sootblower in operation as it traverses into the boiler.

A large kraft recovery boiler has about 100 sootblowers. Sootblowers rotate into and out of the

space between tube platens (see figure 6), and are operated a few at a time in a strategic

sequence intended to maximize deposit degradation. The insertion and retraction of a typical

8

sootblower into a boiler takes about 4 minutes, while the preset sequence for all sootblowers

may take as long as several hours to complete. The sootblowing requirements of a boiler are

based on feedback parameters, such as pressure and temperature, which are monitored

continuously. Pressure probes are located in between platens to monitor pressure gradients

within the flue gas. An unusually high pressure gradient across a tube bank may be indicative of

plugging. Recovery boiler operators also monitor power to the ID fan, and flue gas exit

temperature as additional indications of plugging

Figure 6. Sootblowers operating near a superheater platen [3].

9

Thesis Objectives 1.2

The objectives of this thesis are:

1. To provide an accessible CFD model that predicts the flow behaviour of sootblower jets

using the commercial software ANSYS Fluent solver in combination with the SJT

turbulence model previously developed by Tandra [1] and Emami [2]. The model is used

to produce 3D steady-state simulations of an underexpanded supersonic sootblower jet

impinging onto complex boiler tube geometries. A comparison of the CFD jet centerline

pressure distribution with experimental data will be used to assess and validate the

Fluent model.

2. To utilize the Fluent model to simulate the sootblower flows studied experimentally by

Pophali [3], within the economizer and generating bank sections of a kraft recovery

boiler, and to compare sootblower performance within those geometries. In particular,

the effect of economizer fins on sootblower flow behavior will be assessed.

Note that sootblowing involves the concurrent operation of many sootblowers in between a

large number of heat transfer tubes. The simulations at hand model instances of sootblowing at

specific orientations to the tubes. An understanding of the complex flows that result from a

supersonic underexpanded jet impinging onto the fins and cylinders of the boiler is a first step in

investigating sootblower efficiency. Furthermore, sootblower flow into the superheater

convective section of the recovery boiler will not be investigated in the present work as it has

been previously studied by Emami [2]. The economizer and generating bank geometries are

more complex and better suited for assessing ANSYS Fluent’s capabilities.

10

Chapter Summaries 1.3

Chapter 2 is a review of the literature and scientific concepts relevant to sootblower operation.

Chapter 3 reviews the governing equations of supersonic turbulent flow that are solved by

ANSYS Fluent. This chapter also presents the implementation of enhancements to the ANSYS

Fluent realizable k-ε turbulence model, appropriate for sootblower modelling.

Chapter 4 presents a comprehensive review of the ANSYS Fluent modelling process. The

governing equations of the solver will be reviewed. The choices of domain and mesh generation,

solver controls and boundary conditions will be presented and justified. There will also be a

section on the various challenges faced during the modelling process.

Chapter 5 presents the results of a free jet simulation, as well as simulations of a sootblower jet

impinging onto the economizer and generating bank geometries at four nozzle-to-tube offsets. A

comparison of the jet centerline pressure values to experimental data will be used to validate the

ANSYS Fluent model. A qualitative comparison of the results to experimental visualization will

be presented and discussed.

Chapter 6 summarizes and concludes the thesis. The implications of the CFD investigation on

sootblower performance are discussed, and recommendations are offered for future work.

11

Chapter 2 Background

An overview of the literature and scientific concepts pertaining to sootblower operation is

presented. Section 2.1 is a detailed review of the work by Pophali [3], particularly the free jet,

economizer and generating bank experiments which were modelled in the present work. There

will be an emphasis on the experimental setup and boiler tube geometries which were modelled

with ANSYS Fluent. The reader may choose Section 2.2 introduces the scientific background

and key physical parameters characteristic of sootblower jets. Finally, section 2.3 presents CFD

investigations, and particularly previous research at the University of Toronto, relevant to

sootblower operation.

Pophali’s Experimental Sootblowing Model 2.1

Figure 7. A schematic of Pophali’s experimental apparatus [3].

Pophali [3] created a ¼ scale experimental model of a sootblower nozzle, and tube arrangements

characteristic of the superheater, generating bank and economizer convective sections of a kraft

recovery boiler. The objective of the experiments was to characterize the interaction of a

supersonic air jet impinging on these tube arrangements. A schlieren flow visualization

technique coupled with a high speed camera was used to image all interactions. Pitot pressure

measurements were also made within the jet core to quantify the jet structure. As shown in

figure 7, a solenoid valve connected to an air tank supplied a supersonic convergent-divergent

12

sootblowing nozzle with compressed air at a supply pressure (Po) of 2.14 MPa, similar to actual

sootblowers. The supersonic nozzle consists of a bell shaped converging portion leading to a

final throat diameter (dt) of 4.5 mm which then diverges to a nozzle exit diameter (de) of 7.4 mm

[3]. A small pitot probe was designed to move freely in the axial direction to measure static

pressure. The supersonic nozzle was adjustable in two directions: into and out of the page, as

well as axially towards the tubes. The offset between the jet and tube centerlines, the diameters

of the tubes, and the distance between the nozzle and tube were varied to examine their effects

on jet/tube interaction. The subsequent discussion in this section pertains to aspects of the

aforementioned experiment relevant to the present CFD study: the choice of air as a model fluid

for the experimental sootblower jet, an overview of the schlieren visualization technique, and

the geometries of the model economizer and generating bank tubes.

2.1.1 Air versus steam

Actual sootblowers operate with high pressure steam, but air was chosen as the model fluid for

the experiments for reasons of safety and simplicity. Pophali designed the experimental nozzle

to create a supersonic air jet geometrically and dynamically similar to actual steam sootblower

jets. The justification for using air as the model fluid is as follows:

Pophali [3] shows that both air and superheated steam are both homogenous fluids.

The heat capacity ratio,

, for air is 1.4 and similar to for steam.

The jet exit Mach number has been shown to be the most important parameter for

creating a dynamically similar jet [9]. Consequently, with a supply pressure (Po) of 2.14

MPa, the experimental nozzle produced a nozzle exit Mach number of 2.5,

corresponding to that of an actual sootblower jet.

The ¼ scale geometry using air resulted in a lab jet Reynolds number of 1.6 x 106, a

value close to the actual jet Reynolds number of 1.9 x 106.

Another characteristic to consider is the spreading rate of the supersonic jet, which is

mainly affected by the jet exit Mach number and the ratio of the ambient fluid density to

13

the density of the fluid within the jet core. Pophali imposed flow conditions similar to an

actual sootblower to ensure that the experimental jet expanded at a similar rate.

Field trials in Sweden [10] measured sootblower jet forces that were consistent with lab

scale experiments using air as a model fluid.

As a consequence of the above design choices, Pophali claimed that the results of the

experimental work were applicable to actual sootblowing inside a kraft recovery boiler.

2.1.2 Schlieren technique

Figure 8. Schematic of a schlieren visualization apparatus in operation [3].

The schlieren technique, invented by August Toepler, has long been used to visualize invisible

fluid mechanics phenomena such as shock waves [11]. The basic principle of the schlieren

visualization technique is to shine a collimated source of light, where the light rays are strictly

parallel, onto an area of interest. A transparent target medium, such as air, will bend each light

ray differently due to variations in the local refractive index. It has been shown [12] that the

local reflective index of air is directly proportional to its local density. Consequently, a density

gradient, such as the one occuring across shock wave, will result in a variation of light intensity

as light bends dissimilarly. Figure 8 shows an apparatus that facilitates the imaging of such flow

visualization. Note that the variation in how light rays are deflected as they pass through the

medium, in this case the supersonic air jet, makes it difficult to focus the resultant image. As a

result, a critical component of schlieren visualization is the placement of a knife edge at the

14

focal point of the second mirror (M2) to block half the light. Light rays that have been deflected

sufficiently to pass by the knife edge illuminate the focusing lens, brightening certain regions of

the focused image. This creates a contrast across the final schlieren image corresponding to a

change in the density gradient (first derivative of the density) in the direction normal to the knife

edge. In the absence of a knife edge, the resultant image would be a shadowgraph.

Shadowgraphs simply reflect the shadows of a transparent material exhibiting a fluid density

variation and are often observed in nature (hot air casting shadow on a nearby surface). The

variation of light intensity in a simple shadowgraph represents the second derivative of the

density gradient [13].

2.1.3 Tube geometries

Figure 9. Pophali's experimental generating bank model [3].

Figure 10. Experimental economizer model: (a) schematic of one row of tubes; (b) experimental setup [3].

15

The two tube geometries studied by Pophali that are of interest here are the economizer and

generating bank sections. Both tube configurations comprise an array of cylindrical tubes, with

the key difference being that fins interconnect the tubes of the economizer. In a kraft recovery

boiler, the fins are intended to extend the heating surfaces to maximize heat transfer.

As shown in figure 9, the generating bank model consists of a 40 tube array with a surface-to-

surface spacing of 12.7 mm. The tubes are arranged in four parallel rows of 10 tubes, with each

tube having an outer diameter of 14.3 mm. The distance between the nozzle exit and the leading

tube of the model bank is 48.35 mm. The economizer model is shown in figure 10, and consists

of two platens, 12.7 mm apart. Each platen consists of six 11 mm (outer diameter) tubes

connected by 1.2 mm thick welded fins. The tubes in each platen are a surface-to-surface

distance of 22 mm apart, and two additional fins, 11 mm in length, are welded on the windward

(facing the nozzle) and leeward (away from the nozzle) ends of each platen. The distance

between the nozzle exit and the leading fin (on the windward side) is 39 mm.

Despite the different tube diameters in the economizer and generating bank models, the fins are

of central importance in dictating the difference in flow behaviour as the sootblower jet

impinges onto the tube banks. In addition to comparing sootblower flow into the generating

bank and economizer, this difference offers an opportunity to characterize the effects of the

leading fin, essentially a flat plate, in its interaction with a turbulent supersonic jet.

Finally, experiments involving a free jet in the absence of any obstacles were also performed by

Pophali. The free jet results will be used to validate the CFD model, and to compare with jet

propagation results midway between two rows of economizer and generating bank tubes.

Key Concepts 2.2

The following section is a review of the underlying physics and key parameters of the

experimental sootblower model of Pophali, which will be examined with the CFD results of the

present work.

16

2.2.1 Shock waves

In compressible flows, substantial pressure and temperature gradients lead to variations in the

density of the flow field. The Mach number (M), the local ratio of flow velocity to the speed of

sound (a), is an indicator of compressibility within a flow field at values higher than about 0.3.

A Mach number value higher than 1 is supersonic, meaning that the local flow velocity exceeds

the speed of sound. The local speed of sound for an ideal gas such as air is directly proportional

to the square root of the absolute temperature.

Figure 11. In the presence of a supersonic flow, an oblique shock is formed at the tip of an object [14].

Figure 12. A jet flow diverges as it interacts with tube curvature, forming an expansion shock wave [3].

17

Figure 13. As a blunt body moves right to left in a supersonic wind tunnel, a nomal shock propogates

perpendicular to the impinging surface [15].

The Mach number of the Pophali jet at the nozzle exit was 2.5. A characteristic of such a flow is

the formation of oblique shock and expansion waves as the flow attempts to adjust to sudden

disturbances caused by sharp pressure gradients. An oblique shock occurs when a flow is turned

into itself and is compressed. The static pressure, which is equivalent to the pressure measured

by a pitot tube stagnating the flow, increases across an oblique shock. Figure 11 shows the

propagation of an oblique shock in a supersonic flow. Conversely, expansion shock waves are

formed when the flow adjusts to a sudden divergence or turning away of the flow, such as the

Coanda effect-induced divergence of a supersonic jet interacting with tube curvature (see figure

12). The Coanda effect refers to the tendency of a flow to be attracted to a nearby solid surface

and can lead to deviations in the flow direction. An expansion shock wave is associated with a

decrease in the static or pitot tube pressure across its shear layer.

In addition to oblique and expansion shock waves, a normal shock wave forms upstream of a

supersonic flow impinging directly onto an obstacle, such as a tube or deposit. A normal shock

wave occurs when a flow is turned to such a degree that it cannot remain attached to the

impinging body, and propagates perpendicular to its surface. Normal shocks always result in a

deceleration of the flow velocity to subsonic conditions (Mach number becomes lower than 1).

Figure 13 shows the formation of a normal shock as a supersonic flow impinges onto a blunt

object.

2.2.2 Peak impact pressure

The parameter that is considered representative of sootblower jet effectiveness is the “Peak

Impact Pressure” (PIP). PIP is the pressure a jet would exert, upon impingement, on a deposit

18

positioned somewhere along its centerline, and varies with distance from the nozzle exit. Emami

[2] defines PIP as “as the stagnation pressure on the downstream side of a normal shock wave

(when the local Mach number is greater than one), or the stagnation pressure itself (in subsonic

regions of the flow)”. To justify the applicability of PIP, Emami also shows that the force

exerted by a supersonic sootblower jet on a perpendicular flat plate [2] agrees well with the

value calculated by multiplying the plate surface area by the PIP of a free jet. Experimentally,

PIP is simply measured by probing a point along the jet centerline with a pitot tube pressure

transducer. Pophali was able to measure PIP with great repeatability [3]. To exactly replicate

this measurement in a CFD simulation, one would have to model a small cylinder, having the

diameter of the experimental probe, at various locations of interest in the computational domain.

This is not feasible considering the number of simulations one would have to run to obtain a

reasonable number of data points along the jet centerline. An alternate approach is to assume an

infinitely small tube diameter, and evaluate the effect of a normal shock wave normal to the

flow direction. This is a reasonable assumption for the Pophali experiments considering that the

nozzle exit diameter is 2.5 times that of the 3 mm probe tip. On the basis of the above

assumption, we can approximate PIP using the Rayleigh pitot tube equation which calculates the

total pressure downstream of a normal shock as a function of the upstream total pressure, the

ratio of specific heats ( ), and the upstream Mach number, as follows:

represents the local total pressure, M represents the local Mach number, and is

the heat capacity ratio of air. Using post processing tools, we can extract the local total pressure

and Mach number from a CFD result to “virtually” probe along a jet centerline. Note that the

PIP distribution on walls within the computational domain, where flow velocity is zero due to

the no-slip condition, is equivalent to the total pressure.

19

2.2.3 Off-design jets

Figure 14. Multi-cell shock structure of a supersonic underexpanded jet (nozzle exit on the left) [16].

The supersonic nozzles at the end of a sootblower lance tube are intended to operate at a certain

design pressure, to create a fully expanded jet. A study by Jameel et al. [17] showed that fully

expanded nozzles increase the jet energy exerted on deposits for removal and are therefore

desirable. However, fluctuations in the supply pressure (Po), and perhaps nozzle manufacturing

defects will produce “off-design” jets. If the static pressure of the jet at the nozzle exit plane is

higher than the ambient pressure, the jet is underexpanded. Conversely, if the static pressure at

the nozzle exit is lower than the ambient pressure, an overexpanded jet is produced. An

important characteristic of these “off-design” jets is the formation of multi-cell shock structures.

As displayed in figure 14, sudden pressure fluctuations in the form of conical expansion and

compression waves occur as an underexpanded jet acclimatizes to the ambient pressure. Upon

leaving the nozzle exit, an underexpanded jet expands rapidly to match the ambient conditions,

creating the initial bulging of the jet in figure 14. These expansion waves propagate to the

constant pressure boundaries of the jet and reflect back as compression waves to form an

adjacent oblique shock. These compression waves then reflect off the jet boundary as expansion

waves. This process repeats itself to form the diamond shock structure seen in figure 14. As the

jet radially expands, these shock cells interact with the turbulent shear layer and decay

downstream of the nozzle exit. The experiments performed by Pophali were conducted at an exit

pressure ratio of 1.2, which is a mildly underexpanded jet. The resultant shock structures have

significant implications on the CFD modelling that is presented in Chapter 3 and 4.

20

2.2.4 Supersonic impingement

Figure 15. Three key parameters of incompressible jet impingement onto a cylinder [3].

The Pophali experiments of jet/tube interaction exmained supersonic jet impingement onto

cylindrical surfaces. In the economizer model, there is the additional complication of flow

impingement onto the tip of the fin. The impingment of an incompressible jet onto cylindrical

surfaces has been studied extensively. However, the underexpanded supersonic equivalent of

this flow has not been widely studied. The shock structures characteristic of underexpanded

supersonic flows complicate flow behaviour. Nonetheless, a review of jet impingement onto

cylindrical surfaces provides insight into the interactions which we model in this thesis. Figure

15 is a schematic showing the three key governing parameters of incompressible jet

impingement onto a cylinder: the nozzle-cylinder distance, the jet diameter relative to the tube

diameter, and the offset of the nozzle centerline with respect to the tube centerline [18][19][20].

Based on these studies, the most important parameter in the Pophali generating bank

configuration is the small distance between the nozzle and the leading tube. The leading tube of

the experimental model is situated in the jet core (the region downstream of the nozzle exit

where the jet retains its properties).

Aside from the findings of Pophali, which have been discussed in detail, we are unaware of

other studies of the impingment of supersonic underexpanded jets onto finned tubes.

Furthermore, there is no research on the impingement of a supersonic jet onto the edge of a flat

plate. Much of the research on flat plate impingement involves a supersonic jet impinging onto a

normal flate plate. However, this flow behaviour is not representative of the one encountered in

an economizer. The results of this interaction will be presented in Chapter 5.

21

Relevant CFD Investigations 2.3

The University of Toronto has been involved with CFD modelling of sootblowers for the last

decade or so. Tandra [1] initiated the development of a numerical model to describe the

interaction of a fully-expanded turbulent supersonic sootblower jet with tube banks and

deposits. Tandra used this model to study a sootblower jet propagating between superheater

platens. In conjunction with laboratory experiments, he also studied the feasibility of using less

expensive low pressure steam for sootblowing operation. In the initial stages of his work,

Tandra recognized the lack of numerical models able to adequately describe the turbulence

within a supersonic sootblower jet, and so developed modified k-ε turbulence model that he

incorporated into the open source CFDLib code (developed at the Los Alamos National

Laboratory). This modification incorporated the effect of compressibility on reducing the

turbulent kinetic energy redistribution [21], into the standard k-ε model. The resulting

simulations of a fully expanded supersonic sootblower jet were in good agreement with

laboratory measurements of a free jet, and jet flows between superheater platens. An important

finding of this work is that by increasing the nozzle dimensions and steam flow rate, low

pressure sootblowing can exert forces on deposits comparable to those of high pressure

sootblowing.

Figure 16. A comparison of the computed axial velocity distribution along the centerline of a free supersonic

jet [4] and corresponding experimental data [22]. ue and D represent the nozzle exit velocity and diameter,

respectively.

0 5 10 15 200.4

0.5

0.6

0.7

0.8

0.9

1

1.1

x / D

u /

ue

Simulation

Experimental Data

22

Emami [2] built on the work of Tandra [1] by accounting for the effects of turbulence

realizability and shock unsteadiness. The improved model predicted jet characteristics more

accurately, producing results of a supersonic jet impinging onto solid surfaces that agreed well

with experimental results. Figure 16 shows an axial velocity distribution of a fully expanded jet,

modelled by Emami, compared to the experimental data of Panda and Seasholtz [22]. The

Emami model was also used to study the impingement of underexpanded sootblower jets onto

cylindrical deposit geometries. An essential finding of this work was the central importance of

the position along the multi-cell shock jet structure at which the interaction occurs, due to the

large variations in the centerline PIP within an underexpanded jet. This was confirmed by the

pitot tube PIP measurements of Pophali [3] along the jet centerline. The work of Tandra and

Emami set the groundwork for the CFD investigation in this thesis, and will be referred to again

in Chapter 3.

In addition to the above literature, a large number of CFD investigations were surveyed to

inform the setup of ANSYS Fluent boundary conditions and solver settings (e.g.

[23][24][16][34]). In particular, Garcia [25] used ANSYS Fluent to model high speed

underexpanded jet impingement onto a stationary deflector (flat disk). This work proved a

valuable resource for developing the model presented here. Garcia had success producing

accurate results using the ANSYS Fluent standard k-ε turbulence model. Furthermore, Garcia

included the nozzle as part of the computational domain; that proved to be a solution to

difficulties encountered in the present work.

23

Chapter 3 Theoretical Considerations

This chapter provides an overview of the governing equations for a supersonic compressible

turbulent flow, which are solved by ANSYS Fluent. In section 3.2, the formulations of the

standard and realizable k-e turbulence models are introduced. Section 3.3 presents two

enhancements: the removal of the dilatation dissipation term, and a structural compressibility

correction, to the Fluent realizable k-ε turbulence model, and the implementation of these

enhancements into ANSYS Fluent using User-Defined Functions (UDFs).

Governing Equations 3.1

The flow of a sootblower jet as it exits a lance tube is supersonic, highly compressible and

turbulent. The smallest turbulence scales of a supersonic flow are greater than the molecular

scales [26], rendering the flow a continuum phenomenon. Consequently, the Navier-Stokes (N-

S) equations which govern the conservation of mass and momentum of a continuum fluid can be

used to represent the flow. The N-S equations are solved by ANSYS Fluent to obtain the

velocity and pressure fields within a domain, and for compressible flows, Fluent also solves the

conservation of energy equation to couple the velocity and static temperature field. Finally, the

pressure and static temperature fields are used to determine the density field using the ideal gas

equation. The aforementioned equations are as follows:

Conservation of Mass:

Conservation of Momentum:

Conservation of Energy:

24

Equation of State (Ideal Gas Law):

is the fluid density, is time, ⃗ is the velocity vector, is the static pressure, ̿ is the stress

tensor, is the total fluid energy, is the thermal conductivity of air, is the ambient

pressure of the flow, set to atmospheric pressure of 101.3 kPa, = 286.9 J/(kgK) is the

specific gas constant for air, and is the static temperature.

k-ε Turbulence Model 3.2

The N-S equations describe any turbulent flow and can be solved numerically using the Direct

Numerical Simulation (DNS) technique. However, DNS modelling of a sootblower jet is not

feasible because to the random fluctuations and eddy motions take place over a wide range of

length scales. The grid size of such a simulation, dictated by the smallest Kolmogorov

turbulence scales, would require immense computational resources [1].

An alternative approach is the two-equation k-ε model which requires far less computation, yet

provides the means of capturing the mean-flow features of turbulence relevant to the present

research objectives. The standard k-ε model describes flow turbulence using two transport

equations for the turbulent kinetic energy (k) and rate of dissipation (ε), as follows:

is the velocity component, is the production of k due to the mean velocity gradients, is

the production of k due to buoyancy, is the contribution of the fluctuating dilatation in

compressible turbulence to the overall dissipation rate, is the viscosity, and is the turbulent

viscosity which is assumed to be constant. is a user-defined source term for modifying the

turbulent kinetic energy equation. The rest of the parameters are constant values fitted to

various turbulent flows: σk = 1, σϵ = 1.3, C1ϵ= 1.44, C2ϵ = 1.92 and C3ϵ = 0.09 as per the ANSYS

Fluent User Guide [27].

25

The standard k-ε model cannot accurately capture flow fields with adverse pressure gradients,

separation and complex secondary flow features, all of which are present in a sootblower jet

flow. The realizable k-ε (RKE) model, a variation of the standard k- ε model addresses these

limitations [28]. The term ‘realizable’ refers to satisfying mathematical constraints on the

Reynold stresses which are consistent with the physics of a turbulent flow. To achieve this, RKE

replaces the standard k-ε dissipation rate transport equation with an improved one “derived from

an exact equation for the transport of the mean-square vorticity fluctuation” [28]. Furthermore,

RKE introduces a variable formulation for the turbulent viscosity term that is a constant in the k

and ε equations. This new turbulent viscosity formulation is a function of the mean strain and

rotation rates as well as the turbulence field (k and ε).

Enhancements to the RKE model 3.3

The robustness of the RKE model comes at the price of accuracy when capturing certain aspects

of sootblower jet flow. There are two aspects of supersonic flow in particular with which the

RKE model struggles: the compressibility of high Mach number flows, and the shock structure

of an underexpanded jet.

The k-ε model was initially developed assuming that compressibility effects are negligible [1],

and as reported by Thies & Tam [29], results depart significantly from experimental data at

supersonic Mach numbers. Furthermore, as reported by Sinha et al [30] and Liou et al [31], the

k-ε model fails to accurately describe flows within shock waves as it overpredicts the k

production across each shock. Consequently, to model sootblower jet flow one must suppress

the amplification of k across shocks [1].

To address the aforementioned shortcomings of the k-ε model, Emami [32] incorporated the

corrections into two User Defined Functions (UDFs), which are presented next. The UDF codes

are in Appendix A.

Removing the Dilatation Dissipation term

Sarkar [33] proposed an additional “Dilatation dissipation” term to the turbulent kinetic energy

equation to account for the failure of the k-ε model to “predict the observed decrease in

spreading rate with increasing Mach number for compressible mixing and other free shear

layers”. This correction term, previously presented on the right hand side of equation (3.5), is:

26

As reported by Gross [35], the addition of this term yields a solution that “does not exhibit

sufficient mixing at the higher Mach numbers seen for the 3-D jet because it suppresses

turbulence growth excessively.” It has been shown that this term is not necessary for

sootblowing simulations [32].

The first UDF code in Appendix A implements the Sarkar correction term (3.7) into the right

hand side of equation (3.5) as the user defined source (Sk) term. The addition of this term

effectively eliminates the Fluent implementation of the Sarkar term (in the form of the term

YM). In other words, adding the correction term through the source term Sk removes it from the

k transport equation.

Structural Compressibility Correction

Compressibility strongly reduces the growth of turbulent kinetic energy in supersonic flows. As

one of the first to address this problem, Heinze [21] used the results of the DNS compressible

flow simulations performed by Pantano and Sarkar [36] to obtain an empirical expression

relating the k production to Mach gradients. As the structural compressibility (Mach gradients)

increases, the turbulent viscosity reduces significantly. This results in a reduction of the

turbulent stresses and suppresses the turbulent kinetic energy production, a phenomenon

neglected by ANSYS Fluent.

Tandra [1] implemented the empirical expression into the k-ε model to obtain an expression for

the turbulent viscosity μt as a function of and the Mach gradient Mg, as follows:

The second UDF code in Appendix A implements the turbulent viscosity formulation of

equation (3.8) into the ANYS Fluent solver.

27

Chapter 4 Methodology

The approach to modelling sootblower jet flows, defined as the steady-state impingement of a

3D turbulent, highly compressible, supersonic (Mach 2.5) underexpanded jet onto complex

geometries, with ANSYS Fluent is presented. First, various challenges of using the ANSYS

Fluent software for modelling supersonic flow over complex geometries are discussed. Then the

modeling process is presented, starting from choices of geometry and mesh generation, to

boundary condition selection, solution initialization and finally solution convergence.

With ANSYS Fluent, one is constrained by the parameters the software provides, and often it is

through trial and error that the best setup for a particular problem is found. Consequently, this

chapter serves as an overview of ANSYS Fluent capabilities and limitations in predicting under-

expanded supersonic flow over complex geometries.

ANSYS Modelling Challenges 4.1

Prior CFD sootblowing models developed at the University of Toronto were generated using the

CFDLib code from the the Los Alamos National Laboratory. Tandra implemented the k-ε

modifications of Chapter 3 into CFDLib and Emami further incorporated a realizability and

shock unsteadiness condition into the standard k-ε model. In what turned out to be important to

the present work, Emami modelled fully-expanded and underexpanded sootblower jets from the

nozzle exit onwards (result shown on figure 17).

Figure 17. Mach contours of fully-expanded (top) and underexpanded (bottom) sootblower jets [2].

28

This earlier CFD work served as the starting point for the ANSYS Fluent modelling. In section

3.4, the final preprocessing for the simulations in this thesis will be presented to the reader.

However, to provide the reader with a clearer picture of the modelling process, we first present

various difficulties and obstacles encountered while working with ANSYS Fluent, which

informed the development of the final model.

4.1.1 Initial mesh generation

Figure 18. 3D perspective view of economizer tubes.

The economizer geometry consists of rows of cylindrical tubes connected by fins that resemble

flat plates. Although this geometry is comprised of simple shapes, it is a complex geometry to

mesh. Initially, the geometry was blocked into ten rectangular subcomponents and meshed with

1.8 million elements. The outer blocks, where there would little to no flow, were meshed with

hexahedral elements. The core blocks aligned with the economizer fins were meshed with

tetrahedral elements and refined near high curvatures. Furthermore, the mesh was refined within

the jet core, in the space between the nozzle exit and the leading fin. Despite several versions of

the tetrahedral mesh with inflations around the cylinders and fins, a quality mesh was not

obtained. All simulations with this hybrid tetrahedral mesh diverged due to the low mesh

quality. Figure 19 and 20 illustrate a cross sectional view of the hybrid mesh and shows that

large size variations exist between adjacent elements, which lead to numerical errors and thus a

low quality mesh. Nonetheless, through appropriate blocking of the geometry, a higher quality

29

hexahedral mesh was developed. The details of this mesh will be presented in section 3.3 when

discussing the final modelling process.

Figure 19. A top view of the hybrid mesh.

Figure 20. Cross sectional view of the hybrid mesh showing large size variation between elements which

leads to an overall low quality mesh.

30

4.1.2 Divergence with the Density-based Solver

ANSYS Fluent offers two solvers, the density-based solver (DBS) and the pressure-based solver

(PBS). In both approaches, the governing momentum equation (3.2) is solved to obtain a

velocity field. However, the DBS then uses the continuity (3.1) equation to determine the

density field, while the pressure field is determined via the equation of state (3.3). Consequently,

the DBS solves the energy equation to determine the temperature field used in equation (3.3).

On the other hand, the PBS manipulates the N-S equations to determine a pressure correction

equation which it uses to obtain the pressure field. Traditionally, the PBS is favored for

incompressible or slightly compressible flows (around Mach 0.3 or less), while the DBS

approach was designed for highly compressible and supersonic flows. Over the years,

improvements to both approaches have made them capable of solving a broad range of flows.

For instance, similar to the DBS, the coupled PBS [37] couples velocity and pressure, solving all

equations simultaneously. This makes the coupled PBS an alternative to the DBS that is

applicable to compressible flows. However, for a supersonic underexpanded sootblower jet, the

DBS offers the advantage of better shock resolution and therefore greater accuracy of results

[38].

Figure 21. Dimensions and boundary conditions for the Economizer model from the jet exit onwards.

31

For this reason, the DBS was the first choice for modelling sootblower jet flow into an

economizer. The boundary conditions displayed in figure 21 were implemented into ANSYS

Fluent and solved with DBS starting from an initial zero-velocity solution. The resulting

simulations diverged or plateaued at high residuals. Figure 6 shows that the flow field stagnated

shortly after entering the domain.

Figure 22. Velocity (m/s) contour of a DBS simulation for the economizer model from the jet exit onwards.

4.1.3 Pressure-based Solver shortcomings

As mention, the coupled PBS offers an alternative DBS solver for modelling supersonic

compressible flows. The problem setup presented in figure 21 solved by the coupled PBS

resulted in similar divergence issues previously discussed in section 3.2.2.

Convergence stability is hard to achieve in compressible flows due to the high degree of

coupling between velocity, density, pressure and energy. The ANSYS User Guide [39] offers

multiple strategies to address this solution instability. One suggestion offered by the Guide is to

start by solving with a reduced inlet to outlet pressure ratio, for example one that corresponds to

Mach 0.3. That solution can then be used to initialize a higher inlet Mach number simulation

until the desired value of 2.5 is reached. Using this approach with the coupled PBS, a converged

second order solution was finally obtained for the underexpanded Mach 2.5 sootblower jet into

an economizer (see figures 23 and 24).

32

Figure 23. Mach contours of PBS economizer simulations in order of increasing inlet Mach number

Figure 24. Mach contours of the Mach 2.5 underexpanded jet into an economizer, as solved by the PBS

33

Figure 25. Visual comparison of experimental schlieren image (left) to the CFD Mach field (right)

As displayed in figure 25 the PBS simulation of a Mach 2.5 underexpanded jet into an

economizer is in good qualitative agreement with the schlieren visualization in terms of the flow

separation points on the impinging leading fin. However, as expected, the PBS struggles with

resolving the shock structure, resulting in smeared shocks. The major shortcoming of the PBS

simulation, however, is that it fails to predict a reasonable pressure field within the core of the

underexpanded jet. A centerline profile (figure 26) shows that the jet total pressure remains at a

constant value of 2.14 MPa, the pressure specified at the simulation inlet.

Figure 26. Centerline total pressure distribution from the coupled PBS economizer simulation.

p0 = 2.14 MPa and de = 7.4 mm

34

4.1.4 The addition of a nozzle

A look at similar simulations of underexpanded jet modelling using ANSYS Fluent, by Garcia

[25], Brown [40] and Munday [41], prompted the idea of including the converging-diverging

nozzle in the computational domain. Subsequently, a personal communication with an ANSYS

developer [42] confirmed that including the nozzle is crucial for capturing the flow features of a

supersonic underexpanded jet.

Figure 27. Side-view of the converging-diverging nozzle used by Pophali.

Figure 28. Mach contour of flow within the experimental nozzle with a supply pressure of 2.14 MPa

The bell shaped converging-diverging nozzle used by Pophali [3] was measured and modelled

with ANSYS Workbench. Note that adding the nozzle changes the mass flowrate inlet

boundary condition, previously presented in Figure 21, to a nozzle inlet pressure boundary

condition of 2.14 MPa. This value is reported by Pophali [3] as the average supply pressure of

the compressed air tank, used to produce the experimental model sootblower jet. To confirm the

35

accuracy of the nozzle geometry for generating the desired conditions at the nozzle exit, an

independent 3D steady state simulation of the flow inside the nozzle was performed. A highly

refined mesh of 1 million tetrahedral elements was generated and a boundary condition of 2.14

MPa was imposed on the nozzle inlet. The Mach contour plot in figure 28 shows that the Mach

number at the nozzle exit plane is 2.5, as is expected. Furthermore, the static pressure

approximately 0.5 mm downstream of the nozzle exit plane reached an approximate value of 19

kPa gauge. This result is in agreement with the outlet to ambient pressure ratio of 1.2 measured

by Pophali [3].

Geometry and Mesh Generation 4.2

This section describes the geometrical modelling and meshing that was done for the simulations

presented in this thesis. All geometries were modelled using SolidWorks 2012 and imported into

ANSYS Workbench using the .sat file format. All meshes were generated using ANSYS

Workbench.

4.2.1 Free Jet

Figure 29. Computational domain for the free jet simulation. Dt = 11 mm is the economizer tube diameter.

36

Pophali [3] measured the centerline PIP values of a free jet up to 46 nozzle exit diameters from

the nozzle exit. The free jet simulation serves as a source of validation for the subsequent

economizer and generating bank simulations. A free jet was modelled in 2D using the ANSYS

Fluent axisymmetric solver, but a converged solution could not be obtained. Consequently, a 3D

cylindrical quarter geometry, with two planes of symmetry, was generated for the free jet

simulation. As shown in figure 29, the cylindrical domain is scaled in the radial direction by 8

nozzle diameters and 42 nozzle diameters in the axial direction.

Figure 30. Side view of the cylindrical quarter model free jet mesh.

Figure 31. Front view of the free jet mesh showing the radial refinement near the jet core.

37

The domain was meshed with 0.1 mm tetrahedral elements in the nozzle region and hexahedral

elements in the remainder. From the nozzle exit onwards, the mesh spacing was controlled in

the radial direction by 80 divisions with an inflation growth rate of 5%, in the angular direction

by 70 equal divisions, and in the axial direction by 360 divisions with an inflation growth rate of

1%. The resultant quarter model mesh consists of 3.6 million elements with an orthogonal

quality of 0.91 (shown in figures 30 and 31).

4.2.2 Economizer

Figure 32. Computational domain of a sootblower jet impinging head-on onto an economizer fin Dt = 11 mm.

Pophali’s ¼ scale economizer model consists of two finned tube platens separated by a tube-to-

tube spacing of 23.7 mm. All other dimensions of the experimental economizer platens are

presented in figure 10a of Chapter 2. A 3D rectangular geometry, scaled with respect to the 11

mm tube diameter, as shown in figure 32, was generated as the computational domain for the

economizer simulations. In order to minimize the computational costs, only the first three finned

tubes of each platen were included in the domain. The centerline of the nozzle was aligned with

the centerline of the leftmost platen in order to simulate the head-on economizer experiment.

38

Figure 33. Top view of the economizer geometry blocks.

To create a high quality mesh, the domain was blocked to establish greater control over mesh

sizing. As shown in figure 33, blocks were sliced to segregate regions of prominent flow

features from outer blocks where the velocities are near zero and pressure gradients are small.

The rectangular volume around each finned tube was sliced into eight smaller quadrilateral

sections. Once sliced, the element growth rate along the slice lines was used to control the radial

growth of the mesh around each tube.

Figure 34. Symmetry plane view of the economizer mesh for the head-on case.

39

Figure 35. Front view of the economizer mesh displays the mesh sweeping in the vertical direction, with an

inflation bias towards the symmetry plane.

Figure 36. a) Top view of the mapped nozzle mesh; b) O-grid mesh refinement around finned tubes

Once the geometry was blocked, the meshing process involved imposing the number of element

divisions on the resultant edges. The choices of element sizing were made to ensure a smooth

transition from refined areas of interest to the coarse inconsequential blocks. The symmetry

plane mesh was replicated (defined as “sweeping” by ANSYS) in the vertical direction with a

growth rate of 4% (see figure 35). As shown on figure 36a, the nozzle surfaces were mapped

(following the nozzle topology) and a sizing of 0.2 mm was imposed on all elements throughout

the body. Figure 36b shows a close-up of the O-grid mesh (element size refining as they

approach the tube circumference) with the leading cylinder having greater radial refinement.

The final mesh (top view shown in figure 34) comprised of 4.8 million elements, with an

40

average orthogonal quality of 0.96, and a minimum of 0.22. The orthogonal quality represents

the deviation of the element edges from the perfect orthogonal orientation of a cuboid element,

having an orthogonal quality of 1 [43]. Using this blocking approach, we were able to create a

high quality mesh consisting entirely of hexahedral elements from the nozzle exit onwards.

4.2.3 Generating Bank

Figure 37. Computation domain of a sootblower jet impinging head-on onto a generating bank cylinder.

The generating bank model created by Pophali was a 4 x 10 array of 14.3 mm wide cylindrical

tubes separated by 12.7 mm (surface to surface) in all directions. A 2 x 3 representation of the

array was chosen for the CFD model since the prime area of interest is the flow interaction with

the leading and secondary cylinders. The reader may refer to the economizer computational

domain of figure 32 for the dimensions not shown in the generating bank domain of figure 37.

41

Figure 38. Top view of the generating bank geometry blocks.

Figure 39. Symmetry plane view of the generating bank mesh for the head-on case.

Figure 40. O-grid mesh and radial refinement around generating bank cylinders.

42

The generating bank geometry and mesh were generated in a similar way to that of the

economizer. The lack of fins allowed for easier blocking (shown in figure 38) around the

cylinders. This resulted in a smooth meshing surrounding the leading and secondary cylinders,

as shown in figure 40. The edge size divisions throughout the meshing process were chosen to

create a mesh consistent with that of the economizer. The final mesh (shown in figure 39)

comprised of 4.6 million elements with an average quality of 0.97 and a minimum of 0.22.

4.2.4 Offset Models

Figure 41. The following offset cases were selected for CFD modelling.

Pophali performed schlieren visualizations of offset cases for both the generating bank and

economizer models. Starting from the initial head on case, the nozzle was offset in increments

of 2 mm towards the final mid-platen position. Pophali performed visualizations of eight offset

cases for each of the generating bank and economizer models, of which we chose four for CFD

modelling.

43

Figure 42. The final mesh of the generating bank mid-platen offset case

Using ANSYS Workbench, the nozzle body was selected and translated by the necessary

increment in the Y-direction (as defined in figures 34 and 39). Adjustments were made to the

blocking of each offset case to accommodate the shifting of prominent flow features. Figure 42

shows an example of this accommodation in a mesh for the mid-platen offset case of the

generating bank, where the elements around leading cylinder of both platens are equally refined.

The number of elements, and the quality of all offset meshes were close to the values previously

presented for the head on cases.

Preprocessing and Solving 4.3

This section outlines the boundary conditions and setup parameters for implementing an

accurate and convergent sootblower jet model into Fluent. How the solving process is initiated

and monitored to achieve convergence, and how shock resolution is enhanced through grid

adaption, are also discussed.

4.3.1 Setup

All results presented in Chapter 5 are second-order accurate steady-state simulations using the

Density-Based Solver (DBS) along with the energy equation. The density of air was modelled

using the ideal gas law. Explicit and implicit formulations were both used throughout the

simulations, depending on convergence behavior. A total temperature value of 293 K, as per the

Pophali experiments, was imposed on all boundary conditions. ROE-FDS was used as the

convective flux type for all simulations. Both the Green-Gauss and node-based gradient

44

evaluation approaches were used, depending on convergence behavior. A very low Courant

number (0.1 < CFL < 0.01), and under-relaxation, were used throughout the simulations to

maintain convergence of flow residuals. Finally, the two UDFs previously discussed in Chapter

3 were implemented into ANSYS Fluent:

The Heinze structural compressibility model was set to define the turbulent viscosity.

The Sarkar dilatation dissipation term was eliminated from the turbulent kinetic energy

equation by subtracting it via a source term.

4.3.2 Boundary Conditions

Figure 43. Boundary conditions imposed on the economizer domain.

Figure 44. A wall was created around the nozzle exit to avoid backflow into the surrounding outlet surfaces.

45

The boundary conditions shown in figure 43 were imposed in order to produce an undexpanded

sootblower jet into the economizer geometry. A pressure inlet boundary condition at a uniform

value of 2.14 MPa gauge was imposed on the distal surface of the nozzle. Using the nozzle exit

diameter of 7.4 mm as the flow hydraulic diameter and a turbulent intensity of 1%, the turbulent

kinetic energy at the inlet was initialized to a calculated value of 49 m2/s

2 with a dissipation rate

of 2.2 x 105 m

2/s

3. The nozzle and tube surfaces were defined as no slip walls. The top surface

of the domain was defined as a symmetry boundary condition as only half of the nozzle was

included in the domain. Finally, all other surfaces were defined as pressure outlets at 0 kPa

gauge. The turbulent kinetic energy at the outlet was initialized to a value of 1.0 m2/s

2 with a

dissipation rate of 1.0 m2/s

3 as these values were determined to be inconsequential to the

simulation results. An additional wall surface, shown in figure 44, was defined surrounding the

nozzle exit in order to prevent backflow into the immediately adjacent pressure outlet. The same

The boundary conditions of the economizer model in figure 43 were also applied to the

generating bank and free jet models, with only a change in geometry.

4.3.3 Solving

In order to determine convergence of CFD simulations, the residual behavior of the energy,

velocity, turbulence and continuity terms are usually monitored with respect to the number of

solver iterations. The residuals for all simulations were monitored to reach an order of 10-2

. The

residual behavior was constantly monitored and under-relaxation factors adjusted to achieve an

optimal balance between solution stability and convergence acceleration. However, the ANSYS

User Guide [44] points out that “there are no universal metrics for judging convergence” and

that “residual definitions that are useful for one class of problem are sometimes misleading for

other classes of problems”. Consequently, in addition to monitoring residuals, the overall mass

balance of each simulation was monitored (an example of this is shown in figure 45).

Monitoring the mass ensures that the difference between the outlet and inlet mass fluxes

represents at most a 5% mass imbalance.

Figure 45. The Fluent mass balance report for the generating bank simulation.

46

4.3.4 Solution Initialization

In the case of complex flows, such as that of a sootblower jet impinging onto the finned tubes of

an economizer, an appropriate initial solution is critical for establishing and accelerating

convergence. One approach is to initialize all variables in interior domain cells to those of the

inlet, except for the velocity which is set to zero. The logic behind this technique is that the

velocity field will develop from the inlet onwards, making it an appropriate initial guess. In the

preliminary stages of running simulations, we struggled to achieve solution convergence with

the Density-Based Solver using this initialization technique.

An alternative initialization technique, as suggested by the ANSYS Tutorial Guide on modelling

external compressible flow [38], is to utilize the Full Multigrid (FMG) feature that involves

constructing a number of grid levels of varying coarseness. The flow is solved quickly on the

coarsest grid level; this provides a rough solution of the major flow features, which is

interpolated onto a finer mesh in a subsequent iteration. This process is repeated until a solution

is obtained on the finest level available, which the original grid. The default settings of the FMG

feature were used to initiate all simulations.

Figure 46. Mach contour of an initial economizer solution, as determined by FMG initialization.

As seen in figure 46, the FMG initialization creates a rough, qualitative solution for the solver to

iterate on. This can help to accelerate convergence, but may also lead to difficulty achieving

very low residuals, as certain values are quite close to those of the converged solution.

47

4.3.5 Gradient-based Mesh Adaption

Achieving a mesh independent solution, one for which a parameter of interest does not differ

appreciably as the mesh is refined, is desired for all CFD simulations. For simple geometries,

such as external flow over a single cylinder, this can be easily done by refining a mesh until

further computational costs are not justified by the change in solution accuracy. Furthermore,

the parameter of interest is usually a single value such as the drag coefficient on the cylinder. In

the case of sootblower jet flow onto economizer and generating bank geometries, there are many

meshing parameters to alter and many field variables to monitor. To add to this complexity,

offset simulations can have refinements that differ from one another. Consequently, it is very

difficult to investigate mesh independence by generating multiple meshes of varying refinement

for each case.

One solution to this problem is to use solution-adaptive mesh refinement determined by the

numerical solution. Fluent offers a Gradient Adaption feature that refines a mesh using gradients

of any particular field variable. Refining with respect to gradients of total pressure is a suitable

choice for resolving the shocks of an underexpanded jet and progressing to a mesh-independent

solution. The maximum pressure gradient was calculated and all cells within 10% of this value

were selected for refinement. Figure 47 shows the improvement in shock resolution after using

Gradient Adaption. A total pressure-based Gradient-based mesh Adaption was performed on all

simulations in this thesis.

Figure 47. The effects of shock resolution on the Mach contour of the head-on economizer simulation.

48

Chapter 5 Results and Discussion

ANSYS Fluent results of sootblower jet flow into economizer and generating bank geometries

are presented. With the convergence criteria described in section 3.4.3, each simulation took 4-5

days to complete on an Intel i7-3770 3.4 GHz machine with 24 GB of RAM.

To validate the ANSYS Fluent model, the results of a free jet simulation are compared with

experimental data. Then density gradient and Mach contours of the simulation results are

qualitatively compared to schlieren visualizations of Pophali [3]. Finally, PIP distributions of the

following flow scenarios are examined:

a primary jet impinging on a leading tube, for all simulations,

a primary jet impinging on the leading fin of the economizer geometry,

the impingement of a secondary jet onto interior tubes, and

the propagation of a free jet midway between tubes.

Additionally, we also present the values and location of the maximum PIP exerted on the

impinging surfaces.

49

Free Jet Validation 5.1

Figure 48. Jet centerline PIP distribution: CFD vs. experimental measurement [3].

Figure 38 illustrates a comparison of jet centerline pitot tube measurements with PIP values

calculated from the Fluent free jet model results using the Rayleigh pitot tube formula (eq 2.1).

The PIP to supply pressure (Po) ratio at the nozzle exit is 0.46 for both results. As the

underexpanded jet leaves the nozzle, it completes its first expansion outside the nozzle and thus

the PIP decreases. The ensuing oscillations represent compression / expansion waves of the

shock structure. Note that each peak-to-peak variation of the PIP represents one shock cell. A

comparison of the plot in figure 48 to that of the fully-expanded jet in figure 16 shows the

importance of the location of jet impingement on the flow behaviour. Depending on the position

50

of the shock cells, at impingement positions only one nozzle diameter apart a deposit may

experience a 50% difference in PIP.

The experimental results exhibit 8 shock cells. The first four dissipate very little as they reach a

similar peak PIP value; the last four shock cells gradually dissipate as the jet weakens. Fluent

predicts 5 shock cells within the jet core which dissipate gradually, similar to to the last four of

the experimental results. Overall, the CFD predicted shock cells diffuse in strength and size at a

faster rate than the experimental data.

Capturing shock cells of a supersonic underexpanded jet is notoriously difficult and the above

represents our best effort using the modelling process presented in Chapter 4. A possible cause

of the accelerated shock cell diffusion in the Fluent result may be due to an overprediction of the

turbulence generated in the shear layer. This overprediction may be attributed to the choice of

inlet turbulence boundary conditions. The initial inlet turbulence parameters (k and ε) of all

simulations were calculated by Fluent based on our input of 1% turbulent intensity and a

hydraulic diameter of 7.4 mm (equal to nozzle exit diameter). These input values were based on

an investigation of turbulence in external flows over a bluff body, similar to the flow considered

here [23]. Furthermore, note that the Fluent results are subject to the limitations of the Rayleigh

equation (eq. 2.1) that assumes a perfect normal shock on an infinitely small pitot tube.

Nonetheless, the ANSYS Fluent free jet does a good job at capturing the general trend observed

in the centerline PIP distribution of the experimental free jet results. As a result, the Fluent

model is deemed appropriate for a study of the relative performance of a sootblower jet

impinging onto the economizer and generating bank geometries at various offsets. It should be

noted that the results far downstream of the nozzle exit, at about 35 nozzle diameters, are

distorted by the limited domain size. This is inconsequential to the investigations of the present

work, as impingement in the economizer and generating bank occur in at about 5 to 6 nozzle

diameters downstream of the nozzle.

51

Figure 49. Radial PIP distribution of the Pophali [3] experimental jet 10.8 diameters from the nozzle exit.

Another source of validation for the Fluent model is the jet spreading rate measured by Pophali

[3]. One way to characterize the spreading rate of a supersonic jet is to determine the effective

jet radius at various axial positions. Pophali [3] defines jet radius as the radial distance between

the centerline and the point where PIP decreases to 5% of its maximum value at that cross

section. Pophali measured PIP, in increments of 1 mm across the jet radius, at various axial

distances. For example, figure 49 shows the radial PIP distribution at an axial position of 10.8

nozzle diameters, along with an indication of the jet radius. Using radial PIP profiles at various

axial positions selected by Pophali , a set of corresponding jet radii were determined from the

Fluent results. A comparison of the results is presented in figure 50, and shows a strong

agreement between the Fluent model and two experimental data sets. The additional

experimental data comes from Kweon et al [45] who studied jet spreading of a slightly more

underexpanded jet under similar operating conditions. As seen in the plot of figure 50, the jet

radius initially increases due to expansion at the nozzle exit; further downstream the jet radius

increases due to the entrainment of the surrounding air and turbulent mixing. Overall, the jet

spread is small as is expected with a focused highly supersonic jet.

52

Figure 50. A comparison of the jet radial expansion: CFD vs. experimental results [3].

53

Free Jet, Economizer and Generating Bank: 5.2

Comparison with Schlieren Visualization

Figures 51-53 provide a visual comparison of Fluent results, in the form of density gradient

magnitude and Mach number contours, to schlieren images of a free jet, and jet flows into

economizer and generating bank tube geometries. The offsets that are specified in figures 52 and

53 are defined in figure 41 of section 3.3.4.

Figure 51. Flow visualization of a free jet (Top to bottom: experimental, density gradient magnitude, Mach

number).

54

Figure 52. Visualization of flow into an economizer at various offsets (left to right: Mach number, density gradient magnitude, experimental).

55

Figure 53. Visualization of flow into a generating bank at various offsets (left to right: Mach number, density gradient magnitude, experimental).

56

Comparing these figures, the Fluent simulations are in reasonable agreement with the schlieren

images, exhibiting similarly located shock cells, normal shock waves and points of separation

from the impinging surfaces.

The free jet simulation exhibits fewer and wider shock cells in comparison to the experimental

results. As previously observed on the centerline PIP distribution, Fluent predicts 5 observable

shock cells in the free jet core. The “midway between tubes” offset does not impinge on any

surface, and so is similar to that of the free jet. Expansion waves, that look like arrow heads,

form on the leeward (the side opposite the surface facing the jet) side of the first and second

tubes for the case of jet flow midway between tubes. This expansion wave, associated with a

sudden pressure drop, may be caused by the supersonic jet adjusting to the Coanda effect as the

flow diverges (following the tube curvature). This pressure drop was calculated (using Fluent

results) as the difference between PIP values upstream and downstream of the shock apparent

shear layer. A visual comparison of the “midway between tubes” results (bottom row of figures

52 and 53) shows that the CFD model has resolved the boundaries of these expansion waves

with reasonable accuracy.

One prominent visual discrepancy, present on the zero and slight offset generating bank and

economizer simulations, is the diffusion of the secondary jet following impingement. This

diffusion causes the secondary jet to form at a very different angle than in the schlieren images.

Conversely, the secondary jet of “top half of first tube” is in surprising agreement with the

schlieren image. Recall the free jet centerline PIP distribution comparison of figure 49: the jet

impinges in the region between 5 to 6 nozzle diameters. At 5 nozzle diameters downstream, the

Fluent sootblower jet is at the peak of its expansion (PIP is at a local minimum) while the

experimental model is at the peak of its compression (PIP is at a local maximum). However, the

PIP values of the Fluent and experimental model are in better agreement further downstream.

The third offset case is nearly one nozzle diameter above the leading tube centerline and

experiences impingement much closer to 6 nozzle diameters downstream of the jet core.

This explains the weak secondary jet behavior of the first two offset cases, while explaining the

agreement observed in the “top half of first tube” case. For the purposes of the study at hand,

this is the only offset for which the secondary jet behavior will be quantitatively characterized.

57

Economizer and Generating Bank: 5.3

Pressure Distribution on Impinging Surfaces

Figure 54. The pressure distribution on the tubes and fins of the economizer.

Figure 55. The pressure distribution on the tubes of the generating bank.

A 3D simulation of a sootblower jet allows for investigation of the pressure distributions on the

tubes and fins. As a sootblower impinges onto the geometry, a portion of its kinetic energy is

transferred to the impacted surface and the weakened jet is then deflected in three dimensions.

Although sootblowers are installed on most upper floors of a recovery boiler, a common issue is

the inability to effectively reach and clean deposits in transitional regions between two

58

sootblowers. This issue is exacerbated by the focused nature (low spread) of highly supersonic

jets. To visualize the effectiveness of a jet in cleaning a tube length, figures 54 and 55 present

pressure contours of the tubes in the vertical direction (away from the nozzle mid-plane), for

three offsets. The “midway between tubes” offset was omitted as there is very little interaction

between the jet and the tubes. Note that the black lines to the left of the tubes represent one tube

diameter. The flow velocity on all surfaces is zero due to the no-slip wall boundary condition.

Recall that at subsonic conditions the total pressure is equivalent to the PIP.

In the generating bank, the zero and slightly offset jets essentially imprint their radial pressure

profile on the windward face of the leading tube. However, as the jet is offset to the top half of

the leading tube, it can be felt further down the tube length. In the economizer cases, the

presence of the leading fin reduces the average pressure value on the impinging surface but

extends the jet reach in the vertical direction as well as along the tube curvature. The

economizer case, where the nozzle is offset to the top half of the leading tube, is the most

effective in the vertical direction, imposing a reasonable pressure distribution, as far as two

economizer tube diameters down. Another feature of this case (indicated by the red streak) is the

high pressure values along the junction of the fin and tube geometry. This may imply that

deposits are less likely to accumulate at the tube-fin junction.

Effect of Economizer Fins 5.4

The presence of interconnecting fins, as well as different tube diameters, mark the key

differences between the generating bank and economizer tube bank geometries. However, at a

ratio of 1.3 (generating bank to economizer tube diameter), the latter does not significantly alter

the flow field. On the other hand, the leading fin dramatically changes the flow field, as the

supersonic jet is split by the flat plate (the leading fin) and impinges onto an immediately

adjacent cylinder (leading tube). Moreover, the leading fin of the economizer is nearly one

nozzle diameter closer to the nozzle exit than the leading tube of the generating bank.

In this section, PIP distributions on the impinging surfaces are presented and discussed. The

focus is on characterizing the effect of the leading fin on sootblowing performance. For all

subsequent discussions, GB (generating bank) and EC (economizer) will be used to distinguish

between the two sets of data.

59

5.4.1 PIP Distribution: Leading Tube

Figure 56. PIP distribution on the top quadrant of the leading tube EC tube.

60

Figure 57. PIP distributions on the top quadrant of the leading GB tube.

The angular PIP distributions on the top windward quadrant of the leading tube for all GB and

EC offsets are presented in figures 56 and 57. Note that these measurements are from the mid-

plane of the jet core. The location of maximum PIP for each offset is marked by thin dashed

lines. Table 1 summarizes notable observations regarding the above plots.

Table 1. A summary of observations from the PIP distributions on the leading tubes.

Offset GB - Max PIP EC - Max PIP Shock

Zero 842 kPa @ 18 degrees 300 kPa @ 64 degrees GB - Oblique @ 31 degrees

Slight 870 @ 31 degrees 392 kPa @ 41 degrees

GB - Oblique @ 41 degrees

EC - Oblique @ 42 degrees

Top half of first tube 1000 kPa @ 20 degrees 648 kPa @ 18 degrees GB - Oblique @ 87 degrees

61

The following are additional observations pertaining to the plots in figures 56 and 57:

Figure 57, for the GB, indicate that the “zero offset” and “slight offset” cases reach zero

PIP at 65 and 70 degrees respectively. These are points of flow separation. In all other

simulations, separation takes place at angular positions greater than 90 degrees. This can

be confirmed by referring to the visualizations in section 4.3.

The shocks specified in Table 1 correspond to a sudden increase in PIP for an oblique

shock and a sudden drop in PIP for an expansion wave.

The following is a list of remarks regarding the above observations:

As the nozzle is offset away from the initial head on position, the average value of the

angular PIP distribution increases. This occurs because a larger portion of the resultant

jet, split upon impingement, comes in contact with the top quadrant of the leading tube

windward face.

When the offset is “midway between tubes” for both tube geometries, the PIP is two

orders of magnitude smaller than at other offsets, and so sootblowing is inconsequential.

Oblique shock waves exist on the surface of the leading tube for all GB offsets. As the

nozzle is offset away from the “head on” position, the oblique shock tends to shift

towards the leeward side. An oblique shock is the response of a supersonic jet to the

flow turning inwards and into itself. Therefore, these shocks occur where the curvature

of the tube surface is “felt” by the supersonic jet. Oblique shocks are associated with a

sudden increase in pressure and may be considered as provide a small boost to the PIP

distribution.

On the EC tubes, the angular position of the maximum PIP is shifted towards to the

windward face as the nozzle is offset away from the “head on” position. This reflects the

fact that as the nozzle is offset, the deviation of the primary jet by the leading fin

decreases. On the other hand, the angular position of the maximum PIP on the GB

leading tube increases (towards the leeward side) between the “zero” and “slight” offset

cases, but then shifts back towards the windward side with the final offset. Looking back

at figure 52, it may be that the primary jet does not split when it impacts the top half of

62

the first tube, and so the increased jet radius capable exerts its maximum PIP value at a

more windward angular position.

Conversely, an expansion wave occurs in the “slight offset” case on the EC leading tube.

As seen in figure 52, upon impingement the leading fin creates a substantially deviated

yet strong resultant jet on its top surface. This causes the flow to turn away from itself, to

which the supersonic jet responds with an expansion wave. As expansion waves are

associated with a sudden pressure drop, this behavior may be detrimental to sootblowing

performance. Note that this behavior is limited to the small offset range in between the

“head on” and “top half of first tube” cases.

Overall, the GB leading tube experiences higher PIP forces than the EC leading tube,

because the leading fin reduces the maximum PIP exerted on the top quadrant of the

leading tube. The leading fin of the EC tube reduces the maximum PIP by 64%, 55% and

35% for the “zero”, “slight” and “top half of first tube” offset cases respectively. This

difference is expected as the leading fin of the EC splits the primary jet, so that a

weakened and deflected jet impinges onto the leading tube surface. However, based on

the PIP distributions at various offsets, the aforementioned primary jet breakup also

leads to a more uniform PIP distribution on the top windward quadrant of the EC leading

tube. For all offsets onto of the GB leading tube, PIP drops by about 800 kPa (peak-to-

trough) in the angular direction. The corresponding PIP variation on the EC leading tube

is no more than 100 kPa.

On the basis of the above discussion, there exists substantial evidence that the maximum PIP

value exerted on the leading tube in the presence of a leading fin is reduced, but that the

resulting angular PIP distribution tends to be more uniform.

63

5.4.2 PIP Distribution: Leading Fin

Figure 58. PIP distribution on the top surface of the EC leading fin.

Figure 58 presents the PIP distribution on the top surface of an EC leading fin, and shows that

the average PIP value on the leading fin for each offset case is lower than the corresponding

average PIP value on the leading tube surface. The PIP distribution is rather erratic and perhaps

indicative of shock wave formation near the fin surface. However, the PIP distribution for the

“top half of first tube” offset case displays an intriguing behaviour. There exists a sudden

fourfold increase in the PIP value at approximately the midway point of the fin length.

Referring back to the corresponding visualization for this offset, a possible explanation for this

behaviour is as follows. A unique characteristic of this offset case is that at some point in its

expansion, the jet shear layer boundary becomes coincident with the top surface of the leading

fin. As the jet expands radially in the downstream direction, the effective jet radius increases to

a value equivalent to the nozzle offset with respect to the fin top surface. Midway along the fin

64

length, the jet effectively shears the top surface, imprinting a strong PIP distribution. The sizable

and uniform nature of the PIP distribution on both the leading fin and the leading tube for the

“top half of first tube” offset case suggests that it is likely to maximize sootblowing efficiency.

5.4.3 Maximum PIP

Figure 59. Position of maximum PIP for the GB and EC “slight offset” cases.

Brittle breakup is one of two mechanisms by which sootblowers remove deposits. Brittle

breakup is a sudden fracture due to large local internal stresses within a deposit, stressed

induced by a sootblower jet. As a result, maximum PIP is a key parameter for gauging

sootblower effectiveness.

As an example, figure 59 shows the location of maximum PIP exerted on the impinging surface

of the “slight offset” case. For the EC, as the offset changes, the maximum PIP may occur at the

tip of the fin, or the top surface of the leading fin, or the leading tube surface. For the GB cases,

the maximum always occurs on the leading tube.

Table 2 shows the maximum PIP values in the GB and EC geometries, for all offset cases. The

location of maximum PIP is indicated in brackets below the values.

65

Table 2. Maximum PIP values associated with each simulation.

Boiler section Zero Offset Slight Offset Top Half of First Tube

Generating

Bank

842 kPa

(leading tube)

870 kPa

(leading tube)

1000 kPa

(leading tube)

Economizer

780 kPa

(fin tip)

787 kPa

(fin top surface)

648 kPa

(leading tube)

Notice that the maximum PIP values of the “zero” and “slight” EC offsets are comparable to

those of the corresponding GB simulations. The “top half of first tube” offset possesses the

lowest maximum PIP value (occurring on the leading tube).

5.4.4 Free jet vs Midway offset

Simulations of a sootblower jet propagating midway between the EC and GB tubes are

compared with free jet results. At this offset, there is no direct impingement onto a surface, and

so a free jet forms between the tubes. However, tubes adjacent to the supersonic jet alter its

behavior further downstream, leading to a more rapid decay of the centerline PIP. In the case of

the GB, the open gaps between arrays of tubes result in a fraction of the jet flow diverging and

forming a wall jet around the cylinders. This is due to entrainment of surrounding air into the jet

core, as well as to the Coanda effect, the natural tendency of a fluid to be attracted to a nearby

obstacle. Conversely, the fins of the EC form a planar confinement through which the free jet

flows. This confinement prevents the entrainment of surrounding air and reduces the decay of

PIP in the axial direction. Consequently, the jet centerline PIP distribution through the EC

decays at a slower rate than through the GB. This phenomena is documented by Pophali [3] in a

plot of PIP versus axial position in the EC and GB (figure 60). Figure 61 is a similar plot of the

present CFD results. Note that the dashed blue line indicates the position of the leading fin’s tip,

and the dotted red line indicates the front edge of the GB leading tube. Note that due to the

excessive computational cost of modelling the entire length of the experimental domain, the EC

and GB simulations were only 22 nozzle diameters long, which explains the strange jet behavior

near the domain boundary. Nonetheless, the general trend of the CFD results confirms that the

jet in the GB decays quicker.

66

Figure 60 Experimental centerline PIP distribution for a free jet, and jets midway between tubes of EC & GB [3].

Figure 61. CFD centerline PIP distribution for a free jet, and jets midway between EC and GB tubes [3].

67

Secondary Jet Characterization 5.5

Figure 62. A Mach contour plot showing the secondary jets for the "top half of first tube" case of EC (a) and GB (b).

Primary jet impingement onto an obstacle can create a weaker deflected “secondary jet”. At

certain nozzle offsets, the relatively close spacing of the GB and EC tube banks may lead to the

formation of a secondary jet that impinges onto an interior tube, which we refer to as the

“secondary tube”. Figure 62 visualizes impingement of the secondary jet onto a secondary tube

surface for the “top half of first tube” offset cases of the EC and GB.

Due to their reduced velocities and a smaller jet core radius, it is not clear whether secondary

jets actually contribute to effective sootblowing. Using the “top half of first tube” offset as a

case study, the plots in figures 63 and 64 compare the angular PIP distribution of a secondary jet

to that of the corresponding primary jet, for both the GB and EC. Note that the primary jet

results are on the top windward quadrant of the leading tube, whereas the secondary jet impacts

the bottom windward quadrant (theta defined in figure 62) of the secondary tube. The secondary

68

jet angular PIP distribution exhibits a relatively consistent profile, similar to that on the EC

leading tube. The maximum PIP values are 196 kPa (at 28 degrees) and 212 kPa (at 67 degrees)

for the EC and GB secondary tubes respectively. These values reflect a significant reduction in

the maximum PIP of the secondary jet when compared to the primary jet impinging onto the

leading tube. The reduction is 70% for the EC and 79% for the GB.

Figure 63. The angular PIP distributions on the leading and secondary tubes of EC.

69

Figure 64. The angular PIP distributions on the leading and secondary tubes of GB.

Model Limitations 5.6

In this chapter, possible reasons for specific discrepancies between the numerical and

experimental results were presented. The following list summarizes the limitations of the

ANSYS Fluent, which pertain to all simulations in this work:

The schlieren images were captured from a top view and are representative of a 3D flow

in all planes along the tube length. In the post processing of the CFD results, the

contours are from jet mid-plane. This may lead to qualitative discrepancies when

comparing the CFD contours to the schlieren images. Also, the PIP distributions

presented in this chapter are from the jet mid-plane, where we assume them to be at a

maximum.

70

As discussed in section 2.1.2, there is no CFD contour plot that corresponds directly to

the schlieren images. A density gradient contour would have to be resolved onto the

normal component of the knife edge, a direction vector that is unknown. This creates a

challenge in directly comparing Fluent CFD results with the corresponding schlieren

images. However, since visualizations are largely used for a qualitative assessment of

flow behaviour, a contour of the density gradient magnitude (first derivative) should

reproduce a flow field that corresponds to the schlieren visualization. This is why we

also presented Mach contours, that represent the change in density and velocity of the

jet.

To avoid excessive computational costs, the length of the computational domain for the

EC and GB simulations are of approximately half of the distance examined

experimentally. The experimental GB model consists of a 40 tube array of which only 6

are modelled. The geometry of the economizer experiment also consists of 6 tubes with

fins at both ends of each platen. In the CFD EC model, we included only the leading fin

and the first three interior tubes. This may explain discrepancies between the CFD and

experimental results near the distal boundary of the computational domain (around 15

nozzle diameters downstream). A similar limitation holds true for the free jet simulation,

although the effects of the boundary are observed much further from the nozzle exit

(around 35 nozzle diameters downstream).

The dimensions of the experimental geometry are based on measurements of limited

accuracy. This is not consequential for the larger dimensions, such as tube diameters and

the economizer fin length. However, the nozzle dimensions, such as the throat and

nozzle exit diameters, may be less accurate.

In the Pophali experiments, there are energy losses within the converging-diverging

nozzle, and the nozzle supply pressure fluctuates [3]. The CFD model cannot account for

changes in jet behaviour caused by the aforementioned phenomena.

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Chapter 6 Closure

Summary 6.1

An ANSYS Fluent model was created to predict the flow behaviour of a supersonic sootblower

jet and its interaction with complex tube geometries characteristic of a recovery boiler.

Turbulence model corrections, developed over a number of years at the University of Toronto,

were implemented into the Fluent realizable k-ε model as two UDFs. Using the Fluent model,

second-order accurate 3D steady-state simulations were run of a supersonic (Mach 2.5)

underexpanded sootblower jet propagating freely and impinging onto lab-scale economizer and

generating bank geometries. The generating bank and economizer simulations were run at four

nozzle-to-tube centerline offsets ranging from head on impact to jet propagation midway

between tubes.

The solution methodology involved obtaining a preliminary solution, followed by a grid

adaption of regions of high pressure gradients to improve the resolution of shock structures in

the flow. A summary of the modelling challenges, geometry definition and mesh generation

processes, and the Fluent solver controls was presented to help guide future sootblower jet flow

research using ANSYS Fluent. Comparisons of the CFD free jet centerline PIP distribution and

spreading rate to experimental data were used to validate the model. There is a need for further

validation of the current model using more accurate experimental measurements. Nonetheless,

the model was shown to produce an acceptable level of stability and accuracy in capturing

prominent flow features. The PIP distributions exerted by the sootblower jet on leading

impinging surfaces were presented and analyzed. The results and analysis clearly demonstrate

the efficacy of this accessible ANSYS Fluent model for further studies of sootblower jet

interactions with complex tube geometries.

72

Conclusions 6.2

Sootblower jet interaction with complex tube geometries is strongly affected by the large PIP

fluctuations that occur due to the shock structures that are present in an off-design jet. As a

result, it is difficult to draw conclusions on sootblower jet interaction produced by offsetting the

nozzle with respect to the tube centerline.

Mach and density gradient magnitude contours were used to compare the CFD results to the

experimental schlieren visualizations of Pophali [3], and were shown to be in good qualitative

agreement.

PIP distributions on tube surfaces were presented to assess the effectiveness of a sootblower jet

impinging onto tubes with (economizer) and without (generating bank) fins. The results suggest

that the presence of fins in the economizer reduces the maximum PIP generated by the

sootblower jet on the leading tube but creates a more uniform PIP distribution on its surface.

Pressure contours of tube surfaces in the vertical direction show a sharp decline (one order of

magnitude or more) of PIP within approximately one tube diameter from the nozzle mid-plane.

As previously shown in the experimental work of Pophali, a quantitative comparison of a free

jet propagating midway between the economizer and generating bank tubes suggests that the

fins preserve the jet strength downstream of the nozzle. Finally, PIP distributions exerted on an

interior tube by a secondary jet were presented. The results show that secondary jets are often

much weaker, by an order of magnitude or so, than the primary jet.

73

Implications on Sootblowing 6.3

The results presented in this thesis clearly highlight the limitations of sootblowing into the

closely-spaced geometries of the economizer and generating bank. A sootblower jet is fairly

focused and so a majority of the substantial PIP force, that is capable of deposit removal, is

exerted on small areas of the leading tube surfaces. The secondary jet structures that reach the

interior tubes are often weaker and cannot be expected to effectively remove deposits. The

leading edges of the economizer fins tend to alleviate this problem by deflecting the primary jet

to create a slightly weaker yet more uniform interaction. Additionally, the fins enclose the space

in between economizer platens resulting in the preservation of secondary jet structures that

could contribute to deposit erosion.

Recommendations for Future Work 6.4

CFD is a powerful tool for predicting the flow behaviour of sootblowers, as well as many

similar complex supersonic impingement applications. With further research and development

on CFD algorithms, more accurate and stable means of conducting CFD studies will become

available to the wider engineering community. The ANSYS Fluent model presented here must

be improved to better capture the number of shock structures within the sootblower jet core.

More computationally expensive methods such as LES and DNS would provide more accurate

flow predictions.

In recent years, sootblower suppliers have begun to experiment with inclined sootblower

nozzles that direct steam jets at an angle to heat transfer surfaces. The computational model of

the present work provides a means to investigate the feasibility of installing inclined

sootblowers to improve the removal of fouling in the more complex generating bank and

economizer tube geometries.

Finally, a more comprehensive study would be to improve and couple the current CFD model

with a solid mechanics Finite Element Analysis (FEA) that models deposit breakup. This model

would provide a powerful means of investigating the underlying principles that determine

sootblower effectiveness in removing deposits.

74

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APPENDIX A: Turbulence Correction UDF Codes

79