An Experimental Investigation of High Temperature Particle Rebound and Deposition ...

An Experimental Investigation of High Temperature Particle Rebound and Deposition Characteristics Applicable to Gas Turbine Fouling

THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Michael James Lawrence, B.S. Graduate Program in Aeronautical and Astronautical Engineering

The Ohio State University 2013

Master's Examination Committee: Dr. Jeffrey P. Bons, Advisor Dr. Jen-Ping Chen

Copyright by Michael James Lawrence 2013

Abstract A high temperature combustion rig was used to impact bituminous and lignite coal fly ash particles on an impingement plate at conditions similar to those found in the hot section of a gas turbine engine. Individual particles were tracked using particle shadow velocimetry as they either rebounded from or deposited on the plate surface. The effects of particle size, particle impact velocity, impact angle, particle temperature, and plate temperature were explored. Particle diameter ranged from 30-800µm, impact velocity ranged from 5-160 m/s, impact angle ranged from close to 0° to 90°, and temperatures ranged from ambient conditions to 2100°F. Increasing diameter, impact velocity, and plate temperature were all shown to decrease the total coefficient of restitution. The angular coefficient of restitution was shown to decrease with increased impact angle for bituminous ash. The total coefficient of restitution versus both impact angle and particle temperature yielded unexpected trends. For bituminous ash, a peak in coefficient of restitution occurred for all temperature cases at an impingement angle of 40°. Both higher and lower impact angles resulted in a decrease in coefficient of restitution. A peak in coefficient of restitution occurs between 1250-1500°F for both the bituminous and lignite ash, decreasing at both higher and lower temperatures. Possible explanations for these unexpected results are discussed.

ii

Dedication

Dedicated to my parents James Lawrence Betty Lawrence

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Acknowledgments First, I would like to acknowledge my family, especially my parents for their love, encouragement, and sacrifice. Without their support, none of this would have been possible. I would also like to thank Dr. Jeffrey Bons for his guidance and expertise, and the entire team: Steven Whitaker, Brian Casaday, Carey Clum, Carlos Bonilla, and Blair Peterson. Lastly I acknowledge God who is constantly at work in my life.

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Vita June 2011……………………………..B.S. Aeronautical and Astronautical Engineering The Ohio State University March 2012 to present………………...Graduate Research Assistant, Department of Mechanical and Aerospace Engineering, The Ohio State University

Publications "Computational Modeling of High Temperature Deposition in Gas Turbine Engines with Experimental Validation." Michael J. Lawrence, Steven M. Whitaker, Brian P. Casaday, Derek Lageman, and Jeffrey P. Bons. Proc. of 51st AIAA Aerospace Sciences Meeting, Grapevine, Texas, USA. “Deposition with Hot Streaks in an Uncooled Turbine Vane Passage.” Brian P. Casaday, Robin Prenter, Carlos Bonilla, Michael J. Lawrence, Carey Clum, Ali Ameri, Jeffrey P. Bons. ASME Turbo Expo 2013, San Antonio, Texas, USA. “The Effect of Film Cooling on Nozzle Guide Vane Deposition.” Carlos Bonilla, Carey Clum, Michael J. Lawrence, Brian P. Casaday, and Jeffrey P. Bons. ASME Turbo Expo 2013, San Antonio, Texas, USA. Fields of Study Major Field: Aeronautical and Astronautical Engineering Specialization: Experimental Fluid Dynamics and Heat Transfer v

Table of Contents

Abstract ............................................................................................................................... ii Dedication .......................................................................................................................... iii Acknowledgments.............................................................................................................. iv Vita...................................................................................................................................... v Table of Contents ............................................................................................................... vi List of Tables ...................................................................................................................... x List of Figures .................................................................................................................... xi Nomenclature ................................................................................................................... xiv Chapter 1: Introduction ....................................................................................................... 1 Chapter 2: Existing Models ................................................................................................ 7 2.1 Critical Velocity ........................................................................................................ 9 2.2 Critical Viscosity ..................................................................................................... 10 2.3 Elasto-Plastic Model ............................................................................................... 11 2.4 Elastoviscoplasticity Models ................................................................................... 14 2.4.1 Energy Elastoviscoplasticity............................................................................. 15 vi

2.4.2 Integration Elastoviscoplasticity....................................................................... 15 Chapter 3: Experimental Setup ......................................................................................... 18 3.1 Hot CoR Rig ............................................................................................................ 18 3.1.1 Fuel-Air Injection, Ignition, and Combustion .................................................. 19 3.1.2 Flashback Arrestor ............................................................................................ 19 3.1.3 Flame Holders................................................................................................... 20 3.1.4 Combustion Chamber ....................................................................................... 20 3.1.5 Particle Injection and Impingement .................................................................. 21 3.1.6 Instrumentation ................................................................................................. 23 3.1.7 Particle Shadow Velocimetry ........................................................................... 25 3.2 Uncertainty Analysis ............................................................................................... 28 3.2.1 Temperature Uncertainty Analysis ................................................................... 28 3.2.2 Velocity Uncertainty Analysis .......................................................................... 29 3.2.3 Particle Size Uncertainty Analysis ................................................................... 29 Chapter 4: Data Processing ............................................................................................... 31 4.1 Image Processing..................................................................................................... 31 4.1.1 Reading Images and Initial Image Manipulation ............................................. 31 4.1.2 Particle Detection ............................................................................................. 33 4.1.3 Three Particle Trajectory Formation ................................................................ 34 vii

4.1.4 Particle Rebound Detection .............................................................................. 35 4.1.5 Detecting Particle Deposit Events .................................................................... 36 4.1.6 Particle Sizing ................................................................................................... 37 Chapter 5: Results and Discussion .................................................................................... 39 5.1 Experimental Overview........................................................................................... 39 5.1.1 Ash Composition .............................................................................................. 39 5.1.2 Thermal Expansion Testing .............................................................................. 41 5.1.3 Bituminous Ash Two Angle Data Set .............................................................. 42 5.1.4 Bituminous Ash Three Angle Data Set ............................................................ 44 5.1.5 Lignite Ash Data Set......................................................................................... 46 5.1.6 Bituminous Ash with Backside Heating ........................................................... 47 5.2 Experimental Rebound Results ............................................................................... 49 5.2.1 Impact Velocity, Impact Angle, and Diameter Distributions ........................... 49 5.2.2 Effect of Particle Diameter on Total Coefficient of Restitution ....................... 54 5.2.3 Effect of Temperature on the Coefficient of Restitution .................................. 55 5.2.4 Effect of Particle Impact Velocity on Total Coefficient of Restitution ............ 59 5.2.5 Effects of Impact Angle on Total Coefficient of Restitution ........................... 61 5.2.5 Effect of Impact Angle on Angular Coefficient of Restitution ........................ 65 5.2.6 Effect of Backside Heating ............................................................................... 67 viii

5.3 Experimental Deposit Results ................................................................................. 69 Chapter 6: Conclusion....................................................................................................... 76 References ......................................................................................................................... 78

ix

List of Tables

Table 1: Example material properties ............................................................................... 16 Table 2: Thermocouple uncertainty values ....................................................................... 29 Table 3: Major chemical components of tested ash species ............................................. 40 Table 4: Bituminous ash two angle test matrix, taken with Dimax© color camera ......... 44 Table 5: Bituminous ash three angle test matrix, taken with v311 monochrome camera 45 Table 6: Lignite ash 60° impingement angle test matrix, taken with v311 monochrome camera ............................................................................................................................... 47 Table 7: Bituminous ash with backside heating test matrix, taken with v311 monochrome camera ............................................................................................................................... 48

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List of Figures Figure 1: Diagram of a particle impacting a flat surface .................................................... 8 Figure 2: Normal coefficient of restitution plotted against the normal impact velocity for the elasto-plastic model from [17]. Compared to experimental data from [20]. .............. 14 Figure 3: Coefficient of restitution versus particle impact velocity trends plotted for various particle impact models. Note that the dashed line indicates increased temperature. ........................................................................................................................................... 17 Figure 4: Hot CoR Rig Schematic .................................................................................... 18 Figure 5: Normalized particle temperature versus the streamwise distance (in meters) from the particle injection point. ....................................................................................... 23 Figure 6: Hot CoR Rig Instrumentation............................................................................ 25 Figure 7: PSV Schematic .................................................................................................. 26 Figure 8: Image acquired with the PCO Dimax© high speed color camera, showing grid pattern. .............................................................................................................................. 27 Figure 9: Image acquired with the Vision Research Phantom® v311 high speed camera. ........................................................................................................................................... 28 Figure 10: Sample images from the initial processing procedure. (a) Raw image. (b) Averaged or background image. (c) Background subtracted and scaled image. (d) Contrast enhanced image. ................................................................................................. 32 xi

Figure 11: Particles detected using the threshold method ................................................ 34 Figure 12: Thermal expansion test results ........................................................................ 42 Figure 13: Impact velocity histogram for all four data sets .............................................. 50 Figure 14: Impact angle histogram for all four data sets .................................................. 52 Figure 15: Particle effective diameter histogram for all four data sets ............................. 53 Figure 16: Total coefficient of restitution vs. particle diameter with lines representing data at different particle temperatures. Bituminous ash three angle data set. ................... 55 Figure 17: Total coefficient of restitution vs. particle temperature. ................................. 59 Figure 18: Total coefficient of restitution vs. particle impact velocity with lines representing data at different particle temperatures. Bituminous ash three angle data set and data from Whitaker et al. [21] .................................................................................... 61 Figure 19: Total coefficient of restitution versus particle impact angle for the bituminous ash three angle data set. Additional data from Reagle et al. [20]. .................................... 64 Figure 20: Total coefficient of restitution versus temperature with lines of averaged coefficient of restitution with angle for the bituminous ash three angle data set ............. 65 Figure 21: Angular coefficient of restitution versus impact angle for the bituminous ash three angle data set. Comparison data from Whitaker et al. [21]. .................................... 66 Figure 22: Total coefficient of restitution versus impact velocity for bituminous ash with backside heating. ............................................................................................................... 69 Figure 23: Histogram total number of detected particles, including both deposits and rebounds, versus particle normal kinetic energy............................................................... 71

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Figure 24: Probability of sticking versus temperature applying the critical viscosity model ........................................................................................................................................... 74 Figure 25: Sticking efficiency versus particle normal impact kinetic energy .................. 75

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Nomenclature A

=

constant used to define critical viscosity model

B

=

constant used to define critical viscosity model

=

drag coefficient

D

=

particle diameter

E

=

modulus of elasticity

e

=

coefficient of restitution

KE

=

kinetic energy

=

constant used to determine particle drag coefficient

=

constant used to determine particle drag coefficient

=

constant used to determine particle drag coefficient

k

=

apparent plastic flow consistency

m

=

particle mass

N

=

number of instances

Nu

=

Nusselt number

n

=

apparent plastic flow index

Pr

=

Prandtl number

PS

=

probability of particle sticking

Re

=

Reynolds number xiv

r

=

particle radius

SE

=

sticking efficiency

T

=

temperature

=

critical velocity

=

particle velocity

=

work of adhesion

=

particle impact/rebound angle

=

surface energy adhesion parameter

=

ratio of initial tangential velocity to initial normal velocity

=

particle Poission’s ratio

=

surface Poission’s ratio

=

normalized particle temperature

=

viscosity of particle

=

coefficient of friction

=

particle density

=

flow stress

=

yield stress

=

uniaxal yield stress

η



̂

Subscripts 1

=

pre-impact velocity

2

=

rebound velocity xv

crit

=

critical

n

=

normal

p

=

particle

r

=

rebound

s

=

surface/sticking

t

=

tangential

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Chapter 1: Introduction Rapidly expanding aircraft fleets, as well as an increased interest in alternative fuels such as coal-derived synthesis gas, have led to an increased exposure of gas turbines to ash and other particulates. These particles, which can be present in the air due to manmade pollution or volcanic ash, or present within the fuel itself, can deposit on the internal walls of the engine and degrade the system over time. Increased surface roughness resulting from such deposition augments the heat transfer from the high temperature fluid to the surfaces, further increasing part degradation. Removal of the deposits is expensive and time consuming. Understanding how the particulate adheres to the walls and under what conditions is crucial to reducing the amount of deposition. Reducing deposition will reduce the time spent cleaning the engine and prolong the life of the hardware. There have been many studies looking into the causes and effects of deposition on turbine hardware. Small-scale deposition has been shown to increase the surface roughness. Bons [1] concluded that increases in surface roughness can decrease turbine performance. Abuaf et al. [2] supported the finding that losses are associated with increased roughness and found that the heat transfer was increased with additional roughness. Large-scale deposition was found to be even more damaging to turbine hardware. Kim et al. [3] conducted experiments exploring the effects of volcanic ash on 1

turbine hardware. They found that deposition can clog film cooling holes and can lead to failure of the turbine vanes. Dunn et al. [4] also studied the effects of volcanic ash and found that damage due to deposition was related to the turbine inlet temperature, concentration of particulate and the material properties of the volcanic ash. Ash preferentially deposited in the hottest regions of the turbine, determined by the location of the upstream combustors and associated regions of hot gas paths. Dunn et al. confirmed that deposition can clog film cooling holes and that deposition is a major issue for modern engines with high combustor temperatures. Dunn et al. also noted that aircraft engines that ingest particle laden flow have increased difficulty in restarting and that engines exposed to sufficient levels of particulate can be damaged beyond repair. Sundaram and Thole [5] studied the effects of deposition on film cooling and found that film cooling effectiveness degrades as deposition forms near and in film cooling holes. Lewis et al. [6] found that the location of deposition around film cooling holes can affect the heat transfer. Deposition that forms between and downstream of film cooling holes causes the high temperature free stream to flow into the deposition valleys and increases heat transfer into the surface. Lawson et al. [7] conducted experiments in a low speed wind tunnel using low melt wax to investigate the deposition mechanism and formation of deposits on a flat plate. Jensen et al. [8] and Crosby et al. [9] constructed the Turbine Accelerated Deposition Facility (TADF) and observed the growth of deposits on one inch coupons. This facility was operated at actual engine temperatures and used coal fly ash for particulate. Smith et al. [10] constructed the Turbine Reacting Flow Rig (TuRFR) and tested actual turbine hardware at engine temperatures and velocities. Deposition from 2

coal fly ash was found to form on the pressure surface and leading edge of the turbine vanes. The negative effects of deposition have demanded that the mechanisms of deposition formation be better understood, yet the difficulties in conducting experiments at engine operating conditions have supported the need for the modeling of deposition. However, modeling of turbine deposition presents its own unique challenges Several efforts have been made to model particle deposition, each with unique strengths and weaknesses. The critical velocity model, developed by Johnson et al. [11], Dahneke [12], and Brach and Dunn [13], defined a critical velocity based on the adhesion forces. Below this velocity, the particle adhered, while above this velocity, the particle rebounded. Although useful for low speed and low temperature flows, the critical velocity model does not account for energy loss due to plastic deformation. Tafti and Sheedharan [14] developed a particle deposition model based on a particle viscosity, which is a function of temperature. However, the critical viscosity model has no dependence on several important parameters, such as particle size and impact velocity. In an effort to create a model that accounts for most of the important parameters for particle deposition, elastoviscoplasticity (EVP) models were created. Fu et al. [15] created an EVP model for the deposition of wet granules, and Adams et al. [16] created another EVP model for soft agglomerates. While promising, the EVP models have not yet been applied to the high temperature environment of a gas turbine engine. Perhaps the most applicable high temperature model is the elasto-plastic adhesion model developed by Singh and Tafti [17]. In this model, the energy loss from plastic deformation and adhesion forces are used to calculate a normal and tangential coefficient of restitution 3

(CoR). Rebounds occur for a coefficient of restitution greater than zero, while a zero or imaginary coefficient of restitution represents a deposit. This is the only known coefficient of restitution model validated by high temperature data, specifically sand particles impacting a stainless steel plate. Validation of a particle deposition model would ideally be performed on a particle by particle basis: i.e. data would be available for individual particle rebound and deposit events at a range of temperatures, particle impact velocities, particle impact angles, and particle sizes. The applicable literature is sparse. In the early 1960’s, Mok and Duffy [18] investigated the effect of temperature and velocity on the coefficient of restitution of a steel ball impacting an aluminum and lead surface. The authors showed trends of decreased coefficient of restitution with increased velocity and increased temperature. However, the steel spheres used were ½” or 1” diameter, much larger than particles in a gas turbine environment. About 20 years later, Brenner et al. [19] impacted iron spheres between 0.05-0.15 cm in diameter onto an iron plate at elevated temperatures (up to 1470°F). They showed that below a critical velocity, the iron balls welded to the plate, while above this critical velocity, the welds were broken and the balls rebounded. The authors noted that this critical velocity was not an absolute value for all observed impacts; instead, the events were probabilistic and the critical velocity could vary from particle to particle, even under the same impact conditions. Although informative, the particles size and composition used in this study are not typical of a gas turbine environment, and the temperatures are somewhat low.

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The most relevant high temperature coefficient of restitution study was performed by Reagle et al. [20] in 2013. Sand particles (commonly referred to as Arizona road dust) with a diameter between 20-40 µm were impacted on a stainless steel plate at temperatures of 500°F, 1100°F, and 1470°F. In this study, the authors used a particle image velocimetry (PIV) system to acquire individual particle trajectories from image pairs, where the images are separated by a small time gap. While individual pre- and post-impact particle trajectories could be determined, the low repetition rate of the system (~7 Hz) prevented the authors from following an individual particle through the impact and rebound phases, as most particle moved out of the imaging window between image pairs. To determine individual coefficients of restitution, an average impact velocity and angle was calculated. Then, individual rebound trajectories were compared to this average impact trajectory to create individual coefficients of restitution. The extent to which this method is valid is unknown, though it may be reasonably accurate since the rebound process is probabilistic in nature. Another limitation on the experiments presented by Reagle et al. was a constant mass flow at all of the temperature conditions, which causes a significant change in flow velocity and therefore particle velocity. With these caveats in mind, the authors found that the total coefficient of restitution did decrease with temperature, but this was likely due more to the increased velocity than the increased temperature since the tests were performed at temperatures below what the authors call the “critical temperature” regime where temperature begins to dominate the decrease in coefficient of restitution. The authors also found that the total and normal coefficient of restitution decreased with increasing impact angle, the tangential 5

coefficient of restitution increased non-monotonically with increased impact angle, and that plastic deformation was the primary energy loss mechanism. Although this study acquired a great deal of useful data, it would have ideally included higher temperatures, as well as the ability to track individual particles throughout the entire impact and rebound process. The goal of the present study is to acquire coefficient of restitution and adhesion data for individual ash particles at gas turbine engine conditions and use this data to determine which, if any, of the above models best describes the deposition process in a gas turbine engine. With a more realistic model, better predictions of ash deposition in gas turbine engines can be made.

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Chapter 2: Existing Models When a particle collides with a surface, several interactions combine to result in a change in the particle’s energy. Forces such as adhesion and friction, along with deformation of the particle and impact surface, culminate in a net loss of kinetic energy from the particle during impact. This can result in either the particle rebounding from the surface at a lower velocity, or the particle adhering to the surface. In the case of a rebound, the particle properties before and after impact are characterized by the coefficient of restitution. There are numerous definitions for the coefficient of restitution of impacting particles, though there is no consensus on which is most appropriate when considering many factors that affect impact dynamics. In this study, the total coefficient of restitution (ratio of outgoing to incoming velocity), normal coefficient of restitution (ratio of outgoing to incoming normal velocity) and the angular coefficient of restitution (ratio of rebound to impact angle) will be examined. It is important to note that particle impact dynamics are governed by the conditions at the point of impact. Figure 1 shows a diagram of a particle impacting a surface. Often when examining these impacts, as in the models in the following sections, it is assumed that particles are spherical in nature and rotation is often neglected. In this situation, the velocities and angles described above refer only to the linear motion of the 7

particle. If, however, a particle is rotating prior to impact, the velocity at the point of impact also has a contribution from the rotational motion. In addition, non-spherical particles not only have unique impact angles, but also a propensity to either increase or decrease rotational rates upon impact depending on their orientation. The added complexity of rotation and non-spherical particles has been neglected in both the modeling and experimental portion of this work, as it is currently impractical to include all of these effects.

Figure 1: Diagram of a particle impacting a flat surface

When examining the coefficient of restitution or deposition parameters of particle impacts, it is important to understand the mechanisms by which the particle loses kinetic energy. The initial speed, size, material properties, angle, and temperature of the particle can all affect the amount of energy loss, and therefore the impact response. The models

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detailed in the following sections use some or all of these parameters in an effort to describe the impact response.

2.1 Critical Velocity The critical velocity model was developed by several authors, including Johnson et al. [11], Dahneke [12], and Brach and Dunn [13]. The coefficient of restitution, e, defined as the ratio of the rebound velocity after impact to the initial velocity before impact, shows an exponential decrease as the particle initial velocity decreases. Only elastic deformation is considered in the critical velocity model. As such, the main mechanisms to decrease the coefficient of restitution below unity are adhesion forces. If the incoming particle has enough kinetic energy to overcome the adhesion forces, it will rebound off of the surface. A particle with insufficient kinetic energy will adhere to the surface. The velocity corresponding to the transition between rebounding and adhering is termed the critical velocity. An initial particle velocity below the critical velocity will adhere, and an initial particle velocity above the critical velocity will rebound. The normal critical velocity is given by: (

where

is the normal critical velocity,

)

(1)

is the work of adhesion, η is the ratio of

initial tangential velocity to initial normal velocity, m is the mass of the particle, and the coefficient of restitution based on the normal incoming and outgoing velocities. The work of adhesion is given as:

9

is

[ where

is the particle density,

surface, radius, and

and

( and

)]

(2)

are the Poission’s ratios for the particle and

are the moduli of elasticity of the particle and surface, r is the particle

is the surface energy adhesion parameter. The modulus of elasticity is

dependent on temperature and particle composition; therefore, an empirical or theoretical expression for the modulus of elasticity as a function of temperature must be found for each particle composition being studied. While this method works reasonably well for low speed, low velocity particle impacts, it does not account for the plastic deformation that occurs at higher temperatures and velocities, such as those experienced in a gas turbine engine. To account for these, the critical viscosity model was created.

2.2 Critical Viscosity Tafti and Sheedharan [14] developed a deposition model based on the particle viscosity. The particle viscosity changes with temperature and the relationship can be predicted based on the coal ash properties. They based their model on the probability of the particle sticking or depositing. The ash softening temperature is the critical sticking temperature, TS. Particles above this temperature are assumed to have a sticking probability of one. Particles with temperature much less than the critical sticking temperature will have a sticking probability of zero. For particles with temperatures inbetween, the probability function is found using: 10

( where

)

(3)

is the particle temperature, μcrit is the viscosity of the particle at the critical

sticking temperature and μTp is the viscosity of the particle at the current particle temperature. Senior and Srinivasachar [17] developed a method to determine the coal ash particle viscosity based on the coal ash chemical composition. N’Dala et al. [23] have shown that the temperature dependence of viscosity of silicate and aluminosilicate melts can be described by: (

)

(4)

where A and B are constants which depend on the chemical composition. Senior and Srinivasachar conducted experimental tests to develop a curve fit for determining A and B. The model is described in further detail in [17]. The critical viscosity model defines the sticking probability based on the viscosity of the ash, but is limited in that it is not dependent on other parameters, such as particle impact velocity, particle mass, or angle of impact. Ideally, a model capable of taking all of these parameters into account would be used. It should also be noted that the critical viscosity model makes no prediction of the coefficient of restitution for particles that do not deposit, making it unique out of the models presented in this study.

2.3 Elasto-Plastic Model The elasto-plastic model, derived by Singh and Tafti [17] was created specifically for high temperature environments. It was found to have moderate agreement with the 11

data obtained by Reagle et al. [20] where sand particles were impacted on a stainless steel plate at temperatures up to 1472°F. In the elasto-plastic model, four stages of impact are considered: 1. Elastic compression stage- Begins when the particle impacts the plate and ends when plastic deformation begins to occur. Deformation is purely elastic in this stage. 2. Elasto-plastic compression stage- Starts when plastic deformation begins and ends when the center of the particle comes to an instantaneous stop. The contact area is at a maximum at this point. 3. Restitution stage- Begins when the center of the particle comes to an instantaneous stop and ends when the particle leaves the surface of the plate. During this stage, the particle recovers some of its kinetic energy. 4. Adhesion breakup stage- Occurs simultaneously with the restitution stage. During this stage, the particle attempts to break the adhesion forces holding it to the surface. It is assumed that energy lost from adhesion is independent of the energy lost from plastic deformation. By analyzing each of these four stages, the authors derive expressions for both a normal and tangential coefficient of restitution (

and

respectively):

(

)

(

)(

12

⁄

(5)

)

⁄

(6)

where

is the coefficient of friction,

restitution after the restitution stage, and

is the impact angle,

is the coefficient of

is the work of adhesion given in Eq. (2). The

full derivation, along with a method to determine

, is provided in [17].

Figure 2 is a plot from Ref. [17], showing the normal coefficient of restitution versus the normal impact velocity. The model shows a sharp decrease in coefficient of restitution at very low velocities, and a gentler drop off at higher velocities. The model shows moderate agreement with the experimental results from Reagle et al. [20].

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Figure 2: Normal coefficient of restitution plotted against the normal impact velocity for the elasto-plastic model from [17]. Compared to experimental data from [20].

2.4 Elastoviscoplasticity Models In an effort to create a more physical rebound and deposition model, the elastoviscoplasticity models were derived. As the name suggests, these models account for the elastic, viscous, and plastic effects during particle impact and rebound. This paper will consider two of these models, one derived by Fu et al. [15], which will be referred to

14

as the Energy Elastoviscoplasticity (EEVP) model, and the other by Adams et al. [16], which will be referred to as the Integration Elastoviscoplasticity (IEVP) model. 2.4.1 Energy Elastoviscoplasticity The EEVP model develops relations for the elastic energy of deformation, the plastic energy of the deformation and the work of adhesion. These relations are then substituted into the definition of the coefficient of restitution. The full derivation, by Fu et al. can be found in [15]. The final expression for the coefficient of restitution is given as: √

√ where

√

(7)

is the yield stress, E is the effective elasticity, m is the particle mass, and

is

the work of adhesion, which is found using Eq. (2). The effective elasticity is given as: (

)

(8)

2.4.2 Integration Elastoviscoplasticity The IEVP model essentially equates the kinetic energy to the integration of the pressure over the range of displacement. The full derivation by Adams et al. can be found in [16]. The final expression for the coefficient of restitution is given as: √ where

̂

(

̂

)

̂

(9) ( ̂ )

is the uniaxal yield stress, and ̂ is the flow stress, which, for a Herschel-

Bulkley material, can be found with the following expression:

15

̂

( )

(10)

where k is the apparent plastic flow consistency, n is the apparent plastic flow index, and D is the particle diameter. The work of adhesion can again be found using Eq. (2). This relation is substituted into Eq. (9) in order to arrive at the final equation which can be used knowing the physical properties of the particle and the impacting velocity. Using the example material properties listed in Table 1, the behavior of the critical velocity, EEVP, and IEVP models are plotted in Figure 3. (Note: The critical viscosity model prediction is not shown in Figure 3 since it is not dependent on particle impact velocity and does not predict the coefficient of restitution.)

Table 1: Example material properties ⁄

The two EVP models show overall similar trends, where the particle rebounds at low velocity and deposits at high velocity, but the transitional velocity, and the slope of the coefficient of restitution, vary significantly between the models. The EVP trend is the reverse of the critical velocity trend. This discrepancy arises due to the differing assumptions made in each of the models; both of the EVP models assume the particle always yields, while the critical velocity model assumes the particle never yields. The dashed lines in Figure 3 represent an increase in temperature, assuming a 90% reduction 16

in both the yield stress and modulus of elasticity. Although it is generally true that the modulus of elasticity and yield stress decrease most materials with increased temperature, there is no data on these properties for ash particulate in the temperature range of this study. Throughout this study, these models, along with the critical viscosity model and elasto-plastic model, will be examined to determine if any of them are capable of describing the deposition and/or rebound trends observed in the high temperature coefficient of restitution data.

Figure 3: Coefficient of restitution versus particle impact velocity trends plotted for various particle impact models. Note that the dashed line indicates increased temperature.

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Chapter 3: Experimental Setup

3.1 Hot CoR Rig To simulate engine temperatures and conditions, a high temperature combustion rig, dubbed the Hot CoR Rig, was designed and constructed. A schematic of the Hot CoR Rig is shown in Figure 4. The operation of the rig is detailed in the following sections.

Figure 4: Hot CoR Rig Schematic

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3.1.1 Fuel-Air Injection, Ignition, and Combustion High pressure air from a shop air system is fed to plumbing made of galvanized steel pipe. The air is split into two streams—one stream is used as dilution air and is fed directly into the combustion chamber, while the other stream is mixed with propane (stored in a 20 pound pressurized propane cylinder) and fed through a flashback arrestor, followed by eight swirling flame holders. The fuel-air mixture exiting one of the flame holders is passed over a diesel engine glow plug, which is connected to a 12 volt car battery. The glow plug is pre-heated so that the fuel-air mixture ignites when it passes over the glow plug. The remaining flame holders quickly light from the first flame holder, as they are in close proximity to one another. After ignition, the glow plug is turned off. During this process, the pressure relief valve is open to prevent a buildup of pressure during the ignition of the fuel-air mixture. The propane flow is controlled with a 0-40 psig pressure regulator, while each of the air streams are separately controlled with ball valves. These controls allow for precise adjustments to the fuel-air ratio, overall combustion efficiency, flow temperature, and flow rate. A viewport with a high temperature quartz glass window was installed to allow the operator to actively observe and adjust the flame structure and combustion efficiency. 3.1.2 Flashback Arrestor A flashback arrestor was designed and built to prevent a potentially dangerous flashback event. The device consists of a galvanized steel pipe tee filled with 4.5mm spherical copper coated steel BBs. The BBs are held in place with a stainless steel mesh

19

at the three openings in the tee. This design provides a thermal and flow velocity barrier preventing a potential flashback from propagating upstream into the air or propane lines. 3.1.3 Flame Holders Several iterations of flame holder designs were tested before choosing the final design. For each design, several criteria were considered: 1) the ability to easily and safely ignite, 2) stable combustion over a wide range of operating conditions, 3) the ability to produce flow exit temperatures of at least 2000°F, and 4) the ability to survive at these high temperatures. Designs considered included a sintered stainless-steel pipe fitting commonly used as a muffler, pipe fittings with V-gutters and other obstructions installed, perforated metal tubing, and a swirling design with a section of an auger bit inserted in a pipe nipple. While all of the designs worked well in the open atmosphere, all except the swirling flame holders failed to meet all of the above criteria when installed in the combustion chamber. The sintered metal flame holders provided stable combustion, but melted when temperatures above 1800°F temperatures were reached. The V-gutter designs could not hold a stable flame at the required flow conditions, and the perforated metal tubing could not consistently reach the required 2000°F exit temperatures. The swirling flame holders met all of the test criteria, and eight were installed in the combustion chamber. 3.1.4 Combustion Chamber A hydraulic reservoir was repurposed into the shell of the combustion chamber. The walls of the reservoir are made of 11 gauge steel, and the removable top plate is ¼” 20

steel. A two inch thick layer of small river rocks, typically used in landscaping, was spread on the bottom of the combustion chamber to disperse the dilution air. Extra high temperature rigid ceramic insulation, with a maximum temperature of 2300°F, was installed on the side walls and lid of the reservoir, to protect the steel from the extreme temperatures, and to retain more heat from the combustion process. Holes were drilled and tapped for the air and propane plumbing, instrumentation, the viewport, and glow plug ignition system. An eighth-inch thick ultra-high temperature millboard gasket was used to seal the top plate of the reservoir. Four turnbuckles were used to clamp the top plate in place. The combustion chamber is capable of producing sustained exit temperatures above 2000°F. 3.1.5 Particle Injection and Impingement The hot combustion products are fed through a 60 cm long, ¾” NPT stainless steel pipe lined with a high temperature non-porous high-alumina ceramic (1/2” inner diameter) tube, threaded into the side of the combustion chamber. This equilibration tube is wrapped in a flexible high temperature ceramic insulation to reduce the heat loss. An auger bit driven by a stepper motor pulls particulate from a hopper and drops it into a vertical stainless steel pipe, where gravity feeds the particulate into the hot flow. This setup is shown schematically in Figure 4. The feed rate can be controlled by varying the rotation rate of the motor. The particulate is allowed to reach thermal equilibrium before impacting an eighth-inch thick Inconel® 625 plate. Three impingement plates were made at three different impingement angles: 30°, 60°, and 90°. Note that it is important for the particles to reach thermal equilibrium with the flow before impacting the plate, as the 21

particles are assumed to have the same temperature as the flow. To ensure the equilibration tube was long enough to allow the particles to reach thermal equilibrium, a simple equilibrium analysis was performed assuming a stationary particle is injected into ) of the particles, which were

a 50 m/s, 2000°F hot gas stream. The drag coefficients (

assumed to be spherical, were calculated using the following Reynolds number correlation from Morsi and Alexander [30]: (11) where

,

, and

numbers, and

are constants provided in Ref. [30] for a variety of Reynolds

is the Reynolds number. The Nusselt number (Nu) was calculated using

the following correlation from Ranz and Marshall [31]: ⁄

where

⁄

(12)

is the Prandtl number. A normalized particle temperature, , is plotted against

the streamwise distance from the injection point in Figure 5. This normalized particle temperature is defined as: (13) where

is the flow temperature,

is the particle temperature, and

is the initial

particle temperature at the injection point. Even particles of up to 1000 µm in diameter reach thermal equilibrium within 30 cm of the injection point, half of the available 60 cm.

22

Figure 5: Normalized particle temperature versus the streamwise distance (in meters) from the particle injection point.

3.1.6 Instrumentation Several thermocouples, a pressure transducer, and a rotameter were used to measure and monitor the conditions present in the Hot CoR Rig. A schematic showing the locations of the instrumentation is provided in Figure 6. In total, five K-type sheathed thermocouples, were used to measure the stagnation temperature in the combustion chamber, the combustion chamber wall temperature (between the rigid ceramic insulation and the steel wall), the flow temperature at the injection point, the flow temperature at the 23

exit of the equilibration tube, and the flow temperature at the surface of the impingement plate, in the center of the jet. The temperature uncertainty of the thermocouples is the larger value between ±2.0°F or ±0.4%. A King Instrument Company 2-20 standard cubic feet per minute (SCFM) (accuracy ±0.4 SCFM) rotameter is used to measure the total volume flow rate of air through the combustion chamber. This is corrected to a mass flow with the line pressure, measured upstream of the rotameter using a 0-50 psig pressure transducer, and knowing the nominal temperature of the supplied shop air. A LabVIEW Virtual Instrument (VI) program was created to display and record all of the measurements obtained with the above described instrumentation.

24

Figure 6: Hot CoR Rig Instrumentation

3.1.7 Particle Shadow Velocimetry The technique known as Particle Shadow Velocimetry (PSV) was used to track individual particles exiting the equilibration tube and impacting the impingement plate. PSV is a powerful but relatively simple technique where particles are backlit with a bright light source, creating shadows which are recorded with a high speed camera. A schematic of this process is shown in Figure 7. Using PSV, the pre- and post-impact particle velocity, particle size, impact angle, and rebound angle can be determined for each particle impact.

25

Figure 7: PSV Schematic

Initial tests in the Hot CoR Rig were performed with a PCO Dimax© high speed CMOS color camera. While this camera was capable of imaging the particle shadows, a grid pattern, visible in Figure 8, complicated particle detection and sizing. The grid pattern was caused by the different sensitivity of each of the four color pixels (red, blue, and two green) to the supplied light. The original blue LED light source was replaced with a white LED, but the problem persisted.

26

Impingement Plate

Particle Shadows

Plate Surface

Figure 8: Image acquired with the PCO Dimax© high speed color camera, showing grid pattern.

After taking initial data with the PCO Dimax© color camera, a monochrome Vision Research Phantom® v311 high speed CMOS camera was acquired for testing. No grid pattern was visible with the v311 since it is a monochrome camera. In addition, the v311 has a slightly higher throughput, allowing for a higher frame rate at a given camera resolution. The bulk of the data presented in this paper was taken with the v311. For all tests with both cameras, a Nikkor 200mm f/4 macro lens was used to image the particles.

27

Figure 9: Image acquired with the Vision Research Phantom® v311 high speed camera.

3.2 Uncertainty Analysis 3.2.1 Temperature Uncertainty Analysis The uncertainty in particle temperature is based on the uncertainty in the thermocouple measurement, assuming that the thermocouple is accurately measuring the flow temperature and that the particles reach thermal equilibrium with the flow. From Figure 5, the particles will reach thermal equilibrium with the flow before impacting the plate. The thermocouple should accurately read the flow temperature since it is immersed in the flow and is mounted in the equilibration tube, preventing significant radiation

28

effects. The K-type thermocouple uncertainty is the greater value between ±2.0°F or ±0.4%. Table 2 provides a list of uncertainty values for temperatures typical of this study.

Table 2: Thermocouple uncertainty values Uncertainty Nominal Temperature (°F) 80 1000 1250 1500 1750 2000 2100

°F 2 4 5 6 7 8 9

% 2.5 0.4 0.4 0.4 0.4 0.4 0.4

3.2.2 Velocity Uncertainty Analysis The uncertainty in the velocity measurements, and the coefficient of restitution measurements based on the velocity measurements, is caused by the uncertainty in the centroid location. It is difficult to quantify an exact uncertainty in the centroid location, but ±2 pixels is a reasonable estimate. From this, frame rate dependent velocity uncertainty can be easily calculated. For frame rates of 40,550 and 23,280 frames per second, values typical in this study, the velocity uncertainty is 2.8 and 1.6 m/s respectively. The contribution to the velocity uncertainty from the frame rate is negligible. 3.2.3 Particle Size Uncertainty Analysis The most difficult uncertainty value to quantify is the uncertainty of the particle size, determined using the particle shadow velocimetry system. One difficulty arises from 29

the fact that the particles are not perfectly spherical, and may be rotating between images, causing their apparent size to change between frames. Another issue is that a typical particle is only represented by a few pixels, so that an uncertainty of only a single pixel could potentially lead to a large error. Finally, there is no feasible technique to measure the accuracy of the system, due to the inherent difficulties in dealing with small particles. With these limitations in mind, a conservative estimate of the uncertainty in the particle size is one pixel, or approximately 30 µm. For most instances however, the error is likely less than this since multiple particle instances are sized in each trajectory.

30

Chapter 4: Data Processing

4.1 Image Processing A MATLAB® code was written to process the high speed particle shadow velocimetry images for particle rebounds and deposits. The following sections explain the operation of the code. 4.1.1 Reading Images and Initial Image Manipulation After declaring the various constants and pre-allocating variables, the code begins reading images into memory in 40 image batches. The background, including the impingement plate, is removed from each image by subtracting the average of the 40 image batch. The pixel intensity values of the resulting images are scaled from zero to one. To reduce the effects of density gradients of the air in the images (the dark and light spots in the background of an image, caused by a shadowgraph-like effect), pixels intensities within 2.5 standard deviations of the mean pixel intensity value are scaled from 0.9-1.0. The remaining pixels are scaled from 0-0.9, effectively increasing the contrast between the background and the particle shadows. This processed image set, referred to as the Image 2 set, is saved to memory for use in particle detection and trajectory creation. A separate contrast enhanced image set, referred to as the Image 3 set and used for particle sizing, is also saved. In this image set, the scaled intensity values are 31

cubed and a median filter is applied. Figure 10 shows the results of this initial processing for a typical image.

(a)

(b)

(c)

(d)

Figure 10: Sample images from the initial processing procedure. (a) Raw image. (b) Averaged or background image. (c) Background subtracted and scaled image. (d) Contrast enhanced image.

32

4.1.2 Particle Detection After removing the image background and performing initial processing on the images, particles are detected using a pixel intensity technique. First, all pixels downstream of the surface of the impingement plate are set to the maximum intensity value (one in the images scaled from zero to one) to ensure that none of the pixels in the plate shadow are counted as particles. Then the minimum pixel intensity value in the image is found and checked against the threshold value, defined at the beginning of the code, and adjusted for each image set. If this pixel intensity falls below the threshold, then the pixel is considered a particle and its position is saved. To prevent that particle from being counted multiple times, a 5x5 pixel square around the dark pixel is set to the maximum intensity value. The process of finding the minimum pixel intensity and comparing it to the threshold continues until threshold value is met, meaning that all remaining pixels in the image are above the threshold. The particles detected in a representative image are highlighted by red circles in Figure 11. This detection scheme is applied to all images in the image batch so that a matrix of pixel locations is obtained for each image.

33

Figure 11: Particles detected using the threshold method

4.1.3 Three Particle Trajectory Formation With particle locations determined, the next step is correlate individual particle instances into three particle trajectories. A three particle trajectory was chosen, as opposed to a two or four particle trajectory, because three is the minimum number of instances that provides high confidence that the trajectory does in fact represent a single particle. The process for forming the trajectory is as follows. First, a two particle trajectory is created between two particles in adjacent frames. A velocity is calculated, and the position of a third particle is predicted. The next frame is checked to see if a particle lies within a tight tolerance from this prediction. If a particle is found, then the three particle trajectory is created and the data, including the centroid location, velocity,

34

and image number, is saved. If a particle is not found, then another two particle trajectory is checked, until all possible combinations have been explored. 4.1.4 Particle Rebound Detection In this section of the code, pre- and post-rebound trajectories are correlated into a single particle rebound event. First, the point in time and space that each trajectory intersects the impingement plate is determined from the intersection of the linear function defining the trajectory and the linear function defining the plate surface. Pairs of trajectories are compared to determine if they intersect the plate at the same point in time and space. If a match is found, the following criteria are checked to reduce the occurrence of false positives: 

The impact must occur within the bounds of the image (i.e. the impact location on the impingement plate must occur on a portion of the plate that is in the image).



The x-velocity (horizontal direction) of the incoming trajectory must be positive, or moving towards the plate.



The absolute velocity of the incoming particle trajectory is greater than the absolute velocity of the outgoing particle trajectory.

If the rebound meets all of the above criteria, then the rebound data, including the particle positions and velocities are saved, and four of the six particle instances are sent to the sizing function—the first and third instance in both the incoming and outgoing trajectory. Only performing the sizing on four of the particle instances reduces the computation time, while still accounting for changes in the apparent particle size due to the rotation of any non-spherical particles. 35

4.1.5 Detecting Particle Deposit Events After all of the particle rebounds have been found in a particular image set, the remaining unused trajectories are examined to determine if the particle deposited on the surface of the impingement plate. Note that this process is not performed on every data set, specifically the lower temperature cases, as few particles deposit at low temperature, and it is extremely time consuming. The overall theory for deposit detection is to examine an individual incoming trajectory to see if it passes several exclusion criteria, and if it does, the user visually examines the images to determine if a deposit occurs. The exclusion criteria are as follows: 

The third point in the trajectory is no closer than 50 pixels from the bottom or top edge of the image. This is done to reduce the number of trajectories that are in fact rebounds, but the outgoing trajectory moves off screen before the three particle trajectory can be formed.



The x-velocity (horizontal direction) of the incoming trajectory must be positive, or moving towards the plate.



The impact must occur within the bounds of the image (i.e. the impact location on the impingement plate must occur on a portion of the plate that is in the image).



Only trajectories that end close to the plate (based on the particle velocity) are considered, to reduce the number of particles that move out of focus before reaching the plate.

If the trajectory meets the above criteria, then the images are presented to the user, with the particle locations and predicted impact location highlighted, for the user to visually 36

inspect. The user looks to see if the particle does rebound, but the rebound trajectory was not detected, if the particle moves out of focus, preventing the rebound trajectory from being detected, or if the detected trajectory either was not made up of the same particle or was made up from non-particles (most commonly image artifacts caused by density gradients in the air). If the trajectory passes all of these criteria, then the trajectory data, including the particle positions and velocity are saved, and all three particle instances are sent to the sizing function. 4.1.6 Particle Sizing After a rebound or deposit has been detected, individual instances of the particle from the three particle trajectories are sent to the sizing function to determine the particle width, height, effective diameter, eccentricity, and centroid location. First, a 30x30 pixel window around the particle from the contrast enhanced image (Image 3 set) is defined. All sizing operations are performed in this window. Next, the window is converted from greyscale to binary using a threshold based on the minimum intensity detected in the window. A Canny based edge detection method is applied to find the outer edge of the particle. The image is dilated in a disk pattern to connect any small gaps in the edge lines, and any closed shapes within the window are filled in. Any shapes connected to the border of the window are deleted, unless the only shape detected is connected to the border. The remaining shapes are eroded in a disk pattern to return the particle to its original size. Using the built in Matlab function ‘regionprops’, the width, height, diameter, eccentricity, and centroid location of any shapes in the window are calculated. If multiple shapes remain in the window, the one closest to the center of the window is 37

assumed to be the actual particle. The process is repeated for all four particle instances sized for a rebound or all three particle instances sized for a deposit. The results are averaged, and a new velocity is calculated based on the updated, more accurate centroid locations. Finally, the particle size is adjusted for any blur caused by the non-zero exposure time, by calculating the distance the particle would move within the exposure time, and subtracting the resulting value from the width and height. With these new values, the effective diameter can be re-evaluated, and the data is saved. For the pixel resolution used in this study (approximately 30-35 µm), most particles detected fall between 50-200 µm. At least two pixels are typically required to detect a particle, but the final size of the particle can be less than this after image blur is accounted for. After the blur correction, a small number of particles down to approximately 20 µm are detected.

38

Chapter 5: Results and Discussion

5.1 Experimental Overview In total, four separate data sets were acquired with the Hot CoR Rig. Three of these data sets used bituminous ash while the fourth used a lignite ash. 5.1.1 Ash Composition Two different ash species were used in the high temperature coefficient of restitution testing—a bituminous ash derived from coal mined in West Virginia, and a lignite ash derived from coal mined in Mississippi. The samples were obtained from the hot gas filter hopper in operating coal-fired power plants. The ash composition was analyzed with wavelength dispersive X-ray fluorescence. The results from this test are presented in Table 3.

39

Table 3: Major chemical components of tested ash species Component (wt. %) SiO2 CaO Al2O3 Fe2O3 MgO TiO2 SrO SO3 K2O Na2O Density (kg/m3)

Bituminous 25.3 2.3 13.5 52.7 0.6 1.9 0.1 0.6 2.0 0.3 2892

Lignite 32.8 31.7 14.2 9.8 3.6 2.6 1.3 1.2 1.0 0.9 1114

The bituminous ash used in these tests is primarily made up of iron oxide, silicon dioxide, and aluminum oxide, while the lignite ash is primarily composed of calcium oxide, silicon dioxide, aluminum oxide, and iron oxide. In a study by Webb et al. [27], the deposition of bituminous and lignite ash (from the same sources used in the present study) on turbine nozzle guide vanes was investigated. The authors found that lignite ash deposited more readily at lower temperatures compared to bituminous ash, and they partially attributed this to the ratio of network modifiers, such as calcium oxide, magnesium oxide, sodium oxide, and potassium oxide, to network forming species, such as titanium dioxide and silicon dioxide. This molar ratio is 1.2 for the lignite ash, but only 0.18 for the bituminous ash, which can result in a lower viscosity glass at high temperatures in the lignite ash compared to the bituminous ash. While Webb et al. were specifically interested in the bulk deposition patterns of these ashes, their results would point towards a higher coefficient of restitution for a bituminous ash particle compared to 40

a lignite ash particle at high temperature, all other conditions constant, as well as a higher sticking efficiency for lignite ash compared to bituminous ash at a given condition. 5.1.2 Thermal Expansion Testing The bituminous and lignite ash samples were also run through a thermal expansion test to determine the sintering temperature for each ash type. A sample of each ash was heated, and the change in volume was observed. Figure 12 plots the percent volume change with temperature. The bituminous ash begins to change volume as low as 400°F with a significant decrease in volume occurring after 1700°F. The steepest slope occurs at 2200°F, marking the sintering temperature for the bituminous ash. The lignite ash volume remains relatively constant until starting to decrease at about 1870°F, with a sharp drop at 2100°F marking the sintering temperature. The lower sintering temperature of the lignite ash compared to the bituminous ash is another indicator that the lignite ash will likely begin depositing at a lower temperature. This matches the results seen in the study by Webb et al. [27], where it was observed that the lignite ash deposited at a lower temperature, and in a much larger amount compared to the bituminous ash.

41

Figure 12: Thermal expansion test results

5.1.3 Bituminous Ash Two Angle Data Set The first data set was acquired using bituminous ash at 45° and 60° impingement angles. The full test matrix is provided in Table 4. The PCO Dimax© color camera was used to record images at a frame rate of 22,151 frames per second, an exposure time of 1.454 µs, and an image size of 432 x-pixels by 268 y-pixels (except the 45° impingement plate angle, 1100°F particle temperature test, which was run at 23,454 frames per second, an exposure time of 1.454 µs, and an image size of 384 x-pixels by 268 y-pixels). One notable disparity between the various tests, even those performed at the same 42

impingement angle, is in the number of rebounds detected. For instance, in the 1445°F testing, 1863 rebounds were detected in the 60° impingement angle case, but only 147 were detected in the 45°case even though only twice as many images were taken for the 60° case than the 45° case. This disparity is also present in many of the other tests presented in the following sections. The primary cause is a wide variance in the particle density injected into the system. For some tests, a large number of particles are injected, so a large number of rebounds are detected. In other tests, the number of particles injected is relatively small, causing fewer particles to be detected. A secondary cause of this disparity is the varying image quality, especially between different particle temperatures. While not ideal, this disparity does not prevent a sound analysis of the data. After these tests were completed, the following modifications were performed on the Hot CoR Rig before subsequent testing: the fuel source was changed from natural gas to propane, thermocouples were installed at the particle injection point and on the surface of the impingement plates, a pre-mix system was added to mix the fuel and air prior to injection in the combustion chamber, the flame holders were modified, and a viewport was added to the combustion chamber to monitor combustion. As such, the flow temperature, used to determine the particle temperature, was taken at the exit of the equilibration tube instead of using the injection point thermocouple reading, and no impingement plate surface temperature was recorded. All data sets were processed for particle rebounds.

43

Table 4: Bituminous ash two angle test matrix, taken with Dimax© color camera Nominal Particle Temperature

1115°F

Nominal Plate Angle

45°

60°

Image Scale (µm/px)

29.62

34.27

Actual Particle Temperature (°F) Pixel Resolution (µm/px)

1100

1130

31.68 10,000

34.07 20,000

251

1,173

Actual Particle Temperature (°F) Pixel Resolution (µm/px)

1430 33.76

1460 34.07

# Images Processed

10,000

20,000

# Rebounds Detected

147

1,863

Actual Particle Temperature (°F) Pixel Resolution (µm/px)

1865

1800

33.76 21,000

34.07 20,000

183

835

# Images Processed # Rebounds Detected

1445°F

1830°F

# Images Processed # Rebounds Detected

5.1.4 Bituminous Ash Three Angle Data Set The largest data set was taken after performing the modifications to the Hot CoR Rig described in the above section. Bituminous ash was used, and data was taken at three impingement plate angles: 30°, 60°, and 90°. Table 5 shows the full test matrix for this data set. The Phantom® v311 monochrome camera was used to acquire the images at a frame rate of 40,554 frames per second, an exposure time of 2.8µs, and an image size of 256 x-pixels by 256 y-pixels. All data sets were processed for particle rebounds, while only the 2000°F and 2100°F data sets were processed for particle deposits. In total, 34,428 rebounds were detected.

44

Table 5: Bituminous ash three angle test matrix, taken with v311 monochrome camera Nominal Particle Temperature

30°

60°

90°

29.62

34.27

34.63

76

82

88

Plate Temperature # Images Processed

76 30,000

83 30,000

88 20,000

# Rebounds Detected

6,395

11,392

2,648

Actual Particle Temperature Plate Temperature # Images Processed

997 30,000

1,010 766 30,000

1,041 812 30,000

# Rebounds Detected

1,022

1,825

729

Actual Particle Temperature

1,250

1,267

1,252

Plate Temperature # Images Processed

30,000

904 30,000

963 30,000

# Rebounds Detected

1,725

486

261

Actual Particle Temperature Plate Temperature

1,510 -

1,482 1,049

1,482 1,141

# Images Processed

30,000

30,000

30,000

# Rebounds Detected

2,271

730

320

Actual Particle Temperature Plate Temperature # Images Processed

1,739 30,000

1,721 1,202 30,000

1,770 1,340 30,000

340

682

531

Actual Particle Temperature Plate Temperature

2,007 -

2,006 1,388

2,000 -

# Images Processed # Rebounds Detected

30,000 464

30,000 425

30,000 466

# Deposits Detected

14

13

23

2,094 30,000 281

2,105 1,475 30,000 533

2,150 1,517 30,000 902

26

18

25

Nominal Plate Angle Image Scale (µm/px) Actual Particle Temperature

80°F

1000°F

1250°F

1500°F

1750°F

# Rebounds Detected

2000°F

2100°F

Actual Particle Temperature Plate Temperature # Images Processed # Rebounds Detected # Deposits Detected

45

5.1.5 Lignite Ash Data Set A single data set was acquired with lignite ash with a 60° impingement plate. The Phantom® v311 monochrome camera was used to acquire 30,000 images per data set at a frame rate of 23,286 frames per second with an image size of 512 x-pixels by 256 ypixels. A brighter, blue LED light source was used for this test, allowing the exposure time to be reduced to 1.0 µs. The image quality achieved with this brighter LED was noticeably better than in the previous data sets. Specifically, the intensity distortions caused by density gradients in the air were significantly reduced. Unfortunately, due to limited availability of the LED, it was not used in subsequent testing. All temperature cases were processed for particle rebounds, while only the 2000°F data set was processed for particle deposits, as the image quality of the 2100°F test was too poor to detect a significant number of deposits. In total, 7,575 rebounds were detected.

46

Table 6: Lignite ash 60° impingement angle test matrix, taken with v311 monochrome camera Nominal Particle Temperature

Nominal Plate Angle Image Scale (µm/px)

80°F

1000°F

1250°F

1500°F

1750°F

2000°F

33.5

Actual Particle Temperature (°F)

88

Plate Temperature (°F)

88

# Rebounds Detected

4,572

Actual Particle Temperature (°F)

1002

Plate Temperature (°F)

739

# Rebounds Detected

298

Actual Particle Temperature (°F)

1261

Plate Temperature (°F)

932

# Rebounds Detected

617

Actual Particle Temperature (°F)

1480

Plate Temperature (°F)

1059

# Rebounds Detected

1,239

Actual Particle Temperature (°F)

1749

Plate Temperature (°F)

1245

# Rebounds Detected

247

Actual Particle Temperature (°F) Plate Temperature (°F) # Rebounds Detected

2020 1390 391

# Deposits Detected 2100°F

60°

35

Actual Particle Temperature (°F) Plate Temperature (°F)

2083 1452

# Rebounds Detected

211

5.1.6 Bituminous Ash with Backside Heating In the final data set, bituminous ash was impinged on the 60° plate. A MAPP (methylacetylene-propadiene propane) fuel torch was used to heat the backside of the plate. The torch head was placed approximately one inch from the back of the 47

impingement plate and the torch flame was centered with the hot jet exiting the Hot CoR Rig. As in previous tests, the plate temperature was monitored with a flush mounted thermocouple. Table 6 shows the full test matrix for this data set. Notice the higher plate temperatures compared to the same tests performed with no backside heating (see Table 5). The Phantom® v311 monochrome camera was used to acquire the images at a frame rate of 23,286 frames per second, an exposure time of 2.4µs, and an image size of 512 xpixels by 256 y-pixels. All data sets were processed for particle rebounds. In total, 862 rebounds were detected, considerably less than in other image sets. The reduction in rebounds detected at each temperature was caused primarily by the reduced image quality from the additional density gradients (and therefore intensity variations in the images) caused by the flame impinging on the backside of the plate.

Table 7: Bituminous ash with backside heating test matrix, taken with v311 monochrome camera Nominal Particle Temperature

80°F

1750°F

2000°F

Nominal Plate Angle

60°

Image Scale (µm/px)

32.22

Actual Particle Temperature (°F) Plate Temperature (°F)

75 1038

# Rebounds Detected

650

Actual Particle Temperature (°F) Plate Temperature (°F)

1745 1557

# Rebounds Detected

118

Actual Particle Temperature (°F) Plate Temperature (°F)

1989 1689

# Rebounds Detected

48

94

5.2 Experimental Rebound Results 5.2.1 Impact Velocity, Impact Angle, and Diameter Distributions An impact velocity histogram, showing the impact velocity distribution of the four data sets discussed above, is provided in Figure 13. All four data sets have impact velocity distributions starting close to 0 m/s. The bituminous ash with backside heating, bituminous ash two angle, and lignite ash data sets all have a maximum impact velocity close to 160 m/s, while the bituminous ash three angle data set has a maximum velocity of approximately 140 m/s. These maximum values are within the maximum velocity that the imaging system is capable of capturing, indicating proper operation of the particle tracking code. The bituminous ash with backside heating, bituminous ash two angle, and lignite ash data sets have an impact velocity centered at 52 m/s. The bituminous ash three angle data set has a primary peak at 22 m/s, but a significant number of rebounds occur at an impact total velocity between 20-60 m/s. This distribution is a result of the relatively low velocity the room temperature tests for the bituminous ash three angle data set were run at, compared to the high temperature tests. Since approximately 60% of the rebounds detected were during room temperature tests (due to the high image quality without density gradients in the air causing intensity fluctuations in the images), there is a large peak in the impact velocity distribution corresponding to the lower velocity that the room temperature tests were run at. This was corrected for in subsequent tests by running the room temperature experiments at a higher mass flow.

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Figure 13: Impact velocity histogram for all four data sets

A similar plot is shown in Figure 14 for the distribution of impact angles. Three peaks are observed in the bituminous ash three angle data set, corresponding to the three impingement plate angles: 30°, 60°, and 90°. The 90° peak is the smallest, since fewer rebounds were found at this condition. Overall, there is a distribution ranging from a glancing, nearly 0° impact to a completely normal, 90° impact for the bituminous ash three angle data set. For both the bituminous with backside heating and lignite ash data sets, a majority of the impacts occur near 60°, which is expected since both of these tests were performed 50

with the 60° impingement plate. The slight offset of the peaks (57° for the lignite ash data set, 62° for the bituminous ash with backside heating data set) can be attributed to a slight change in the impingement plate angle between the two tests. The impact angle histogram for the bituminous ash two angle data set is by far the flattest, implying a relatively even distribution of impact angles. This is a significant departure from the other data sets, but can be explained by changes made to the Hot CoR Rig itself between the bituminous ash two angle test and subsequent tests. In the bituminous ash two angle tests, a 1/8” diameter thermocouple was placed in the center of the jet at the exit of the equilibration tube, which would cause increased turbulence and deflect particles from their stream-wise trajectory. These effects would distribute the particles over a wide band of impact angles, explaining the distribution seen in Figure 14. In subsequent tests, the exit thermocouple was placed 2-3 inches into the equilibration tube from the exit. The thermocouple was also flush with the bottom surface of the ceramic liner, so the core of the jet would remain relatively undisturbed.

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Figure 14: Impact angle histogram for all four data sets

The final histogram of particle effective diameter is shown in Figure 15. Here, the diameters of all four data sets are primarily concentrated between 50-200 µm. The peaks for the bituminous ash three angle, bituminous with backside heating, bituminous ash two angle, and lignite ash data sets are 90 µm, 90 µm, 100 µm, and 110 µm respectively. Using a centrifugal particle size analyzer, the mass mean diameter for the bituminous and lignite ash was found to be 14.12 µm and 12.51 µm respectively. This large discrepancy is caused by the limits of the PSV system, which requires at least one pixel, and usually more, to pick up a particle. Since the individual pixel size ranges from 30-35 µm for a 52

given test, the code is unable to detect particles smaller than this. (Note that it is possible to image a smaller particle after accounting for the blur caused by the exposure time of the image. For instance, a two-pixel particle moving quickly may only actually be ½ a pixel in size after accounting for blur.) Overall, the PSV technique is only able to detect a very small percentage of the total number of particle impacts.

Figure 15: Particle effective diameter histogram for all four data sets

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5.2.2 Effect of Particle Diameter on Total Coefficient of Restitution Figure 16 shows the trend of total coefficient of restitution with diameter plotted using the bituminous ash three angle data set at all tested particle temperatures. At diameters between 30-100 µm, the total coefficient of restitution decreases strongly with particle diameter for all temperatures. At diameters between 100-200 µm, this trend begins to level out. Essentially, two processes are at play here. First is the adhesion force, which is proportional to the contact area (diameter squared). As the diameter increases, the adhesion force increases, decreasing the coefficient of restitution as observed between 30-100 µm. The second process is that as the diameter increases, the kinetic energy of the particle for a given velocity increases with diameter cubed, since the kinetic energy is proportional to the mass and in turn volume for a given particle density. As the increase in kinetic energy begins to outpace the growth in adhesion forces, the coefficient of restitution trend begins to level out, as seen in the 100-200 µm range of Figure 16. Essentially, the adhesion force requires less energy to overcome, relative to the total energy available, allowing the CoR trend to level out as diameter increases. Note that the increased variation in the coefficient of restitution at higher particle diameters is due to less rebound data at these diameters. Overall, there is no apparent trend with temperature.

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Figure 16: Total coefficient of restitution vs. particle diameter with lines representing data at different particle temperatures. Bituminous ash three angle data set.

5.2.3 Effect of Temperature on the Coefficient of Restitution Of significant interest to the present study is the effect of the particle temperature on the coefficient of restitution. Figure 17 plots the total coefficient of restitution versus the particle temperature for three data sets—the bituminous ash three angle data set, bituminous ash two angle data set, and the lignite ash data set. Because only three temperatures were acquired for the bituminous ash with backside heating data set, this data set was not included in the plot. In addition to these three data sets, a fourth curve is 55

included, showing the 60° impingement plate portion of the bituminous ash three angle data set, allowing easy comparison to the lignite ash data set which was run only at 60°. All rebounds at each temperature were averaged into a single value. Although the absolute coefficient of restitution values vary somewhat, all four of the data sets show a similar trend. At low temperatures (between room temperature and 1000°F), the coefficient of restitution stays relatively constant before rising at 1250-1450°F. After leveling off, the coefficient of restitution then drops back down at 1750-2000°F. The full three angle bituminous ash data set then increases slightly at 2000°F before dropping down again at 2100°F, while the coefficient of restitution for the two 60° data sets (lignite ash and the 60° data from the full three angle bituminous ash data set) decrease at 2000°F. Overall, this does not match the expected trend of a monotonically decreasing coefficient of restitution with temperature. Indeed, in the only other study available to compare coefficient of restitution of micro particles at elevated temperatures, Reagle et al. [20] found that the coefficient of restitution of Arizona road dust particles impacting a stainless steel plate decreased by 12% at 500°F, 15% at 1100°F, and 16% at 1472°F, compared to ambient temperature. However, this study was run at a single mass flow, so that as the gas temperature increased, the flow velocity also increased. Due to this increase in velocity, the authors attribute the observed decrease in coefficient of restitution primarily to an increase in plastic deformation caused by increased velocity, as opposed to temperature. In addition, the highest temperatures run in the study by Reagle et al., were well below the highest temperatures run in this test.

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While unexpected, this general trend appears in all three of the data sets presented. Since this trend is clearly repeatable, and there is no reason for it to consistently appear between tests, there is a high likelihood that this is a real trend, at least within the conditions created by the Hot CoR Rig. One possible explanation of this trend is as follows. Over a wide range of low temperatures, from 80-1000°F, there is little change in material properties, resulting in little change in the coefficient of restitution. Then, as the temperature increases further into the 1000-1250°F range, the particulate undergoes a rapid change in mechanical properties due to, for instance, a change in the crystal structure of the chemical constituents. This change causes an increase in the yield stress and/or modulus of elasticity, increasing the coefficient of restitution. This process was considered by Reagle et al. [20], but no concrete conclusions were made. However, other researchers [32] have observed a trend of increased modulus of elasticity with increased temperature for multi-component silicate glasses. These silicate glasses have some chemical components in common with the bituminous and lignite ashes used in this study, such as silicon dioxide, so this stiffening of material properties is certainly feasible, though more research would be needed to determine the precise property variation with temperature of the ash varieties study here. Another possible explanation for the sudden rise could be from a weakening in the adhesion forces due to the increased temperature. Either way, these effects would continue to dominate the rebound behavior of the particles until temperature effects begin to significantly increase plastic deformation in the 1750-2000°F range, marked by the

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rapid decrease in the total coefficient of restitution observed in Figure 17. Note that it is also in this range when deposits begin to form. Initially, these results may seem to discount all of the models discussed in Chapter 2. However, the models are only as good as their inputs. Implicit in the discussion of the model trends with temperature is an understanding of how the material properties are changing. Even the trends provided in Figure 3 assume that the modulus of elasticity and yield stress decrease with temperature. If the material properties are changing in unexpected ways, then the coefficient of restitution trends in the models may not be intuitive.

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Figure 17: Total coefficient of restitution vs. particle temperature.

5.2.4 Effect of Particle Impact Velocity on Total Coefficient of Restitution Another important factor in particle rebound behavior is the particle impact velocity. The total coefficient of restitution for the bituminous ash three angle data set is plotted against the particle impact velocity in Figure 18. From this plot, a strong trend of decreasing coefficient of restitution with increasing velocity is observed, which agrees well with data from Whitaker et al. where crushed quartz particles impacted an aluminum plate at ambient temperature conditions. This is expected for the velocity range of these experiments, because as the velocity increases, the plastic deformation of the particle 59

increases, resulting in a decrease in the coefficient of restitution. Note that at high velocities (above 90 m/s) the data becomes noisier, because less data are available at these velocities. There is no clear temperature trend, but it is observed that the general trend follows that of Figure 17. This trend agrees well with the trends observed for the elasto-plastic model in Figure 2 and the EVP models in Figure 3, but is the opposite of the critical velocity trend, where the coefficient of restitution increases with velocity. However, the purely elastic collision assumption in the critical velocity model is likely not met here; it is possible that at lower velocities, where the collision would be closer to purely elastic, the critical velocity trends would be observed.

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Figure 18: Total coefficient of restitution vs. particle impact velocity with lines representing data at different particle temperatures. Bituminous ash three angle data set and data from Whitaker et al. [21]

5.2.5 Effects of Impact Angle on Total Coefficient of Restitution The impact angle is another important factor in particle rebound characteristics. For a rigid, perfectly smooth surface, it would be expected that the total coefficient of restitution would decrease as the impact angle increases to 90°, holding the total velocity constant, because the normal velocity is effectively increasing. A higher normal velocity results in increased plastic deformation, and a decreased coefficient of restitution. The coefficient of restitution models discussed in Chapter 2 all predict this monotonically 61

decreasing trend. The results of the three angle bituminous ash data set, presented in Figure 19, do not show this expected monotonic decrease in coefficient of restitution. Rather, for most temperatures, the coefficient of restitution starts between 0.4-0.5 at low angles before peaking between 0.5-0.65 at approximately 40° and then dropping off again as the impact angle increases towards 90°. One possible explanation for the observed trend deals with the frictional forces experienced by the particles as they impact the plate. At low angles, the energy lost to friction is high because there is a large component of tangential velocity. As the impact angle increases, this tangential velocity component decreases, decreasing the energy loss due to friction. Under this theory then, low coefficients of restitution at low impact angles would be caused primarily by energy loss due to friction, while low coefficients of restitution at high impact angles would be caused primarily by energy loss due to plastic deformation. At mid-range angles, the particles would be affected by both friction and plastic deformation, but the overall energy loss would be at a minimum. Hussainova and Schade [28] found that friction was a major contributor to net energy loss in the impact of glass beads on a ceramic-metal (cermet) plate. Data from Reagle et al. [20], where sand particles were impacted on a polished stainless steel plate, are presented in Figure 19. Between 40°-60°, the two data sets show good agreement. At high angles (60°-90°), both data sets begin to level out, though the magnitude of the coefficient of restitution is higher in the presents study. At lower angles, below 40°, there is a significant departure in both trend and magnitude. However, the particle type and impingement plate material and finish (Inconel 625, unpolished mill 62

finish in the present study versus polished stainless steel in the Reagle et al. study) is also different, making it difficult to make a direct comparison. Another interesting aspect of Figure 19 is the temperature dependence, specifically the high coefficient of restitution at low angles for the 1250°F and 1500°F cases compared to the other temperature cases. This matches the trend observed in Figure 17 where the coefficient of restitution spikes up at 1250-1500°F before dropping off again at 1750°F. However, this same trend is not observed at higher angles. Another way to visualize this data is shown in Figure 20. Again, it is observed that the lowest angle has the highest dependence on temperature, while higher angles have a much weaker dependence on temperature. At the highest angle, the trend is actually reversed, causing the coefficient of restitution to decrease at 1250°F. One possible explanation for this trend is an unexpected change in the mechanical properties of the particulate, such as an increased shear modulus between 1250-1500°F. At shallow impact angles, changing the shear modulus would cause a more significant change in the coefficient of restitution, when compared to a more normal impact angle, because most of the energy is contained in the tangential direction. The particle’s temperature dependence on frictional forces or adhesion forces, as discussed previously, or a combination of these effects, could also play a role in this coefficient of restitution trend with temperature.

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Figure 19: Total coefficient of restitution versus particle impact angle for the bituminous ash three angle data set. Additional data from Reagle et al. [20].

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Figure 20: Total coefficient of restitution versus temperature with lines of averaged coefficient of restitution with angle for the bituminous ash three angle data set

5.2.5 Effect of Impact Angle on Angular Coefficient of Restitution The angular coefficient of restitution, defined as the ratio of the rebound angle to the impact angle, is plotted against impact angle in Figure 21. At all test conditions there is a large spike in the angular coefficient of restitution at small impact angles, which decreases exponentially towards the normal impact case. This can be explained by considering the definition of the angular coefficient of restitution; at low impact angles, even a small deviation from the impact angle will cause a large angular coefficient of 65

restitution. On the other hand, a small deviation from a moderate to large impact angle will not affect the total coefficient of restitution to nearly the same extent. This trend is also observed in the data from Whitaker et al. [21], where crushed quartz particles were impacted on an aluminum plate. Comparing the various temperatures reveals no major particle temperature influence on the angular coefficient of restitution.

Figure 21: Angular coefficient of restitution versus impact angle for the bituminous ash three angle data set. Comparison data from Whitaker et al. [21].

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5.2.6 Effect of Backside Heating Heating the impingement plate has the effect of reducing the total coefficient of restitution. Figure 22 shows the relationship between the total coefficient of restitution and the particle impact velocity for two ambient conditions: one with backside heating and one without backside heating. Note that the plate temperature was 1038°F for the heated case and 88°F for the unheated case. The increased plate temperature has the clear effect of decreasing the coefficient of restitution. Two possible mechanisms exist for this. First, heating the plate will change the mechanical properties of the plate, specifically the yield stress and modulus of elasticity, which will increase the plastic deformation of the plate and the contact area between the particle and plate surface, reducing the coefficient of restitution. By interpolating in the mechanical property variation with temperature for an annealed Inconel 625 1/8” plate data provided in Ref. [33], the variation in plate properties can be quantified: the modulus of elasticity decreases from ambient temperature to stress decreases from

psi at

psi at 1038°F (a 16.6% reduction), and the yield psi at ambient temperature to 56.6

psi at 1038°F

(a 22.9% reduction). These data clearly show a change in the mechanical properties of the plate for the temperature range of this experiment. The modulus of elasticity appears in the denominator of the work of adhesion term for all of the coefficient of restitution models. A decrease in the modulus of elasticity would cause a subsequent increase in the work of adhesion, and decrease the coefficient of restitution, as observed in Figure 22. For the EVP and elasto-plastic models, which include the effects of plastic deformation, a

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decreased yield stress causes a decreased coefficient of restitution, again matching the trends observed in Figure 22. Another mechanism for this reduction is the thermal boundary layer produced by the hot, relative to the jet, plate. As the particles traverse the boundary layer, their temperature will increase somewhat, potentially causing a change in the mechanical properties of the particles. It is doubtful that this has a significant effect though, since the temperature increase of the particles would be relatively small for the large particle diameters observed in this study [29] (which would traverse the of order 4 mm thick thermal boundary in order 10-5 seconds). In addition, previously discussed results (Figure 17) indicate that the particle temperature does not have a significant impact on the coefficient of restitution in this temperature range.

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Figure 22: Total coefficient of restitution versus impact velocity for bituminous ash with backside heating.

5.3 Experimental Deposit Results All data for the bituminous ash three angle data set at 2000°F and 2100°F, as well as the data for the lignite ash data set at 2000°F were processed to detect individual particle deposits. In total, 50 and 69 deposits were detected at 2000°F and 2100°F respectively for the bituminous ash data, and 35 deposits were detected for the 2000°F lignite ash data. Of primary interest in the critical velocity and EVP models is the kinetic energy based on the normal impact velocity, 69

, defined as

(14) where

is the mass of the particle, and

is the normal velocity of the particle. Note

that the mass is calculated from the effective diameter, assuming a spherical particle, and the density of the ash. A histogram of this normal kinetic energy is plotted in Figure 23 for each data set. Both of the bituminous ash data sets are heavily skewed to low normal kinetic impact energies below approximately 10 µJ. The lignite ash data set, which contains far fewer particle instances, has a flatter distribution, though most particles still fall below a normal kinetic energy of 10 µJ.

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Figure 23: Histogram total number of detected particles, including both deposits and rebounds, versus particle normal kinetic energy

To effectively compare the number of detected deposits at various particle normal kinetic energies, a sticking efficiency,

, was defined as: (15)

where

is the number of particle sticks or deposits detected, and

is the number of

particle rebounds detected. This particle sticking efficiency is plotted against the particle normal impact kinetic energy in Figure 25. All deposits for the three analyzed data sets occurred below a particle normal kinetic energy of 10 µJ, well below the cutoff of 71

approximately 1000 µJ seen in Figure 23, which would imply a strong dependence between the propensity of a particle to deposit and the particle’s normal impact kinetic energy. Looking at the bituminous ash data sets, there appears to be a slight downward trend as the normal kinetic energy increases from close to zero to 3µJ and 6 µJ for the 2000°F and 2100°F cases respectively. A secondary spike then occurs for each bituminous ash data set at 8µJ and 9 µJ, though it should be noted that these spikes represent only one particle deposit each, since the total number of rebounds and deposits at the specified normal kinetic energies is relatively low (see Figure 23). The lignite ash results show a much higher sticking efficiency, peaking at approximately 52% at low normal kinetic energies. The lignite ash is expected to deposit more readily and at a lower temperature, as discussed in sections 5.1.1 and 5.1.2, so this result is expected. The critical velocity defines a velocity below which particles deposit, and above which, particles rebound. Similarly, the elasto-plastic model has a low velocity threshold below which particle deposit, and above which particles rebound. Comparing the critical velocity model (Figure 3) and the elasto-plastic model (Figure 2) to the trend seen in Figure 25 shows good agreement with this general trend, since the data shows particles depositing at low kinetic energies. However, both models predict a hard cutoff velocity, whereas Figure 25 reveals the probabilistic nature of particle deposition. For these models to be applied to these conditions, a deposition probability would need to be included. The EVP models have a trend where particles rebound at low velocities and then deposit above some threshold velocity. This is not seen in the conditions of the testing performed in this study. 72

The critical viscosity model, which has no dependence on the particle kinetic energy, is clearly not supported by this data, since a strong trend with the normal kinetic energy is observed in Figure 25. One possible way to still utilize the critical viscosity method would be to apply it at a given particle normal kinetic energy. To explore this possibility, the following work was performed. Using the critical viscosity model, where the sintering point found in Figure 12 is used as the critical temperature (2100°F for lignite ash and 2200°F for bituminous ash), the sticking probability was plotted against temperature in Figure 24. The constants A and B, used to determine the particle viscosity as a function of temperature, were determined using Ref. [17] from the chemical composition provided in Table 3. From Figure 24, the probability of sticking at 2000°F is 36% for the lignite ash and 14% for the bituminous ash, a factor of approximately 2.5 lower. At 2100°F, the probability of sticking for the bituminous ash rises to 39%, which is similar to the probability of sticking for the lignite ash at 2000°F. Comparing these probabilities of sticking to the sticking efficiency in Figure 25 shows poor agreement. At low normal kinetic energies, there is a ten-fold difference in the experimental sticking efficiency compared to only a 2.5 fold difference in the probability of sticking from the critical viscosity. In addition, comparing the bituminous ash data at 2100°F to the lignite ash data at 2000°F, the experimental data again shows an approximately ten-fold difference at low normal kinetic energies, but the critical viscosity model predicts that the probability of sticking is almost the same for these two conditions. These comparisons are presented with the caveat that the probability of sticking is not necessarily the same as the sticking efficiency, especially in the context of these experiments where a relatively 73

small number of particle deposits were detected. Overall though, from these results as well as the simple observation of a dependence of deposition on particle normal impact kinetic energy, it would appear that the critical viscosity model is not effectively capturing the deposition behavior.

Figure 24: Probability of sticking versus temperature applying the critical viscosity model

While good agreement is observed between the three data sets, the number of deposits detected is relatively low, making it difficult to have full confidence in the data presented above. Ideally, more testing would be performed to confirm these results. 74

However, the process of detecting the deposits is extremely time consuming, as the operator must manually confirm a particle deposit when the image processing code finds a potential trajectory. A fully automated code would be ideal, though without improved image quality such a code may not be feasible.

Figure 25: Sticking efficiency versus particle normal impact kinetic energy

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Chapter 6: Conclusion This study has examined the rebound and deposition of ash particulate on an impingement plate at conditions relevant to the hot section of a gas turbine engine. Tests were run using bituminous and lignite ash at particle temperatures between ambient and 2100°F. Particle shadow velocimetry was used to measure the size and velocity of individual particles impacting on and rebounding from an impingement plate. Increasing particle size and impact velocity were shown to decrease the total coefficient of restitution. The dependence of the coefficient of restitution on impact angle and temperature was unexpected. For the impact angle, the coefficient of restitution started low at low impact angles and increased to a peak value at 40° before dropping off again at higher angles. Friction between the particle and plate surface was presented as a possible explanation for this trend. When plotted against particle temperature, the coefficient of restitution started low at low temperatures, reached a peak value between 1250-1500°F, before again decreasing at high temperatures. A non-intuitive change in particle mechanical properties was presented as a possible explanation for this trend. Finally, increased impingement plate temperature was shown to decrease the coefficient of restitution. Individual particle deposits were also detected using particle shadow velocimetry. It was observed that particles predominantly deposited at low particle kinetic energies, 76

based on the normal impact velocity. However, the number of deposits detected was low, making it difficult to draw any strong conclusions. Of all of the models discussed in Chapter 2, the elasto-plastic model was the only that matched both the trend of coefficient of restitution with particle impact velocity, and the trend of deposition with kinetic energy. The critical velocity model was able to predict the deposition pattern seen in this study but predicted a reverse trend of coefficient of restitution with impact velocity. The EVP models had the opposite problem, where they were able to predict the coefficient of restitution trend with velocity, but did not capture the deposition behavior. The critical viscosity model, which only predicts the trend of deposition, did correctly predict deposition occurring at high temperature, but failed to capture the dependence on kinetic energy. Ideally, future work would investigate the mechanical properties of the particulate at various temperatures. Knowing the modulus of elasticity, the yield stress, and possibly the dynamic mechanical properties of the particles would provide significant insight into the trends observed, especially the coefficient of restitution trend with temperature. With these values available, the process of creating a comprehensive particle rebound and deposition model would be within reach.

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[27] Webb, J., Casaday, B., Barker, B., Bons, J.P., Gledhill, A.D., Padture, N.P., “Coal Ash Deposition on Nozzle Guide Vanes—Part I Experimental Characteristics of Four Coal Ash Types,” Journal of Turbomachinery, Vol. 135, (2013). [28] Hussainova, I., Schade, K.P. “Correlation between Sold Particle Erosion of Cermets and Particle Impact Dynamics,” Tribology International Vol. 41 (2008): 323-330. [29] Richards, G.A., Logan, R.G., Meyer, C.T., Anderson, R.J. “Ash Deposition at CoalFired Gas Turbine Conditions: Surface and Combustion Temperature Effects,” Journal of Engineering for Gas Turbines and Power Vol. 114 (1991): 132-138. [30] Ranz, W.E., Marshall, W.R. “Evaporation from Drops, Part II,” Chemical Engineering Progress Vol. 48 (1952): 173-180. [31] Morsi, S.A., Alexander, A.J. “An Investigation of Particle Trajectories in TwoPhase Flow Systems,” Journal of Fluid Mechanics Vol. 55 (1972): 193-208. [32] Personal communication with Dr. E. Lara-Curzio, Oak Ridge National Laboratory, 08/14/2013. [33] Battelle Columbus Div. Ohio, Deel, O. “Mechanical-Property Data Inconel 625. Annealed Sheet.” (1971)

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