Luận văn thạc sĩ vaporisation of single and binary component droplets in heated flowing gas stream and on solid sphere

59Figure 3.4 Transient change of FCC feed droplet diameter predicted by four different homogeneous models - ITC, AS, FTC & ETC compared with the base case of Buchanan [Buc 1].. The princ

Vaporisation of single and binary component droplets in heated flowing gas stream and on solid sphere

A thesis submitted for the degree of

Doctor of Philosophy

By

Thi Bang Tuyen Nguyen

Discipline of Chemical Engineering

School of Engineering

Faculty of Engineering & Built Environment

The University of Newcastle

March, 2018

i

DECLARATIONS

I hereby certify that the work embodied in the thesis is my own work, conducted under mal supervision

nor-The thesis contains no material which has been accepted, or is being examined, for the award

of any other degree or diploma in any university or other tertiary institution and, to the best of

my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text I give consent to the final ver-sion of my thesis being made available worldwide when deposited in the University’s Digital Repository, subject to the provisions of the Copyright Act 1968 and any approved embargo

ii

ACKNOWLEDGEMENTS

Firstly, I would like to express my sincere gratitude to Prof Geoffrey M Evans who brought

me to Australia, to pursue my desired PhD program

I would like to thank my supervisors, Prof Geoffrey M Evans, Dr Subhasish Mitra and Dr Mayur Sathe, for their continued support and guidance I would also like to express my sin-cere appreciation to Dr Subhasish Mitra for being a supportive senior colleague prior to his currently supervising role and for his great effort in self-fabricating a number of delicate ex-perimental setups in our laboratory

I am grateful to all my friends in Nier A Block for keeping a friendly atmosphere and being

an everyday life support

I would also like to acknowledge the financial support provided through the linkage project from British Petroleum, Kwinana refinery, Western Australia and Australian Research Coun-cil that made this work possible

Finally, I would like to thank my daughter Binh-Minh, who recently has asked me “Are you a doctor, mummy? – not yet but really soon – oh no I don’t like needles.”, and “why you keep putting party pies in my lunch box everyday mummy?”; my baby boy Quang-Minh, whose face expressions can clear all the work’s hardship when I am home every day and my hus-

band Cuong, for his daily support, encouragement and love

iii

SELF-PUBLISHED WORK INCLUDED IN THE THESIS

No Full bibliography Journal/

Conference Status

Contribution

to thesis

1 Nguyen, T T B., Mitra, S., Sathe, M J.,

Pareek, V., Joshi, J B., & Evans, G M

(2018a) Evaporation of a sessile binary

droplet on a heated spherical particle

Experimental Thermal and Fluid Science

Journal,

Exp Therm

Fluid Sci

Published Chapter 5

2 Nguyen, T T B., Mitra, S., Sathe, M J.,

Pareek, V., Joshi, J B., & Evans, G M

(2018) Evaporation of a suspended binary

mixture droplet in a heated flowing gas

stream Experimental Thermal and Fluid

3 Nguyen, T T B., Mitra, S., Pareek, V., Joshi, J.,

& Evans, G (2015) Comparison of

vaporization models for feed droplet in

fluid catalytic cracking risers Chemical

Engineering Research and Design, 101,

82-97

Journal, ChERD

Published Chapter 3

4 Nguyen, T T B., Mitra, S., Pareek, V., Joshi, J

B., & Evans, G M (2016) Modelling

evaporation of mono and binary

component alkane droplets in different

convective flow conditions Paper

presented at the Proceedings of the 10th

Australasian Heat and Mass Transfer

Conference (AHMT 2016) Brisbane, Qld

14-15 July, 2016

http://hdl.handle.net/1959.13/1329006

Conference, AHMT

droplet on a spherical particle in film

boiling regime Chemical Engineering

Science, 149, 181-203

Journal, CES

Published Chapter 3

6 Nguyen, T B T., Mitra, S., Pareek, V., Joshi, J B.,

& Evans, G M (2017) Evaporation at the

three phase contact line of a highly wetting

droplet on a superheated surface Chemeca

conference 2017

Conference, Chemeca

Presented Appendix F

iv

TABLE OF CONTENTS

DECLARATIONS i

ACKNOWLEDGEMENTS ii

SELF-PUBLISHED WORK INCLUDED IN THE THESIS iii

TABLE OF CONTENTS iv

LIST OF TABLES vii

LIST OF FIGURES viii

ABSTRACT xiii

NOMENCLATURE xvi

Notation xvi

Dimensionless numbers xvii

Greek letters xviii

Subscripts xix

Chapter 1 Introduction 1

1.1 Background of the study 1

1.2 Homogeneous vaporisation 2

1.3 Heterogeneous vaporisation 3

1.4 Problem statement 5

1.5 Objectives of thesis 7

1.6 Thesis outline 9

Chapter 2 Literature review 11

2.1 Vaporisation of droplets in multiphase (gas-solid fluidised bed) system 11

2.2 Vaporisation of a suspended droplet in heated flowing gas stream 18

2.3 Vaporisation of a droplet on a heated substrate 29

2.4 Internal convections inside an evaporating droplet 34

Chapter 3 Comparison of vaporization models for feed droplet in fluid catalytic cracking risers 38 3.1 Homogeneous vaporization models 39

3.1.1 Governing equations: 39

3.1.2 Homogeneous models: 41

3.1.3 Estimation of thermos-physical properties: 44

3.2 Heterogeneous vaporization models 46

3.2.1 Existing heterogeneous models 46

3.2.2 Proposed heterogeneous droplet-particle collision (DPC) model 48

3.3 Results and Discussions 57

3.3.1 Validation of homogeneous vaporization models 57

3.3.2 Predictions of vaporization time for gas oil droplets by homogeneous models 61

3.3.3 Heterogeneous vaporization time predictions for gas oil droplets 67

3.4 Conclusions 74

Chapter 4 Evaporation of a suspended binary mixture droplet in a heated flowing gas stream 76 4.1 Modelling 77

4.1.1 Droplet evaporation rate 77

v

4.1.2 Droplet temperature 80

4.1.3 Estimation of thermo-physical properties 81

4.2 Experimental 83

4.2.1 Apparatus 83

4.2.2 Procedure 84

4.2.3 Materials 87

4.2.4 Image analysis 88

4.3 Results and discussions 90

4.3.1 Evaporation of hydrocarbon mixtures 90

4.3.2 Evaporation of water-glycerol mixtures 99

a) Reduction in droplet size 99

b) Variation in droplet temperature 109

4.4 Scaling analysis 112

4.4.1 Internal motions in the droplet 112

4.4.2 Unsteady heating/cooling stage of the droplet 115

4.5 Conclusions 117

Chapter 5 Evaporation of sessile binary droplet on a heated spherical particle 120

5.1 Experimental 121

5.1.1 Apparatus 121

5.1.2 Image analysis 125

5.2 Results and discussion 130

5.2.1 Droplet evaporation rate 131

5.2.2 Droplet temperature 138

5.2.3 Unsteady heating-up stage 145

5.2.4 Wetted contact area 147

5.2.5 Transient variation in contact angle 155

5.2.6 Internal motion within droplet 163

5.3 Conclusion 168

Chapter 6 Conclusions and recommendations 171

6.1 Conclusions 171

6.2 Recommended future work 175

6.2.1 Evaporation model accounting for internal motions in binary droplets on a heated curved substrate 175

6.2.2 Effect of surface curvature on the sessile droplet evaporation on heated substrate 175

6.2.3 Temperature dependency of contact angle in non-boiling evaporation 175

6.2.4 Evaporation at the three-phase contact line 176

REFERENCES 178

Appendix A Evaporation rate of a suspended droplet 189

Appendix B Evaporation rate of a sessile droplet 191

Appendix C Temperature dependent physical properties of fluids 194

Appendix D Lennard–Jones Potential Model Constants 198

Appendix E Contact angle of an evaporating sessile droplet 199

Appendix F Evaporation at the three-phase contact line 202

vi

F.1 Background 202

F.2 Modelling 203

F.3 Results and Discussion 207

F.4 Conclusions 211

Appendix G Supplementary results of Chapter 5 212

G.1 Standard deviations used for error bars 212

G.2 Additional results of water-glycerol, water-IPA and water-butanol droplets 215

vii

LIST OF TABLES

Table 2.1 Typical numerical studies including the droplet vaporisation under film boiling

regime, particularly in FCC riser and fluid coker operating conditions 13

Table 2.2 Development of heat and mass transfer correlations for droplet evaporation 19

Table 2.3 A comparative summary of modelling studies on multicomponent droplet evaporation 24

Table 2.4 Summary of experimental studies on multicomponent droplet evaporation 28

Table 2.5 Experimental contact angle of water droplet on metal surface at different temperature 32

Table 3.1 Homogeneous models for droplet vaporization 41

Table 3.2 FCC feed (vacuum gas oil) liquid and vapour properties in a typical FCC riser (Buchanan, 1994) 62

Table 3.3 Operating conditions of a typical FCC riser (Buchanan, 1994; Nayak et al., 2005)63 Table 3.4 Droplet vaporization times (ms) for different size of FCC feed droplets predicted by homogeneous models (operating conditions are: d p = 65 µm, T d0 = 561 K, T B = 700 K, T G = T p = 922 K) 66

Table 3.5 Vaporization times (ms) predicted by the heterogeneous models for FCC feed droplet (Operating conditions are: d p = 65 µm, T d0 = 561K, T B = 700K, T G = T p = 922K) 69 Table 4.1 Physical properties of the liquid and gas mixture 82

Table 4.2 Operating conditions of binary hydrocarbon droplet evaporation 90

Table 4.3 Operating conditions of the water-glycerol systems 99

Table 4.4 Time scales for droplet internal motion 114

Table 4.5 Comparisons between characteristic time scales and actual unsteady heating times 116

Table 5.1 Case studies 131

Table 5.2 Comparison of liquid-solid interface temperature predicted with experimental measurement Operating conditions: 90 % water - 10 % glycerol droplet T S = 323-358 K, d p = 10 mm, T a = 296 K, RH = ~ 50 % d 0 = 2.75 mm 141

Table 5.3 Comparison of thermal diffusion time with the actual heating time (case “gly10”) 147

Table 5.4 Duration of pinning mode at different concentrations (TS = 323 K) 149

Table 5.5 Parameters evaluating the convection inside droplet 166 Table 5.6 Reduction in surface tensionsubject to temperature and glycerol concentration 167

viii

LIST OF FIGURES

Figure 1.1 Schematic of the two feed droplet vaporisation regimes in a typical FCC unit 5Figure 2.1 Schematic of a suspended evaporating droplet 18Figure 3.1 Droplet-particle collision mechanism 49Figure 3.2 Validation of the four homogeneous model predictions with the vaporization data

of water (Ranz & Marshall, 1952b) Conditions are: T d0 = 282 K T G = 298 K T B = 373.15

K d d0 = 1.1 mm Re d0 = 0 (a) Vaporization data of hexane (Downingm, 1966) Conditions

are: T d0 = 281 K T G = 437 K T B = 344.6 K d d0 = 1.76 mm Re d0 = 110 (b) Vaporization

data of heptane (Nomura et al., 1996) Conditions are: T d0 = 298 K T B = 371.42 K T G = 741

K d d0 = 0.80 mm Re d0 = 0 (c) Vaporisation data of decane (Wong & Lin, 1992) Conditions

are: T d0 = 315 K T G = 1000 K T B = 447.1 K d d0 = 2 mm Re d0 = 17 (d) 58Figure 3.3 Comparison of transient change of decane droplet temperature predicted by

homogeneous models and experimental data of Wong and Lin (1992) Conditions are: T d0 =

315 K T G = 1000 K T B = 447.1 K d d0 = 2 mm Re d0 =17 (a) Temporal change of volume

averaged temperature T d versus surface temperature T ds of decane droplet predicted by FTC

model Conditions are: T d0 = 315 K T G = 1000 K T B = 447.1 K d d0 = 2 mm Re d0 =17 (b) 59Figure 3.4 Transient change of FCC feed droplet diameter predicted by four different homogeneous models - ITC, AS, FTC & ETC compared with the base case of Buchanan

[Buc (1)] Conditions are: d d0 = 300 µm, d p = 65 µm, T d0 = 561 K, T B = 700 K, T G = T p =

922K (a) Conditions are: d d0 = 300 µm, d p = 65 µm, T d0 = 561 K, T B = 700 K, T G = T p =

922 K (b) 65

Figure 3.5 Transient change of FCC feed droplet diameter predicted by the four

heterogeneous models – Buc (2), Buc (3), Nayak (phi = 14) and DPC Conditions are: d d0 =

50µm, dp = 65 µm, T d0 = 561K, T B = 700K, T G = T p = 922K (a) Conditions are: d d0 =

50µm, dp = 65 µm, T d0 = 561K, T B = 700K, T G = T p = 922K All the model predictions

could be seen attaining the saturation temperature limit (b) 68Figure 3.6 FCC feed droplet vaporization time predicted by the proposed DPC model with

two different formulation of the droplet-particle contact time Conditions are: d 0 = 50 µm, d p

= 65 µm, T d0 = 561K, T B = 700K, T G = T p = 922K Larger vaporization time is predicted

when the contact time of droplet on particle surface decreases 71Figure 3.7 Effect of advancing contact angle variation on FCC feed droplet vaporization time

in the proposed DPC model Conditions are: d d0 = 50 µm, d p = 65 µm, T d0 = 561K, T B =

700K, T G = T p = 922K Vaporization time varies insignificantly when the advancing contact

angle of the droplet on particle surface changes from 150o to 180o 73Figure 4.1 Experimental setup (1) rotameter, (2) column, (3) inline heater, (4) temperature controller, (5) stainless-steel needle, (6) one-way control valve, (7) silicon tube, (8) syringe, (9) syringe pump, (10) droplet, (11) high speed camera, (12) transparent quartz windows, (13) back light, (14) computer, (15) pitot tube, (16) T-type thermocouple, (17) manometer, (18) data logger 84Figure 4.2 Image analysing process - a) raw nozzle image b) raw nozzle-and-droplet image c) binary image d) logical image e) holes filled image f) nozzle-free-droplet binary-scale image

ix

g) droplet boundary and nozzle polynomial fitting curve h) polynomials fitting curve on left and right side of droplet boundary 89Figure 4.3 Model predictions of temporal diameter and temperature validated against experimental data of a decane droplet reported by Daif et al (1999) Operating conditions of

Case 1: d 0 = 1.386 mm; T G = 348 K; T d0 = 317 K; Re d0 = 215 91Figure 4.4 predictions of temporal droplet size and temperature validated against experimental data of a heptane-decane mixture droplet (75 % heptane and 25 % decane)

reported by Daif et al (1999) Operating conditions of Case 2: d 0 = 1.334 mm; T G = 348 K;

T d0 = 293 K; Re d0 = 214 93Figure 4.5 Model prediction in temporal change of evaporation rate (a) and mass fraction of species (b) of heptane-decane mixture droplet (75 % heptane and 25 % decane) Operating

conditions of Case 2: d 0 = 1.334 mm; T G = 348 K; T d0 = 293 K; Re d0 = 214 95Figure 4.6 Predicted variation in droplet (75 % heptane and 25 % decane) diameter profile based on both ideal and non-ideal assumption, max standard deviation ~ 0.8×10-3 (a) Activity coefficient of each species in the liquid mixture (b) Operating conditions of Case 2:

d 0 = 1.334 mm; T G = 348 K; T d0 = 293 K; Re d0 = 214 96Figure 4.7 Model prediction of temporal reduction of heptane-decane mixture droplet (20 % heptane and 80 % decane), validated against experimental data of Gökalp et al (1994) and

modelling of Zhang and Kong (2010) Operating conditions of Case 3: d 0 = 1.563 mm; T G =

372 K; T d0 = 295 K; Re d0 = 107 97Figure 4.8 Temporal reduction in droplet size for hexane-decane droplets at different

compositions (operating conditions of Case 3: d 0 = 1.563 mm; T G = 372 K; T d0 = 295 K; Re d0

= 107) 98Figure 4.9 Model prediction of temporal change of droplet size and temperature of water-glycerol mixture droplet (82.5 % water and 17.5 % glycerol), validated against experimental

data of Davies et al (2012) Operating conditions of Case 4: d 0 = 0.042 mm; T G = 298 K; T d0

= 298 K; Re d0 = 1.07 100Figure 4.10 Comparison of model predicted droplet diameter reduction for pure water system with present experimental data (Error: 0.073 – 0.104 mm in 95% confidence interval) Inset plot shows high-speed visualizations of droplet size reduction Operating conditions of Case

5: d 0 = 2.61 mm; T G = 353 K; T d0 = 310 K; Re d0 = 714 102Figure 4.11 Model prediction for temporal droplet (70 % water and 30 % glycerol) diameter reduction validated against present experimental data (a); and predicted change in species mass fraction with time (b) (Error: 0.013 to 0.05 mm in 95% confidence interval); inset plot

shows a complete evaporation Operating conditions of Case 6: d 0 = 2.61 mm; T G = 353 K;

T d0 = 317 K; Re d0 = 708 103

Figure 4.12 Temporal variation of evaporation rate for a) water species and b) glycerol species in the binary mixture droplet (70 % and 30 % glycerol) Operating conditions of Case

6: d 0 = 2.61 mm; T G = 353 K; T d0 = 317 K; Re d0 = 708 105Figure 4.13 Transient change in droplet diameter predicted using ideal and non-ideal assumptions A max standard deviation of 0.0023 mm (more visible in the inset) is the

difference between these two assumptions (a), variation in activity coefficient of each species

in the liquid mixture (b) Operating conditions of Case 6: d 0 = 2.61 mm; T G = 353 K; T d0 =

317 K; Re d0 = 708 106

temperature (b) Operating conditions of Case 5: d 0 = 2.61 mm; T G = 353 K; T d0 = 310 K;

Re d0 = 714 (Error: 0.07 – 1.57 K in 95% confidence interval) 110Figure 4.16 Model prediction of transient droplet (70 % water and 30 % glycerol) temperature validated against present experimental data (a); and heat ratio interpreting the

change in droplet temperature (b) Operating conditions of Case 6: d 0 = 2.61 mm; T G = 353

K; T d0 = 317 K; Re d0 = 708 (Error: 0.09 – 4.95 K in 95% confidence interval) 111Figure 4.17 Unsteady stages during the predicted temporal temperature of droplets Unsteady stage of pure droplets is shorter than that of mixture droplet Operating conditions of Case 2:

d 0 = 1.334 mm; T G = 348 K; T d0 = 293 K; Re d0 = 214 117Figure 5.1 Schematic diagram of the experimental set up – a) brass particle b) 200 W cartridge heater placed inside the grooved heating billet c) heating billet with insulation d) 1.0

mm OD T type thermocouple e) temperature controller f) variac with transformer g) droplet h) nozzle assembly containing hypodermic needle i) syringe pump j) diffuser screen k) light source l) height adjustment facility with scale m) Phantom v311 camera n) computer o) 0.5

mm OD T type thermocouple p) translation stage q) data logger 122Figure 5.2 Scanning electron microscopy (Phenom) image of brass particle surface Average

surface roughness R a = 189 nm and R z = 345 nm 124

Figure 5.3 Image processing showing raw image from camera was converted into a binary image, droplet and particle boundaries were then separated for other detailed calculations 126

Figure 5.4 Definitions of measured parameters: d 0 is initial diameter of the droplet before

impact; d w is length of the arc from point A to B or wetted diameter; ϕ is spreading angle;

V cap,P is volume of the wetted spherical cap on particle side; V cap,L is volume of the liquid

portion; h L is height of the liquid cap excluding solid portion (a) Image analysis for a typical image: (1) circle fitted on particle surface; (2 and 3) polynomials fitted on the left and right side of the droplet interface used for volume calculation; (4) maximum spreading angle; (5) left-side contact angle; (6) right-side contact angle (b) 127

Figure 5.5 Uncertainties in the image processing (Pure water droplet, T S = 323 K), a) effect

of the polynomial degree for curve fitting on the measured contact angle, b) effect of asymmetry in droplet deposition on contact angle, c) comparison of the two methods determining equivalent droplet diameter 130Figure 5.6 Transient reduction normalised liquid cap height with time of water-glycerol

droplets Glycerol concentration from 0.0 to 35.0 % Operating conditions: T S = 343 K, d p =

10 mm, T a = 296 K, relative humidity RH = ~ 50 % Average standard deviations ‘std.’ that

were calculated from three experimental sets are mentioned in brackets 132Figure 5.7 Transient reduction of normalised liquid cap height with time for water-IPA

droplets IPA concentration from 0.0 to 15.0 % (b) Operating conditions: T S = 343 K, d p = 10

mm, T a = 296 K, relative humidity RH = ~ 50 % Average standard deviations ‘std.’ that were

calculated from three experimental sets are mentioned in brackets 134

xi

Figure 5.8 Measured droplet volume reduction with time, at three different solid temperatures

T S : 90 % water - 10 % glycerol droplet T S = 323-358 K, d p = 10 mm, T a = 296 K, RH = ~ 50

%, d 0 = 2.75 mm, T L,0 = 299.5 K Dash lines present the linear regression during the early stage of evaporation 135Figure 5.9 Measured droplet volume reduction with time, at three different solid temperatures

T S at 323, 343 and 353 K d p = 10 mm, T a = 296 K, RH = ~ 50 % Other operating conditions

stated in Table 5.1 136Figure 5.10 Measured droplet volume reduction with time, at three different solid

temperatures T S at 323, 343 and 353 K water 95 % - IPA5 % droplet (a) and water 90 % -

IPA 10 % droplet (b) d p = 10 mm, T a = 296 K, RH = ~ 50 % Other operating conditions

stated in Table 5.1 137

Figure 5.11 Measured temperatures of the liquid cap at various positions at (a) T S = 323 K,

(b) T S = 343 K and (c) T S = 358 K Operating conditions: Mixture of 90 % water – 10 %

glycerol, d 0 = 2.75 mm Locations of the thermocouple’s tip: ‘pos (1)’ indicates positions 1a and 1b on the particle surface; ‘pos (2)’ indicates positions 2a and 2b, ‘pos (3)’ indicates positions 3a, 3b and 3c and ‘pos (1)’ indicates positions 4a and 4b located at a distance of 0.4

mm, 0.6 mm and 0.8 mm respectively, from particle apex point (uncertainty ±0.1 mm ‘std’ indicates the average standard deviation obtained from two or three data sets corresponding

to different measurement locations (a, b, c) 140

Figure 5.12 Liquid temperature distribution at different solid temperature 90 % water - 10 %

glycerol droplet, T S = (323, 343, 358) K, d 0 = 2.75 mm (a) 95 % water - 5 % IPA droplet, T S

conditions: T S = 323 K, d p = 10 mm, T a = 296 K, relative humidity RH = ~ 50 % 150

Figure 5.15 Experimental relationship between normalised maximum spreading diameter and solid temperatures Mixture of purified water and glycerol with glycerol concentration from

0.0 to 35.0 % Operating conditions: T S = 323 K, d p = 10 mm, T a = 296 K, relative humidity

RH = ~ 50 %; surface temperature normalised by boiling temperature T b = 373 K for gly00,

T b = 373.9 K for gly10; Tb 375.3 K for gly25 and T b 376.4 K for gly35 (Glycerine Producers Associations, 1963) 152Figure 5.16 Transient change in spreading diameter of “Butanol05” droplet Operating

conditions: T S = 353 K, d p = 10 mm, T a = 296 K, relative humidity RH = ~ 50 % 153

Figure 5.17 Measured contact angle and spreading diameter reduction with time, at three

different solid temperatures Operating conditions: 90 % water - 10 % glycerol droplet d 0 =

2.75 mm, d p = 10 mm T L,0 = 299.5 K T S = 323-358 K 158Figure 5.18 Contact angles of water-glycerol droplets at different concentration of glycerol

from 0 to 35 % Operating conditions: T S = 323 K, d p = 10 mm, T a = 296 K, relative humidity

RH = ~ 50 % The contact angle decrease rate found at 0.16 o/s, 0.14 o/s, 0.12 o/s and 0.10 o/s for gly00, gly10, gly25 and gly35 respectively 160

xii

Figure 5.19 Contact angles of water-IPA droplet at different IPA concentration from 0 to 15

% Operating conditions: T S = 343 K, d p = 10 mm, T a = 296 K, relative humidity RH = ~50

% 161Figure 5.20 Transient change in contact angles of “Butanol05” droplet Operating conditions:

T S = 353 K, d p = 10 mm, T a = 296 K, relative humidity RH = ~ 50 % 162

Figure 5.21 Experimental relationship between the pinned spreading diameter and contact angle at solid temperatures from 323 - 358 K and glycerol concentrations from 0 – 35 %

Operating conditions: d p = 10 mm, T a = 296 K, relative humidity RH = ~ 50 %; 163

Figure 5.22 Reduction in normalised droplet volume with normalised time for three different binary mixtrue droplets compared with pure water droplet, at the same surface temperature at

323 K Operating conditions: d p = 10 mm, T a = 296 K, relative humidity RH = ~ 50 %; 165

xiii

ABSTRACT

Droplet vaporisation is significant to a number of multiphase process engineering plications which include but not limited to Fluid Catalytic Cracking (FCC) process for pro-ducing transport fuel; fluid coking for producing fuel gas, distillate and petroleum coke; spray coating of tablets in pharmaceutical industry; drying of seeds in spouted bed in food industry and spray drying of milk in dairy industry The principal aim of this study was to improve the physical understanding the droplet vaporisation in a multiphase environment due to both con-vective (homogeneous vaporisation) and conductive heat transfer (heterogeneous vaporisa-tion) with the aid of experimental measurement and numerical modelling The principal aim was met first by numerically quantifying the feed droplet vaporisation time in a typical multi-phase application (FCC riser) including both homogeneous and heterogeneous modes; and then separately investigating these two modes by experimentally quantifying the vaporisation behaviour of a suspended droplet in a hot convective flow and on a heated spherical particle, respectively

ap-A comprehensive quantitative comparison of the existing models (both homogeneous and heterogeneous) was conducted to predict FCC feed droplet vaporisation time under typi-cal industrial operating conditions Noting a dearth of suitable physical model that accounts for the conductive heat transfer between feed droplets and catalyst particles, a new vaporisa-tion model based on the particle-droplet collision mechanism was proposed which provided a reasonable agreement with the available heterogeneous models It was noted that all homoge-neous models predicted a larger droplet vaporisation time compared to the heterogeneous models which could be attributed to the large difference in the Nusselt number in these two modes of heat transfer

Evaporation behaviour of binary mixtures droplet in high Reynolds number (~ 714)

xiv

environment was next studied experimentally and a numerical model was developed ent change in droplet size and temperature were measured for both pure component system (water) and a polar binary system (70 % water and 30 % glycerol) at free stream temperature

Transi-~ 353 K and superficial gas velocity Transi-~ 4.3 m/s Reasonable agreements with the model dictions were obtained for single component system however some deviation was noted for binary system specifically at the transition stage which was attributed to the liquid phase dif-fusional resistance due to high system viscosity Transient droplet temperature measurements were performed which showed an unsteady heating stage followed by a thermal equilibrium stage The unsteady heating stage was shown to be within the two limits of characteristic thermal convection and mass diffusion time scale

pre-Heterogeneous vaporisation behaviour was examined by the experimental studies of binary mixture droplets evaporating on heated spherical particle Effect of liquid composition for three different binary system droplets (water-glycerol, water-IPA and water-butanol) and sol-

id surface temperature (range) on the droplet vaporisation rate were studied It was observed that droplets exhibited pinned mode evaporation (i.e evaporation with constant wetting area and reducing contact angle) for major duration of its lifetime, at ~95 % for pure water and a major time for binary systems A model was given to determine time varying theoretical con-tact angle based on droplet evaporation rate incorporating the effect of Marangoni flows which provided good agreement with the experimental data Furthermore, local temperature measurements of the droplet showed a short initial unsteady heating duration followed by a longer thermal equilibrium stage regardless droplet compositions and solid surface tempera-ture; the actual heating duration was found to be less than 10 % of the droplet lifetime and fell within the range of the calculated thermal diffusion time-scales Finally, a scaling analy-sis was carried out to quantify the internal motions within the droplet It was shown that un-der the given operating conditions, surface tension driven flow component (thermal Maran-

xv

goni flow) dominates over the convective flow component due to density difference leigh flows) which justifies inclusion of the additional Marangoni number based correction factor in the evaporation model to correctly predict the vaporisation rate

(Ray-This study aimed to shed light on the two different modes of droplet vaporisation cess in multiphase system and it is expected that some of the models developed in this study can be incorporated in CFD framework to aid design of the relevant process equipment

C p,m heat capacity of the vapour/air mixture, J/kgK

col freq collision frequency, 1/(m 3 s)

d droplet, m

d p diameter of the particle, m

d w wetted diameter, m

d equiv equivalent spherical diameter of the droplet, m

d max maximum spread diameter, m

D v binary diffusion coefficient of vapour into carrier gas, m 2 /s

D L self-diffusion coefficient of the liquid phase, m 2 /s

e film vapour film thickness, m

k thermal conductivity, W/mK

h L height of the liquid cap(excluding solid portion), m

h col heat transfer coefficient based on droplet-particle collision, W/m 2 K

h eff effective heat transfer coefficient used in model of Nayak et al (2005), W/m 2 K

h heat heat transfer coefficient in the heating up stage, W/m 2 K

h vap heat transfer coefficient in the vaporization stage

L V latent heat of vaporization, J/kg

d

m vaporization rate, kg/s

n d number of droplet, 1/m 3

n p number of particle, 1/m 3

r c half of the chord length cap

Q col heat transferred by each collision, J

Q total total heat transferred by collisions, W/m 3

R 0 initial droplet radius, m

T average temperature used for characteristic thermal diffusion time estimation, K

xvii

T S,L solid-liquid interface temperature, K

T S bulk solid temperature, K

T L temperature of the liquid, K

T a ambient temperature, K

v slip droplet-gas slip velocity, m/s

v slip_dp droplet-particle slip velocity, m/s

v slip_pg particle-gas slip velocity, m/s

V cap,L volume of the liquid cap (after subtracting the solid portion), m 3

V cap,P volume of the wetted spherical particle cap, m 3

V volume of entire spherical cap including liquid and solid portion, m 3

Dimensionless numbers

B M mass transfer number

B T heat transfer number

B’ T modified heat transfer number used in the AS model

Ma Marangoni number

Ra Rayleigh number

RH ambient relative humidity, %

Y s mass fraction at the droplet surface

Y G mass fraction far away from droplet surface

χs mole fraction at droplet surface

G heat transfer correction factor

/

Sh=Kd D Sherwood number based on Ranz and Marshall (1952)

where K is mass transfer coefficient

/

Nu=hd k Nusselt number based on Ranz and Marshall (1952)

where h is heat transfer coefficient

Sh* Modified Sherwood number

Nu* Modified Nusselt number

Nu eff Effective Nusselt number used in model of Nayak et al (2005)

Nu heat Nusselt number used in heating up stage

Red =ρG slip v d d /µG Reynolds number of gas phase

ReL =ρL slip v d d /µL Reynolds number of liquid phase

βΤ thermal expansion coefficient, K -1

ε holdup (chapter 3) mass fraction ratio (chapter 4)

γ activity coefficient

∈ voidage used in the model of Buchanan (1994)

∞ carrier gas phase, far from the droplet surface

φΝ phenomenological factor used in model of Nayak et al (2005)

φ correction factor used in model of Abramzon and Sirignano (1989)

θ droplet-particle contact angle, deg

κ change in surface tension with respect to temperature

Λ change in surface tension with respect to mole fraction

m mixture vapour/air except “m” used in Table 2.2

Re m “modified” Reynolds number using free-stream density (Table 2.2)

f film conditions (vapour film at the droplet interface – Table 2.2)

∞ free-stream density (Table 2.2)

Chapter 1 1

Chapter 1 Introduction

This chapter presents the aims of the thesis followed by a brief background of the search problem which highlights the significance of droplet vaporisation in many practical applications A particular focus is given to the feed stock vaporisation in fluid catalytic crack-ing process, a typical multiphase application involving complex hydrodynamics with phase change A number of physical factors affecting the related heat and mass transport processes between the vaporising droplet and the surrounding environment are presented Investigation

re-of some re-of these factors are identified as objectives re-of this study which are further developed into individual chapters of this thesis and outlined in the thesis organisation section

1.1 Background of the study

Besides its importance in everyday life such as evaporation of body perspiration, rain drops on leaves, droplet evaporation has significant practical applications such as spray com-bustion in internal combustion engines; fluid catalytic cracking (FCC) process for producing transport fuel; fluid coking for producing fuel gas, distillate and petroleum coke; spray coat-ing of tablets in pharmaceutical industry; drying of seeds in spouted bed in the food industry and spray drying of milk in the dairy industry

In most of the natural evaporation phenomena, the diffusion process largely governs droplet evaporation which occurs due to concentration gradient of evaporating species be-tween droplet interface and surrounding ambience In engineering applications involving a typical multiphase system, droplet evaporation however can occur under very different oper-ating conditions based on different mechanisms For example in spray coating, interactions between droplets and the solid-particles often occur at relatively low temperatures (~ 320 K);

heat transfer mechanisms For this reason, the two vaporisation models namely homogeneous and heterogeneous are commonly assumed to describe the vaporisation of feed droplets in

gas-solid fluidised bed systems Homogeneous vaporisation describes the heat transfer

result-ed from convection of the hot gas flow whilst heterogeneous vaporisation describes heat

transfer resulting from direct contact between droplets and catalytic particles (Martin, 1990)

In the following section, a brief description of fluid catalytic cracking process is presented to illustrate droplet vaporisation behaviour in a typical multiphase flow system which involve complex interactions of all three phases

1.2 Homogeneous vaporisation

In homogeneous mode of vaporisation, droplets are sprayed into a hot connective flow environment Modelling of individual droplets vaporisation has been conducted in many studies Droplet collisions and coalescence are considered in dense spray whereas it is usually ignored in dilute spray if the space between droplets is larger than the mean free path of colli-sions The vaporisation rate of a suspended droplet exposed to a flowing gas is strongly de-

Chapter 1 3

pendent on the gas phase conditions such as pressure, temperature and Reynolds number and usually quantified through the transient change in droplet size and temperature Mathemati-cally, these two phenomena are modelled based on mass transfer and heat transfer rate, re-spectively For multicomponent droplet system, depending on the chemical characteristics of the droplet i.e polar or non-polar, additional consideration of ideal or non-ideal mixture be-haviour also needs to be taken into account which may play a significant role in the vaporisa-tion rate A comprehensive numerical treatment on droplet vaporisation in a convective envi-ronment can be found in the work of Law (Law & Law, 1982), Sirignano (Sirignano, 2010) and Sazhin (Sazhin, 2014)

Frequently, a suspended droplet vaporizing in a flowing gas stream is considered as

an analogous approach to a moving droplet in a gaseous environment as long as the gas relative velocity remains identical This approach has been used in many experimental studies on droplet vaporisation to overcome the difficulty of injecting and subsequently moni-toring a moving droplet Although a number of experimental work investigated the droplet vaporisation behaviour over last five decades (Daıf et al., 1998; Downingm, 1966; Ghassemi

droplet-et al., 2006b; Gökalp droplet-et al., 1994; Halldroplet-ett & Beauchamp-Kiss, 2010; K Han, Yang, droplet-et al., 2016; Ranz & Marshall, 1952b; Stengele et al., 1999; Volkov et al., 2017; Wong & Lin, 1992; Y Zhang et al., 2017), the ultimate target of studying a system as in the real applica-tions comprising high temperature and pressure, high velocity and fine size droplet (< 100 µm), is difficult to be met due to experimental limitations

1.3 Heterogeneous vaporisation

In typical multiphase process applications, it is more challenging to understand the vaporisation in a heterogeneous regime due to the presence of the additional solid phase Of-ten, droplet vaporisation in such cases is quantified by the conduction heat transfer at solid-

Chapter 1 4

liquid interface and convective heat/mass transfer at liquid-vapour interface Theoretically, the presence of a solid particle in the system creates a number of complex factors affecting the vaporisation such as droplet-particle impact dynamics, particle surface wettability (char-acterised by wetted area and contact angle) and movement of the three-phase contact line These physical complexities associated with droplet vaporisation are briefly described next in

a typical multiphase system, fluid catalytic cracking unit

In an FCC unit, the low calorific value heavy vacuum gas oil feedstock (mixture of long-chain hydrocarbons) is injected in atomised state into an upward flowing fluidised cata-lyst particles stream to have intimate contacts and mixing with the hot catalyst particles (see Figure 1.1) Vaporisation of the feed droplets takes place in a very short time followed by cracking reaction which occurs within ~1.5 to 4.0 s (Buchanan, 1994) Along with the con-vective heat transfer from fluidising medium (steam), droplets also receive heat from the hot catalyst particles Close interactions with catalyst particles is essential to accelerate the vapor-isation rate and ensure all the cracking reactions take place within the aforesaid residence time

Vaporisation here is characterized by a number of factors – multicomponent diffusion both inside and at the interface of droplet, conductive and convective heat transfer at liquid-solid and gas-liquid interface, respectively, droplet-particle interaction mechanisms, mass transfer at the gas-liquid interface and internal motion within the droplet Although critical, studies on vaporisation of feedstock in FCC riser has been either ignored or treated in a sim-plified manner (Mitra, 2016) Simple modelling approaches are reported in many studies without considering the physical interactions between droplets and particles (Behjat et al., 2011; Gan et al., 2011; Gao et al., 1999; Lopes et al., 2011; Wu et al., 2010) In fewer FCC modelling studies however heat transfer due to droplet-particle interactions is accounted

Chapter 1 5

(Buchanan, 1994; Martin, 1990; Mirgain et al., 2000; Mitra, 2016; Mitra et al., 2016; Nayak

et al., 2005) These studies nonetheless do not account for the droplet-particle interaction mechanisms in the heat transfer coefficient modelling explicitly as described in Ge and Fan (2007) and Mitra (2016) based on the interacting droplet-particle size ratio

Figure 1.1 Schematic of the two feed droplet vaporisation regimes in a typical FCC unit

1.4 Problem statement

In practical multiphase applications involving all three phases, both homogeneous and heterogeneous vaporisation modes occur simultaneously While convective heat transfer modelling is rather straightforward using based some variations of Ranz-Marshall (1952) cor-relation, heat transfer modelling at solid-liquid interface is a challenging one Solid surface characteristics (roughness, hydrophobicity and curvature) and droplet-particle size ratio de-termine the wetted contact area for heat transfer There are numerous studies focusing on

Chapter 1 6

droplet impact behaviour on flat surface (Burton et al., 2012; Chandra & Avedisian, 1991b; Chandra et al., 1996; Ge & Fan, 2005; Liang et al., 2016; Pasandideh‐Fard et al., 1996) Ex-perimental studies published in the literature in high temperature conditions include heat transfer below droplet saturation temperature (P Chen et al., 2017; P Chen et al., 2016; Crafton & Black, 2004; Di Marzo & Evans, 1986; Diddens et al., 2017; Misyura, 2016, 2017), heat transfer under nucleate boiling regime (Liang et al., 2016; Nikolopoulos et al., 2007) and in film-boiling regime (Biance et al., 2003; Mitra et al., 2016) Such studies on droplet-particle system are rather limited (Charalampous & Hardalupas, 2017; Ge & Fan, 2007; Mitra, 2016; Mitra et al., 2017; Mitra et al., 2013) In the experimental scheme, vapori-sation time is unmeasurable for a multicomponent droplet vaporising in such a complex three-phase system involving heat transfer

In gas-solid fluidized bed system, some conceptual interaction mechanisms were suggested in Mirgain et al (2000) between a liquid film coated particle and a dry particle depicting three possible pathways for sharing liquid content due to particle-particle collisions Ge and Fan (2007) suggested four possible mechanisms for droplet-particle interactions which include droplet rebound from particle surface, droplet deposition on particle, film formation around particle and agglomerate formation These interaction mechanisms have been reviewed com-prehensively in the recent work of Mitra (2016) Associated droplet evaporation behaviour on solid surface has been addressed in detail in the review work of Erbil (2012) Although there are several works reported for pure component system evaporating on flat solid surface (Chandra et al., 1996; P Chen et al., 2017; Crafton & Black, 2004; Di Marzo & Evans, 1986; Sefiane & Tadrist, 2006), evaporation on curved surface using binary or multicomponent sys-tems (P Chen et al., 2017; P Chen et al., 2016; Misyura, 2016; Sefiane & Tadrist, 2006) which is a better representative for the practical applications, remains largely unexplored

Chapter 1 7

In a multicomponent system, in the liquid phase itself, internal diffusion plays a erning role in the vaporisation behaviour due to the different physical/chemical properties of each component in the mixture From thermodynamic perspective, non-ideal behaviour of the mixture (non-unity activity coefficient leading to positive or negative deviation from Raoult’s law) is another aspect that influences vaporisation behaviour solution however studies on this aspect are still limited in the literature

gov-Further, atomised droplets in the riser experience shear stress from the up-flowing idizing gas due to their relative motions which results in internal motions within the droplets Additionally, temperature gradient inside the droplet, surface tension difference due to both temperature and composition differences also contribute to internal motion through Rayleigh and Marangoni flows These internal motions increase the apparent thermal conductivity of droplet and influence droplet vaporisation behaviour Many investigations have been devoted

flu-to study the dynamics of these interior motions especially using flow visualisation Particle Image Velocimetry – PIV method (Cao et al., 2000; Kinoshita et al., 2007; Mandal & Bakshi, 2012; Prakash & Sirignano, 1978), however implementation of internal motions on droplet vaporisation remains rather limited (P Chen et al., 2017; Diddens et al., 2017; Tam et al., 2009)

1.5 Objectives of thesis

This study is aimed at improving the physical understanding of the droplet tion characteristics in a typical multiphase process application A number of aspects related to

vaporisa-droplet vaporisation in a typical multiphase environment have been detailed in the problem

statement section From the application perspective, research need to focus on quantifying

vaporisation behaviour in a multi-component mixture having fine droplet size, high slip locity and high ambient temperature to improve the physical understandings of the related

ve-Chapter 1 8

heat and mass transport process However, it is extremely challenging taking into account all the aforesaid operating conditions and related physics in either a modelling framework or a quantitative experiment Nonetheless, fundamental insights to this problem can be achieved through controlled study is of the underlying mechanisms

The main objectives of this work were to study the vaporisation behaviour of a binary mixture droplet with and without the presence of hot particle(s) using a combination of exper-imental and numerical techniques Specifically:

1) To validate the published homogeneous vaporization models at different operating ditions for pure component droplets with reported experimental data,

con-2) To quantify vaporization times for typical FCC feed droplets using these validated mogeneous models,

ho-3) To quantify vaporization times for same size of feed droplets using heterogeneous models and comparing with predictions of homogeneous models,

4) To develop a mechanistic heat transfer model for heterogeneous vaporization mode volving droplet-particle collision

in-5) To develop a lumped parameter evaporation model for binary mixture droplet system based on the rapid mixing assumption to predict temporal variation in droplet diameter and temperature accounting for non-ideal behaviour in binary mixture

6) To experimentally investigate the evaporation behaviour characterized by variation in droplet size and temperature with time for polar binary mixture droplet comprising wa-ter and glycerol in a heated convective environment at high gas velocity so that droplet Reynolds number is higher than reported in the available literature

Chapter 1 9

7) To experimentally quantify variations in droplet size, temperature, wetted contact area and contact angle as a function of time for different particle temperatures below the liq-uid saturation point in a binary system involving different droplet liquid compositions 8) To quantify the dynamics of internal motions inside the droplet represented by Peclet number, Rayleigh number and Marangoni numbers using the measurements of gas flow velocity and temperature within the droplet

1.6 Thesis outline

The structure of this thesis is organized as follows:

Chapter 2 presents a comprehensive review providing a sufficient background of the lem In this chapter, first presented is a brief review of previous studies on droplet vaporisa-tion in gas-solid fluidised bed Next, selected studies on the vaporisation of both single and binary mixture droplets in a heated convective environment are reviewed Vaporisation of a sessile droplet on a heated solid substrate heated below droplet saturation temperature is re-viewed in the third section Finally presented is a review of typical work on the motions which occurs inside an evaporating droplet, with or without the presence of a solid substrate The main body of this work presented in Chapter 3 to Chapter 5 which have already been submitted or published in peer reviewed conferences/journals

prob-Chapter 3 presents a numerical modelling of feed vaporization in a fluid catalytic cracking riser The first section depicts the theoretical background of different homogeneous and het-erogeneous models which have been proposed in the literature followed by the development

of a new physical heterogeneous vaporisation model accounting for the explicit particle contact Next, validations of homogeneous models with published vaporization data are then presented followed by an analysis of the new model predictions applied for the vac-

Chapter 5 explores evaporation of a sessile binary droplet on a heated spherical particle The influence of solid surface temperature and liquid composition on the vaporisation are present-

ed through the temporal variations in droplet size, temperature, wetted contact area and phase contact angle This is followed by an empirical model predicting the change in contact angle of an evaporating droplet Next, a qualitative analysis on the internal motions inside droplet resulted from Marangoni flows is drawn and conclusions are shown in the last sec-

three-tion

Chapter 2 11

In this chapter, first presented is a brief review of the previous studies on droplet porisation in a typical multiphase process application - fluid catalyst cracking riser to underlie the background knowledge of the vaporisation behaviour of a droplet with and without the presence of hot solid particles Next, some selected numerical studies on the vaporisation of both single and binary mixture droplets in heated convective environment are reviewed fol-lowed by a summary of the published experimental work that confirms the need for this the-sis Vaporisation of a droplet deposited on a heated solid substrate at low temperature is re-viewed in the third section Finally presented is a review of the studies on internal motions which take place inside an evaporating droplet with or without the presence of a solid sub-strate

va-2.1 Vaporisation of droplets in multiphase (gas-solid fluidised bed) system

In gas-solid fluidised bed, solid particles come into contact with a gaseous flow with a range of velocities which is dependent on the applications In fluidised bed granulation, liquid coating materials are sprayed as atomised droplets into a particle bed and vaporisation of the liquid film takes place when droplet are in contact with the granules (T.-J Wang et al., 2001)

In petrochemical operations, fluidised bed plays important roles in fluid coking and fluid alytic cracking unit In fluid coking process, bitumen or heavy petroleum fractions are inject-

cat-ed as atomiscat-ed liquid into a fluidizcat-ed particles bcat-ed; interaction between the hot coke particles and liquid droplets enable the quick vaporisation followed by cracking to yield distillate products from the coker feeds (Gray et al., 2001; McMillan et al., 2005)

In fluidized catalytic cracking risers, droplets are injected in to a gas-solid flow cluding hot steam and catalysts which are preheated well above the boiling temperature of the

in-Chapter 2 12

feedstock Vaporisation of the feedstock is then completed through heat received from both hot steam flows and catalysts when droplets are in contact with the catalyst particles The commonly used approaches describing the droplet vaporization process under these condi-tions are homogeneous mode wherein droplets receive heat only from the surrounding hot gas, and heterogeneous mode wherein vaporization process involves direct collision between droplet and hot solid particles Numerous studies have been conducted on homogeneous va-porization of droplets involving both mono and multi-component droplets especially in rela-tion to the spray combustion in internal combustion engines and liquid fuelled burners which

is reflected in the recent studies of Sazhin (2014) and Sirignano (2010) A review of the vant literature on homogeneous vaporisation is presented later in section 2.2

rele-Although critical, a large number of studies reported on the numerical simulations of FCC riser apparently ignore the feed vaporization phenomenon because of instantaneous na-ture of the process (Gan et al., 2011; Gao et al., 1999; Lopes et al., 2011; Wu et al., 2010) Some other studies include rather simpler vaporization models without considering the drop-let-particle interactions in their numerical modelling (Behjat et al., 2011; Gan et al., 2011; Gao et al., 1999; Lopes et al., 2011; Wu et al., 2010) Possibly, the complex nature of such interactions in the feed vaporization zone coupled with simultaneous heat and mass transfer process appears to be quite challenging to formulate the suitable physical models to include

in the numerical modelling studies A summary of typical numerical studies which include simple vaporisation approaches was presented in Table 2.1 to reflect the status of the droplet vaporization process modelling under film boiling conditions

Gao et al (1999) Instantaneous

I.-S Han et al (2000) The feed vaporization section is modelled as pseudo heat transfer system in which two streams (catalyst and

feed) join The catalyst temperature after feed vaporization is calculated by the energy balance assuming batic operation, and the vapour temperature is calculated by the Antoine equation

adia-Gao et al (2001) Vaporization was calculated by dividing mass of single droplet by fixed vaporization time (0.2 s) (simplified

d 2 law) Both sensible heat transfer and latent heat transfer were considered

Gupta and Subba Rao

(2001)

Sensible heat transfer between solid and liquid and latent heat transfer between gas and liquid considered

Bowman et al (2002) The model was based on the fundamental physics of stationary single droplet vaporization and then modified

for large groups of droplets in a convective environment using correlations

S.-L Chang and Zhou

Chapter 2 14

X Wang et al (2004) Droplet vaporization in gas phase was considered Droplet-solid heat transfer was accounted indirectly by

in-corporating a modified Nusselt number which accounted for influence of vapour and solid particles

Lopes et al (2011) Instantaneous

Behjat et al (2010) Vaporization of droplets was considered to occur in gas following three different stages – inert heating,

vapori-zation and boiling The reduction in heat transfer coefficient from droplet to gas phase due to presence of the vapour film around the droplet was accounted

Gan et al (2011) Instantaneous

Behjat et al (2011) Vaporization of droplets was considered to occur in gas following three different stages – inert heating,

vapori-zation and boiling The reduction in heat transfer coefficient from droplet to gas phase due to presence of the vapour film around the droplet was accounted

Pougatch et al (2012) Two mechanisms of liquid spreading in the fluidized bed were considered: first, by random motion of particles,

and second, by liquid exchange during a collision Interfacial heat transfer between droplet and gas phase was obtained through the use of the Nusselt number correlation by Ranz and Marshall correlation

J Chang et al (2012) Fixed droplet diameter was considered and droplet vaporization time considered to be proportional to square to

droplet diameter Ahsan (2015) Instantaneous vaporization of the feed droplets which are in contact with the hot catalyst particles was consid-

ered The resulting heat transfer involves removal of both latent heat of vaporization and sensible heat from the hot catalyst and vapour thus formed remains in thermal equilibrium with the catalyst particles

Q Yang et al (2016) Complete vaporisation assumed just after injection

John et al (2017) Instantaneous

Li et al (2017) Instantaneous

Chapter 2 15

Only very few studies have focused on the detailed droplet-particle interaction anism and the subsequent vaporisation approaches (Buchanan, 1994; Martin, 1990; Mirgain

mech-et al., 2000; Mitra, 2016; Nayak mech-et al., 2005) which are discussed below

Martin (1990) was possibly the first time to propose two different heterogeneous heat transfer mechanisms in FCC riser In the first mechanism, it was assumed that feed droplets are larger than the catalyst particles and direct contact heat transfer at particle surface area occurs through the thermal conduction during collision In the second mechanism, Lei-denfrost effect was assumed to occur during the collision of feed droplet and catalyst particle which prevents direct contact between the droplet and hot particle due to presence of a thin vapour film at the droplet-particle contact area No quantification in terms of physical model-ling of these mechanisms however was reported

Later on, in the same line of thought, Buchanan (1994) proposed two physical models

of the heterogeneous vaporization process to represent the two limiting cases of ous heat transfer process during droplet-particle collision: (i) infinitely fast heat transfer be-tween droplets and particles where the entire heat was assumed to be transferred instantane-ously from the catalyst particle to the feed droplet during collision; (ii) hard sphere model where a pair of droplets and particles was assumed to undergo an elastic collision due to presence of a thin vapour film (Leidenfrost effect) at the solid-liquid contact area No physi-cal collision model however was proposed and the presence of solid catalyst particles was accounted through modification of Reynolds number in the expression of Ranz-Marshall cor-relation (1952) for convective heat transfer by inclusion of solid volume fraction

heterogene-In these two cases analysed by Buchanan (1994), the thermal history of a droplet was divided into two distinct phases: heat-up and vaporization In the first phase, droplet is heated from initial temperature to its boiling temperature without vaporization; and during the sec-

Chapter 2 16

ond phase, only the vaporization was assumed to occur without any change in temperature Total vaporization time was therefore calculated by summing up the heating and vaporization time These two limiting cases i.e (i) and (ii) also set the maximum and minimum possible heat transferred to droplets during collisions with catalyst particles hence the minimum and maximum possible vaporization time respectively

Contrary to the theory proposed by Martin (1990) and Buchanan (1994), Mirgain et

al (2000) argued that Leidenfrost effect possibly does not occur during droplet-particle

colli-sion in FCC riser primarily because of high Weber number (We> 5000) of the injected lets They reasoned since the critical We number for droplet breakup is reported to be ~ 80 in

drop-Leidenfrost regime (Wachters & Westerling, 1966), droplet must break upon interactions with particles under the FCC operating conditions It is critical to know if feed droplets could

be vaporised completely within the typical residence time in riser The residence time in an industrial scale FCC riser is usually defined as the time since the feed is injected into the bot-tom of the riser reactor until the product vapours come out at the top of the riser This resi-dence time includes time for both feed vaporization and subsequent cracking reactions Mirgain et al (2000) critically analysed the effect of homogeneous and heterogeneous heat transfer modes on the vaporization time in FCC riser and showed that within the typical resi-dence time in a riser, complete vaporization of the feedstock is not possible without including the heterogeneous mode which accounts for the enhanced heat transfer coefficient Three dif-ferent droplet-particle collision mechanisms were proposed between a liquid-covered and a liquid free catalyst particle: (i) two particle stay bonded by the liquid film (ii) liquid film is shared between the two particles and (iii) liquid film is completely transferred to the other particle These interactions mechanisms provide realistic insights to heterogeneous vaporiza-

Recently Mitra et al (2016) showed that in a droplet-particle system in film boiling regime (particle temperature 250 to 350 oC), Leidenfrost effect is limited to only up to a

range of impact Weber numbers Beyond this range (We ~ 34 to 146), a clear transition from

rebound to disintegration regime was noted The observed transition indicates that direct tact between droplet and particle is inevitable when relative velocity exceeds a threshold val-

con-ue Also shown was the effect of impact Weber number on the droplet-particle contact time which exhibited a decreasing trend with increasing Weber number up to the transition thresh-old and then indicated much less dependency on the Weber number once the droplet under-goes disintegration The above discussion shows that limited research is indeed available on the droplet-particle interaction mechanisms related to vaporisation of feed droplets in multi-phase systems like FCC units There are different modelling approaches reported which may provide different vaporisation times and a comprehensive comparison of these models is es-sential to identify an operation window Also, there is a pressing need to develop more phys-

Chapter 2 18

ics based models as opposed to empirical correlations that capture the underlying nisms of phase interactions for more complete description of the multiphase vaporisation pro-cess Section 2.2 and 2.3 review the two important aspects of droplet vaporisation process - convective (homogeneous mode) and conductive (heterogeneous), respectively, to provide an adequate background of the problem undertaken in this study

mecha-2.2 Vaporisation of a suspended droplet in heated flowing gas stream

Vaporisation of droplet in a convective environment is of interest in spray combustion

or in FCC risers wherein droplets are injected at a high velocity into the hot gaseous or solid environment respectively Vaporisation occurs owing to the convective heat received from the hot gas stream Studies of the vaporisation of a moving droplet in a stagnant gas en-vironment have been analogised to a suspended droplet vaporising in a flowing gas stream using identical relative velocity between droplet and the gas flow This section first presents a review of typical numerical modelling studies of both single and multicomponent droplet va-porising in heated gas flows, followed by a review of selected experimental work in the same field

gas-Figure 2.1 Schematic of a suspended evaporating droplet

Chapter 2 19

Figure 2.1 shows a suspended droplet vaporising in a flowing gas wherein heat and mass transfer take place at the droplet interface The vaporisation rate can be obtained using Fick’s law assuming thermodynamic vapour-liquid equilibrium exists at the liquid-gas inter-face whilst heat transfer represented by transient temperature of the droplet can be obtained from the energy balance between convective heat gained and heat loss due to evaporation (see Appendix A for the full derivation) Sherwood and Nusselt number via Ranz-Marshall (or modified Ranz-Marshall) correlations are utilised to represent mass and heat transfer of the droplet the respectively Selected reports of Sherwood and Nusselt numbers in the litera-ture which based on the originally Frossling’s (Frossling, 1938) mass transfer correlation was reviewed in Table 2.2 with corresponding operating conditions

Table 2.2 Development of heat and mass transfer correlations for droplet evaporation*

ty in the Reynolds number which is the free stream densi-ty)

Chapter 2 20

(*): the used subscript “m” means “modified” Reynolds number using free-stream density, “f” means film ditions (vapour film at the droplet interface) and “∞” means free-stream density

con-Numerical approaches for the gas phase characterised by Sherwood and Nusselt number

is strongly coupled to the liquid phase calculations through the linked parameters, which is temperature and mass fraction at the liquid-vapour interface According to Sirignano (2010), heat transfer inside the liquid droplet can be classified into six different modelling approaches

of increasing complexity (i) constant droplet temperature models which yield the

well-known d 2 law relating the linear relationship between droplet diameter or radius with time); (ii) infinite liquid thermal conductivity models wherein droplet temperature is considered homogeneous but time-varying; (iii) spherically symmetric transient droplet heating model (diffusion limit) wherein droplet temperature is inhomogeneous and time-varying; (iv) effec-tive thermal conductivity model which considered droplet temperature to be inhomogeneous and time-varying and internal motions accounted by introducing an effective thermal diffu-sivity; (v) vortex model; (vi) complete solution of the Navier-Stokes equation

Aggarwal et al (1984) compared available droplet evaporation models and suggested the use of the diffusion limit model which assumes a temperature gradient in the liquid phase for negligible droplet Reynolds number Also, suggested in this work was the simplified vor-

2 0.6 Rem Sc f / B M

( )0.5 0.33