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Discharge of buoyant fluid jets and particle-laden jets into stratified ambient fluid Kim, Sunkyoung Annie 2002

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DISCHARGE O F BUOYANT FLUID JETS AND P A R T I C L E - L A D E N JETS INTO STRATIFIED A M B I E N T FLUID by Sunkyoung Annie K i m  B . A . Sc., Chungnam National University, Korea, 1994 M . A . Sc., Chungnam National University, Korea, 1996  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies Department of C i v i l Engineering  W e accept this thesis as conforming to the requited standard  T H E U N I V E R S I T Y O F BRITISH C O L U M B I A October 2001 © Sunkyoung Annie K i m , 2001  In presenting this thesis  in partial fulfilment  of the  requirements  for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes department  or  by  his  or  her  representatives.  may be granted It  is  by the head of my  understood  that  copying  or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  ^  v  1  1  E V v * y rl eeHt^v.  The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  0c\  , M>0  \  Abstract Extraction o f petroleum from o i l sands generates a vast quantity o f fine tailings. A common form o f tailings treatment involves discharging the tailings at an angle o f minus a few degrees into a tailings pond. Tailings ponds generally have a two-layered structure involving an upper layer o f clear water separated by a pycnocline from a lower layer o f sludge.  Discharge o f fine tailings into such ponds raises concerns about the release o f  petroleum residuals into the upper layer and hence into the surrounding environment.  This study investigates the dynamics o f fluid jets and particle-laden jets discharged downward at an angle o f 3° into stratified ambient fluid. This in turn allows identification of the discharge conditions that minimize the release o f undesirable substances into the upper layer o f the pond. A series o f laboratory experiments were conducted for round buoyant fluid jets and particle-laden jets, the latter consisting o f buoyant interstitial fluid and varied particle concentration.  Important parameters affecting the behavior o f fluid jets in two-layer systems were found to be the buoyancy flux, the magnitude o f the density step, and the discharge distance to the pycnocline.  These were combined into a dimensionless parameter, W, which was then  used to determine three flow regimes: the weak impingement, strong impingement and penetration regimes.  Buoyant jets impinged weakly on the pycnocline and proceeded  horizontally when *F < 0.5, the upper layer being undisturbed by the discharge. However, for *F > 0.9, buoyant jets penetrated to the water surface after discharge and spread above the pycnocline. During penetration, the entrained fluid from the lower layer was transported and mixed throughout the upper layer. For the transition regime, 0.5 < *F < 0.9, buoyant jets caused significant mixing in the upper layer but no density change occurred at the surface.  ii  The small discharge angle (-3°) was found to not significantly affect the behavior o f buoyant jets relative to horizontal discharge.  Backflows occurred along the pycnocline  when the jet angle at the pycnocline was greater than 7° for the weak and strong impingement regimes.  For the penetration regime *F > 0.9, some jet flow accumulated  along the pycnocline and backflows also formed at the surface o f the upper layer. Coanda bottom attachment occurred, independently o f the ambient fluid conditions, when the dimensionless parameter h/£  M  > 0.22.  The dimensionless maximum rise height and the top o f the spreading layer were found to increase linearly with *F in the strong impingement regime but were constant in the weak impingement regime. A l s o , the spreading layer thickness increased with a dimensionless momentum term regardless o f the presence o f the density step.  Particle-laden jets with low particle concentration were found to behave like fluid jets, whereas those with high particle concentration behaved like negatively buoyant fluid. The particles were found to move with interstitial fluid and thus get transported to the upper layer during penetration.  A l s o , grouping behavior o f individual particles was observed.  After the source momentum decays, the behavior o f particle-laden jets was determined by a density difference ratio ( R ) and *¥.  Four flow regimes were classified based on R and ¥ . When 0 < R < 1, all particle-laden jets penetrated into the upper layer or strongly impinged on the pycnocline, depending on the magnitude o f *F . However when R < - 2 . 0 , jets plunged to the bottom and propagated as a turbidity current regardless o f Y . After significant settling, eventually the interstitial fluid rose but remained trapped under the pycnocline. When - 2.0 < R < 0 , jets initially plunged but after particle settling, formed an intermediate level gravity current.  The analysis o f gross flow characteristics indicated that particles reduce the potential o f buoyant interstitial fluid to rise or significantly penetrate into the upper layer.  iii  Table of Contents  Abstract  ii  T a b l e o f Contents  iv  L i s t o f Figures  ix  L i s t o f Tables  xv  Notation  xvi  Acknowledgement  xxi  Chapter 1  Introduction  1  1.1  Background  1  1.2  Objectives and Applications  4  1.3  Scope and Methodology  5  1.4  Organization  6  Chapter 2  Literature Review  9  2.1  Introduction  9  2.2  Jets and plumes  9  2.2.1  Simple jets, plumes and buoyant jets  9  2.2.2  Theoretical background for buoyant jets  11  2.2.3  Entrainment  14  2.2.4  Important parameters  15  2.2.4.1 Characteristic length scales  15  2.2.4.2 Dimensionless parameters  17  Effect o f source geometry  18  2.2.5.1 Discharge angle  18  2.2.5.2 Proximity to the adjacent horizontal bed  18  2.2.5  iv  2.3  Dynamics o f buoyant jets in various ambient conditions  19  2.3.1  Classification o f ambient fluid  19  2.3.2  Stratified ambient fluid  20  2.3.2.1 Linearly stratified ambient fluid  20  2.3.2.2 Two-layer system  21  2.4  Previous experimental studies  23  2.5  Behavior o f particle-laden flow  24  2.5.1  Particle clouds without source momentum  24  2.5.2  Characteristic o f particles in flow  26  2.5.2.1 Particle settling  26  2.5.2.2 Effect o f particle size and concentration  27  2.5.2.3 Density and buoyancy  28  2.5.3  Gravity current 2.5.3.1 Particle-laden flow with reversing buoyancy  2.5.4 2.6  2.7  Experimental conditions o f previous studies  29 29 30  C O R M I X (Cornell M i x i n g Zone Expert System)  32  2.6.1  32  CORMIXlv3.2  Summary  Chapter 3  Experimentation  34  36  3.1  Introduction  36  3.2  Experimental apparatus  36  3.2.1  Physical set-up  36  3.2.1.1 M a i n experimental tank  37  3.2.1.2 Jet discharge system  39  3.2.1.3 Ambient fluid stratification system  40  Instrumentation  41  3.2.2.1 P M E conductivity and temperature probe  41  3.2.2.2 Calibrationof a P M E probe  42  3.2.2  3.2.2.3 Anton Paar density meter  43  3.2.2.4 M A C H Spectrophtometer  43  Material  44  3.2.3.1 Jet and ambient fluid  44  3.2.3.2 Particles  44  Experimental conditions  48  3.3.1  Fluid jet  48  3.3.2  Particle-laden jet  52  3.2.3  3.3  3.4  Experimental procedures  52  3.4.1  Preparation  52  3.4.1.1 Stratification o f ambient fluid  52  3.4.1.2 Calibration o f the P M E probe and flow visualization  56  Measurement and sampling  56  3.4.2.1 Fluid jet  56  3.4.2.2 Particle-laden jet  57  3.4.2  3.5  Data acquisition and processing  58  3.5.1  Data acquisition  58  3.5.1.1 Dye concentration measurement  58  3.5.1.2 Suspended particle concentration  58  3.5.1.3 B u l k density  59  3.5.1.4 Density profile  59  Density data processing  61  3.5.2.1 Fluid density estimation  61  3.5.2  Chapter 4  Results and Discussion: Fluid Jets  65  4.1  Introduction  65  4.2.  Buoyant fluid jet in a two-layer system  65  4.2.1  Behavior o f buoyant jets  66  4.2.1.1 Weak impingement  66  4.2.2  4.2.1.2 Strong impingement  66  4.2.1.3 Penetration  68  Determination o f flow regimes  72  4.2.2.1 Penetration/impingement parameter, *F  72  4.2.2.2 Density relation  76  4.2.2.3 Comparison o f flow regimes with prediction o f CORMIX1  78  4.2.3  Backflow  79  4.2.4  Coanda bottom attachment  82  4.2.4.1 Comparison with previous studies  84  4.2.4.2 Comparison with C O R M I X prediction  86  Analysis o f gross flow characteristics  88  4.2.5  4.2.5.1 M a x i m u m rise height and the top o f the spreading layer ..89 4.2.5.2 Spreading layer thickness 4.3  Summary o f fluid jets  Chapter 5  Results and Discussion: Particle-laden jets  94 96  98  5.1  Introduction  98  5.2  Particle-laden jets in two-layer systems  98  5.2.1  Behavior o f particle-laden jets  99  5.2.2  Determination o f flow regimes  101  5.2.3  Particle distribution and interstitial fluid dilution  103  5.2.3.1 Particle distribution in ambient fluid  103  5.2.3.2 Dye concentration profile  105  5.2.3.3 Effect o f R on the characteristic width (b)  109  Analysis o f gross flow characteristics  111  5.2.4  5.2.4.1 M a x i m u m rise heigh and the top o f the spreading layer .113  5.2.5  5.2.4.2 Spreading layer thickness  117  Comparison with C O R M I X prediction  119  vii  5.3  Chapter 6  5.2.5.1 Flow classification  119  5.2.5.2 Centerline concentration  121  Summary o f particle-laden j ets  Comparison between Fluid Jets and Particle-laden Jets  122  125  6.1  Homogeneous ambient fluid  125  6.2  Two-layer system  128  6.2.1 M a x i m u m rise height and penetration  128  6.2.2 Top o f the spreading layer  130  6.2.3 Spreading layer thickness  131  Chapter 7 7.1  Conclusions and Recommendations  133  Conclusions  133  7.1.1  Buoyant fluid jets in two-layer system  133  7.1.2  Particle-laden jets in two-layer system  135  7.2  Contributions  137  7.3  Recommendations for future research  138  References  140  Appendix A . Buoyant jets in linearly stratified ambient fluid  147  Appendix B . Particle-laden jets i n linearly stratified ambient fluid  157  Appendix C . Comparion o f fluid jets and particle-laden jets in linearly stratified ambient fluid Appendix D . Overview o f the experimental set-up  160 164  List of Figures Chapter 1 Figure 1.1  A sketch of a tailings pond (After M a c K i n n o n , 1989)  2  Figure 1.2  Overview of the present study  7  Chapter 2 Figure 2.1  A sketch of a jet geometry and flow regions  Figure 2.2  Schematic diagrams for ambient condition based on the density profile:  10  (a) linearly stratified fluid, (b) two-layer system with the pycnocline and (c) two-layer system with a linearly stratified lower layer (Jirka and Doneker, 1991) Figure 2.3  20  F l o w pattern in shallow and deep ambient fluid (a) a buoyant jet with initial Coanda attachment and transition to surface jet, (b) buoyant jet and transition to surface jet without bottom attachment, (c) confined surface jet and (d) surface jet (After Sobey et al., 1988)  22  Figure 2.4  Behavior of a particle cloud (After Ruggaber, 2000)  24  Figure 2.5  C O R M I X 1 flow classification for buoynat submerged discharge in uniform density layer (Jirka et al., 1996)  Figure 2.6  33  Summary o f the scope of the present study in relation to the range of possible related studies  35  Figure 3.1  Experimental facility  37  Figure 3.2  A sketch of the main experimental tank  38  Figure 3.3  A sketch of discharge system  39  Figure 3.4  Ambient fluid stratification system  40  Figure 3.5  P M E conductivity and temperature probe  41  Chapter 3  ix  Figure 3.6  Anton Paar D M A 500 density meter  43  Figure 3.7  M A C H Spectrophotometer  43  Figure 3.8  Particle size distribution o f glass beads  45  Figure 3.9  Shape o f particles (a) fine tailings, (b) mixture o f fine tailings and glass beads and (c) glass beads  Figure 3.10  Experimental conditions for fluid jets: (a) two-layer system and (b) linearly stratified fluid  Figure 3.11  47  49  Experimental conditions for particle-laden jets (a) two-layer system and (b) linearly stratified ambient fluids  54  Figure 3.12  Vacuum filter system  58  Figure 3.13  Definition sketch o f parameters  60  Figure 3.14  Calculation procedure o f fluid density (After Head, 1983)  63  Chapter 4 Figure 4.1  Sketches o f behavior o f buoyant jets and density profiles in two-layer systems: (a) weak impingement ( A 19) (b) strong impingement (A71) and (c) penetration (A70), ( — ) : density profile before discharge, ( — ) after discharge  Figure 4.2  Density profiles before ( — ) and after (—) a buoyant jet discharge along the tank for weak impingement (A19)  Figure 4.3  69  Impingement o f buoyant jets in two-layer system: (a) weak impingement (A3 7) and (b) strong impingement (A51)  Figure 4.4  67  70  Process o f a buoyant jet penetration in two-layer system (A33): (a) penetration, (b) lateral-horizontal spreading and (c) horizontal spreading71  Figure 4.5  A buoyant jet in two-layer system  72  Figure 4.6  F l o w regimes o f buoyant jets in two-layer systems  75  Figure 4.7  Dimensionless density (y) o f buoyant jets in two-layer systems  77  Figure 4.8  Backflows in two-layer systems: (a) no-backflow (A24,  - 0.34,  F =30.1, and (b) backflow (A40, T = 0.52, F = 8.9)  80  Figure 4.9  Development o f a backflow at the pycnocline  81  Figure 4.10  Backflow o f fluid jets in two-layer systems  83  Figure 4.11  Conanda bottom attachment (A45, F = 33.4, h/£  Figure 4.12  Coanda attachment in various ambient fluid conditions  Figure 4.13  Comparison o f the Coanda attachment with previous studies (Sobey et al.,  d  d  d  = 0.21)  u  85 86  1988; Johnston et al., 1994) and C O R M I X prediction  87  Figure 4.14  Definition sketch o f parameters in a two-layer system  88  Figure 4.15  Dimensionless maximum rise height (Z /h  92  Figure 4.16  Location o f maximum height o f rise ( X / d ) in two-layer systems  Figure 4.17  Trajectory o f the top o f the spreading layer in two-layer system:  m  ) in two-layer systems  i  m  A4(A,./</=18.4 F =\6.1), d  A21  10.2 F =93), d  A 3 8 (h /d= i  A\l{h ld= i  18.4  92  F =%.9), d  A 2 3 (/?,-1d= 10.2  F =\%.\), d  5.1 F = 18.7), A41 (h, Id= 5.1 F = 16.0) d  d  93  Figure 4.18  Dimensionless top o f the spreading layer ( Z / h ) o f buoyant fluid jets ..94  Figure 4.19  Dimensionless spreading layer thickness ( T /h )  t  f  i  l  o f buoyant fluid jets i n  two layer systems  95  Chapter 5 Figure 5.1  Behavior of particle-laden jets i n two-layer systems:(a) penetration (P20), (b) impingement (P24), (c) weak plunging (P22) and (d) strong plunging (P23)  100  Figure 5.2  F l o w regimes for particle-laden jets in two-layer systems  104  Figure 5.3  Relative dye concentration and particle distribution for (a) Penetration (P57), (b) Weak plunging regime (P58)  106  Figure 5.4  Dye concentration profile and Gaussian distribution for (a) Penetration (P5 7) and (b) Impingement (P24)  Figure 5.4  107  (continued) Dye concentration profile and Gaussian distribution for (c) Weak (P22) and (d) Strong plunging (P23)  108  Figure 5.5  Jet centerline displacement (s) along the jet trajectory (x/ L)  110  Figure 5.6  Centerline displacement and the concentration characteristic width (b) o f particle-laden jets  Figure 5.7  Ill  Definition o f parameters o f a particle-laden jet in a stagnant two-layer system  Figure 5.8  112  Dimensionless maximum rise height ( Z / h •) o f particle-laden jets in m  two-layer systems Figure 5.9  115  Dimensionless top o f the spreading layer ( Z , / h j ) o f particle-laden jets in two-layer systems  Figure 5.10  116  Dimensionless spreading layer thickness ( T / h ) o f particle-laden j ets i n f  (  two-layer systems Figure 5.11  118  Relative error between the experimental results and C O R M I X 1 prediction  122  Chapter 6 Figure 6.1(a) Behavior o f a buoyant fluid jet in homogeneous ambient fluid (A47) .... 126 Figure 6.1(b) Behavior o f a particle-laden jet with buoyant interstitial fluid in homogeneous ambient fluid: (i) momentum-dominant jet behavior, (ii) plunging, (iii) detrainment o f interstitial fluid and bulk particle settling and (iv) forming a horizontal spreading layer after particle settling (P61) Figure 6.2  Centerline dye concentration and Gaussian distribution o f (a) a fluid jet and (b) a particle-laden jet in homogeneous ambient  Figure 6.3  127  Comparison o f the maximum rise height (Z /h ) m  particle-laden jets in two-layer systems  i  fluid  129  between fluid jets and 130  Figure 6.4  Comparison o f the top o f the spreading layer ( Z /h t  {  ) between fluid jets  and particle-laden jets in two-layer systems Figure 6.5  131  Comparison o f the spreading layer thickness ( T /h ) f  i  between fluid jets  and particle-laden jets in two-layer systems  132  Appendix Figure A . 1  Buoyant jets in linearly stratified ambient fluid (a) A 1 3 (F TV = 0.76), ( b ) A 5 3 ( F  Figure A . 2  =22.9,  d  r f  =17.7, N = 0.75)  148  Density profiles before (—) and after (— ) a buoyant jet discharge along the jet trajectory in linearly stratified ambient fluid (A12)  149  Figure A . 3  A definition sketch o f a buoyant jet in a linearly stratified fluid  150  Figure A . 4  Dimensionless maximum height o f rise (Z /f ) m  b  in linearly stratified ambient  fluid Figure A . 5  152  Dimensionless location o f the maximum height o f rise in linearly stratified fluid  152  Figure A . 6  Dimensionless top o f spreading layer in linearly stratified fluid  154  Figure A . 7  Dimensionless spreading layer thickness in linearly stratified fluid  155  Behavior o f particle-laden jets in a linearly stratified fluid (a) fluid jet like Figure B . l  behavior, (b) intermediate (c) plunging in the near-field and (d) detrainment of interstitial fluid i n the far  field  158  Dimensionless gross flow characteristics o f particle-laden jets i n linearly Figure B.2  Figure C . 1  stratified  fluid  159  Comparison o f the dimensionless maximum rise height (Z /£' ) m  b  between  fluid jets (Wong, 1984; present study) and particle-laden jets i n linearly stratified fluids  161  Figure C.2  Comparison o f the dimensionless top o f the spreading layer (Zj£  )  N  between fluid jets (Jirka, 1991; present study) and particle-laden jets Figure C.3  Figure D . 1  Comparison o f the dimensionless spreading layer thickness (T /t ) (  b  162 between  fluid jets and particle-laden jets in linearly stratified fluids  162  Overview o f the experimental set-up  164  xiv  List of Tables Table 2.1  Properties o f turbulent round jet and pure plume (Fischer et al., 1979)  12  Table 2.2  Summary o f previous experimental studies on horizontal buoyant jets in twolayer systems and homogeneous shallow ambient fluid  23  Table 2.3  Experimental conditions o f previous studies on particle-laden flow  31  Table 3.1  N a C l standard solution for calibration (After Weast, 1985)  42  Table 3.2  Experimental conditions for fluid jets in two-layer systems  50  Table 3.3  Experimental conditions for fluid jets in homogeneous ambient fluid  51  Table 3.4  Experimental conditions for fluid jets in linearly stratified fluid  51  Table 3.5  Experimental conditions for particle-laden jets in two-layer systems  55  Table 3.6  Experimental conditions for particle-laden jets in linearly stratified ambient fluids  55  Table 3.7  Summary o f experimental parameters and measurement techniques  59  Table 5.1  Classification o f particle-laden jets  Table 5.2  Comparison o f C O R M X I 1 prediction and experimental results for flow classification  103  120  XV  Notation The following symbols are used in this thesis:  A . Fluid jets  A  nozzle cross-sectional area  B  source buoyancy flux; B = Qg'  b  characteristic width o f concentration at a radical position where c/c  b  characteristic width o f velocity  b  experimental constant for a round plume (b  0  m  u  2  2  C  s  salt concentration  2 5  conductivity at 25 °C  C c  = exp(-l)  = 0.35, Fischer et al. 1979)  maximum concentration  m  C  dye concentration at source  c,  experimental constant o f maximum rise height for fluid jets  c  experimental constant o f top o f the spreading layer for fluid jets  0  2  D  molecular diffusion coefficient, m Is  d  nozzle diameter  2  F  source densimetric Froude number; F = uj-Jg' d  G  circuit gain o f a P M E conductivity-temperature probe  g  gravitational acceleration  g'  modified gravitational acceleration  g'  modified gravitational acceleration at the centerline  d  m  d  0  xvi  g'  0  modified acceleration based on the difference between jet and ambient fluid density; g' = g(p 0  g'  a  -Pj)/p  a  a  modified acceleration based on the difference between lower and upper layer density;  g' = g(p a  2  /?,)/' p  2  H  total water depth above the nozzle  h  discharge height above the bed  /z,  upper layer thickness in two-layer system  h  proximity to the pycnocline from a discharge nozzle in a two-layer system  h  half-thickness o f density interface  h,  half-thickness o f spreading layer  t  x  2 J  calibration constant o f a P M E probe  K  calibration constant o f a P M E probe  L  length o f experimental tank  i'  length scale characterizing the relative importance o f the buoyancy to ambient  b  stratification ; £' = B  £  M  B /N U3  length scale characterizing the relative importance o f the momentum and buoyancy o f a buoyant jet; £  £  length scale characterizing the relative importance o f the momentum to  N  ambient stratification; £  N  £  =M /^ 3M  M  q  length scale characterizing the relative importance o f the jet source geometry; £  Q  M  =M  =M/4B  source momentum flux; M = Qu  M  M o l a r concentration at 25 °C  M  vertical momentum  0  v  xvii  m  specific momentum flux  m  horizontal momentum  m  momentum flux due to buoyancy for a plume  N  Brunt-Vaisala frequency buoyancy frequency; N =  h  v  — j? dc —-—V Po d  P  impingement height above the pycnocline  Q  source kinematic volume flux; Q = ftd u/4  r  radius o f a jet  d  2  R  Reynolds number; R = ud/v  s  centerline displacement  t  time  T  water temperature (°C)  e  T  final spreading layer thickness  u  time-averaged j et velocity  u  initial mean jet velocity  u  maximum time-averaged velocity  f  m  V  electrical voltage o f a P M E probe  X  volumetric concentration o f particles  x  downstream distance  0  X  locations where maximum height o f rise occurs  z  vertical distance from the jet centerline  m  Z  b  Z  m  bottom o f spreading layer maximum height o f rise  Z  top o f spreading layer  a  entrainment coefficient; a - 0.057 + 0 . 5 F r sin 9  P  specific buoyancy flux  t  z  - 2  xviii  y  non-dimensional density o f fluid jets; y = p -pjp -  p  volume flux at distance z  v  kinematic viscosity  9  discharge angle  9  p  jet angle at the pycnocline  Pj  density o f jet at the source  p  density at the pycnocline  p  density o f the ambient fluid at discharge level  /?,  density o f upper layer in a two-layer system  p  density o f lower layer in a two-layer system  p (T)  density o f fresh water at T °C  Ap  density difference between the ambient fluid and jet fluid at discharge level;  x  t  a  2  W  p  2  i  (Pa-Pj) Ap  density difference between the lower layer and the upper layer; ( p  Ap  density increment due to N a C l  CT(T)  conductivity at T °C in Figure 3.14  cr(ref)  reference conductivity  %  interface thickness g = j4nDt  *¥  impingement-penetration parameter; F = B  a  s  v  2 / 5  /g^  3 / 5  h  2  - p) x  i  B . Particle-laden jets B  b  initial bulk buoyancy flux; B = Q\ b  Pa  V  J (  B  f  buoyancy flux o f the interstitial fluid; B = Q(\ - X)\ g  P -P ^ a  f  f  V  Pa  J  XIX  (B  f  = 5 in fluid jets)  B  p  bulk density o f a particle cloud  c  3  experimental constant o f maximum rise height for particle-laden jets  c  4  experimental constant o f top o f the spreading layer for particle-laden jets  p  particle diameter  d  E  R  Relative error between measured dye concentration ( C ) and C O R M I X 1 M  prediction ( C ) ; E c  R  =C  -C /C  M  C  M  R  dimensionless density o f particle-laden jets; R = p -  R  size o f a particle cloud  R  non-dimensional density o f particle-laden fluid; R  a  c  h  w  s  h  particle settling velocity; w = s  — ^ \%p v  pj p b  a  p  = pj- - p jp  f  a  b  -  p  a  p  a  X  volumetric particle concentration  z  critical depth o f the transition o f a particle cloud  c  p  bulk density o f the particle-laden jet at the source  p  density o f the interstitial fluid o f particle-laden jet at the source  p  particle density  b  f  XX  Acknowledgement I would like to thank my primary supervisor Dr. Greg Lawrence for his invaluable intellectual guidance, patience and generosity, and my co-supervisor Dr. Loretta L i for her warm encouragement and sincere supervision. Without Dr. Lawrence and Dr. L i , my P h . D . would not have been possible. I wish to also show my sincere appreciation to my thesis committee, Dr. Peter Ward, Dr. Susan A l l e n and Dr. Noboru Yonemitsu and the university examiner, Dr. Rob M i l l a r for their kindness and valuable comments on my thesis.  I would also like to thank Kurt Nielson, Scott Jackson, Douglas Hudniuk, Douglas Smith and Herald Schempp o f the C i v i l Engineering Hydraulic Laboratory, for their assistance in constructing the experimental facility, the data acquisition instrument and their constant help without any hesitation.  Special thanks go to my parents in Korea for their continued prayer and love, and Dr. Dongil Seo for his encouragement. A l s o , I wish to thank my classmates Violeta Martin and T i m Fisher for their constant help and friendship throughout the program.  Most o f all, I would like to particularly express my gratitude to my husband, Charles Hyde, for his love, encouragement and his direct advice on my thesis. I also have to thank h i m for his sacrifice o f his career in Australia to be with me over the past two years.  xxi  Chapter 1 Introduction  1.1 Background The increase in production o f petroleum extracted from o i l sands has resulted in a vast quantity o f o i l sand tailings. A s a result, the disposal o f tailings has been one o f the most sensitive environmental issues confronting the mining industry (Lawrence et a l , 1991; Ward et al., 1994). Adequate discharge schemes and appropriate maintenance o f fine tailings is essential for preventing environmental disasters. Sub-aqueous disposal is a common final treatment o f oil sands tailings. This involves discharging the fine tailings into a pond through a pipeline.  The end o f discharge pipe usually follows the trend o f the  bottom slope o f the tailings pond at an angle o f minus a few degrees (Ward, 2001). The tailings are a slurry consisting mainly o f water, fine sand, silt and clays, asphaltenes and residual bitumen, and unrecovered solvent (Petroleum Communication Foundation, 2000)  In practical applications, there are several structures o f tailings pond such as a clear water layer with a linearly stratified sludge layer or a clear water layer with a uniform sludge layer. This study focuses on the two-layer structure consisting o f a clear water layer and a homogeneous sludge layer. The tailings pond (see Figure 1.1) consists o f an upper layer o f clear water and a lower layer o f sludge containing particulate substances from 10 % to about 50 % (Mackinnon, 1989). These two layers are separated by an intermediate thin layer called a pycnocline, where a dramatic density change occurs.  The sludge layer is  often divided into an immature sludge layer consisting mainly o f fine silts and clays and a  1  mature sludge layer with coarse silts and fine sands (Mackinnon, 1989).  Generally, the water quality o f the upper layer is important from both an environmental and industrial perspective. This is because the upper layer comes into direct contact with the surrounding environment and the upper layer is also recycled for industrial use (Petroleum Communication Foundation, 2000). Therefore, it is important to minimize the disturbance o f the lower layer and pycnocline during the discharge in order to prevent undesirable substances from rising into the upper layer.  Figure 1.1 A sketch o f a tailings pond (After M a c K i n n o n , 1989): Vertical scale is exaggerated.  There has been a great deal o f research on the discharge o f turbulent jets into homogeneous and linearly stratified receiving water (Abraham, 1965a, 1965b; Fan and Brooks, 1966, 1969; Hirst, 1972; List and Imberger, 1973; Wallace and Wright, 1984; Fischer et al., 1979; Lee and Jirka, 1981; Turner, 1973, 1986; Roberts, 1987; Sobey et al., 1988; G u and Stefan, 1988a; Jirka and Doneker, 1991; W o o d et al., 1993). Typically,  2  wastewater is discharged as a turbulent buoyant jet through a round nozzle or a diffuser into ambient fluid. The primary goal is to achieve high initial dilution o f contaminated fluid adjacent to the discharge structure and thus to prevent a spreading layer o f undiluted wastewater. Consequently, understanding the behavior o f a buoyant jet and its mixing characteristics under a given discharge scheme and ambient fluid condition is essential prior to commencing wastewater disposal.  The dynamics o f buoyant jets are controlled by three important factors: the discharge condition, geometrical factors and the receiving water condition. The discharge condition includes initial jet properties such as the volume and velocity o f discharge and the density difference between the jet and the ambient fluid. The geometrical factors are associated with the source geometry configuration, the angles o f the jet inclination, and proximity to the adjacent boundaries. Ambient conditions include the presence and type o f density stratification, the cross-flowing current, and ambient turbulence (Fischer et al., 1979).  A turbulent buoyant jet initially has both source momentum and buoyancy. The initial momentum and geometry o f discharge is the dominant factor affecting the entrainment and trajectory o f a buoyant jet at the near field. However as the jet proceeds, its behavior is increasingly determined by the local buoyancy o f the jet fluid and the ambient fluid condition (Fischer et al., 1979). In homogeneous ambient fluids, a jet grows linearly with distance and the total volume flux grows continuously with distance. Entrainment into the jet can come from the entire water depth. However, the stratification o f the ambient fluid suppresses the vertical motion o f jet fluid and thus the entrained flow is constrained vertically. A s the jet velocity decays, the jet collapses vertically and then spreads laterally. Entrainment essentially ceases after collapse and the jet forms a horizontal spreading layer with a finite thickness (Manins, 1976; Brooks, 1980; Roberts, 1987; W o n g and Wright, 1988). In contrast to the research on buoyant jets in homogeneous and linearly stratified ambient fluid, there has been surprisingly little research on buoyant jets in a two-layer system.  3  In many cases o f industrial discharge such as fine tailings, the flow is not solely fluid but rather fluid associated with suspended particles. Hereafter, jets carrying particles are termed particle-laden jets and jets without particles are termed fluid jets. Most previous studies o f jets and plumes have focused on fluid jets with little attention being paid to particle-laden fluid jets. The particle-laden flow behavior is more complicated due to 1) the particle sedimentation that occurs and 2) the buoyant jet processes due to the interstitial fluid. Depending on the particle concentration, the jet trajectory and flow characteristics o f particle-laden jets can be significantly different from those o f fluid jets. It is important to comprehend not only the characteristics o f turbulent fluid jets but also the fundamental mechanisms o f particle/interstitial fluid interaction and its combined effect on the gross flow characteristics. However, most previous research associated with particles in flow has been focused on particle clouds without source momentum, and turbidity currents ( K o h and Chang, 1973; Rahimipour and Wilkinson, 1992; N o h and Fernando, 1993; Ruggaber, 2000a, 2000b; Bonnecaze, 1993; Hallworth et al, 1996, 1998; Huppert et al., 1991, 1993, 1995; Hogg etal., 1999).  1.2 Objectives and Applications To understand the behavior o f fine tailings discharged into a tailings pond, it is necessary to understand the dynamics o f particle-laden jets i n two-layer systems.  However, as  mentioned i n the previous section, little information is available on both buoyant jets i n two-layer systems and particle-laden jets.  Therefore, the present study examines 1) the  dynamics o f buoyant fluid jets and 2) the dynamics o f particle-laden jets with buoyant interstitial fluid i n two-layer system and linearly stratified ambient fluid.  The specific  objectives are:  • T o understand the behavior o f buoyant fluid jets o f 3° downward discharge angle in two-layer systems  4  • T o investigate the effect o f particles on turbulent flow •  To identify important factors affecting the behavior o f buoyant jets and particle-  laden jets in two-layer systems •  To define the flow regimes and examine the gross behavior o f both buoyant jets  and particle-laden jets.  B y achieving these objectives, this study provides a guide for the discharge o f fine tailings so as to prevent upper layer disturbance and thus contamination o f the pond surface.  The present study is also relevant to situations where the density interface (pycnocline or thermocline) should not be affected by the discharge flow such as hypolimnetic aeration in a stratified lake. Here aerated water is injected as a jet below a thermocline that is to be preserved. Another example is the discharge o f warm water generated from a power plant into stratified receiving water. A third example is the dynamics o f sediment-laden river plumes carrying nutrients into reservoirs.  1.3 Scope and Methodology The objectives are achieved by a series o f laboratory experiments for buoyant fluid jets and particle-laden jets. Dimensional analysis is also carried out and compared with the experimental results. The experimental results are also compared with previous research and C O R M I X (Cornell M i x i n g Zone Expert System) predictions.  A  physical discharge model was set up in a rectangular experimental tank and  experiments with fluid jets and particle-laden jets were performed under various discharge schemes. Jets inclined downward at 3 ° ( 5 % slope) are discharged into the stagnant twolayered ambient fluid, where the bottom bed is inclined at 5 % slope. This setup is a  5  simulation o f a typical tailings pond and discharge angle. Linearly stratified fluid, two-layer stratified fluid and homogeneous ambient fluids are simulated, although the majority o f experiments are conducted in a stagnant two-layer system. Jets are discharged only into the quiescent lower layer under a density step. The overview o f the present study is summarized in Figure 1.2  1.4 Organization Relevant previous studies on buoyant round fluid jets and particle-laden flows are reviewed in Chapter 2. Basic characteristics of jets, plumes and buoyant jets under various ambient conditions are discussed and the behavior o f particle-laden flows such as particle clouds and turbidity currents are described. In Chapter 3, the experimental apparatus and instrumentation used in the laboratory experiments are presented and the experimental conditions, detailed experimental procedures, data acquisition and processing are presented.  Experimental results and discussion o f fluid jets are presented i n Chapter 4. The behavior o f fluid jets in a two-layer system is described and dimensional analysis is conducted on the gross flow characteristics such as maximum rise height and horizontal spreading layer thickness. The important parameters are identified from the experimental results and asymptotic solutions are found. The results for buoyant jets in linearly stratified fluids are presented by means o f the characteristic length scale technique and compared with previous investigations.  Chapter 5 presents the experimental results and dimensional analysis for particle-laden jets. The presentation and interpretation o f experimental results follows the same format as in Chapter 4. The results are also compared with the predictions o f C O R M I X 1 v3.2 and its suitability for particle-laden flow is examined.  6  Main purpose of the present study is to understand the dynamics of buoyant fluid jets and particle-laden jets with buoyant interstitial fluid in stratified ambient fluid  1) to understand the behavior of buoyant fluid jets of 3° downward discharge angle in two-layer systems 2) to understand the behavior of particle-laden turbulent jets 3) to identify important factors affecting the behavior of buoyant jets and turbulent particle-laden jets 4) to define the flow regimes and examine gross behavior of buoyant jets and particle-laden jets  Objectives  Fluid jets • Laboratory experiments • Dimensional analysis • Comparison with CORMIX prediction  Methodology  Parameters  Results and Discussion  • • • • •  Particle-laden jets • Laboratory experiments • Dimensional analysis • Comparison with CORMIX prediction  Density of jet fluid and ambient fluid Velocity of jet Discharge height above the bottom bed Distance from the jet nozzle to a pycnocline Density difference between the upper and lower layer  • Define flow regimes based on the identified influential parameters • Investigate Coanda attachment and backflows • Evaluate dimensionless maximum rise and its location, top of the spreading layer and final layer thickness  1  »Bulk density of particle-laden jets »Density of interstitial fluid  • Identify the effect of particles on turbulent flow • Evaluate the feasibility of using CORMIX for particle-laden jets  I Understanding the behavior of buoyant fluid jets and particle-laden jets and identifying the discharge condition to prevent penetration of jets into the upper layer  Figure 1.2 Overview o f the present study  7  A comparison o f the behavior o f fluid jets and particle-laden jets is given in Chapter 6. Chapter 7 summarizes the main conclusions and the contributions o f the present study. Recommendations for future research are also made.  The results and discussion o f the behavior o f buoyant jets in linearly stratified ambient fluid are presented in Appendix A . Appendix B contains the results relating to the behavior of particle-laden jets in linearly stratified fluid, while the comparison between the two types of jet is made i n Appendix C . A overall experimental setup are sketched in Appendix D .  Chapter 2 Literature Review 2.1 Introduction In order to predict the behavior o f fine tailings discharged into a tailings pond it is essential to understand the characteristics o f jets, plumes and buoyant jets and their behavior in various ambient conditions. In addition, it is necessary to understand the effect of particles on turbulent flow and gross behavior o f particle-laden jets. A s noted in Chapter 1, however, there has been little research on buoyant jets in two-layer systems and particle-laden turbulent jets.  This chapter discusses the existing body o f knowledge relating to the behavior o f buoyant jets in homogeneous  fluid and stratified ambient fluid. For particle-laden jets, past  experimental studies on particle-laden flows such as particle clouds and turbidity currents are investigated.  2.2 Jets and plumes 2.2.1 Simple jets, plumes and buoyant jets Discharges into ambient fluid are classified as jets, plumes and buoyant jets depending on the influence o f the source momentum and buoyancy. A pure jet is discharge with initial momentum through a nozzle and two distinct regions are formed after discharge: the Zone o f F l o w Establishment (ZFE), and the Zone o f Established F l o w (ZEF). In the Z F E , the shear forces due to the interaction between the jet and ambient fluid do not affect the core of the jet. Thus the centerline velocity remains the same as the velocity at the jet nozzle.  9  This zone is often neglected because o f its relatively short length (approximately six times the diameter o f the jet nozzle) for a deeply submerged jet (Fischer et al., 1979). In the Z E F , the centerline velocity, temperature and density begin to decay due to the continuous entrainment o f surrounding fluid.  The time-averaged velocity and concentration profiles  across a jet cross-section form Gaussian distributions (Fischer et al., 1979). A schematic diagram o f the flow region is shown in Figure 2.1.  Initial flow condition at nozzle  ZFE Zone o f F l o w Establishment  Mean concentration and  ZEF Zone o f Established F l o w  Figure. 2.1 A sketch o f a jet geometry and flow regions  A plume is a discharge driven solely by the buoyancy due to the density difference between entering fluid and the ambient fluid. Thus, the local flow properties such as velocity and concentration are dependent on the initial buoyancy, the mass flux and the downstream distance.  Buoyant jets are typical o f many environmental discharges having both initial momentum and buoyancy. Initially, a buoyant jet is dominated mostly by the source momentum and geometry, and after some distance the behavior is determined by the buoyancy and the ambient fluid condition. The centerline concentration decays after a short distance due to entrainment. Sufficiently far from the source all buoyant jets behave like plumes. I f the  10  initial momentum o f a jet is not i n the direction o f buoyancy, the jet trajectory becomes curved.  2.2.2 Theoretical background for buoyant jets The dynamics o f jets, plumes and buoyant jets have been well established. For a turbulent round buoyant jet, initial volume flux Q, momentum flux M and buoyancy flux B are given by Fischer et al. (1979):  (2.1)  M  where  —d u  (2.2)  4  d : jet nozzle diameter u : initial mean jet velocity,  The initial density difference between a jet and the ambient fluid at the source can be represented by modified gravitational acceleration g' : Q  Pa-Pi Pa  g  (2.3)  where p:  density o f ambient fluid  p.:  density o f jet  g:  gravitational acceleration  a  11  Therefore, initial buoyancy flux B is given as  B =  Qg' =uA  Pa-Pj  0  .  Pa  (2.4)  g  where A : cross sectional area o f a nozzle  If the density o f the jet is close to that o f the ambient fluid, the effect o f the density difference is negligible on the inertia force, but it exerts a considerable effect on the buoyancy force. This Boussinesq approximation is generally valid when —— < 0.1 (Baines Pa and Hopfinger, 1984).  Table 2.1 shows the relevant parameters to the present study for round jets and plumes in homogeneous ambient fluid.  Table 2.1 Properties o f turbulent round jet and pure plume (Fischer et al., 1979)  Parameter  M a x i m u m time-averaged velocity  (u ) m  Momentum flux (m)  where  Round Jet  o  Round Plume  (i  M  \  [z  )  m = M (constant)  £ : characteristic length (£ Q  Q  = Q/4M  u  ={A.l±02)B z~ m  m  m = oB 2  m  z  )  z : distance from source  12  b  2  : experimental constant b « 0.35 (Fischer et al., 1979) 2  The gross buoyant jet behavior has been commonly described by integrating a set o f ordinary differential equations o f volume, momentum and buoyancy over the jet cross section. (Fan and Brooks, 1969; Hirst, 1972; List and Imberger, 1973; Wright and Wallace, 1979; Fischer et al., 1979; Lee and Jirka, 1981; Turner, 1986):  Volume flux  JU = \ udA = 2n\ urdr  (2.5)  Momentum flux  m = \ u dA  (2.6)  Buoyancy flux  A  2  A  2K\u rdr  A/7 P - \g A  where  =  2  00  udA = 27r\ug'rdr P  (2.7)  o  A  the cross- sectional area o f the jet  u  time averaged velocity in axial direction  M  specific volume flux  m  specific momentum flux  P  specific buoyant flux  Ap:  density difference between jet and ambient fluid  r :  radius o f a jet  8' •  modified gravitational acceleration  The time-averaged profiles o f velocity and passive tracer concentration are generally expressed as simple Gaussian distributions:  13  u(r,s) = u exp m  - — K r  (2.8)  - — b  (2.9)  L  c(r,s) = c exp  r  m  where b and b are the characteristic widths o f the velocity and concentration (or density) u  profiles, respectively. The w and c m  m  represent the local centerline velocity and the  concentration.  2.2.3 Entrainment Entrainment, the ingestion o f ambient fluid into a turbulent jet fluid, is the fundamental mechanism for dilution o f discharged wastewater. A s a jet leaves the source, shearing action between the jet and the ambient fluid develops and the neighboring fluid is accelerated. Entrainment primarily results from the engulfment o f non-turbulent fluid by the large-scale eddies across the edge o f a turbulent jet or plume (Fischer et al., 1979; Baines,  1975; Schneider, 1980; Lee and Jirka,  1981). The subsequent small-scale  turbulence and diffusion is however, relatively insignificant to the overall mixing rate (Turner, 1986). For the final stage o f external fluid ingestion into the turbulent flow, the viscous diffusion o f vorticity plays an important role (Baines, 1975).  The classical entrainment hypothesis is that the mean inflow velocity o f diluting fluid into a jet is proportional to the maximum local time-averaged velocity or the spatial-averaged velocity over the section o f the turbulent flow (Rajaratnam, 1976; Fischer et al, 1979; Turner, 1986, Wright and Wallace, 1979). The inflow velocity at the edge o f the flow is some fraction (a) o f the maximum mean velocity (u ) given as — = 27i> au , where a is dz m  u  m  the entrainment coefficient. For a horizontal discharge, or = 0.057 (Wong, 1984).  14  2.2.4 Important parameters 2.2.4.1 Characteristic length scales Characteristic length scales are often useful tools to express and interpret the gross behavior o f flows. A l s o , the relative magnitude o f the length scales is useful i n identifying the dominant mechanisms under the prevailing jet and ambient conditions. A l o n g with the important parameters for jet and ambient fluid, several useful characteristic length scales have been formed and used by many researchers (Fischer et al., 1979; Schneider, 1980; Roberts and Mathew, 1982, 1984; Wong, 1984; Lee and Cheung, 1986; Roberts, 1987; Sobey et al., 1988; W o n g and Wright, 1988; Johnston and Volker, 1993; Johnston et al., 1994b; Jirka and Doneker, 1991; Jirka et al., 1996). Geometric length scale For a simple turbulent round jet, a characteristic length describing the relative importance of the source geometry, £  Q  can be formed (Fischer et al, 1979).  (2.10)  l  Q  characterizes the distance from the nozzle over which the source volume flux affects  the flow field. I f downstream distance is much greater than £  Q  (i.e. z » £ ), the influence Q  of the initial volume flux is insignificant and the properties o f the jet are independent o f the source conditions.  Jet/plume transition scale  W i t h distance buoyant jets undergo a transition from momentum-dominant to buoyancydriven flow. This relationship associated with source momentum and buoyancy can be defined as  15  (2.11)  £  M  is a measurement o f a characteristic distance at which the transition from jet-like  behavior to plume-like occurs. I f z « £  M  ,  the momentum flux dominates and the flow  behaves like a jet. For downstream distance greater than I , M  the source momentum effect  becomes negligible and the buoyant jet behaves like a plume over the entire trajectory.  Jet/linear stratification length scale  If the ambient fluid is linearly stratified and a jet is initially momentum-dominant, a characteristic length scale £  N  can be defined as  where N is a buoyancy frequency given as  (2.13)  £  N  is a length scale characterizing the strength o f the source momentum flux relative to  the ambient linear stratification.  Plume/stratification length scale  If the source buoyancy is much stronger than the initial momentum, the momentum is ignored. A characteristic length £' incorporating only buoyancy and ambient stratification b  16  can be formed (Wright and Wallace, 1979; Lee and Cheung, 1986; Jirka and Doneker, 1991):  7jl/3  n = ^  t'  b  (2.i4)  measures the distance at which a plume becomes strongly affected by the ambient  stratification. In fact, i'  b  and t  are interdependent for a buoyant jet and its relationship  N  can be expressed in the form o f I  M  = —^-. ^b  2.2.4.2 Dimensionless parameters It is also useful to express the research results as familiar dimensionless parameters. Reynolds Number  The Reynolds number defined below indicates whether the jet is laminar or turbulent.  „  pdv  R= — e  fd  ud  =—  o  (2.15)  where v is the kinematic viscosity o f discharged fluid. In most cases, in nature, the flow generated by the discharge is turbulent. I f the number exceeds 4,000 the flow is considered turbulent (Fischer, 1979).  Densimetrlc Froude Number The densimetric Froude number is widely recognized as an influential parameter for buoyant jets. The Froude number relevant to the present study is a densimetric Froude number  F: d  17  where g' is modified gravitational acceleration due to the density difference between the 0  jet fluid at discharge level ( p . ) and the ambient fluid ( p ) . a  2.2.5. Effect of source geometry 2.2.5.1 Discharge angle The most significant difference between horizontal jets, downward inclined jets and vertical jets is difference i n the direction o f initial momentum and buoyancy. I f the direction o f initial momentum and buoyancy o f a buoyant jet is different, the jet trajectory becomes  curved when  z l £  M  » \  (McCorquodale et al., 1992). The flow spreads  predominantly i n the direction o f the discharge due to the initial horizontal momentum, while the vertical momentum due to buoyancy is modified as it rises or sinks to the neutrally buoyant level. Thus the discharge angle significantly influences the dilution o f inflow (Johnson et al., 1989). Hofer and Flutter (1981) suggested that the negative initial jet angles cause substantially larger undulations in the jet trajectory than positive angles.  2.2.5.2 Proximity to the adjacent horizontal bed If a buoyant jet is discharged sufficiently close to the bed, the jet is deflected toward the floor for some distance. This phenomenon is called the Coanda effect. A s a jet propagates along the bed, constant bottom friction reduces the horizontal momentum. Consequently, at some point the buoyancy force becomes dominant and the jet rises to its neutral buoyancy (Sharp and Vyas, 1977; Sobey et al., 1988; Johnson and Volker, 1993; Johnston et al., 1994a; Doneker and Jirka, 1991; Jirka and Doneker, 1991).  18  Sobey et al. (1988) suggested that proximity o f the boundaries has a considerable influence on the near-field flow pattern. For h/£  M  above the bottom,  initial jet  development  < 0.1, where h is discharge height  is predominantly  influenced by Coanda  attachment until buoyancy eventually prevails. They also indicated that the influence o f the Reynolds number and densimetric Froude number on the Coanda bottom attachment to the bed is insignificant. Johnston and Volker (1993) also discovered that the jet path could be greatly influenced by the distance between discharge exit and the bed, and also the densimetric Froude number. When h/£  M  >0.\,  the Coanda effect did not occur as  observed by Sobey et al.(1988).  2.3 Dynamics of buoyant jets in various ambient conditions 2.3.1 Classification of ambient fluid  The receiving water conditions play a significant role in the dilution and trajectory o f buoyant jets. A s buoyant jets spread into the ambient water, the initial source characteristics weaken and the ambient fluid condition begins to influence the flow dynamics. In a homogeneous ambient fluid, a round horizontal jet exhibits an axisymmetric flow pattern and the entrainment o f ambient fluid can occur from the entire water depth (Fischer et al, 1979; Abraham, 1965a; Fan and Brooks, 1969). However, in stratified ambient fluid the mixing and entrainment o f jet fluid are constrained vertically due to the stratification.  Jirka and Doneker (1991) classified stratified ambient water into three categories based on  the  characteristics  o f the  density  stratification:  linear  stratification,  two-layer  stratification and two-layer stratification with a linearly stratified lower layer. The schematic diagrams o f the ambient water conditions are shown in Figure 2.2. The two-layer system consists simply o f a uniform upper layer (epilimnion) and a uniform lower layer  19  (hypoliminion). A two-layer system with a stratified lower layer may or may not be separated by a density jump (pycnocline) between the two layers.  Figure 2.2 Schematic diagram for ambient fluid condition based on the density profile: (a) linearly stratified fluid, (b) two-layer system with a density step and (c) twolayer with a linearly stratified lower layer (Jirka and Doneker, 1991)  A tailings pond has a two-layer system with a linearly stratified lower layer or a two-layer system with a homogeneous lower layer. Thus this study focuses on the linearly stratified ambient fluid and two-layer system.  2.3.2 Stratified ambient fluid  2.3.2.1 Linearly stratified ambient fluid  The behavior o f a jet in a linearly stratified ambient fluid is significantly different from its behavior in a homogeneous ambient fluid. In the immediate vicinity o f the jet exit, the influence o f stratification on the jet is rather insignificant and the width o f the jet initially grows linearly with distance as in the case o f an unstratified fluid (Roberts, 1987; W o n g and Wright, 1988). However, at some distance the jet entrains ambient fluid selectively from a finite thickness, collapses vertically and proceeds as a horizontal density current (Maxworthy, 1973; Manins, 1976; Brooks, 1980; Roberts and Mathews, 1984; Roberts, 1987).  20  2.3.2.2 Two-layer system A jet trajectory in a two-layer system is different from that in homogeneous system or linearly stratified fluid due to the presence o f a layer o f rapid density change. When discharged into the lower layer, a buoyant jet rises to the pycnocline, which inhibits the vertical transport o f energy and mass and diverts it horizontally. Entrainment across the density step is determined by the characteristics o f the turbulence within the flow at impingement on and at a density interface (Baines, 1975). In addition, entrainment is affected not by the density o f ambient fluid but only by the presence o f a density step across the pycnocline.  The proximity between a discharge exit and the density step is a critical factor affecting vertical movement o f the flow (Schneider, 1980). The spreading layer thickness decreases as the ratio o f half thickness o f interface depth (h  L  ) to half thickness o f spreading layer  2  (/z ) increases. A l s o , at approximately h x  L  2  2' /  lh = 1 , mixing at the front o f the flow ceases L  2  (Britter and Simpson, 1981).  If the density step Ap  a  is large, the jet trajectory and mixing become trapped under the  pycnocline and the role o f upper layer becomes insignificant (Schneider, 1980). In such cases, the lower layer o f the two-layer system can be regarded as shallow homogeneous ambient fluid. Sobey et al. (1988) indicated that in shallow water, both proximity to an upper boundary (h ) and bottom (h) significantly influence the jet path. The flow patterns {  occurring in an initially stagnant ambient fluid are illustrated in Figure 2.3. I f the free surface parameter  h /£ (  M  > 0.05  and bed parameter  hl£  M  < 0 . 1 , then a buoyant jet  initially experiences Coanda attachment to the bottom and then rises (Figure 2.3(a)). O n the other hand, i f h I £ t  M  < 0.05 and hi £  M  < 0.1, then a buoyant jet is confined in the shallow  ambient fluid and no rising to the surface occurs (Figure 2.3(c)).  21  (c) Coanda bottom attachment 0.0  (d) No Coanda bottom attachment 1  1  0  •  H  —  1  Figure 2.3 F l o w patterns in shallow and deep ambient fluid (a) a buoyant jet with initial Coanda attachment and transition to surface jet, (b) buoyant jet and transition to surface jet without bottom attachment, (c) confined jet and (d) surface jet (After Sobey et al., 1988)  Jirka and Doneker (1991) suggested that i f t l h < \ , the flow is dominated by M  i  buoyancy after a short distance and has no interaction with the water surface. I f £  M  I h > 1, t  the flow is dominated by momentum in relation to /z, and the surface interaction for a horizontal discharge depends on the discharge angle.  Balasubramanian and Jain (1978) found that when a jet with high momentum and low buoyancy is injected in shallow water conditions, the energy input into the receiving water may be so strong that a unstable flow can be formed due to insufficient buoyancy. Consequently, this results in recirculation near the jet discharge leading re-entrainment o f partially diluted fluid into the discharge. However, rising buoyant jets with low  F  d  submerged in a deep receiving water entrain only ambient fluid but not the partially diluted jet fluid. Re-entrainment o f partially diluted fluid occurs i f H/h< 0.36F  d  where H is total  water depth and h is the distance between discharge and the bottom boundary.  22  2.4 Previous experimental studies There has been little research on buoyant jets in two-layer system. Table 2.2 summarizes previous experimental studies o f horizontal buoyant jets in two-layered stagnant ambient fluid and experiments o f Coanda attachment in homogeneous shallow water.  Table 2.2 Summary o f the previous experimental studies on horizontal buoyant jets in two-layer systems and homogeneous shallow ambient fluid  Conditions Investigators  Schneider (1980)  Ambient fluid two-layer system  Density relations  Parameters and measurement techniques  Pj = Pa discharge into the lower layer  entrainment flux across the interface (shadow graph), a single-electrode resistivity probe and a thermistor  Roberts and Mathew(1984)  two-layer system with a linearly stratified lower layer  Pj = Pa discharge into the lower layer  spreading level, collapsed layer thickness and volume flux, entrainment location and thickness; density profile using a two-wire conductivity probe photographs of dye streaks  Sharp and Vyas (1977)  Homogeneous shallow ambient fluid  Pj < Pa  velocity profile using hydrogen bubble generator  Balasubramanian and Jain (1978)  Homogeneous shallow water  Pj < Pa  density profile by thermistors, velocity distribution using a orifice meter  Sobey et al.(1988)  Homogenous shallow water with two boundaries: the bed and free surface  Pj = Pa  thermistor probes  Johnston and Volker(1993)  Shallow water with two boundaries: the bed and the free surface  Pj = Pa  Johnston et al. (1994b)  Shallow water with two boundaries: the bed and the free surface  Pj < Pa  Pj , p  a  jet trajectory, temperature profile and velocity distribution laser doppler velocimeter, thermistors, planimeter jet trajectory, temperature profile and velocity distribution in horizontal and vertical direction thermistor probes  : density of jet fluid and ambient fluid  23  2.5 Behavior of particle-laden flow 2.5.1 Particle clouds without source momentum  The sedimentation o f particles from a turbulent jet is a complicated process. The particles in the jet flow constantly settle due to gravity but the turbulence o f the jet maintains the particles in suspension. Therefore, prior to analyzing the complex dynamics o f a particleladen jet, it is useful to understand the fundamental behavior o f a cloud o f dense particles released without initial momentum in the ambient fluid.  K o h and Chang (1973) categorized the gross behavior o f dredged particulate material discharged into open water through a barge into three regimes: convective descent, dynamic collapse and passive diffusion regime illustrated in Figure 2.4. 5L  <  >  Convective Descent  Dynamic Collapse in Water Column  Encounter neutral buoyancy  I  •  Long-term Passive Diffusion  Diffusive spreading greater than dynamic Spreading  Figure 2.4 Behavior o f a particle cloud (After Ruggaber, 2000a)  24  • Convective descent: the released dense particulate moves downward due to its negative buoyancy and creates a particle cloud in the water column.  • Dynamic collapse: depending on the local buoyancy o f the particle cloud, the cloud may reach the bottom o f the water basin or approach its neutral buoyancy level in the water column. When the vertical motion o f the cloud ceases, it collapses and spreads horizontally.  • Passive diffusion: after the dynamic spreading due to initial mixing in the vertical and horizontal directions, the particle cloud moves with the ambient fluid.  The convective descent phase in a homogeneous ambient fluid has been intensively investigated while the dynamic collapse and passive diffusion regimes have been little studied. The convective descent phase includes initial acceleration, cloud and dispersive (particle-settling) regimes.  • Initial acceleration: the released particle-laden fluid accelerates due to initial buoyancy.  Shear force due to the density and velocity difference at the boundary  causes entrainment o f ambient fluid and the cloud expands.  Typically, a particle  cloud enters the second phase o f motion when its travel distance approaches  1-3  initial cloud diameters (Baines and Hopfmger, 1984).  • Cloud (thermal): during this phase the size o f the cloud continues to increase with time, however its velocity decreases with the rapid entrainment o f less dense ambient fluid caused by large eddies. A conspicuous internal circulation in the cloud occurs (Rahimipour and Wilkinson, 1992). The spherical vortex is formed as the cloud descends. The particle cloud becomes flattened and forms a mushroomshape structure due to the induced internal circulation (Ruggaber, 2000a).  The  mixture o f fluid and particle clouds descends as a swarm o f individual particles and  25  gradual separation between particles and parent fluid occurs (Noh and Fernando, 1993). In addition, as the particle cloud descends, re-entrainment o f the particles suspended in the ambient fluid into the cloud can occur at the edge o f the cloud (Carey and Sigurdsson, 1988; Ruggaber, 2000b)  • Dispersive (particle-settling): in this regime, the particle cloud  decelerates  toward the settling velocity o f individual particles. Thus, internal circulation is suppressed  and  becomes  insufficient to  keep  the  particles  in  suspension.  Consequently, active settling o f particles occurs although the cloud continues to expand at a lower velocity (Rahimipour and Wilkinson, 1992; Ruggaber, 2000a). The descending velocity o f the cloud is dependent either on the individual particle settling velocity or the motion o f the cloud (Noh and Fernando, 1993).  2.5.2 Characteristics of particles in flow  2.5.2.1 Particle settling  The Stokes' free settling velocity o f an individual spherical particle, w is expressed as s  g(p -Pa)d ™ = rz \%p v  2  P  p  (2.17)  s  a  where p  p  and p are the density o f the particle and ambient fluid and d a  P  is an equivalent  particle diameter and v is its kinematic viscosity. Strictly speaking, the Stake's velocity is valid only for spherical particles o f dp < 60pm.  The important factors affecting the  particle settling velocity include the particle size, density, shape and roughness. Dietrich (1982) found that for large particles, particle roughness and shape are both influential, but the latter has more effect on the particle settling behavior. For small size particles, smooth  26  surface o f particles result in a large reduction in settling velocity. For example, particles with pointed ends settle faster than those with flat ends (Ilic et al., 1992)  Rahimipour and Wilkinson (1992) indicated that the behavior o f particles within a cloud and the cloud itself is determined by the relative magnitude o f the individual particle settling velocity ( w ) to the internal circulation velocity defined as ^B s  is bulk density o f a particle cloud and R  c  IpR  2  p  a  c  , where  B  p  the size o f the cloud. O n release all particles are  incorporated into the cloud and remain until the cloud velocity approaches the particle settling velocity (Ruggaber, 2000a, 2000b)  2.5.2.2 Effect of particle size and concentration  Particles with smaller settling velocity than the flow velocity initially move with fluid. However, significant separation o f particles occurs as the settling velocity approaches the flow velocity (Hinze, 1972). The movement o f particles is due primarily to large eddies, which promote the formation o f a group o f particles, resulting in large-scale fluctuations o f concentration within the flow (Hinze, 1972). A l s o , particles with small size at large viscosity tend to move together with the fluid as a particle cloud (Noh and Fernando, 1993). The presence o f small amounts o f fine particles in a coarse-grained current enhances flow velocity because the fine particles remain suspended and maintain an excess current density for a longer time (Gladstone et al., 1998).  The concentration o f particles is another influential factor on particle-laden flows. In a very low concentration, the effect o f presence o f particles is insignificant and thus the main flow pattern o f the fluid remains unchanged (Owen, 1969). K a n a and Hanatty (1960) found that particles with volume concentration less than 2.5 % have no significant impact on the diffusion rate unless the slip velocity between particles and the fluid is large. A t high concentrations, however, particles tend to be less mobile than at low concentrations.  27  Individual particles collide with each other and behave as a group. The grouping behavior o f particles can significantly modify the flow pattern (Hinze, 1972; Kada and Hanratty, 1960). Moreover, at very high concentration the interaction o f the particles can cause turbulent motion to halt (Hallworth and Huppert, 1998).  If particle concentration is high but w  is small, a flow plunges as a particle cloud. For  s  low concentration but large w , the particles sink as individual particles leaving interstitial s  fluid (Noh and Fernando, 1993).  2.5.2.3 Density and buoyancy  If the density o f the interstitial fluid is less than that o f the ambient fluid, the behavior o f the particle-laden fluid is determined by its initial bulk density. Turner and Huppert (1992) proposed a stability parameter (R ), h  which is a ratio o f the density difference between the  interstitial and ambient density to the difference between the bulk density o f the suspension and the ambient density. R h  =  Pf~Pa  (  2  1  8  )  Pb-Pa  where p , f  p  a  and p  b  represent the density o f interstitial fluid, ambient fluid and the bulk  density o f suspension.  A two-phase jet such as a particle-laden jet can be characterized by two buoyancy fluxes; initial bulk buoyancy flux (Bb) and the buoyancy flux o f the interstitial fluid (B ) (Carey f  and Sigurdsson, 1988). The initial density o f a particle-laden jet is a function o f particle concentration and the density o f the interstitial fluid.  28  f Q  g  Pa ~Pb Pc a (2.19)  B  7  2d  f  x)\g V  Pa-Pf Pa  J  where X is the volumetric concentration o f particles.  2.5.3 Gravity current A gravity current is driven by the density difference between inflow and the ambient fluid. The density difference can be attributed to dissolved or suspended material or temperature difference. A turbidity current is one type o f gravity current due to suspended particles such as mud and silt in its interstitial fluid (Simpson, 1982). In general, three types o f gravity currents occur in nature: surface overflow, underflow and intermediate flow. I f the entering fluid is denser than the ambient fluid, the current plunges and then forms an underflow. If the entering fluid is lighter than the ambient fluid, it forms a gravity current at the surface o f the ambient water body (i.e. surface overflow). In addition, a current with an intermediate density forms an intermediate level intrusion at the level o f neutral buoyancy (Fischer et al., 1979; Simpson, 1982).  2.5.3.1 Particle-laden flow with reversing buoyancy If the bulk density o f particle-laden flow exceeds that o f the ambient fluid, the flow plunges down to the bed and forms an underflow regardless o f the interstitial fluid density. A s the flow propagates, the suspended particles settle out and the flow decelerates rapidly. Consequently, the buoyancy reverses due to sedimentation. This type o f flow is called a turbidity current with reversing buoyancy. The remaining interstitial fluid rises through the upper surface o f the flow while the particles descend continuously (Huppert et al., 1991;  29  Sparks et al., 1993; Hiirzerler, 1994; Rooij et al., 1999; Hogg et al., 1999; Hairworm and Huppert, 1998).  While the detraining interstitial fluid ascends, it carries fine particles into the overlying ambient fluid (Fischer and Smith, 1983; Carey and Sigurdsson, 1988; Rooij et al., 1999). Particle re-entrainment occurs at the edge o f a particle-laden flow, causing denser margins than the ambient fluid. This convective instability enhances the sedimentation (Carey and Sigurdsson, 1988). After the particles settle out, the entrainment o f ambient fluid into the intrusion becomes the dominant mechanism (Rooij et al., 1999). However, the spreading rate o f the particle-laden flow decreases continuously due to the detrainment. The flow eventually lifts off from the bed and develops a surface overflow downstream (Hurzeler et al., 1996).  2.5.4 Experimental conditions of previous studies Table 2.3 summarizes the experiment conditions o f particle-laden flow from previous investigations.  30  Table 2.3 Experimental conditions o f previous studies on particle-laden flow  Researchers  Type, Size (u,m) Density (kg/m ) of particles  Hallworth et al(1998)  Silicon carbide 9, 17,23,37, 53 1,019-1,957 kg/m  Carey and Sigurdsson (1988)  Silicon carbide 7-120 1,000-1,060 kg/m  Green(1987)  Taconite tailings < 10 specific gravity 2.07  Hogg et al. (1999) Hiirzeler et al. (1994)  3  3  3  Silicon carbide 23 um 3,217 kg/m Silica flour 28.59 um 2,650 kg/m  Measurement Position of flowfront, sediment distribution on the floor  Lock exchange A homogeneous ambient fluid  Density, particle concentration profiles  Buoyant plume of fresh water and solid particles in a salt ambient fluid  Lift-off distance  3  3  Conditions  Vertical density structure, spreading velocity  Lock-release, a mixture of warm water and taconite tailings into a cold clear ambient fluid, Interstitial fluid: methanol + fresh water ambient fluid, Lock-release Lock-release, freshwater + particles propagating into saline ambient water Interstitial fluid: Methanol & fresh water Ambient fluid: fresh & saline water, fixed volume of dense jet with/without particles by lock-release technique  Sparks et al. (1993)  Alumina particles 66.5 um, 3,985 kg/m  Lift-off distance tracking of the current front  Popper et al. (1974)  Oil droplets < 50 (um)  Velocity distribution of oil droplets  Oil particles in air jet  Goldschmidt et al. (1972)  Nitrogen gas bubble and oil droplets 343, 527, 780 and 970 (um)  N2 gas bubble concentration and velocity profile  Water jet with N2 gas bubbles in homogeneous ambient air  Rooij et al. (1999)  Silicon carbide 23, 37(um), 3,217 kg/m  Spreading velocity of saline and particle laden flow, bottom sediment distribution  Saline fluid and particle-laden flow releasing along the density step in two-layer system  3  3  31  2.6 CORMIX (Cornell Mixing Zone Expert System) The mixing model C O R M I X v3.2 was used to compare with the experimental results for fluid jets and particle-laden jets in two-layer systems. The suitability o f the model for particle-laden jets is also examined.  2.6.1 C O R M I X v3.2  C O R M I X is a dimensionless length scale-based model developed by Cornell University for the U S E P A . The program can be used for the analysis, prediction and design o f discharge into an aqueous environment (Jirka et al., 1996). C O R M I X consists o f three integrated submodels: C O R M I X 1, C O R M I X 2 and C O R M I X 3 .  C O R M I X 1 is a model  used for positively and negatively buoyant submerged single port discharges. C O R M I X 2 is used for submerged multiport diffuser discharges and C O R M I X 3 for buoyant surface discharges. The models can simulate steady and unsteady ambient fluid with various density stratification types (Jirka et al., 1996).  The core o f C O R M I X is a flow classification, which provides a generic qualitative description o f the discharge flow in the given ambient fluid condition. The C O R M I X model classifies the discharge configuration with regard to discharge conditions and ambient conditions into a generic flow classification by means o f length scale analysis. A n example o f the schematic diagram o f a flow classification is shown in Figure 2.5 for buoyant jets. Once the flow classification has been performed, a sequence o f hydrodynamic simulation submodels are executed to predict the jet trajectory, dilution characteristics, position and width o f the plume (Jirka et al., 1996).  32  a.  i,  • o — Q J 1  J*  Mm  J 3  2.7 Summary There have been numerous investigations into problems o f turbulent buoyant jets discharged into homogeneous and linearly stratified ambient fluids. However, only a limited number o f studies on the dynamics o f jets in two-layer systems have been published. Moreover, most o f research was conducted on fluid jets and little information on particle-laden jets are available. Although in the 1970's a small number o f studies on the trajectory o f individual particles in an air jet were conducted, the particle concentration was low and thus the effect o f particles on the jet behavior was insignificant. In addition, most studies on the flows associated with particles have been on behavior o f particle clouds without source momentum such as ocean dumping o f dredged material or turbidity current proceeds along the bottom bed.  Figure 2.6 shows a summary o f the scope o f the present study in relation to the range o f possible related studies.  34  Homogeneous (section 2.3, 4.2.4) Ambient Stratification  Linearly stratified fluid (section 2.3.2, Appendix A . B . C . ) Two-layer (section 2.3.3, Chapter 4, 5) Vertical Horizontal  Orientation  Inclined: -3° Negatively buoyant Positively buoyant  Fluid  r jets  Turbulent Jets  Nonbuoyant  Flow bulk buoyancy  <  Interstitial fluid buoyancy  f Negatively buoyant  Negatively buoyant Positively buoyant (section 5.2, 5.3) Nonbuoyant Negatively buoyant  Particle-laden jets  Positively buoyant  Positively buoyant (section 5.2, 5.3) Nonbuoyant Negatively buoyant  Nonbuoyant  Particle laden flows  Positively buoyant (section 5.2, 5.3). Nonbuoyant  Interstitial fluid buoyancy Turbidity current  ^Negatively buoyant J Positively buoyant (turbidity current with reversing buoyancy)  (underflow)  (section 2.5.3.1) Nonbuoyant  Particle clouds (section 2.5.1)  Figure 2.6 Summary o f the scope o f the present study in relation to the range o f possible related studies  ( A r e a o f this study)  35  Chapter 3 Experimentation 3.1 Introduction The present study investigates the behavior o f turbulent fluid jets and particle-laden jets in stagnant receiving water.  Buoyant round fluid jets and particle-laden jets with  buoyant interstitial fluid were injected under various discharge conditions and three different  ambient  homogeneous fluid.  fluid  conditions: two-layer  system,  linearly stratified  fluid  and  A l l jets were discharged at 3° downward inclination, parallel to the  bottom bed. In two-layer systems, the interstitial fluid was kept highly buoyant relative to the lower layer for all experiments so as to simulate the worst possible tailings disposal scenario, where the buoyant jets penetrate into the upper layer. In addition, the bulk density o f particle-laden  jets,  primarily determined  by  particle  concentration,  varied  across  experimental conditions.  3.2 Experimental apparatus 3.2.1 Physical set-up A l l experiments were performed in the C i v i l Engineering Hydraulics Laboratory at the University o f British Columbia. A photograph and a sketch o f the experimental setup is shown in Figure 3.1 and Appendix D . A l s o , the individual components o f the apparatus are discussed in the following subsections.  36  Figure 3.1 Experimental facility  3.2.1.1 Main experimental tank  A l l the experiments were conducted in a main tank 2.4 m long, 0.6 m high and 0.6 m wide in a hydraulics laboratory. The tank was constructed with transparent Plexiglas vertical sidewalls with the bottom o f the bed at 5 % slope. Drainage o f the main tank was accomplished through a 2.54 cm diameter pipe at the bottom. Figure 3.2 shows a schematic diagram o f the main experimental tank.  The tank was equipped with sampling racks and trolley. T w o rails at the top o f the tank allowed a trolley to be moved along the length o f the tank. A computer  controlled  traversing mechanism was mounted on the trolley, which carries a conductivity and  37  temperature probe connected to a 486 P C . The traversing mechanism moved vertically by the signals from the computer while horizontal direction control was achieved manually. Four stainless steel sampling racks were installed along the tank (x = 10, 30, 45 and 75 cm). Each rack holds 16 sampling tubes spaced at 2 - 4 cm intervals. Each sampling tube was connected to a 10 m L syringes for sample collection.  ,  P M E Conductivity & Tefriperature probe  H=60 c m  conditioning  Figure 3.2 A sketch o f the main experimental tank  A t x = 75 cm, 10 copper sampling tubes passing through ten holes with inner diameter of 3.1 m m were fixed at the rear o f the trolley. Each sampling tube was fixed with a tube holder to enable adjustment o f the vertical position. The top o f the tubes were connected to 7016 Masterflex tubes which were in turn connected to an I/P7553-70 Masterflex pump with a maximum capacity o f 600 rpm. The transparency o f the hose facilitated monitoring o f the fluid and particle motion in the tubes. These tubes were bent at right angles and faced upstream on a line perpendicular to and passing though the jet axis.  38  3.2.1.2 Jet discharge system  The discharge system, shown in Figure 3.3, consisted o f a mixing tank, a flowmeter, a flow control valve, a pump and a discharge nozzle. A mixing tank with a 90 L storage capacity was used to supply completely mixed jet fluid. The tank was equipped with a motor, kept at rotation rate o f 60 rpm connected to an arm sufficiently large to provide complete mixing. The mixing tank was connected to the main tank by a pipe. The pump used was a Jet Pump Motor by Dayton Electric M F G C o with a maximum capacity o f 56 J, 60 H z and 3450 rpm. The flow rate was controlled by an inlet valve attached to the main tank and monitored with a flowmeter. The flowmeter used was a ColeParmer P03248-56 by K I N G , with operating range 6.3 - 63 mL/s. This range o f flow rate ensured the jet was fully turbulent at all times for the discharge pipe size used. A n assistant valve was installed in order to remove the residual fluid, gas or particles accumulated in the pipe and the pump prior to commencing experiments.  Mixing tank motor  Main experimental Tank flow control valve jet nozzle =9.8 mm ' fJi&_down slope  Vol.490L  flowmeter  assistant discharge valve V  Figure 3.3 A sketch of discharge system  39  A vertically adjustable discharge nozzle with a 9.8 m m inner diameter was set up 10 cm from the center o f the tank wall. The distance between the nozzle tip and the wall was determined to ensure sufficient mixing area downstream and avoidance o f the turbulence due to the back wall. A n elbow with 3° angle parallel to the bed slope was attached to the end o f the nozzle.  3.2.1.3 Ambient fluid stratification system Two reservoir tanks with capacity o f 500 L were situated approximately 3 m above the ground to achieve sufficient hydraulic head. The filling speed was controlled by a valve attached to the tank (Figure 3.4). A 2.54 cm diameter pipe was used to supply the prepared reservoir fluid to the main tank through a floating spreader. A valve attached to the tank was used to control the filling speed o f the main tank.  One reservoir tank stored fresh  water and the other saline water. These were used to create linearly stratified and two-layer stratified ambient fluid. A motor and two 300 W submersible heaters with thermostat were set up i n the tank ensuring constant water temperature and complete mixing.  40  3.2.2 Instrumentation 3.2.2.1 P M E conductivity and temperature probe Conductivity and temperature measurements were performed using a Model 125 Microscale Conductivity Temperature Instrument manufactured by Precision Measurement Engineering ( P M E ) shown in Figure 3.5. The probe consists o f a conductivity and temperature sensor on a 0.63 c m diameter stainless steel shaft mounted onto a long stainless steel waterproof housing that contains an electronic preamplifier ( P M E , 1999). The sensor provides two analog voltage outputs  that are functions o f the  solution electrical  conductivity and temperature respectively. The sensors are connected to a probe controller which performs amplification and control functions. The controller was connected to an A / D board P C - L P M - 1 6 by National instruments in an I B M 486 P C .  Figure 3.5 P M E conductivity and temperature probe  This A / D board was used to convert analog voltages received from the conductivity sensor to machine-readable digital data. It can accept up to 16 channels o f analog single ended signals. The range o f stable linear conductivity is between 5 m S / c m and 800 mS/cm where the accuracy within this range is ± 1 % . The temperature can be measured from - 1 0 up to 100 °C. A data acquisition program was designed to sample probe measurements at approximately 35 H z and the measured values were recorded in a data file for later analysis.  41  3.2.2.2 Calibration of a P M E probe Conversion o f conductivity and temperature probe electrical readings requires that the probe be calibrated with known conductivity. It was necessary to calibrate the probe prior to each experiment since the probe holds an 8-hour calibration stability. Initially, calibration was conducted by measuring the voltage both from a highest known possible conductivity and the lowest temperature expected during experiments. This procedure was important in that it ensured the measurements do not go out o f the detection range. Once the gain setting was complete, it was necessary to check that the calibrated probe provides linearity between the measured conductivity and the voltage output. This was achieved by testing a series o f solutions o f the conductivity suggested in C R C Handbook o f Physics and Chemistry (Weast, 1985).  The standard solutions for calibration were prepared by addition o f a known mass o f laboratory grade Sodium Chloride (NaCl) to a 250 m l volumetric flask with distilled water at room temperature at 20 °C using Table 3.1. A 1.032 m o l / L N a C l solution was used for the highest conductivity. The calibration curves were obtained to confirm that the conductivity measurement shows linearity.  Table 3.1 NaCl Molar Concentration (g mol/L)  standard solution for calibration (After Weast, 1985) Density  (Df)*  Specific electrical conductance @ 20 °C (mmho/cm, mS/cm)  0.051  1.0004  5  0.172  1.0053  9.8  0.276  1.0096  24.6  0.47  1.0175  39.9  0.613  1.0232  50.7  0.739  1.0282  59.9  1.032  1.0398  80.0  * density ratio at 4°C and 20°C  42  Measured conductivity and temperature were converted into salinity and eventually fluid density using the procedure described in section 3.5.2.  3.2.2.3 Anton Paar density meter The  bulk density o f the particle-laden jets was measured using an Anton Paar  D M A 5 0 0 0 (Figure 3.6). The Anton-Paar density meter vibrates a l m L sample in a U shaped tube and measures the frequency o f oscillation. The U-tube continuously oscillates at the characteristic frequency by a magneto-electrical excitation system. The measured period o f oscillation o f the sample tube is converted into density and displayed on the meter. The uncertainty o f measurement is 10" to 10" kg/m (Anton-Paar, 2000).  Figure 3.6 Anton Paar D M A 5000 density meter  3.2.2.4 M A C H Spectrophotometer Dye concentration was measured using a M A C H  spectrophotometer. It passes a beam o f  broadly polychromatic radiation through the sample and measures the intensity o f power o f radiation as a function o f wavelength. A wavelength o f 520 nm was used.  Figure 3.7 M A C H spectrophotometer  43  3.2.3 Material  3.2.3.1 Jet and ambient fluid  Density modification o f the jet fluid and the ambient fluid was obtained by adding fine granulated sodium chloride from the Canadian Salt Company Limited. The salt was added to water i n all experiments i n order to ensure the conductivity is within the linear range o f the conductivity probe. Thus, the minimum conductivity o f fluid was maintained at 5 mS/cm. Rhodamine dye was added to the jet fluid to provide a qualitative indication o f the extent o f dilution by the mixing process i n the flow. The dye was sufficiently diluted to avoid a density change.  The particle-laden jet consists o f particles and interstitial fluid. The mixing tank was filled  with water and Rhodamine dye, while sodium chloride was added to yield the  minimum conductivity o f 5 mS/cm. The fluid was heated to 30°C to achieve high buoyancy. The particle suspension was sustained by continuously stirring at a fast speed to avoid settling and accumulation o f the particles i n the tank. Completely-mixed jet fluid was pumped at a constant flow rate through a flowmeter into the main experimental tank.  3.2.3.2 Particles  The particles used for particle-laden jets were spherical glass beads with a density o f 2,450 kg/m manufactured by Canasphere Industries Limited, Alberta. The glass beads were used because they have narrow particle size distributions and exhibit uniform behavior and settling velocity. A l s o , these glass beads have no conductivity and are noncohesive in saline solution. The particle settling velocity is determined primarily by the size, shape and specific gravity o f particles i n accordance with Stake's Law. Therefore, it was necessary to investigate the feasibility o f using glass beads as a substitute for fine tailings from Shell tailings pond i n terms o f the particle size distribution and shape.  44  Particle size distribution  The particle size distribution o f glass beads was obtained by a Sedigraph 5100 Particle Size Analysis System. The Sedigraph 5100 determines particle size by the gravity-induced travel rates o f different size particles i n a liquid with known properties. Settling velocity is measured using a finely collimated beam o f x-rays passing through the sample cell to a detector. The particle size is calculated based on Stake's Law. 0.05% Calgon was used as a dispersant for the particles, which has a density o f 0.9941 g/mL and a viscosity o f 0.724 g/mL. The analysis showed that approximately 92% o f the particles ranged between 3060 u m and the mean diameter were 38.72 urn. The detailed particle size distribution is given in Figure 3.8. The mean settling velocity calculated using Stake's law was 1.14 mm/s at 20 °C.  Equivalent spheical diameter (um)  Figure 3.8 Particle size distribution o f glass beads  45  Particle shape  The shape o f the particles is a critical factor for the particle size determination since Stake's law is valid only for spherical shaped particles. Fine tailings taken from a tailings pond in Alberta was used as reference particles.  However, measuring the fine tailings  particle size was not possible due to equipment restrictions and the nature o f the fine tailings. Namely, fine tailings contain bitumen, which exerts a strong viscosity, and they tend to attach to the instrument wall and testing tube. It was also difficult because the shape and size o f tailings are easily modified by a small disturbance.  A s an alternative, photographs o f tailings were taken and compared. The shape o f both glass particles and fine tailings were observed by a N i k o n Microflux E F M (semi-automatic photomicrograph attachment) and photographs were taken. Figure 3.9(a)(b)(c) show the shape o f fine tailings, the mixture o f glass beads and fine tailings and the glass beads respectively. Glass beads show fairly uniform round shape whereas fine tailings are more angular or amorphous. Despite this constraint, fine tailings are roughly spherical and o f similar enough size to glass beads that the latter approximately simulate the fine tailings.  46  Figure 3.9 Shape of particles (a) fine tailings, (b) mixture of fine tailings and gl; beads and (c) glass beads  3.3 Experimental conditions  A l l experiments were conducted with Reynolds number greater than 5,000, ensuring fully turbulent jets.  The experimental conditions for fluid jets and particle-laden jets are  shown i n Figure 3.10 and 3.11 respectively.  3.3.1 Fluid jet A total o f 59 experiments were conducted for fluid jets: 32 experiments for a two-layer system, 14 for a linearly stratified ambient fluid, and 13 for homogeneous ambient fluid. Experiments i n homogeneous  fluid were studied only to examine Coanda bottom  attachment. The individual experimental conditions o f fluid jets are given i n detail in Tables 3.2, 3.3 and 3.4. The details o f the results in the tables w i l l be discussed i n Chapter 4.  Two-layer system •  Densimetric Froude number (F ):  8.1-52.9  •  Density difference between two layers (p  •  Discharge height above the bed ( h ) :  5 - 19.5 c m  •  Distance to the density jump (hi):  3.5 - 18 c m  •  Total water depth at the discharge location (H):  34 c m  d  2  - p ): x  2.9 - 25.6 kg/m3  Linear stratification •  Densimetric Froude Number ( F ) :  8.7 - 55.5  •  Buoyancy frequency ( N ) :  0.58 - 0.78 s"  •  Discharge height above the bed (h):  2 - 15 c m  d  1  48  60.0 (18)  to 50.0 SO £ 5  §  40.0  1<o  30.0  £  20.0  s-  (5)  •(10) • (9-5)  IQ  0*5(17) (18)  10.0  •11  * ? f0  ( 1 7 )  (fl)*(17) 5.0  £5f *  *(11.5) <f6.5)  (6.2)  (3)  0.0 0.0  * (^77)  10.0  *(• - > 4  5  •  11.9 15.0  20.0  25.0  h (cm) • (height from the jet exit to the density jumpjil)  60.0  0.0  2.0  4.0  6.0 h (cm)  8.0  10.0  12.0  14.0  16.0  | • (Buoyancy frequency, N)  Figure 3.10 Experimental conditions for fluid jets: (a) two-layer systems and (b) linearly stratified fluid  49  <N  Jo ro 00  'a'  00  en  s  'So c o  o  o o o o o o o o  ffl d  6  d  d  d  d  d  d  d  <u  d  d  d  d  d  d  d  d  d  d  d  d  d  d  d  d  d  O  O  —  —  — c  — c  r^vo^OininNO'no\cooovO'-HVO©roooinrorocNso©a\^oaNrocNin^Hr^©-H r o ^ © ^ ^ v q ^ i n T f r TJ^ r o iro n ^in v q r o * q © v q o q r o r ^ ~ —>' o —<' o © © © © © d — : tNl^—Io—<' O O O O O O O ^ O ^ O O O O O O O O O O O O O O O  s  •* f i - ' r t u i T t - u i n - . o \ m v o d d d d d d - n ' o O O —I o - H d  as  +-  d  B B B O , OH <u u u 00 ro T)- (S PH PCO H PH oo a \ o - H CN in  S S—  £( D £ S U O  Z Z Z Z Z Z Z Z  a  s  c B B S o o o o  j 5  od  oo  in  r~  d  •rt- CN oo oo m oo ' m * in n  ro ro CN — < ' d  ^  so —< o d p ^ r o T j - o d o o r o r ^ i r i d ^ d T i - o o  od  ro sq vq sq —< CN OS  t - ^ O s o q c o — ; v q © O s — oo in —< CN .-< .-< r o i i n ' o \ v d ^ a o ^ i x J f r i o \ d ^ i n o \ » ^ ' o d r ~ ' H d ' H « o ^ in ^ H r n r-l - H t N ro^H—< • — i ^ —< CN - . ro - - H —< •—i CN  *3 c  a  -4—•  © c s O N r o r - ~ r ^ t ^ ' ^ - v o o \ ' - H C N O O - H O O r o o o s o o \ s o c N O i n r - ~ r o r o m r o o o s o - ^_ - s_ o SO CN Os so -—> ©' r' N l N r o 1r o IoWW ©s so o o ws .s o^ c .o .o -o~o w\ .c vs , c vN O- -o o o o r o ^ H O m ©—O -s c o- r o- - H © o o oo ooo r~ oo rnts^oviNinvorom'O'^iciai^ovortooin  a  ID PH  v  e o  CO  B  5b u cNinincNincNincs©incNrocNininooincsro©ininincNin©cNrocoininco  C O u  u-^-HrtiOrti/-)—<l/->CN-^u->CN'/~>"-*rO—'i/OCN-^-^^-^l/") — — W!CNCN^—*CN  "« e  O ^ ^ O ^ O ^ O r o ^ O O O ^ ^ ^ ^ O O r o ^ ^ ' O O i O i O r o O O ' r i ' / I O  e  sororosorosoroso^roiO^sororoinrosO'^-rorococosororo  -*t  ro ro  C  S  u oo  a f l-H  a W  0 0  > o t ^ t ^ v o t ^ ' o ^ ^ i n i c i ^ - r ^ v i o \ c r i v i > O T f i n t » c > i o o i f i _l~-;i/->i/-}>/->mooi/->ooi/-> ^ d t ^ a o N K ^ i ^ o d o d f A CN CN CN ro ro CN CN CN CN CN CN CN CN ,  CN  oo  oo  ,  oo © Ort i n i n O P - ' i n i n ^ H O S O O O O S S O O O S O i n c O i n i n i n O S C N i n C N i n ^ o! « so ro ro so T(- Tl- so « ici Tf rt  rt  rt  H r^cNroinroininro'* o\ ^' os "~' o d o o '""' ~ *  i n s o s o i n s o i n © © © r o O s o r o c o i n © O i n ^ -  a b  w  m ici  o \ O r H ( s i n ( s v o * o » o ^ o - « a » r t ( s o o o \ o o » i a m ^ i n O N r t O i n r^O\ro©rocNint^OsONin©Os^oqroroON^ ^ • - ' N v d i ^ o d d r t ' o d ^ r n ^ d r M ^ o d m r t i n ' m i ^ o d i ^ i n v i d co CN CN CN CN CN CN CN CNCN CN • — ' C O C N C N C S C N C N C N —. —i (NCNCNCSCN T j - r ^ T j - o s — i H i n , \ e_t. 9—i o o ( s m N O \ n ,^ »- .i " iO N . - ir o Ow O ^-i coroinroOf^ro ^q »q o q r~; • — o r o o o O \ o o i n o \ — m vo 0\ - ^ C N ^ r O T j - O N ^ O ' o d —>' —I CN —<' -•^ ^ ^ r o ^ c N v d r o o d s o d ^ ^ ^ c N ^ T t - d ^ c N K oo od od a i U  a b  a. b  •^••^•oovnvo — " n o s o o o o o — • • ^ - c N u - i r ^ c N O N r ^ - s j - T f r ^ r o - i n oo p c N O - ^ r o r o o q ^ o ^ p c N p r ^ © 0 \ r o r - ~ T i - - « T j - c o o\ ^ ' d d  ^ooor^TfONin^HrocN  — ^  ON in oo ro ro G\ ^ 0\ CNi CN d in i i i d i  ror^-H\00oinTTCNOOsmroo  <1^^<i--'<'CNCNCNrocNt^roro^ininror^r^r^^r^ror^r^^r^Trroro^  c o 0 0  B  5b <u  a u 6  o 6 0  a  t  u  e  5b oi u  3  B  -O cu  r*">  «  m  m  (N  r*">  —  o  ^  —  .  •—<  cn  r-•  c/>  b.  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In addition, 2 experiments were conducted i n homogeneous ambient fluid to observe the difference between fluid jets and particle-laden jets i n the absence o f the effect o f the ambient fluid condition i n Chapter 6. The following is a summary o f the experimental conditions and the individual details are given i n Tables 3.5 and 3.6.  •  Densimetric Froude number ( F ):  •  Dimensionless density ratio (R):  -18.2-0.63  •  Total water depth ( H ) :  34 cm  •  Discharge height above the bed ( h ) :  15 cm  •  Distance to the pycnocline ( h ) :  3.5 - 6.8 c m  d  t  6.6 - 32.8  3.4 Experimental procedures 3.4.1 Preparation Prior to conducting the main experiments, all the individual instruments were carefully tested to avoid experimental errors due to instrumental instability. The jet fluid was prepared and a small amount o f well-mixed fluid was released to remove the residual fluid and particles from the pipe prior to initiation o f the experiment.  3.4.1.1 Stratification of ambient fluid  The reservoir tanks were filled with tap water and salt was added. The stirrer i n the  52  reservoir tank was operated at 120 rpm, ensuring a complete mixing o f ambient fluid. Two submersible heaters were set at room temperature. After ensuring the desired water temperature was reached, the fluid was gradually discharged through a pipe into the experimental tank.  The two-layer density stratified fluid was achieved by slowly releasing the upper reservoir fluid through a floating spreader placed on the top o f the dense lower layer. The spreader floated freely on the water surface as the tank was being filled. The water temperature was maintained constant in order to avoid the double diffusive effects between two layers. This technique has been used by some researchers as an effective method to minimize turbulent mixing at the interface during filling (Maxworthy, 1973; Wong, 1984). The filling rate is a critical factor in creating a sharp interface. Rapid filling can cause turbulent mixing at the density interface. O n the other hand, slow filling rate ensures no turbulence but i f the  filling  is too slow molecular diffusion becomes important. The  interface thickness ( ^ ) can be estimated as (Fischer et al., 1979)  £ = JAxDt  where  (3.1)  m 1s  D: molecular diffusion,  2  D = 1.39 (1 + 0.029 (9 - 20)) x IO" (Schmidt, 1997) 9  T  Oj: water temperature, °C t: time (s)  The filling time for the present experiment was set at 5 hours which was determined through preliminary tests. Using (3.1), the interface thickness increment due to molecular diffusion at 20 °C for 5 hours was estimated at 1.8 cm . After filling, the ambient fluid was allowed to stand for approximately 10 minutes to allow any turbulence to subside.  53  30.0 • R (dimensionless density)  • 0.5 25.0 a  -^.62  20.0  at  • -1.02  a>  u  >>15.0 a « u .4> 13  10.0 5.0  a  • 0.11 • 0.11 0.54 0.15 • -0.73 • -2.4 0.63* \-0.97 • -0.79 * 0.21 " - *-4.49 0.38 T  T3  • -1.35  25  • -18.15  0.0 0.0  5.0  10.0 15.0 20.0 25.0 Densimetric Froude Number (F )  30.0  35.0  d  0.90 • (Dimensionless density, R) -0.47  0.85  •  •  -0.25  3 a> 0.80 -^•43 « 3.55 • -1.04 • -0.20  1*0.75 a  © PS  • -0.49 • -0.45  0.70  0.65 0.0  5.0  10.0  15.0  20.0  25.0  30.0  Densimetric Froude Number (F ) d  Figure 3.11 Experimental conditions o f particle-laden jets (a) two-layer systems and (b) linearly stratified ambient fluids  «  o-  E  N  "3D  ?"  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" 3 -w  u  31.5  o u  3.128  o  -2.33  U 41.8  41.8  ^E  -31.05  X!  c  31.5  u CM  3.167  .©  -3.98  a. u  -67.66  ,o  83.5  «  63.0  a  1315.5  1315.5  5261.9  03  5261.9  —  2.959  877.80 978.80  M *  P H P H P H P H Q H O H C U O H  407.52  413.06  11.7  11.6  20.7  21.4  19.3  OA  Oil  25.4  4>  506.54  1051.13  « •a fa.  83.5  60  63.0  —  -a  2.221  a  -2.12  60  -33.63  « +H  4262.1  </J  75.2  i  56.7  I  00 PH"  w  1.742  0 0  J  -2.04  i  ^ 10.41 10.77 10.74 12.60 11.81 12.13 9.95 10.17  7.60 7.01 9.38 9.27 9.29 9.30 6.96 7.05  )-  4262.1  TJ-  ^ u  ^  75.2  i 0 0  S3  1  56.7  ^ ^ ^  e o  -J  1.391  u  S  14.2  PH  is "j  10.6  (A  £  500.79  £P  483.01  60  1894.3  •o U.  5.0  7.2  9.9  13.9  12.8  16.0  10.1  24.7  5  1315.5  — i  50.1  s  41.8  IS  31.5  0.73  0.75  0.84  0.84  0.76  0.74  0.74  0.75  2 "3  37.8  1  t |  1.888  m  9 1  1.469  i 1  ^ ^ I  -32.28  ii  a '  "! ^ ^ I  -2.20  "E i 1  1  -20.04  £ vo 1  •  0.28  u —H  °! ^ •  -0.96  a o i  ^ ^ •  3.68  s CQ g t 1  -15.57  ^ 1  V (cm/s)  o T—4  Co  1  EXP#  a  EXP# r o o o 0 ^ r ^ t ^ < N ^ t O o O ( N O ^ o a \ O v ^ r ^ v o < N r ^  1  ^  Flow Regime  5.3(b)  5.3(a), 5.4(a)  5.1(b), 5.4(b)  5.1(d), 5.4 (d)  5.1(c), 5.4 (c)  5.1(a)  Figure  Linear stratification was accomplished in a similar manner to the two-layer system. However, the left tank was filled with freshwater and right one with saline water. The dense saline water being discharged from the tank was constantly recharged by freshwater from the left tank by the hydraulic pressure gradient. The motor continuously mixed the freshwater and saline water vigorously. B y this process, the density o f mixed fluid linearly decreases as the tank fills.  3.4.1.2 Calibration of the P M E probe and flow visualization  While the experimental tank was being filled, the conductivity probe was calibrated according to the procedure described i n section 3.5.2. A Panasonic H S video camera was set up in front o f the main tank to take flow images.  3.4.2 Measurement and sampling  Prior to jet discharge, some o f the jet fluid was discarded through an assistant discharge pipe to remove residual fluid. After completing ambient fluid preparation, the density  profile was taken  with  a calibrated conductivity-temperature  probe. The  experiments during discharge were implemented simply by turning on the jet pumping system and setting the flow control valve to obtain the required flow rate.  3.4.2.1 Fluid jet  The measurement locations were chosen based on the characteristics o f jets obtained from preliminary observation.  Measurement o f the density profile was conducted at i)  three points near jet discharge (x = 10, 20 and 30 c m from the jet nozzle), ii) transitional points (x = 45, 60 and 75 cm, and iii) locations considered relatively far from the discharge (x = 90, 105 and 120 cm). Conductivity profiles were taken prior to the discharge, during and after injection o f the jet. Due to the constraints on the dimension o f the main tank, the  56  profiles were obtained before the front o f the spreading flow reached the other end o f tank wall.  The traversing speed o f the P M E probe was set at 50 mm/s to obtain an instantaneous density profile. After each measurement, the trolley was quickly moved to the next location. The measurement time, position, conductivity and temperature voltage output were saved in a text file and loaded into a Matlab file for further analysis. Using the equations described in section 3.5.2, the readings were converted into parameters such as salinity and density.  3.4.2.2 Particle-laden jet The density o f interstitial fluid was estimated using a P M E probe while the bulk density was measured using the D M 5 0 0 0 Anton-Paar. The samples o f particle-laden jets were taken at four locations along the tank: x = 10, 30, 45 and 75 cm. To alleviate the loss o f particles during the sampling procedure, the collected samples were rapidly transferred from the syringes into glass bottles manufactured for spectrophotometer use. Blank samples were also taken from the ambient fluid prior to the discharge. The samples were collected during discharge and the lids placed on immediately after filling and then dated and kept at room temperature for later analysis.  A t x = 75, the samples were initially drawn by a pump sampler. The samples were taken directly into 15 m L mass cylinders through sampling tubes with 3 m m inner diameter. 10 samples were taken at a pump speed o f 300 rpm, which was determined to be the optimum speed based on preliminary tests o f different pumping speeds. It ensures no disturbance o f the ambient fluid due to fast withdrawal and also prevents particles from settling in the tube due to slow sampling speed.  57  3.5 Data acquisition and processing 3.5.1 Data acquisition 3.5.1.1 Dye concentration measurement The particle-laden samples were centrifuged until all particles completely settled to the bottom o f the bottle. The complete separation o f particles and interstitial fluid prevents the fine suspended particles from interfering with light penetration. The bottles were carefully placed in the spectrophotometer cell slot without disturbance. Since red Rhodamine G 6 was used to color the interstitial fluid, the wavelength used was 520 nm, which absorbs red-pink.  3.5.1.2 Suspended particle concentration After completing the dye concentration measurement, the samples were filtered using a vacuum filtering system through a glass fiber filter (G6). Figure 3.12 shows the vacuum filtering system. The filtered particle samples were dried at 103 - 105 °C for over an hour. Then the weight was measured using a four digit electric balance, Mettler A C 100, with accuracy o f ± 0.000 l g . The particle weight was calculated by subtracting the pre-measured precise filter weight from the total weight.  Figure 3.12 Vacuum filter system  58  3.5.1.3 Bulk density The bulk density o f particle-laden jet was measured using the Anton Parr D M 5 0 0 0 described in section 3.2.2. The bulk density o f the particle-laden jets was rather difficult to measure with high accuracy and consistency because the measurement was highly sensitive to particle settling in the inner tube o f the Anton-Paar. In particular, at high concentrations, the measured density difference was relatively large and thus 10 samples were taken from two location: the mixing tank and the discharge nozzle. Individual density was calculated and averaged.  3.5.1.4 Density profile The density profiles o f fluid jets and interstitial fluid o f particle-laden jets were taken using a P M E conductivity and temperature probe before and after discharge. Vertical and horizontal profiles were obtained. Other parameters were obtained by both visual measurement and the density profile analysis. The measurement parameters such as the final spreading layer thickness, the maximum rise height and the location were obtained by video images taken along the jet trajectory against a 5 cm grid on the tank wall. In each experiment, 20 video images were captured using a frame grabber and averaged. The flow images were obtained only before the head o f flow reached the downstream wall. The experimental parameters and measurement methods employed are summarized in Table 3.7.  Table 3.7 Summary o f experimental parameters and measurement techniques  Parameters  Measurement Technique Measurement of density profile using a P M E  Density profile  Bulk  density  micro-scale conductivity and temperature probe and  interstitial  density o f particle-laden fluid  fluid  Measurement of bulk density using Anton-Paar D M A 4500/5000 density meter and interstitial fluid density using P M E probe  59  Maximum location  rise height (X ), m  ( Z ) and m  impingement  the  height  Flow  visualization: video  image  above the pycnocline (Pd), spreading  using a Panasonic video camera  layer thickness(Tf) top and bottom o f  Density profile analysis  capturing  the spreading layer (Z , Zb) t  Centrifuge the samples Dye concentration  Measure the dye concentration using a M A C H spectrophotometer Centrifuge samples and filtrate using a vacuum filtering system, Drying the filter and particles  Suspended particles  Measure the weight using a electric balance Mettler 100  The definition sketch o f parameters is given in Figure 3.13. The symbols hi, h i , and h are the distance to the pycnocline, the upper layer thickness and discharge height above the bed respectively.  y_ j  h,  Figure 3.13 Definition sketch o f parameters  60  3.5.2 Density data processing 3.5.2.1 Fluid density estimation The density estimation procedure is divided into three stages: conversion o f electrical voltage  into  conductivity  and  temperature,  conductivity  into  salinity;  and  salinity/temperature into density. It is essential to obtain temperature and conductivity data simultaneously since conductivity significantly varies with temperature. The first step in the processing o f density data is to extract the electric voltage output from a data file format. A simple calculation program was designed to estimate the density from the raw data file using the Matlab program.  The density o f sodium chloride (NaCl) is a function o f the N a C l concentration and solution temperature. The density o f N a C l solution is estimated as the sum o f fresh water density at temperature (T) and the concentration increase due to N a C l ( A C ) at that S  temperature. The equations Head (1983) suggested were used for the density calculation and the schematic procedure o f density estimation is shown in Figure 3.14. The procedure is divided into two steps: calibration and data conversion from raw experimental data.  STEP I  Conductivity probe calibration consists o f three stages: gain set-up, calibration data acquisition and numerical analysis. From measured conductivity and temperature base electrical voltages (Vc ff and Vioff), the circuit gain G is determined using the following 0  equations.  Vo ( re/ ) = G • a  +V  (3.2)  ) = K + J/T  (3.3)  a  ref  ln(V(T)-V  T o f f  coff  61  where K and J are constants that can be obtained with two reference temperature data points. These coefficients are case-specific and have to be determined for each experiment.  STEP II  Once G , V  T o  ff  and  V  C o  ff  are determined, the probe can be used to measure the electrical  conductivity and temperature o f solutions. The density calculation from  temperature-  compensated conductivity and temperature consists o f two processes: pure water density calculation at temperature T and the computation o f increased density due to sodium chloride (NaCl).  p=p +Ap T  where  (3.4)  s  p : density (kg/m ) 3  px : water density as a function o f temperature (kg/m ) 3  Ap : s  density increment due to N a C l  The density o f pure water (px) as a function o f temperature can be computed to within 0.1% (1 kg/m ) using (Head, 1983): 3  p  = {0.9998395 + (6.7914 • 10" x T) 5  T  + (-9.0894• 10" x T ) +(1.0171-10" x T ) 6  2  7  3  (3-5) + (-1.2816-10" x T ) +(1.1592-10" x T ) 9  4  u  5  + ( - 5 . 0 1 2 5 - 1 0 " x T ) }/0.001 14  6  The measured conductivity value requires a temperature compensation process based on the reference temperature. The temperature compensation equation for N a C l in water is given as:  62  Calibration Vo(<J j), re  CTref,  V  off  Determination of calibration equation for conductivity and temperature V  0  { ° r e  f  HV(T)-V  ) = G -a T o f f  )  cu Su cu  Vo(T), Vo(C)  -•  Conversion of conductivity a(t)  coff  =A+B / T  G, Vcoff, S  V  +  ref  Toff,  (1)  K, J  electrical output and temperature  into (2)  a(t,T)T{t)  a x  W  Calculation of temperature-compensated conductivity cr(t,T) cj{t,T ) rpf  =a(t,T)f(T,T  r p f  )  (3)  a(t,T )T(t) ref  Compute salt concentration C(t) = f(a(t,T )) ref  (4) C(t)T(t)  1£  Estimate density p{t) = f(C(t),T(t))  (5)  Figure 3.14 Calculation procedure o f fluid density (After Head, 1983)  C  2 5  = C / ( 1 + (0.0191 x (T - 25))  (3.6)  T  where C25 and C T are conductivity at 25 ° C and temperature T, respectively. The salinity (wt %) at 25 ° C is obtained by  Salinity(%)  = 0.01498478 +(-0.01458078 x C  1 / 2 2 5  )  + (0.05185288 x C ) + (0.00206994 x C 2 5  + (-0.00010365 x C  2 2 5  3 / 2 2 5  ) + (0.00006269 x C  ) 5 / 2  2 5  (3.7) )  This equation is valid for seawater but it can also be used for N a C l solution with standard deviation o f 0.02% (Head, 1983). Density increment ( Ap )  due to sodium  s  chloride is estimated as:  Ap = (45.5655 x M ) + (-0.2341 x M x T) + (3.4128 • 10" x M x T ) 3  s  0  0  2  0  + (-2.7030-10" x M x T ) + (1.4037 • 10" x M x T ) + ( - 1 . 8 5 2 7 x T ) 5  3  7  4  0  1 5  0  (3.8) + (5.3956• 10" x M l , x T ) + ( - 6 . 2 6 3 5 • 10" x M | ; x T ) + ( - 1 . 6 3 6 8 x M ) 2  5  4  5  2  2  + (-9.5653 • l O x M x T) + (5.2829 • 10' x M x T ) + (0.2274x M / ) - 4  M  0  2  5  2  2  2  5  is the molar concentration calculated from estimated conductivity at 25 °C. Calculation  o f molar concentration ( M ) for N a C l in water is given (Head, 1983) as: c  Salinity(%) . ^ , w x (100-Salinity(%)) M o l a r concentration ( M „ ) = " 0.058443 J V  „ (3.9)  This equation is valid for the temperature range 0 to 50 °C and salinity 0 to saturation (Head, 1983).  64  Chapter 4  Results and Discussion: Fluid Jets  4.1 Introduction To  conduct  wastewater  discharge  into  receiving  water  in  an  effective  and  environmentally-safe manner it is essential to understand the behavior o f buoyant fluid jets under  various discharge  schemes and ambient  fluid  conditions. Understanding  the  dynamics o f buoyant fluid jets also provides a basis to interpret the behavior o f particleladen jets.  Buoyant fluid jets discharged at 3° downward orientation were examined i) to identify the important factors affecting the flow dynamics under various source conditions, ii) to understand the effect o f the ambient fluid condition and, i n particular, the presence o f the pycnocline and iii) to identify discharge conditions preventing buoyant jet fluids from penetrating into the upper layer in two-layer systems.  4.2 Buoyant jet in a two-layer system This section presents the experimental results and dimensional analysis o f buoyant jets discharged into in two-layer systems. The general behavior o f buoyant jets is described and important  flow  regimes  are determined.  Backflow  occurrence  and Coanda  bottom  attachment are investigated. The gross flow characteristics o f buoyant jets such as maximum rise height and spreading layer thickness are analyzed using dimensional analysis and compared with the experimental results.  65  4.2.1 Behavior of buoyant jets  Three flow regimes were observed for buoyant fluid jets: weak impingement, strong impingement and penetration as illustrated i n Figure 4.1. The behavior o f buoyant jets was obtained from flow visualization, and the density and dye concentration profiles. Detailed characteristics o f these flow regimes and analysis o f their behavior are given i n the following sections.  4.2.1.1 Weak impingement  A s a buoyant jet rises and approaches the pycnocline, a density step across the pycnocline suppresses the vertical momentum o f the jet. A s a result, the rising buoyant jet bends immediately after impingement and spreads laterally and horizontally i n the lower layer (Figure 4.1(a)). The buoyant jet does not cause mixing in the upper layer due to substantial reduction in the vertical mixing and the density fluctuation at the pycnocline is also small. Figure 4.2 shows a set o f typical density profiles o f a buoyant jet, showing the weak impingement. The density profiles were taken from five downstream locations along the jet trajectory. In this case, the buoyant jet actively rises and impinges on the pycnocline at approximately x/L - 0 . 1 2 - 0 . 1 9 . Here, x and L are the downstream distance and the length o f the experimental tank respectively. The jet stopped rising at x/L - 0.25, at which point a horizontal spreading layer formed.  4.2.1.2 Strong impingement  When the density o f a jet flow impinging on the pycnocline is slightly smaller or similar to that o f the upper layer, the jet may overshoot across the density step into the upper layer. However, the jet falls back to its neutral buoyancy level immediately and proceeds horizontally (Figure 4.1(b)). The thickness o f the spreading layer grows rapidly until the jet  66  Density profiles for weak impingement  (a)  £ 300  Density (ke/m ) 1  Density profiles for strong impingement  (b)  1015  10P0 Density (kg/m ) 3  Density profiles for penetration  1015  1016  1017  1018  1019  1020 1021  1022  1023  1024 1025  Density (kg/m ) 3  Figure 4.1 Sketches of behavior of buoyant jets and density profiles in two-layer systems: (a) weak impingement (A19) (b) strong impingement (A71) and (c) penetration (A70), (-—): density profile before discharge, ( — ): after discharge  67  reaches the maximum rise height and then it reduces as the jet propagates as a gravity current. The density profiles before and after discharge at x/L = 0.31 clearly indicates that strong impingement o f a jet flow causes permanent mixing in a considerable depth o f the upper layer and significantly increases the density o f the upper layer. However, the density at surface does not change. This is a distinctive difference between weak and strong impingement. Figure 4.3 (a)(b) are photographs showing examples o f weak and strong impingement respectively o f buoyant jets on the pycnocline.  4.2.1.3 Penetration If a highly buoyant jet is injected under a small density step or the density o f a jet impinging on the pycnocline is significantly smaller than that o f the upper layer, the jet can penetrate into the upper layer as illustrated in Figure 4.1 (c). Once a jet penetrated the pycnocline, it spreads above the pycnocline. The density profiles o f a penetrating buoyant jet into the upper layer indicates that the pycnocline became eroded and the upper layer was disturbed significantly by the penetration o f the jet flow. The density significantly increased in the entire upper layer, implying that a considerable amount o f the lower layer fluid was transferred into the upper layer through entrainment and penetration. Since jet fluid is always lighter than the ambient fluid in the lower layer, the density increase in the upper layer is due only to the entrainment o f the lower layer. Figure 4.4 are photographs showing the process o f buoyant jet penetration and spreading in the upper layer. A s the jet reaches the water surface, lateral spreading increases greatly and then it forms a horizontal spreading layer.  68  ON  G cu  CU C  CU  C  CU  c © cu  bx> u 05  C/!  C  05  © 03  CU ^  OS  "O B OS  CU  a  CU -C C/5  _cu  5  ©  a (LULU) q i d e a  c/3 C CU —  -r CU  ex  (a) Weak impingement  (b) Strong impingement Figure 4.3 Impingement of buoyant jets in two-layer systems: (a) weak impingement (A37) and (b) strong impingement (A51)  70  (a) t-36 second  (b) t=65 second  (c) t= 69 second  Figure 4.4 Process of a buoyant jet penetration in two-layer system: (a) penetration (b) lateral-horizontal spreading and (c) horizontal spreading  71  4.2.2 Determination of flow regimes  4.2.2.1 Penetration/impingement parameter, ¥  The direction o f source momentum o f a buoyant jet is fixed at 3° downward in this study. Thus a buoyant jet spreads out predominantly in the source momentum direction and it constantly entrains heavy ambient fluid ( p ) . This results in density increase in jet flow 2  before it bends and rises to the pycnocline as illustrated in Figure 4.5. I f there is sufficient dilution the density o f the jet w i l l approach p  2  as it rises to the pycnocline. However, the  density is always less than the lower layer fluid and the jet rises above the pycnocline.  Figure 4.5 A buoyant jet in two-layer system  Since the direct effect o f source momentum on the jet at the pycnocline is insignificant, a buoyant jet can be approximated as a plume. The rising distance o f a jet above the pycnocline, P  d  depends on the relative strength o f vertical velocity o f the plume when it  impinges on the pycnocline and the strength o f the density step.  72  The balance between kinetic energy and potential energy i n the impingement region yields:  P  d  -  ^  L  —  .  ( 4  ,)  g  If there is sufficient dilution in the jet as it rises towards the pycnocline, then pj —> p . 2  For the purposes o f the derivation o f the most relevant dimensionless this problem, assume Pj = p at the point o f impingement so that: 2  P  d  ~  4"  _ P2 g[, =  where  (4-2)  -Pi  Pi  The time-averaged vertical velocity on the axis o f the plume is given as a function o f the buoyancy flux and the vertical distance (Fischer et al., 1979):  u *(B/z)  (4.3)  , / 3  m  Therefore the ratio o f the rise height above the pycnocline ( P ) to the discharge distance d  (hj) can be rewritten using eq(4.3) as  p  ^  i,  n  2 / 5  * —  '3/5,  (4.4) yy-^J  Subsequently, the ratio can be defined as a dimensionless parameter (*F):  73  *F is a measure o f the ratio o f the strength o f the plume as it impinges on the pycnocline to the resistance offered by the density step. Given the assumptions presented above the impingement height P should increase linearly with increasing *F . d  Baines (1975) presented a similar result for a negatively buoyant plume impinges on a density interface but does not penetrate it. H e expressed his results in terms o f a Froude number F , which has the same general form as * F . In fact, i f the centerline velocity r  u  m  =4.7(B/z)  1 / 3  , see Fischer (1979), then  Y = (F /4.7)  6 / 5  r  . Kumagai  (1984) also  conducted a similar experiments and theoretical investigation on impingement o f pure plumes on the density interface. However, these studies are different from the present study in that this study is associated with 3° downward directed turbulent jets which cause significant entrainment o f the ambient fluid while the previous studies dealt with pure plumes without source momentum. A l s o , the previous studies covered only impingement cases whereas the present study concerned with both impingement and penetration.  Figure 4.6 shows the dimensionless impingement height (P I h ) versus * F , where P is d  t  d  the impingement height above the pycnocline. The flow became trapped under the pycnocline when m < 0.5, which covered the weak impingement regime. The impingement height above the pycnocline (P ) d  was less than 0.3A, from 14 measurements. Penetration  occurred when *P > 0.9 and the strong impingement regime covered 0.5 < *F < 0.9.  74  4.0 A weak irnpingement • strong impingement  3.5  x penetration  3.0  2.5  2.0  1.5  1.0  0.5 A  .  A'  0.0 0.0  0.2  0.4  0.6  0.8  1.0  1.2  1.4  1.6  1.  Figure 4.6 F l o w regimes o f buoyant jets in two-layer systems  75  4.2.2.2 Density Relation To understand under what circumstances a buoyant jet impinges or penetrates the pycnocline, the relationship between the density o f a jet when it reaches the pycnocline and that o f the lower and upper layer is considered. The density ratio / can be defined as:  Y  =  P  x  ~  Pi  where /?,., p  and p  x  2  P  (4.6)  i  -Pi  are the density o f a jet flow at the pycnocline and the density o f the  upper and lower layers respectively. I f /  = 1, the ambient fluid is homogeneous, while  Y > 1 indicates that the ambient fluid is statically unstable since the upper layer is heavier than the lower layer. For a stable two-layer stratified fluid the lower layer density is always greater than that o f the upper layer (p > 2  /?,). A s a buoyant jet ascends it entrains heavy  ambient fluid, however the density o f the lower layer ( p ) is always larger than that at the 2  density step p  t  (p  2  - p > 0 ) . Consequently, a jet can penetrate into the upper layer only i f i  / ? , - / » , > 0, that is: 0 < Y <1  (4.7)  However, i f / ? , - / ? , < 0 , a submerged jet does not penetrate but becomes trapped at the pycnocline. A s the jet rises, it slightly impinges on the density step due to the weak vertical momentum resulting from buoyancy. The weak impingement occurs if:  Y  <  0  (4.8)  O n the other hand, i f p « p ., a jet flow impinges on the pycnocline with varying x  t  strength depending on the density difference with the lower layer, p  2  - p. t  If p  2  > p  t  impingement can occur only weakly since the jet does not obtain sufficient vertical  76  momentum from the lower layer. However, i f p  2  »  p., a strong impingement may occur  due to the strong vertical driving force generated by the large density difference even for p <p x  i  although penetration does not occur. Therefore, i f strong impingement regime  satisfies y ~ 0  (4.9)  However, the definition o f strong impingement is rather vague and thus this regime can be supplemented quantitatively with experimental data in section 4.2.2.1.  Figure 4.7  presents the estimated dimensionless density ratio y showing that the defined regimes agree with the experimental data. Density at the pycnocline p  t  was estimated using  C O R M I X 1.  A  0.0  H9 •1  •i  0  • B  0.5 B  -2.0  •  1.0  1.5  2  •  -4.0  • • •  -6.0  -8.0  •10.0  •  •  • •  • weak impingement  • strong impingement  A penetration  Figure 4.7 Dimensionless density ( / ) o f buoyant jets in two-layer systems  77  4.2.2.3 Comparison of flow regimes with prediction of CORMIX1 C O R M I X 1 v3.2 was run to compare with the flow regimes defined in this study. A l l submerged buoyant jets tested were predicted to be Class H4-0 except for the Coanda bottom attachment condition. When this type o f flow is discharged into the stagnant ambient fluid, the weakly bent buoyant jet impinges on the pycnocline and spreads radially (Jirka e t a l , 1996).  C O R M I X 1 does not explicitly distinguish between impingement and penetration as different flow classes but it recognizes the density step as an internal boundary. The model determines whether (a) the flow penetrates to water surface or (b) bends and propagates under the density step by the following relations: (a) Z , + h > H  s  where Z  t  and (b) Z , + h <  H, s  and h are the vertical height o f rise relative to the discharge elevation and the  discharge height above the bottom respectively. H  s  is a finite layer depth which can be  either total water depth or discharge height to the pynocline depending on the strength o f the density step (Jirka and Doneker, 1991).  When the density step is influential, only lower layer depth is important. Thus, H  s  =h + h, where h is the distance to the pycnocline from discharge level. A s the top o f t  t  the spreading layer approaches the boundary, Z  t  < h , the flow is trapped under the (  pycnocline and i f Z > h , the jet rises to the water surface. t  t  Experiments showed that when Z - h < 1.5 weak impingement occurred along the t  (  pycnocline and i f Z - h > 5.5 the flow rose to the surface regardless o f the presence o f t  t  the pycnocline. The model agreed with the defined flow regimes in the present study except for a strong impingement case (A51). In this exceptional case Z, - h =5.9 and thus the t  model predicted the jet to penetrate to the upper layer. This discrepancy may have occurred because the model underestimates the influence o f the small density step. Once the model  78  determines the effect o f the density step to be negligible, it regards the ambient fluid as homogeneous with average density o f the upper and the lower layer, thus allowing a buoyant jet to rise to the top o f the upper layer.  4.2.3 Backflow  The prevention o f discharge flows back to the intakes is one o f the principal design factors iii many industrial applications. A backflow, an upstream intrusion, is formed when a rising buoyant jet encounters a horizontal pressure gradient. It is necessary to distinguish between a backflow and a return flow for a small scale laboratory experiments, where the limited basin length may affect flow pattern. A return flow forms when a discharged jet pushes the fluid ahead toward the end-wall in the tank resulting in reversing the direction at the end wall (Darden et al., 1972).  For all experimental conditions, backflows occurred when buoyant jets approached the density step. However, there was a great deal o f variation in the thickness and location o f the backflow. Some o f the backflows emerged along the pycnocline immediately near the jet nozzle while some formed far downstream and exerted little impact on the discharge area. Hereafter, the former is termed as backflow and the latter defined as  no-backflow.  Figure 4.8 shows photographs o f both backflow and no-backflow. To identify the condition o f backflow generation, the horizontal momentum, m  h  and  vertical momentum, m o f a buoyant jet are considered. The horizontal momentum o f a jet v  is constant at any cross-section, i.e. m = M cos 0, where M is the source momentum flux. h  For a small discharge angle m =M h  since cos (9 « 1.  The momentum o f a vertically oriented jet can be approximated by the vertical momentum o f a plume:  m =b B v  2  2 / 3  z  4 n  (4.10)  79  (a) No-backflow  (b) Backflow  Figure 4.8 Backflows in two-layer systems: (a) no-backflow (A24, *¥ = 0.34,F =30.1) and (b) backflow (A40, *¥ = 0.52,F = 8.9) d  d  where b is an experimental coefficient to be 0.35 for a round plume (Fischer et al., 1979). 2  The vertical momentum flux at the pycnocline is m = b B hf , 2li  v  where h is the distance  n  2  t  to the pycnocline from a jet nozzle. A sketch o f a buoyant jet forming a backflow is shown in Figure 4.9.  Figure 4.9 Development o f a backflow at the pycnocline  A buoyant jet approaches the pycnocline at the angle 6 , P  relative magnitude o f two momentum i.e. tan 6  m - —-. m  which is determined by the  I f the horizontal momentum is  h  larger than the vertical momentum, the angle becomes small and thus the jet spreads horizontally without forming a backflow. However, i f the relative strength o f vertical momentum to the horizontal momentum is large, then a backflow forms as a jet reaches the pycnocline. The relative momentum is given as:  m  h  M  Eq. (4.11) can be rewritten using a characteristic length scale iM  =M  3  /  4  /B : U2  81  = 0.35  (4.12)  V  *M J  Consequently, the jet angle at the pycnocline becomes functions o f the distance to the pycnocline, h and the characteristic length scale I t  M  :  v 4 / 3  0„ = tan  0.35  (4.13)  V  *M J  The results are likely to be relevant to small angles o f discharge flow since but overall nature of jets are the same as horizontal jets although small angle difference can cause jets to rise to the pycnocline at different locations.  Backflow occurred when the estimated 9 > 7° but no backflow occurred when 6 p  This result was confirmed by experiments as shown in Figure 4.10. backflows was plotted against I  M  fh  i  <1°.  Occurrence o f  and impingement/penetration parameter W. It is  shown that as the relative strength o f the source momentum to the vertical momentum (£ /hi) M  increases, the possibility o f backflow formation at the pycnocline decreases. O n  the other hand, for the penetration regime,  > 0.9, some jet flow accumulated along the  pycnocline with varying degrees while the jet penetrated into the upper layer and a thick backflow formed at the water surface.  4.2.4 Coanda bottom attachment  When a jet is discharged parallel to the bottom bed, the jet clings more abruptly to the boundary due to the increased entrainment demand. Rising o f a buoyant jet is delayed which causes a jet to entrain the more heavy ambient fluid. Thus, the jet trajectory and dilution can be significantly affected. Figure 4.11 shows the Coanda bottom attachment o f a  82  1.6  Penetration  1.4  1.2  1.0  0.8  •  Backflow  0.6 4  •  •  •  •  1  No-backflow  •  0.4 A  0.2s  0.0 0.0  1.0  2.0  3.0  4.0  5.0  L /hi M  • Backflow • No-backflow A Penetration  Figure 4.10 Backflows o f fluid jets in two-layer system  83  buoyant jet in a homogeneous ambient fluid. After an extended bottom attachment, a buoyant jet lifts off from the bed and rises to its neutral buoyancy level.  The Coanda bottom attachment o f buoyant jets discharged at 3° downward was tested for different ambient fluid conditions: homogeneous, linearly stratified fluid and two-layer system. However, the majority o f the experiments were conducted for homogeneous ambient fluid for the purpose o f comparison with past studies. The experimental conditions employed for the Coanda attachment were 0.065 <hl £  M  < 2.1 and 8.7 < F < 55.5. d  The results showed that the bottom attachment occurred when the submergence parameter satisfied hi £  M  <0.22, regardless o f the ambient conditions shown i n Figure 4.12. This is  because the source discharge condition and geometry are influential on the jet development in the vicinity o f the jet exit whereas the ambient fluid condition plays an important role far downstream.  4.2.4.1 Comparison with previous studies A s illustrated i n Figure 3.2, the discharge direction o f the buoyant jet was parallel to the bottom bed but at a 3° downward direction relative to the ambient fluid. The Coanda bottom attachment occurred when hl£  M  < 0 . 2 2 , which is considerably larger than the  value o f 0.1 observed in two previous experiments for horizontal jets by Sobey et al. (1988) and Johnston et al. (1994), shown in Figure 4.13. This difference is probably due to the different range o f densimetric Froude numbers used. The range o f F  d  tested here was 8.7 - 55.5 where most o f cases were F  d  > 15.0  whereas Sobey et al. (1988) and Johnston et al. (1994a) performed experiments for F < 16.0. The definition o f bottom attachment may also have caused the difference in d  results. The previous two studies defined attachment based on the measured density deficit after discharge whereas the present study used the flow visualization. Consequently, the former obtained relatively conservative results.  84  (a) Coanda bottom attachment  (b) Coanda bottom attachment and lift-off  Figure 4.11 Coanda bottom attachment (A45, F = 33.4, h/£ d  M  = 0.21)  0.6  v  A  0.5  u  is  A  O  0.4 S eJ JS  0  0.3 A  0.2  A  A  •  0 A  A  0.1 0.0 0.0  • A  10.0  A  20.0  30.0  40.0  50.0  60.0  Densimetric Froude Number (F^) ANon Coanda - Linearly stratified ONon Coanda- two layer  ONon Coanda - homogeneous  A Coanda - linearly stratified  V Coanda - homogeneous  • Coanda - two layer  Figure 4.12 Coanda attachment in various ambient fluid conditions  4.2.4.2 Comparison with CORMIX prediction C O R M I X 1 was also run in order to provide another comparison. In fact, C O R M I X 1 does not consider jets discharged into ambient fluid with a sloped bottom. However, jets were discharged horizontally to the bed and the discharge angle is small i n this study, it is possible to neglect the discharge angle to the ambient fluid. A simple criteria for bottom attachment by the C O R M I X 1 is given as (Jirka and Doneker, 1991):  t a n # < (0.2-h/£ ) M  (4.14)  86  where 6 is a discharge angle. According to above equation, the Coanda effect occurs i f  hit  M < 0-25 for 3° downward discharge, which agrees with the results observed here.  -Q-  TT  A  • •  Non-Coanda attachmentl  ••o-<&Ep..®.-o  CORMIX prediction  a•  D  A  Coanda attachmentj  ^  o o o ct A  A  A  A A  A & X  0.0  X  10.0  20.0  30.0  40.0  50.0  60.0  Densimetric Froude Number (F ) d  • Non-Coanda attachment  • Conada attachment  AJohnston (1994)-Coanda attachement  XSobey(1988)-Coanda attachment  AJohnston(1994) non-Coanda attachment OSobey(1988) non-Coanda attachment  Figure 4.13 Comparison o f the Coanda attachment with previous studies (Sobey et al., 1988; Johnston et al., 1994b)  87  4.2.5 Analysis of gross flow characteristics  Important independent parameters that were considered for buoyant jets in a two-layer system include 1) the jet properties, such as density (p.)  and velocity (u), 2) the discharge  configuration such as the nozzle diameter ( d ) , the distance from the jet nozzle to the pycnocline ( h ) , the discharge angle (0) and the injection height above the bed ( h ) , and 3) t  the ambient fluid (Ap  a  = p ~Pi) 2  a n  condition characterized by the density step between two layers d the total water depth above the jet discharge nozzle (H).  The  definition sketch o f parameters is shown in Figure 4.14. The dependent parameters ( O ) include the maximum rise height ( Z ) and its location (X ), m  above the density step (P ),  the impingement height  the top and bottom o f the spreading layer ( Z , , Z )  d  spreading layer thickness  m  b  and the  (T ). f  Figure 4.14 Definition sketch o f parameters in a two-layer system  The source condition o f a buoyant jet can be characterized by the initial fluxes o f kinematic momentum M,  kinematic source buoyancy B, and source volume flux  Q.  Since the discharge angle, 0 is fixed at - 3 ° , the dependent variables ( O ) are:  88  0 =  where M,  (4.15)  f{M,B,Q,g' ,h ,H) a  l  B and Q are defined in section 2.3. The parameter  g'  a  is the modified  gravitational acceleration based on the density difference between two layers and is given as g' = g(p a  P\)lP  -  2  2  characteristic length £ experiments  Q  and thus  • The effect o f the initial volume flux becomes negligible when a is small (Wright and Wallace, 1979). In this study £  Q  Q  = 0.87 in all  can be ignored. I f the discharge angle is constant,  the  dimensionless groups can be formed by means o f dimensional analysis:  ( B  2/5  M  h,  ^  3 / 4  (4.16)  g2/5  where  *F = — — — : impingement/penetration parameter, Sa  h-jj:  relative distance o f the jet exit to the pycnocline to the total water depth above the jet exit,  M  3  M  .  relative influence o f the distance to the pycnocline and initial momentum and buoyancy.  4.2.5.1 Maximum rise height and the top of the spreading layer For the impingement and penetration o f the jet on the pycnocline, the vertical momentum o f the flow is most important. Vertical momentum M  v  due to - 3° oriented buoyant jets is  negligible at the pycnocline since the vertical momentum, M  v  M  v  = Msin(-3°))  M the effect o f  due to source momentum  is significantly smaller than the source momentum.  Consequently,  3 / 4  — is insignificant on the jet behavior at the pycnocline.  89  If two homogeneous ambient fluids are separated by a strong density step, a jet impinges slightly on the density step and then it spreads only below the pycnocline. Therefore, the total water depth H is insignificant and only h affects jet behavior. E q . (4.16) can be x  simplified as:  -f-> t  %- = c i  lt  h  c  (4.17)  2  h  The constants c, and c are obtained from the experiments. However, i f a density step is 2  small and the vertical momentum generated due to the positive buoyancy is large, then the B' jet flow can strongly impinge on the pycnocline. In such case, — — — is an important So i 2 5  h  parameter to be considered. Consequently, E q . (4.16) becomes:  Z  Z  k- '  h  :  ( 2/5 B  ~  J  ^ (4.18)  s' h V5  Experimental results Maximum rise height  Figure 4.15 presents the dimensionless maximum rise height {Z /h ) m  i  o f fluid jets  showing two distinctive regimes in a two-layer system. Under the weak impingement regime (*F <0.5), the maximum rise heights o f buoyant jets are constant. Therefore, E q . (4.17) has an asymptotic solution ( c , ) with standard deviation ± 0.2 for the weak impingement regime:  ^=- = 1.17 (± 0.2) h:  (4.19)  90  The constant 1.17 was obtained by averaging across the 14 measurements.  O n the other  hand, for ¥ > 0.5, the maximum height o f rise increases proportionally with *F with standard deviation ± 0.05 :  ^  = (1.53 x ¥ ) + 0.186  (4.20)  In the strong impingement and penetration regimes, the relative strength o f the pycnocline to buoyancy is weak and thus the maximum rise height is primarily influenced by the buoyancy o f the jet flow for a constant discharge depth. Location of maximum height of rise Although initial momentum is unimportant to the vertical component such as the maximum rise height, it has significant effect on the location o f the maximum height o f rise (X ). m  Figure 4.16 shows the locations o f maximum rise height in two-layer systems. X  m  functions o f the densimetric Froude number (F )  and discharge angle (0).  d  is  As F  d  increases, the path length o f the jet is extended and thus buoyancy begins to prevail further downstream. A l s o the negative discharge angle causes the jet flow to stay longer i n the lower layer and rises further downstream later than horizontal jets. However, since X  m  is primarily controlled by initial momentum the influence o f small  negative discharge is less important. Top of the spreading layer  The trajectory o f the top o f the spreading layer ( Z ) versus discharge depth below the (  pycnocline and the densimetric Froude number i n two-layer systems is shown i n Figure 4.17. A s a buoyant jet approaches the pycnocline, the top o f the spreading layer becomes  91  0.0  0.2  0.4  0.6  0.8  1.0  • weak impingement o strong impingement  Figure 4.15 Dimensionless maximum rise height (Z /h m  i  ) i n two-layer systems  90.0 80.0 70.0 60.0 Q-' .«>" •  3 50.0  * 40.0 30.0 20.0  s • Weak impingement  10.0 0.0 0.0  O Strong impingement  10.0  20.0  30.0  40.0  50.0  60.0  Densimetric Froude Number, Fd  Figure 4.16 Location o f maximum rise height ( X / d ) i n two-layer systems m  flat under the density step. For the same hjd  Z /h t  varies with F  (  d  until the jet reaches  the pycnocline but after impingement it becomes independent o f F . Jets with small F d  rises at nearer distance compared with those with large  d  F. d  Figure 4.17 Trajectory o f the top o f the spreading layer i n two - layer system A 4 ( V < / = 1 8 . 4 Fd =  16.7), A 1 7 ( h l d = 18.4 F =S.9), t  A 2 3 (A, / J = 10.2 F = 18.1), A 3 8 (/*,. rf  d  A21 (*,/</= 10.2 </= -3) F  9  5.1 F = 18.7), A41 (h. Id= 5.1 F = 16.0) rf  d  Figure 4.18 shows that the dimensionless top of the spreading layer also has the following asymptotic solution ( c ) for the weak impingement regime: 2  - ± = 1.07 ( ± 0 . 0 4 ) hi The constant c  2  (4.21)  was obtained by averaging across 14 measurements. However, for the  strong impingement and penetration regime the top o f the spreading layer shows a slight increase with the dimensionless parameter *F . The formula obtained by regression analysis is:  93  -^- = 2 . 4 7 x ^ - 0 . 1 9  0.0  0.2  0.4  0.6  • weak impingement  0.8  1.0  (R =0.  (4.22)  2  1.2  1.4  A strong impingement  1.6  1.8  o penetration  Figure 4.18 Dimensionless top o f the spreading layer ( Z / h ; ) o f buoyant fluid jets t  The top o f the spreading layer is primarily influenced by the maximum rise height. For < 0.5, jet flows are confined under the pycnocline and both Z /h m  to the constants c, and c  2  i  and Z,//z - converge (  . However, for *F > 0.5 the higher a jet initially impinges, the  higher the final top o f the spreading layer becomes. This point is important in that the strength o f impingement and penetration determines the elevation o f the final spreading layer.  4.2.5.2 Spreading layer thickness A s the jet proceeds in the homogeneous dense lower layer, the density difference between the jet and ambient fluid constantly decreases with distance due to entrainment. If the  94  density o f a jet flow becomes sufficiently large as it approaches the pycnocline, the rising buoyant flow can be suppressed by even a small density step across the pycnocline. Thus, B ' /g'a' hj 2 5  5  becomes negligible. Consequently, for the spreading layer thickness only the  dimensionless source momentum term is significant. Therefore, E q . (4.16) reduces to:  (  h,'  h -  M  3 / 4  ^  (4.23)  J  t  The experimental results agree with the dimensionless analysis as shown in Figure 4.19.  r  ^ h  3/4  = 0 . 5 0 - ^ ^ + 0.2 h B  (±0.05)  (4.24)  1 / 2  ;  :  3.0 2.5 2.0 1.5 1.0 0.5 • Weak impingement o Strong impingement  0.0 0.0  1.0  2.0  3.0  4.0  5.0  M /(hi*B ) 3/4  1/2  Figure 4.19 Dimensionless spreading layer thickness ( T / h j ) o f buoyant fluid jets f  in two-layer systems  95  4.3 Summary of fluid jets This chapter investigated the dynamics o f buoyant jets in two-layer systems. The findings also provide the basis o f understanding the dynamics o f particle-laden jets with buoyant interstitial fluid. The investigation results o f fluid jets are summarized as follows:  Three parameters were found to have a critical influence on jet behavior at the near-field: the magnitude o f density step, buoyancy o f the jets and the discharge distance to the B pycnocline. These were combined into a dimensionless parameter W (= — — — ) , which 215  S'a  i  h  determines the flow regimes: weak impingement, strong impingement and penetration.  Weak impingement regime: when ¥ < 0.5, a buoyant jet initially rose and reached the pycnocline, where the jet impinged weakly without any significant mixing o f the upper layer. Then it bent and advanced under the pycnocline. This condition was also found to satisfy the condition, y « 0 where y = p - p / p t  ;  2  - pj , in which p , , p  2  and P| are density o f the upper and the lower layer fluid, and density at the pycnocline.  Strong impingement regime: for 0.5 < W < 0.9, buoyant jets overshot the density step and immediately fell back to its neutral buoyancy. Jet  flows  disturbed  considerable depth o f the upper layer, causing density increases by transporting entrained lower layer fluid. However density change does not occur at the surface.  Penetration regime: for  > 0.9, a buoyant jet penetrated  into the upper layer  immediately after the source momentum decays. The penetrated jet flow initially occupied the entire upper layer and proceeded above the pycnocline. While the jet rose it entrained the lower layer fluid, resulting in a significant density increase in the upper layer. This regime also satisfies 0 < y < 1.  96  Backflows occurred along the pycnocline depending on the relative magnitude o f vertical and source momentum flux, which determines jet angles at the pycnocline. Backflow occurred when 0 > 7° but no backflow occurred when O < 1 ° . This result was obtained P  p  from the theoretical analysis and confirmed by experiments. For the penetration regime, *F > 0.9, some jet flow accumulated along the pycnocline and backflows also formed at the surface o f the upper layer.  The Coanda bottom attachment occurred when h/£  M  ambient fluid conditions for constant water depth H/h  0  C O R M I X v3.2 prediction (h/£  M  < 0 . 2 2 , independently o f the  = 34.7. This value is similar to the  < 0.25) but is considerably larger than those from Sobey  et al (1988) and Johnston et al. (1994b) for horizontal jets in shallow water (h/£  M  < 0.1).  The gross flow characteristics suggested that for the weak impingement regime the dimensionless maximum rise height (Z /h m  i  ) and the top o f the spreading layer  {Z fh ) t  i  converged to constants c, =1.17 and c =1.07 respectively. For the strong impingement 3  regime, Z /h m  final  i  and  Z,//J,  linearly increase as B /g' h 2/5  a  spreading layer (Tj- jh )  parameters M  {  3 / 4  /' B h xl2  t  i  increases. O n the other hand, the  was found to be a function only o f the dimensionless  regardless o f the presence o f density step, and increasing with  this dimensionless parameter.  97  Chapter 5 Results and Discussion: Particle-laden jet 5.1 Introduction The dynamics o f particle-laden jets is more complicated than that o f fluid jets because particles settle out o f the jet constantly, thereby modifying the bulk density. Thus, it is important to understand both the characteristics o f fluid jets and the effect o f particles on the interstitial fluid. The primary purpose o f the studies o f particle-laden jets is to understand the effect o f suspended particles on turbulent buoyant flows and to identify whether particles can prevent the penetration o f highly buoyant interstitial fluid.  A series o f experiments were  performed with buoyant interstitial fluid containing spherical glass beads. The conditions o f ambient fluid and jet fluid were kept the same as that o f fluid jets i n order to identify the effect o f particles on flows.  5.2 Particle-laden jets in two-layer systems The qualitative features o f particle-laden jets i n two-layer systems are described and the flow regimes are determined i n this section. The particle distribution and dye concentration profiles o f the interstitial fluid are analyzed. The gross flow characteristics are analyzed by means o f dimensional analysis and compared with experimental results. The flow classification and dilution o f interstitial fluid are compared with C O R M I X v3.2 predictions and the suitability o f this model for particle-laden jets is discussed.  98  5.2.1 Behavior of particle-laden jets When buoyant fluid jets carrying particles are discharged into stagnant ambient fluid, initially the source momentum maintains particles in suspension. However, with increasing distance from the source the influence o f the source momentum weakens and the dynamics of particle-laden jets is determined by the buoyancy o f the jet and the ambient conditions. In the present experimental conditions, when £  M  > 30 cm , all particle-laden jets began to  display plume-like behavior.  Experimental observation showed that when the particle concentration in flow was small, a particle-laden jet behaved like a fluid jet. The jet penetrated into the upper layer (Figure 5.1(a)) or impinged on the pycnocline (Figure 5.1(b)). A s the jet spread along the density step, the interstitial fluid was constantly mixed with the ambient fluid while individual particles settled out o f the jet without significant impact on the jet behavior.  The flow exhibited a distinctive behavior as the particle concentration increased. The bottom o f the jet constantly expanded downward due to the initial discharge angle and active particle settling. Initially, the mixture o f fluid and particle clouds descends as a group o f individual particles and gradual separation between particles and parent fluid occurs as N o h and Fernando (1993) observed. However, the entrainment decreased with distance and thus the internal circulation became insufficient to keep the particles in suspension. Moreover, the constant influx o f particle-laden flow supplied more particles into the spreading layer in which the previously discharged particles were still i n suspension. Consequently, the particles accumulated due to settling at a certain position within the flow, resulting in a wide, U-shaped configuration at the bottom o f the flow as shown in Figure 5.1 (c).  99  Figure 5.1 Behavior of particle-laden jets in two-layer systems: (a) penetration (P20) (b) impingement (P24), (c) weak plunging (P22) and (d) strong plunging (P23)  100  When the bulk density o f a jet was much larger than the ambient fluid density, the jet plunged down to the bed and propagated like a turbidity current (Figure 5.1 (d)). This initial plunging process was similar to the behavior o f negatively buoyant fluid jets except for the separation o f buoyant interstitial fluid from the jet during plunging. Abrupt settling o f particles occurred at the plunging point, where the jet looked and behaved like the turbidity current with reversing buoyancy as described by Simpson (1987), Spark et al. (1993) and Ffiizerler (1996). The buoyant interstitial fluid continuously rose and a backflow was generated on the bottom. Note that a patch o f dyed fluid along the pycnocline in Figure 5.1(d) is an experimental artifact caused by the inevitable release o f interstitial fluid separated from the mixture during initial discharge. Although it is not shown in the figure, the jet flow occupied almost the entire lower layer far downstream. When sufficient particles settled, the flow lifted off the bed and formed a horizontal gravity current under the pycnocline.  5.2.2 Determination of flow regimes Experimental observation indicated that both the initial difference between the bulk density o f a jet and the ambient fluid density and the density difference between the interstitial fluid and the ambient fluid are critical in determining the initial jet behavior. The relationship between the two density differences can be expressed as a non-dimensional density R which is the inverse o f a parameter suggested by Turner and Huppert (1992):  R=  where p  a  ~ Pa ~ Pf P  a  P  b  (5.1)  : ambient fluid density at the discharge level  p : interstitial fluid density f  p  b  : bulk density o f particle-laden jet  101  For fluid jets, R = 1, since p  b  =p  f  and for particle-laden jets R < 1. The present study  considers the case where the interstitial fluid is always buoyant relative to the ambient fluid (i.e. p  a  > p ), f  therefore, i f 0 < R < 1, then the ambient density is always greater than the  bulk density (p  a  > p ). b  Under this condition the influence o f particles on the flow is  insignificant and a particle-laden jet behaves like a buoyant fluid jet regardless o f the particles. Therefore, the flow penetrates or impinges on the pycnocline depending on the dimensionless parameter ¥  defined in fluid jet analysis in section 4.2.2. The former is  defined as penetration regime and the latter as impingement regime. Note that the present experimental condition for particle-laden jets covered only the strong  impingement  (0.5 < *F < 0.9) but not the weak impingement regime.  For R < 0 the jet is initially negatively buoyant, in which case the density difference between p  a  and p  plays a significant role in the behavior o f the jet. Under this  b  circumstance i f R is less than a critical value R , rapid change occurs i n jet trajectory. c  R < R<0 c  If  then the jet flow is initially negatively buoyant but the bulk density is  insufficient to completely sink to the bottom. Thus, the jet begins to rise after sufficient particle settling - this transitional flow regime is classified as weak plunging regime. However, i f R <R <0, c  then the particle-laden jet is significantly heavier than the  ambient fluid and thus it immediately plunges to the bottom and proceeds on the bottom slope - this is defined as strong plunging regime. For weak and strong plunging regimes the ambient fluid condition has little effect on the jet behavior before significant particle settling occurs and the flow rises. Consequently, the behavior o f particle-laden jets in two-layer systems can be classified into four flow regimes based on ¥ as in fluid jets and R . Table 5.1 summarizes the classification o f particle-laden jets. The critical value i? was estimated to be -2.0 from the experiments and the flow regimes c  are shown in Figure 5.2.  102  Table 5.1 Classification o f particle-laden jets  Density Relations Regime  Penetration  Impingement  Rand  Pa> Pf  ( P . - A )  always true  \Pa-Pf)  ¥ (  Behavior of particle-laden jets in two-layer systems  ) ,3/5,  '  {ga  K)  Pa > Pb  0<i?<l, ¥>0.9 Initially buoyant  Pa> Pb  0 < i? < 1, Y < 0 . 9 Initially buoyant  Penetration (Figure 5.1(a)) Impingement on the pycnocline (Figure 5.1(b)) Initial plunging and abrupt group settling, detrainment o f interstitial fluid (Figure 5.1 (c)) Plunge down to the bottom and active detrainment o f interstitial fluid (Figure 5.1 (d))  R <R < 0 c  Weak Plunging  Initially negatively buoyant  Pa<Pb  R <R < 0 c  Strong Plunging  Initially negatively buoyant  Pa « Pb  5.2.3 Particle distribution and interstitial fluid dilution  5.2.3.1 Particle distribution in ambient fluid  Particles carried by the fluid motion start settle out o f the turbulent flow when the particle settling velocity w approaches the flow velocity (u) s  u/w  s  »  (Popper et al., 1974). That is, i f  1, particles move with flow whereas when u/w « s  1, individual particle settling  occurs. The settling velocity o f the glass beads used i n the present study was 1.14 mm/s based on the mean diameter 38.72 pm . The velocity ratio ranged 366.3 < u/w  s  the source, which satisfied u/w  s  < 732.7 at  » 1 to the end o f the tank. In this case, individual  particles were expected to follow the flow motion and the turbulence o f flow due to entrainment also maintains particles i n suspension.  However, jets with high particle  103  concentration exhibited grouping settling behavior near the nozzle. This caused a rapid flow velocity decrease resulting in abrupt settling behavior.  "2:0Penetration * P59  1.5 Strong Plunging  X P57  Weak Plunging  P20  0.9 P23  penjetration line determined from fluid jets  1.0  P60 P58  P18 A A P16  P17  P8  P10  P24  A  P22  A  P9 P6  0.5  A  p  2  1  P25  A  P19  Impingement A  p  5  0.0 -5.0  -4.0  -3.0  -2.0  •1.0  0.0  R = l Fluid jets  R x  Penetration  A  Impingement  A  1.0  Weak plunging  B  Strong plunging  Figure 5.2 F l o w regimes for particle-laden jets in two-layer systems  104  Figure 5.3 (a) (b) shows the particle distribution and interstitial fluid dye concentration profile for penetration and the weak plunging cases respectively. It is shown that the particle distribution follows the motion o f interstitial fluid. When a jet penetrate into the upper layer it transports a significant amount o f particles into the upper layer, where some particles travel in suspension for a considerable horizontal distance (Figure 5.3 (a)). However, for the weak plunging regime, overall particles move with fluid  but  considerable particle settling also occurs under the centerline o f flow (Figure 5.3 (b)). It is probably due to the grouping behavior o f particles in high particle concentration and individual settling o f large particles.  5.2.3.2 Dye concentration profile  The dye concentration profiles were fitted with a Gaussian distribution described by  c = c exp(—-j)  b  m  where  z  : vertical distance from the jet centerline  c: m  b  (5.2)  centerline concentration : characteristic width o f concentration at a radial position where the concentration c/c  m  - e x p ( - l ) = 0.37  Figure 5.4 (a)-(d) show an example o f the dye concentration profiles o f particle-laden jets. Near the jet exit (x/L-0.13),  the concentration profiles o f all particle-laden jets were  identical, however as the source momentum weakened the jets rose or plunged down depending on R . In addition to the constant settling o f the particles, the release o f buoyant interstitial fluid also caused the jet flow to fluctuate as it proceeded along the tank. This centerline displacement was expressed by modifying a Gaussian distribution:  105  o  c c 0 o  3 ? ja a  c  -2 g  1 S rg  ^ S s  8 ^?  5 .2 <u O <H  >o  feci o  2 +H  <U  Cl  <D  OH  >H  Cl '•4-*  *3 13 '€ cS  OH X)  <D  -5 o o a o  >.  Cl 03 Cl  _o  oo -+2-» <n  c fe <L> O  60  c a o 60 o -O  r—I  (U lH  60  (uis) z  PH  o —  10.0 <  o d  15.0 <  d  -1  II  20.0  ©  ©  -o p ©  D  ri  p iri  q O  o  c  ir  in w  c  o ON  d  o  c  II  OH  •\ •' / / •  q  q  q  <N  —  —  • * • o  o  o  o  c  c  c  o *o o 3 c o c •3-  en  o  ••It  ©  •  o d d  (N  q v-i —  o  II  >  • q d  q  o d  —  C c3  i/S  q d  c  C  o  p  1  c  o  O  II  (J  C  o  ;' • _  <u  ^r  o u  <J  ;'  in  ;  1  o d  o d  • —  ,  (UI3) Z (UID) Z  —  •  g '5b  o Cu  o  • T  CU  •  C  'a. E  ©  CN  —  —  T  1  •tf  0.3 2  =0.19  O  o o  -  *  —  ,  —  1  '  -•  ,  o  o ©  o  o o  fS  (UI3) Z  </") O (UID) Z  f  C = C exp m  b  (5.3)  2  J  where s is a constant which describes the centerline displacement from the jet nozzle.  The centerline displacement (s) distance (x/L)  o f the flow regime versus dimensionless downstream  was plotted for all flow regimes in Figure 5.5. The profiles clearly indicate  that as the particle concentration increased the centerline position fell and as the densimetric Froude number (F  d  ) increased the maximum centerline occurred further  downstream. This is consistent with the location o f the maximum rise height ( X ) m  for fluid  jets as discussed in section 4.2.5.  Jets o f penetration and impingement regimes rose to the maximum rise height and fell. Two particle-laden jets o f strong plunging regime have negative centerline positions and depending on R, different particle settling behavior and detrainment o f interstitial fluid caused difference in the centerline displacement. A t x/L = 0 . 1 3 - 0 . 1 9 , the centerline shifted due to plunging. A t x/L = 0.31, the centerline o f P17 rose slightly due to rising buoyant interstitial fluid after sufficient particle settling occurred. However, P23, with larger particle concentration, propagated as a turbidity current without significant rising o f interstitial fluid within the experimental tank length.  5.2.3.3 Effect of R on the characteristic width (b) The relationship between the jet centerline position and the b along the jet trajectory is shown in Figure 5.6. The source momentum-dominant location x/L = 0.04 was excluded in the plot. For penetration and impingement regimes, b is independent o f the centerline displacement, however, b increases proportionally for weak and strong plunging regimes  109  Figure 5 . 5 Jet centerline displacement (s) along the jet trajectory  (x/L)  as the centerline shifts downward. This is because some portion o f buoyant interstitial fluid plunged while particles plunged and some in the upper part o f the flow rose as particle-free fluid.  110  x Penetration A Weak plunging  o Impingement • Strong plunging  Figure 5.6 Centerline displacement and concentration characteristic width (b) o f particle-laden jets  5.2.4 Analysis of gross flow characteristics This section analyzes the gross flow characteristics o f particle-laden jets and also seeks asymptotic solutions to the equations. The experiments for particle-laden jets i n two-layer systems were performed for 0.33 < *F < 1.72, -18.15 < R < 0 . 6 3 , 0 = -3" and h/d = 15.3. According to the flow regimes defined for fluid jets i n section 4.2.3, the experiments covered mostly the strong impingement and penetration regime.  In addition to the independent  variables relevant to fluid jets  (Q,M,B,g' ,h H) a  it  111  described in section 4.2, two important additional parameters need to be considered for particle-laden jets: the distance from the bed (h), and the ratio o f density differences The dependent variables spreading layer ( Z ) t  R.  include the maximum height o f rise ( Z ) , the top o f the m  and the spreading layer thickness ( T ) . A definition sketch o f a f  particle-laden jet in a two-layer system is shown in Figure 5.7.  Consequently, dimensionless groups for particle-laden jets are:  B  2/5  g a h  where — ^ r - . — , — , gfh, H  t  3/4  h,  M  H  hB t  7 2  '  d  (5.4) J  . . . and R are defined in section 4.2 and 5.1. The dimensionless h,B U2  h depth parameter — is defined as the ratio o f the discharge height above the bed to the d nozzle diameter.  112  5.2.4.1 M a x i m u m rise height and the top of the spreading layer  Due to the initial downward discharge angle and particle sedimentation, the direct effect o f the source momentum on the jet behavior at the pycnocline is insignificant, resulting in  M  3 /  7V?  , / 2  ^O. B  , h and — are  215  For the jets o f penetration, impingement and weak plunging regime,  Sa  3/5,.  i  h  H  h and — on the jet dynamics are negligible.  important while the effects o f particles (R)  d  Consequently, E q . (5.4) reduces to:  7  7  r  h, ' h,  B  2IS  (5.5)  J  O n the other hand, for strong plunging regime a particle-laden jet immediately plunges down to the bottom and thus the role o f the pycnocline on the jet behavior is unimportant in the near field. Only the relative distance becomes influential to the plunging particle-laden jets. Therefore,  h  x  h  x  (5.6)  yd;  h Since — is constant in this study, E q . (5.6) becomes:  d  —c , c 3  4  (5.7)  The constants c and c are determined experimentally. 3  4  113  Experimental results Maximum rise height The dimensionless maximum height o f rise ( Z Ih ) o f particle-laden jets in a two-layer m  (  system is shown i n Figure 5.8. The Z Ih for impingement regime increases with the m  t  impingement-penetration parameter ¥ , and tended to be slightly higher than for weak plunging regime. Neglecting the minor difference among the two regimes, regression analysis o f the combined experimental results are:  ^ hi  = 3.43 x^F - 0.31 ( ± 0 . 4 )  (5.8)  O n the other hand, a jet o f strong plunging regime plunged down to the bed and the h  plunging depth became constant as — = 15.3 i n this study. Therefore, the constant ( c ) in d 3  Eq.(5.7) becomes:  = c  3  = - 3 . 0 (±0.01)  (5.9)  hi  However, i f the discharge height above the bed ( h ) increases, the plunging depth is no longer constant but increases with —. d  114  7.0 6.0 5.0 4.0  "A A  3.0 -  2.0  ^  1.0 0.0  (10  0.2  0.4  0.6  0.8  1.0  1.2  1.4  1.6  1.8  21  -1.0 -2.0 4  •—•-  -3.0 -4.0  x Impingement  • Strong Plunging  a Weak Plunging  Figure 5.8 Dimensionless maximum rise height (Z jh ) m  i  A Penetration  o f particle-laden jets  in two-layer systems  Top of the spreading layer  The dimensionless top o f the final spreading layer was plotted in Figure 5.9. In penetration and impingement regimes, it increased linearly with — — — as was observed t 3/5  Sa  7  hi  for the maximum rise height, regression analysis gives:  hi  B  2/5  Z  = 0.95  + 0.66 (± 0.17)  (5.10)  Z'i'\  115  However, for weak plunging regime the top o f the final spreading layer shows an irregular pattern due to the interaction between particle settling and detrainment o f the interstitial fluid and it also tends to lower than that o f impingement regime.  2.5 -,  .  2.0 A  0.5 A  0.2  0.4  0.6  0.8  X Impingement  1.0  1.2  1.4  • Strong Plunging • Weak Plunging  Figure 5.9 Dimensionless top o f the spreading layer (Zjh ) {  o f particle-laden jets  in two-layer systems  On the other hand, jets o f strong plunging regime initially plunge down to the bed and thus the top o f the flow becomes negative relative to the jet exit. However, immediately after considerable settling occurs the jet flow begins to rise due to positive buoyancy o f the interstitial fluid. Thus, the top o f the final spreading layer converges along the density jump. Consequently, Eq.(5.7) has an asymptotic solution ( c ) . 4  c  4  =  = 0.9 ( ± 0 . 0 1 )  (5.11)  h:  116  5.2.4.2 Spreading layer thickness  Particle-laden jets in penetration and impingement regimes behave like buoyant fluid jets and thus the spreading layer increases with M  3 / 4  / V / z - as discussed in Chapter 4. A s / 2  (  particle concentration increases, the flow thickness increases significantly in the near field. However, once a considerable amount o f particles settle out the final spreading layer thickness depends only on M  3 / 4  /B  U 2  h  t  .  For strong plunging regime, jets plunge down and thus initially B /g' h 2/5  and hjH  3/5  i  have little impact on the thickness o f the spreading layer. However, the source momentum and dimensionless distance to the bed (h/d ) are influential. Consequently, i f h/d is constant, the dimensionless final layer thickness is a function only o f M  3 / 4  /B  U 2  h;  regardless o f the flow regime:  T  <M  3 / 4  ^  (5.12)  Experimental results  Initially the spreading layer thickness varies along the trajectory  due to particle  sedimentation. However, as substantial sedimentation occurs the flow spreads out as a layer with a relatively constant thickness. Figure 5.10 shows the dimensionless spreading layer thickness after substantial settling has occurred.  For jets o f impingement and weak plunging regimes, the spreading layer thickness increases with initial momentum and slightly with R. A t a low source momentum R is influential, but it becomes insignificant as momentum increases. Neglecting the minor difference due to R and combining the two regimes, the relationship describing the spreading layer thickness is estimated to be:  117  -f-  = 0.26——  0.96 (+0.4)  (5.13)  For strong plunging regime it was impossible to obtain the final spreading layer thickness because the experimental tank was not long enough for the bottom turbidity current to lose sufficient particles and rise. However, the results imply that jets plunged down and the spreading layer became independent o f the source momentum and was determined mostly by the detrainment o f buoyant interstitial fluid from the bed.  0.0  1.0  2.0  • Impingement  3.0  4.0  A Strong Plunging  5.0  6.0  7.0  • Weak Plunging  Figure 5.10 Dimensionless spreading layer thickness o f particle-laden jets  118  5.2.5 Comparison with C O R M I X prediction C O R M I X 1 v3.2 was run to compare with the present experimental results and thus examine the suitability o f the model for analyzing particle-laden jets. C O R M I X 1 was initially applied to fluid jets without particles and to 19 particle-laden jets in two-layer systems. The comparison was made in terms o f classification o f flow regimes and maximum (centerline) concentration o f the jet flow.  5.2.5.1 Flow classification C O R M I X 1 classified all particle-laden jets as Class N H 1 or Class H 4 . Class N H 1 describes submerged negatively buoyant jets discharged horizontally or near horizontally while Class H 4 describes positively buoyant jets rises and impinges on the upper boundary of the ambient water  •  I f a jet is momentum-dominant near the nozzle, the initial discharge is usually attached  to the bottom. After some distance, the jet flow is vertically mixed over the full layer depth and a re-circulating eddy regime may occur downstream (Jirka, et al 1996).  Penetration, impingement and weak plunging regimes in the present study are equivalent to C O R M I X 1 Class H 4 and the strong plunging regime is equivalent to the C O R M I X 1 Class N H 1 . When the interstitial fluid density ( p ) was applied to the model, all flow f  regimes were determined as Class H 4 as expected. However, the predicted flow class based on the initial bulk density p  b  varied depending on R. Table 5.2 compares the flow regimes  that C O R M I X 1 predicts using bulk density with the experimental results.  The C O R M I X 1 prediction agreed with the flow regime determined in this study for penetration impingement and strong plunging regime, defining them as Class N H 1 . In contrast, the model classified weak plunging regime as Class N H 1 , in which a jet is subject  119  to plunging down to the bottom. However, the experiments showed that these jets did not plunge to the bottom but only locally expanded downward and then spread as a gravity current as described in section 5.2.2.  Table 5.2 Comparison o f C O R M I X 1 prediction and experimental results for flow classification  EXP#  P20 P57 P59 P5 P19 P21 P24 P25 P9 P16 P8 P22 P58 P60 P18 P23 P7 PIO P17  Flow classification  Density ratio (R)  CORMIX prediction  0.63 0.21 0.38 0.5 0.54 0.15 0.12 0.11 -0.19 -1.26 -1.35 -0.73 -0.97 -0.79 -0.05 -2.38 -16.6 -2.63 -2.94  H4 H4 H4 H4 H4 H4 H4 114 NHl NHl NHl NHl NHl NHl NHl NHl NHl NHl NHl  Experiment results (Regime)  Penetration Penetration Penetration Impingement Impingement Impingement Impingement Impingement Weak Plunging Weak Plunging Weak Plunging Weak Plunging Weak Plunging Weak Plunging Strong Plunging Strong Plunging Strong Plunging Strong Plunging Strong Plunging  This discrepancy occurred because the model interprets the particle-laden jets as singlephase fluid (i.e. negatively buoyant fluid jets), not considering the density change due to particle sedimentation. Therefore, i f the initial bulk density is smaller or larger than the ambient fluid density, the model simply classifies the flow as positive buoyant fluid (H4) or negatively buoyant flow ( N H l ) respectively. This limitation can cause a significant prediction error i f the model is applied to particleladen jets, in particular, to heavy particle-laden jets with highly buoyant interstitial fluid.  120  5.2.5.2 Centerline concentration C O R M I X 1 overestimated the dye concentration for all flow regimes, the difference increasing w i t h i ? . In particular, the model overestimated the concentration significantly for strong plunging regime. A s a particle-laden jet proceeded and particle settling continued, the error between the model prediction and the measurements decreased ( x / L = 0.19). A t x/L-  0.31 most particles settled out and the jet behaved like a fluid jet, the C O R M I X 1  prediction becoming closer to the measured concentration. However, for penetration regime and impingement, the model underestimated the dye concentration as in the case o f fluid jets.  Figure 5.11 shows the relative error between the concentration predicted by C O R M I X 1 v3.2 and the measured values for particle-laden jets as the dimensionless density ratio R varied. The bulk density ( p ) h  was applied to the model and subsequently the model  estimated and used the bulk buoyancy flux B . The relative error was calculated using: b  E  R  =  {  C  M  ~  C  C  )  (5.14)  M  where  E  R  C  M  C: c  :  relative error  :  measured dye concentration predicted dye concentration by C O R M I X 1  A s described above, fluid jets and particle-laden jets o f penetration and impingement regimes showed positive error and as R decreased, the error became negative.  121  1.00  s  0.50  tt t * • o  0.00  I• ^  —  —  3 - 0.50 u o s«  Fluid jet  W  -1.00  l  -  L 5  -  <N  *  *  —  x  Strong plunging •  o  o  Penetration Impingement  Weak plunging  o Tt;  ON  —*  ( N  fN  CO  '  o~ *  •  (N  o  *n  ^ o X  *  • X  °  -2.00  -2.50 H Xx/L=0.13 Ox/L=0.19 • x/L=0.31 -3.00  Figure 5.11 Relative error between the experimental results and C O R M I X 1 prediction  5.3 Summary of particle-laden jets The behavior o f particle-laden jets studied is summarized as follows. The difference between fluid jets and particle-laden jets are discussed in Chapter 6.  •  A t the source momentum-dominant zone, the jets behaved like fluid jets regardless o f  the particles. A s jets proceeded, those with low particle concentration exhibited buoyant fluid-jet like behaviors, penetrating into the upper layer or strongly impinging on the  122  pycnocline and propagating horizontally. A s particle concentration increased, jets initially plunged and proceeded like an intermediate jet or plunged down to the bottom and advanced like a turbidity current containing buoyant interstitial fluid.  •  Four flow regimes o f particle-laden jets were identified based on the density difference  ratio R and *F .  - Penetration Regime:  the bulk density o f a particle-laden jet (p ) b  is smaller  than the ambient fluid density ( p ) and the density interstitial fluid is significantly a  smaller than lower layer density. Thus the jet penetrates into the upper layer. This regime satisfies 0 < R < 1 and ¥ > 0.9.  - Impingement Regime: p  a  is greater than p  b  but the jet buoyancy is sufficiently  low relative to the density step that penetration does not occur. Thus the jet strongly impinges on the pycnocline. Active particle settling occurs at the near field. This regime occurs when 0 < R < 1 and  < 0.9.  - Weak Plunging Regime: this regime is transitional, exhibiting both buoyant fluid jet-like behavior and negatively buoyant jet behavior. The jets are initially heavier than the ambient fluid but not heavy enough to plunge down to the bottom. Abrupt group settling o f particles and active detrainment o f interstitial fluid occurs. The ambient condition is insignificant at the near field. This regime occurs when -2.0<i?<0.  -  Strong Plunging Regime: Despite the positive buoyancy o f interstitial fluid,  jets plunge down to the bed and proceed along the bed slope due to having high bulk density. The ambient fluid condition is unimportant until sufficient interstitial fluid is released. This regime occurs when R < - 2 . 0 .  123  •  Concentration profiles and particle distribution o f the particle-laden jets showed that  particles move with flow and a significant amount o f particles were transported to the upper layer and traveled for a considerable distance during strong impingement and penetration.  •  Dimensional analysis and the experimental results indicated that for penetration,  impingement and weak plunging regimes, the dimensionless maximum rise height and the top o f the spreading layer (Z /h ) t  Plunging  Regime  the  parameters  t  increases with B /g'^ h  converge  2,5  constants  c = - 3 . 0 (± O.Ol) 3  c =0.9 ( + 0 . 0 l ) . The dimensionless final spreading layer thickness (Tfjh 4  i  only on M ' /B h 3 4  U2  i  m  j  while for Strong  /5  i  to  (Z /h )  and  ) depended  regardless o f the flow regime. It was also found that penetration o f  particle-laden jets into the upper layer was prevented by the presence o f particles regardless of the buoyancy o f interstitial fluid.  •  The C O R M I X 1 v3.2 predictions o f flow classification agreed with the experimental  results when the particle concentration was either very low (penetration and impingement regimes) or very high (strong plunging regime). However, for intermediate jets (weak plunging regime) the model predicted them to be plunging to the bed (strong plunging regime). In general, the model underestimated the dye concentration o f fluid jets while overestimating for particle-laden jets.  124  Chapter 6 Comparison between Fluid Jet and Particle-laden Jet  This chapter discusses the difference in the flow characteristics o f fluid jets and particle-laden jets. Comparisons are first made in the absence o f the influence o f ambient fluid. The effect o f ambient fluid conditions on the two types o f jet is then considered by comparing the results presented in Chapters 4 and 5.  6.1 Homogeneous ambient fluid Observation o f fluid jet and particle-laden jet behavior in homogeneous ambient fluid provides insight into the effect o f particles on jet trajectory and the role o f the ambient condition. Figure 6.1 (a)(b) shows the behavior o f fluid jets and particle-laden jets in homogeneous ambient fluid. The density o f the fluid jet is identical to that o f the interstitial fluid o f particle-laden jets and less than ambient fluid. Therefore, the density difference between the two jets is due only to the presence o f particles.  A t the near jet exit (x/L = 0.04) where the source momentum was still dominant, both the jets showed similar behavior. A s the jets propagated, however, the fluid jet started to rise due to its positive buoyancy and propagated as a surface jet whereas the particle-laden jet initially sank due to high bulk density. Most interstitial fluid was incorporated into the  125  (i) t = 10 second  (ii) t = 32 second  Figure 6.1 (a) Behavior of a buoyant fluid jet in homogeneous ambient fluid (A47)  (iii)  (iv) Figure 6.1 (b) Behavior of a particle-laden jet with buoyant interstitial fluid in homogeneous ambient fluid: (i) momentum-dominant jet behavior, (ii) plunging, (iii) detrainment of interstitial fluid and bulk particle settling and (iv) forming a horizontal spreading layer after active particle settling (P61)  127  particle settling while the particle-free buoyant fluid at the upper boundary o f the jet flow rose to its neutral buoyancy level. Consequently, the particle-laden jets occupied almost the entire water column in the near field. The fine particles constantly settled along the entire length o f the tank but this had little impact on the jet trajectory. Far downstream, the final spreading layer formed near the surface like fluid jets. Figure 6.2 shows the dye concentration profile for each case. The profiles agree with the description o f the jets above. Two flows behave similarly until x/L - 0.13 but at x/L = 0.19 the fluid jet rises rapidly to the surface.  6.2 Two-layer system 6.2.1 Maximum rise height and penetration The primary concern is the height o f rise and the possibility o f penetration o f a buoyant jet in a two-layer system. fluid  Figure 6.3 shows the dimensionless maximum rise height for  and particle-laden jets in two layer systems. In general, only minor differences  occurred in maximum rise height and penetration for Penetration and  Impingement  Regimes. A l s o , Weak Plunging regime appeared to rise slightly less than the corresponding fluid jets.  However, jets o f Strong Plunging Regime plunged down to the bed and propagated along the bed slope regardless o f  . This behavior is the main difference between the two  jets. Even for the penetration regime where the interstitial fluid is highly buoyant, jets plunged to the bottom. For example, although P7 (*F = 1.3) and P23 ( Y = 0.99) could penetrate into the upper layer but jets plunged down to the bed due to particles. This implies that the presence o f particles in flow above a certain concentration in flow can prevent buoyant interstitial fluid from penetrating into the upper layer. Otherwise, the jet would penetrate and spread out in the upper layer.  128  ON  CN  -J "ft  oo  <  ° 3 o  • »-H -+-»  r/i  =3 O C  S S  o v > o v > © t n o » i " >  =3 a as -S  cn  S  Pi  CD  « O CH  03  o  u  3 m o  Q  CN  II  (mx) z  •  u I-I =s  o "w  SP E  (UI3) Z  I  ft  a  8 e  •  ;  c? <L>  '  1  c3  6.0 X  5.0 4.0 o o  3.0  3  o  ox*  2.0 1.0  0.0, I  1  0  0.2  1  1  0.4  1  0.6  0.8  1  I  1  1  1.0  1.2  1.4  1.6  1  -1.0 •  -2.0  • •  • (P23)  (P7)  •  -3.0 X particle-laden jet(Penetration)  O Fluid Jet  • particle-laden jet (Impingement)  A Particle-laden jet (Weak plunging)  • particle-laden jet (Strong plunging)  Figure 6.3 Comparison o f the maximum rise height (Z  m  jh ) between fluid jets i  and particle-laden jets in two-layer systems  6.2.2 Top of the spreading layer  In the strong impingement regime, Zjhy for the fluid jets increased linearly with *F as shown in Figure 6.4. The particle-laden jets o f Impingement and Weak Plunging Regimes did not rise as high as the fluid jets. In addition, the jets o f Strong Plunging Regime released buoyant interstitial fluid during instantaneous plunging and the interstitial fluid constantly entrained heavy ambient fluid. Eventually, the top o f the final spreading layer was trapped under the pycnocline, which is another unique characteristic o f particle-laden jets relative to the fluid jets.  130  The results also indicate that the difference in the top o f the spreading layer between fluid jets and particle-laden jets is larger than that o f the maximum rise height. It is because the maximum rise height occurs before significant settling occurs, and thus the buoyancy o f the interstitial fluid o f particle-laden jets is still as large as in fluid jets. However, the final spreading layer forms further downstream after the settling and thus the interstitial fluid entrains more heavy fluid in the lower layer. Consequently, as the particle concentration increases, the top o f the spreading layer tends to lower.  0.0  0.2  0.4  0.6  o Fluid jet  O.i  1.0  1.2  1.4  1.6  1.:  • Particle-laden jet (Impingement)  A Particle-laden jet (Weak plunging) • Particle-laden jet (Strong plunging)  Figure 6.4 Comparison o f the top o f the spreading layer ( Z , /h  j  ) between fluid jets  and particle-laden jets in two-layer systems  6.2.3 Spreading layer thickness The particle-laden jets formed an abrupt thick spreading layer in the vicinity o f the  131  nozzle compared to fluid jets. However, surprisingly, the particles exerted little impact on the final spreading layer thickness. Figure 6.5 compares the final spreading layer thickness between fluid jets and  particle-laden  dimensionless parameter M \\B VA  xn  jets showing  . A t low M  3 / 4  that both jets increased  //i,5  with  , Weak Plunging Regime  1 / 2  appeared to have only a slightly thicker spreading layer compared with fluid jets and jets o f Weak Plunging Regime, implying the effect o f particle presence on the final spreading layer was insignificant.  3.0 o  2.5  o  2.0 JS  A  •  y'  o  > 1.5 H  o  •  <>•• <>-• • $•*' o  1.0  ^ °  Y  0.5 0.0 0.0  1.0  2.0  3.0  4.0  6.0  5.0  M /(hi*B ) 3/4  O fluid jet  • Particle-laden jet (Weak plunging)  1/2  • Particle-laden jet (Impingement)  Figure 6.5 Comparison o f the spreading layer thickness ( T /h ) f  {  o f fluid jets  and particle-laden jets in two-layer systems  132  Chapter 7 Conclusions and Recommendations 7.1 Conclusions The dynamics o f buoyant fluid jets and particle-laden jets discharged into two-layered stagnant ambient fluid were studied through a series o f experiments and analysis. The following conclusions were drawn from this investigation.  7.1.1 Buoyant fluid jets in two-layer system Three parameters were identified to have crucial influence on the buoyant jet behavior in two-layer systems: buoyancy o f the jet fluid B , the magnitude o f the density step expressed as a modified gravitational acceleration ( g' ) and the distance o f discharge exit a  B to the pycnocline h . A useful dimensionless parameter *F = — — — was found by g'a i 2/5  t  h  combining these three parameters.  The following flow regimes were identified based on ¥ .  •  < 0.5 : buoyant jets rose and impinged on the pycnocline weakly, causing no  density change in the upper layer. Immediately after impingement, the jet advanced horizontally under the pycnocline, entraining the lower layer fluid.  •  0.5 < ¥ < 0.9: buoyant jets impinged strongly on the pycnocline but did not  penetrate into the upper layer. The upper layer was significantly disturbed and the jet  133  entrained lower layer fluid which was transported into and mixed with the upper layer.  •  ¥ > 0.9: buoyant jets penetrated into the upper layer. O n penetration, rapid  vertical growth occurred and a spreading layer proceeded in the upper layer. A density increase occurred at the surface o f the upper layer due to the entrained fluid from the lower layer.  Once a jet penetrates it spreads above the pycnocline, which is an  important issue for the water quality in the upper layer.  A small discharge angle (-3°) was found to result i n insignificant difference in jet behavior relative to horizontal jets (0°).  Occurrence o f backflows was estimated theoretically and confirmed by experiments. Backflow was found to occur along the pycnocline depending on the relative magnitude o f vertical buoyancy flux and the source momentum flux. The relative strength o f the two momentum fluxes was found to determine jet angles at the pycnocline. When the estimated jet angles at the pycnocline were greater than 7° backflows occurred but when 6  p  < l °  no  backflow occurred. For the penetration regime, *F > 0.9, some jet flow accumulated along the pycnocline and backflows also formed at the surface o f the upper layer.  The ambient fluid condition near the jet appeared to have no influence on Coanda bottom attachment. The bottom attachment occurred at h I £  M  < 0.22 for all the given  experimental conditions. The Coanda effect is a beneficial phenomenon for buoyant wastewater discharged under the pycnocline. This is because discharge flow stays longer in the lower layer, entraining more heavy ambient fluid, resulting in a reduced possibility o f penetration.  The dimensionless maximum rise height and the top o f the spreading layer were found to be constant in the weak impingement regime, whereas they increased with *F in the strong impingement regime. The spreading layer thickness was independent o f the presence  134  and the strength o f the density step and increased with a dimensionless M /h B V4  parameter  . The location o f the maximum rise height ( X ) increased with  U2  x  m  the  densimetric Froude number.  7.1.2 Particle-laden jets in two-layer system The initial concentration o f particles was found to have a significant influence on the behavior o f particle-laden jets. Jets with low particle concentration behaved like buoyant fluid jets whereas those with high particle concentration behaved like negatively buoyant jets regardless o f interstitial fluid buoyancy. Particles tended to be carried by the interstitial fluid and transported downward.  For the source momentum dominant zone, the effect o f particles on the jet behavior was insignificant. However, as source momentum decayed the flow pattern was controlled by the particle concentration, interstitial fluid density and ambient fluid density. A density difference ratio R was found to be the most important factor determining the initial dynamics o f particle-laden jets. The critical value R was found to be - 2 . 0 , under which the c  particle-laden jets plunged to the bed despite the interstitial fluid being highly buoyant.  The behavior o f particle-laden jets were categorized into four flow regimes depending on the critical dimensionless density R and ¥ . The regimes were as follows:  •  Penetration Regime was defined as flow behavior characterized by jet  penetration. For the conditions 0 < R < 1, particle-laden jets behaved like fluid jets regardless o f the presence o f particles. If W > 0.9 J e t s penetrate into the upper layer.  •  Impingement Regime was defined as flow behavior characterized by strong  impingement without penetration.  The conditions 0 < R < 1 and ¥ < 0.9  were  satisfied and active separation o f individual particles from the interstitial fluid  135  occurred. However, the general behavior was similar to that o f buoyant fluid jets.  •  Weak Plunging Regime was defined as flow behavior where the presence o f  particles began to exert a significant impact on the flow patterns. This transitional regime occurred for - 2.0 < R < 0 and involved abrupt group settling and active detrainment o f interstitial fluid. The influence o f the ambient fluid condition was insignificant in the vicinity o f the discharge exit.  •  Strong Plunging Regime was defined as flow behavior with particle-laden jets  that rapidly plunged down to the bed and advanced as a turbidity current and for which - 2.0 < R. The ambient fluid condition had no influence on the flow pattern until the buoyant interstitial fluid rose from the bottom current.  The dimensionless maximum rise height and the top o f the spreading layer increased with  for particle-laden jets o f Penetration, Impingement and Weak Plunging Regimes.  However, the jets plunged to the bottom for the Strong Plunging Regime while the top o f the spreading layer was highly dependent on detrainment o f interstitial fluid and converged along the pycnocline. Moreover, the high particle concentration effectively buoyant interstitial fluid from penetrating into the upper layer.  prevented  O n the other hand, the  thickness o f spreading layer was found only to be a function o f the dimensionless parameter M /B h 3l4  U2  l  , after abrupt particle settling occurred.  A substantial proportion o f the particles and o f the lower layer fluid were found to transport into the upper layer and travel for a considerable horizontal distance during strong impingement and penetration.  The  C O R M I X 1 v3.2 prediction  on  flow  classification was  incorrect  for  the  intermediate jets (Weak Plunging Regime), predicting them as plunging jets (Strong Plunging Regime). The model underestimated  the dye concentration o f fluid jets but  136  overestimated for particle-laden jets. When most particles settled, adversely, the model underestimated the dye concentration o f particle-laden jets. Therefore, using C O R M F X 1 to predict two-phase flow characteristics is questionable.  7.2 Contributions •  This research increases our knowledge o f the behavior o f buoyant discharge flow in  two-layer stagnant ambient fluid. It was found that buoyant jets can either penetrate into the upper layer during discharge or only impinge on the density step but spread horizontally, depending on the source and the ambient fluid conditions. The penetration o f a jet flow can cause serious problems for real-world disposal o f wastewater. A useful dimensionless parameter was identified by combining most influential parameters. This parameter can be applied in practice to predict the trajectory o f discharge in two-layer structured receiving water. It allows discharge conditions to be identified that prevent the penetration o f highly buoyant discharge into the upper layer and minimize the disturbance o f the slurry layer in a tailings pond. In addition, the analysis o f the gross flow characteristics based on the dimensional analysis and experimental results provide a basis for predicting the gross spreading behavior o f buoyant jets such as the maximum rise height, top o f the spreading layer and final spreading layer thickness.  • particles  The present study also provides insights into the significance o f the presence o f in the  discharge,  in particular for particle-laden jets with high particle  concentration. F l o w regimes o f particle-laden jets depending on discharge conditions were identified which allow us to predict whether the particle-laden jets behave like fluid jets or negatively buoyant fluid in the near field. The practical significance o f this is that the penetration o f buoyant discharge flow may be prevented simply by adding sufficient fine particles to the jet. Although eventually the interstitial fluid rises, the constant entrainment of heavy fluid in the lower layer increases the density o f the jet fluid. Thus disturbance o f the upper layer due to discharge activity becomes insignificant, which is a benefit for  137  tailings disposal below the pycnocline.  •  The experimental results indicated that the C O R M I X 1 v3.2 model is unsuitable for  predicting two-phase negative buoyant jets. Thus, the unique flow behavior due to the particles in two-phase flow is not captured by the model, which may result i n significant error in predictions at near-field.  7.3 Recommendations for further research For a better understanding o f the physical processes in buoyant fluid jets and particleladen jets, the following recommendations for future research are made:  •  Large scale experimental facility: it is necessary to perform the experiments in a  sufficiently long and wide experimental tank to achieve the fully developed steady-state and to obtain sufficient measurement time and to avoid side and end wall effects. It is also necessary to use various discharge nozzles and thus examine the effect o f the initial volume flux on the jet dynamics. A sufficiently powerful pump should be used to prevent separation o f particles from the interstitial fluid in the pipe during discharge, especially for the jets with high particle concentration.  •  Realistic ambient conditions: in order to simulate realistic ambient conditions, the  ambient turbulence or crossflow should be considered. A l s o , a two-layer system with linearly stratified lower layer should be simulated.  •  Discharge angles and bottom slopes: the effect o f various discharge angles including  horizontal direction and bottom slope on particle-laden jets and fluid jets should be investigated.  138  •  Discharge above the pycnocline: To investigate the possibility o f tailings disposal  into the upper layer, it is useful to conduct experiments on the discharge o f particle-laden jets above the pycnocline.  •  Velocity profile: vertical velocity distribution along the jet trajectory should be  measured to identify the effect o f particles on the flow field and especially the relation between particle concentration and velocity distribution.  •  Particle-size distribution and types: various sizes and types o f particles (i.e. actual  soils or tailings) should be tested to obtain practically useful results.  •  Theoretical studies on particle-laden jets should be conducted including not only  individual particle settling but also bulk (grouped) settling behavior.  • Implications for prototype such as the effect o f viscosity due to increased Reynolds number in the lower layer should be tested.  • Investigation whether the two dimensionless parameters, R and ¥ can be combined is recommended.  •  Further study on turbulent particle-laden jets in linearly stratified ambient fluid is  also recommended.  139  References Abraham, G . , Horizontal jets in stagnant fluids o f other density, Journal o f the Hydraulic Division, A S C E , V o l . 90, N o . 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S Environmental Protection Agency, Washington, D C , 1973 Kumagai, M . , Turbulent buoyant convection from a source in a confined two-layered region, Journal o f Fluid Mechanics, V o l . 147, pp. 105-131, 1984 Lawrence, G . A . , Ward, P. R. B . , M a c K i n n o n , M . D . , wind-wave induced suspension o f mine tailings in disposal ponds - A case study", Canadian Journal o f C i v i l Engineering, V o l . 18, pp. 1 0 4 7 - 1053, 1991 Lee, J. H . W . and Jirka, G . H . , Vertical jet i n shallow water, Journal o f the Hydraulic Division, V o l . 107, N o . H y 12, pp. 1651-1675, 1981 Lee, J. H . W . and Cheung, V . W . L . , Inclined plane buoyant jet in stratified fluid, Journal of Hydraulic Engineering, Vol.112, N o . 7, pp. 580-589, 1986 List, E . J. and Imberger, J., Turbulent entrainment in buoyant jets and plumes, Journal o f the Hydraulics Division, V o l . 99, pp. 1461-1474, 1973  143  M a c K i n n o n , M . D . , Development o f the tailings pond at Syncrude's O i l sands plant: 1978-1987, A O S T R A Journal o f Research, V o l . 5, pp. 109-133, 1989 Manins, P. C , Intrusion into a stratified fluid, Journal o f Fluid Mechanics, V o l . 74, part 3, pp. 547-560, 1976 McCorquodale, J. A . , Zhou, S. P., Moawad, A . , Yuen, E - M . , Rajaratnam, N . , Near field modeling in the connecting channels o f the Great Lakes, The Industrial Research Institute o f the University o f Windsor for Ontario Ministry o f the Environment Great Lakes Branch, 1992 Maxworthy, T., Experimental and theoretical studies o f horizontal jets in a stratified fluid, International Symposium on Stratified Flows, pp. 611-618, 1973 N o h , Y . and Fernando, H . J. S., the transition in the sedimentation pattern o f a particle cloud, Physics o f Fluids, V o l . 5, N o 12, pp. 3049-3055, 1993 Owen, P. R., Journal o f Fluid Mechanics, V o l . 39, pp. 407, 1969 Petroleum Communication Foundation, Canada's o i l sands and heavy oil, A p r i l , 2000 Popper, J., Abuaf, N . and Hetsroni, G . , Velocity measurements i n a two-phase turbulent jet, International Journal o f Multiphase Flow, V o l . 1, pp. 715-726, 1974 Proni, J. R. and Hansen, D . V . , Dispersion o f particulates i n the ocean studies acoustically: The importance o f gradient surfaces in the ocean, Ocean Dumping o f Industrial Wastes, Plenum Press, N e w York, pp. 161-173, 1981 Rahimipour H . and D . Wilkinson, Dynamic behavior o f particle clouds. Proceedings o f the 11 Australian Fluid Mechanics. Conf. University o f Tasmania, Hobart, Australia, December, pp. 743-746, 1992 th  Rajaratnam, N . , Turbulent jets, Elsevier Scientific Publishing Company, Amsterdam, 1976 Roberts, P. J. W . , T w o stratified jets in linearly stratified fluid se jets i n flowing current, Journal o f Hydraulic Engineering, V o l . 113, N o . 3, pp. 323-341, 2001 Roberts, P. J. W . , Behavior o f low buoyancy jets in linearly stratified fluid, Journal o f Hydraulic Research, V o l . 25, N o . 4, pp. 503-519, 1987 Roberts, P. J. W . and Matthews, R. R., M i x i n g in pumped storage reservoirs, Applying research to Hydraulic Practice, pp. 199 - 2 0 5 , 1982  144  Roberts, P. J. W . , Matthews, P. R., Dynamics o f jets in two-layered stratified fluids, Journal o f Hydraulic Engineering, V o l . 110, N o . 9, pp. 1201-1217, 1984 Rooij de F., Linden, P. F. and Dalziel, S. B . , Saline and particle-driven interfacial intrusions, Journal o f Fluid Mechanics, V o l . 389, pp. 303-334, 1999 Ruggaber, G . J., Dynamics o f particle clouds related to open-water sediment disposal, A thesis submitted to the Department o f C i v i l Engineering in partial fulfillment o f the requirements for the degree o f doctor o f philosophy at the Massachusetts Institute o f Technology, 2000 Ruggaber, G . J. and Adams E . E . , Influential o f initial conditions on particle clouds entrainment, The fifth o f international symposium on stratified flow, V o l . 1, University o f British Columbia, Vancouver, Canada, July, 2000 Schneider, H . H . , Laboratory experiments to simulate the jet-induced erosion o f pycnoclines in lakes, Second international Symposium on Stratified Flows, pp. 697-706, 1980 Schmidt, N , P., Generation, propagation and dissipation o f second mode internal solitary waves, P h . D . Thesis, University o f Canterbury, N e w Zealand, 1997 Sharp, J. J. and Vyas, B . D . , The buoyant wall jet, Proceedings o f international C i v i l Engineers, part 2, V o l . 63, pp. 593-611, 1977 Simpson, J. E . , Gravity currents in the laboratory, atmosphere and ocean, Annual Review of Fluid Mechanics, V o l . 14, pp. 213-234, 1982 Sobey R. J. and Johnston, A . J., and Keane, R. D . , Horizontal round buoyant jet in shallow water, Journal o f Hydraulic Engineering, V o l . 114, N o . 8, pp. 910-929, 1988 Sparks, R. S. J., Bonnecaze, R . T . , Huppert, H . E . , Lister, J.R, Hallworth, M . A . , Mader, H . , and Phillips J, Sediment-laden gravity currents with reversing buoyancy, Earth and Planetary Science Letters, 114, pp. 243-257, 1993 Turner, J. S., Buoyancy effects in Fluid, Cambridge University Press, 1973 Turner, J. S., Turbulent entrainment: The development o f the entrainment assumption, and its application to geophysical flows, Journal o f Fluid Mechanics, V o l . 173, pp.431471, 1986 Turner J. S. and Huppert, H . E . , Sedimentation and mixing at the top o f a suspended particles, Proceedings o f the 11 Australian Fluid Mechanics. Conf. University o f Tasmania, Hobart, Australia, December, pp. 747-750, 1992 th  145  Wallace, R. B . and Wright, S. J., Spreading layer o f two-dimensional buoyant jet, Journal of Hydraulic Engineering, V o l . 110, N o 6, pp. 813-828, 1984 Ward, P. R. B . Personal communication, 2001 Ward, P. R. B . , Lawrence, G . A . , M a c K i n n o n , M . D . , W i n d driven resuspension of sediment in a large tailings pond, Proceedings o f International Symposium on Ecology and Engineering, VI-37 - 12, 1994 Weast, R. C . , C R C Handbook o f Chemistry and Physics, C R C Press Inc., 66th edition: 1985-1986, 1985 Wong, D . R. and Wright S. J., Submerged turbulent jets in stagnant linearly stratified fluids, Journal o f the Research, V o l . 26, No.2, pp. 199-223, 1988 Wong, D . R., Buoyant jet. entrainment o f stratified fluids, P h . D . Dissertation, The University o f Michigan, A n n Arbor, 1984 Wood, I. R., B e l l , R. G . , and Wilkinson, D . L . , Ocean disposal o f wastewater, W o r l d Scientific Publishing C o . Pte. L t d , 1993 Wright, S. J. and Wallace, R. B . , Two-dimensional jets in stratified fluid, Annual Review of Fluid Mechanics, V o l . 105, pp. 1393-1405, 1979  146  Appendix A  Buoyant jets in linearly stratified ambient fluid This section presents the results o f experiments on buoyant jets discharged at 3° downward in stagnant linearly stratified fluids. The gross flow characteristics o f buoyant jets are examined in terms o f the maximum rise height, the top o f the spreading layer and the spreading layer thickness. The results are presented in terms o f dimensionless length scales and compared with previous studies. A total o f 14 experiments were performed and the source and ambient condition were 8.7 < F  d  < 55.5 and 0.58 < N < 0.78  s~ . l  A . l Behavior of buoyant jets Figure A . l presents photographs o f buoyant jets under two different source conditions discharged at 3 degree downward. The flow images show that i n a linearly stratified ambient fluid, initially a buoyant jet grows linearly with distance near the jet exit, as is the case in a homogeneous ambient fluid. However, the ambient stratification constantly suppresses the vertical turbulent motion and the buoyant jet entrains denser fluid and the density difference between the jet and the ambient fluid decreases. Thus, when neutral buoyancy is achieved the jet reaches the maximum height o f rise. Consequently, the jet collapses abruptly and proceeds as a horizontal gravity current. This behavior was also observed by W o n g and Wright (1988) and Roberts (1987).  A typical density profile o f a buoyant jet along the jet trajectory in linearly stratified ambient are presented in Figure A . 2 . A s a turbulent jet rises to its maximum rise height, the density profile becomes significantly distorted vertically and horizontally. The upper and the lower boundary o f the density fluctuation indicate the depth o f entrainment. However, note that the density profiles in this study are not time-averaged profiles but instantaneous.  147  (a)(A13, F =22.9, N = 0.76) d  ( b ) ( A 5 3 , F =17.7, N = 0.75) d  Figure A . 1 Buoyant jets in linearly stratified ambient fluid ( a ) A 1 3 ( ^ = 2 2 . 9 , JV = 0.76), (b)A53 (F  d  =17.7, N = 0.75)  148  CU  es  a; C  fN  3 5=  a  © s C5  E «  •o cu  M cu  C  CU  £  CU  CU  ;>. O _CU  X! '5? c« _CU  s o cn C a CU  < cu  3  Ml  (LULU) L|}dea  DC C  o  A.2 Analysis of gross flow characteristics  The definition o f parameters for a buoyant jet in a linearly stratified ambient fluid is shown in Figure A . 3 . A buoyant jet is discharged at height h above the bed. A s the jet reaches its maximum rise height Z  at the location X  m  m  spreading layer with thickness T . Z and Z f  t  , it bends and intrudes as a  are defined as the top and the bottom o f the  b  spreading layer respectively. The source volume, momentum and buoyancy flux ( Q , M ,B ) are defined in section 2.2.2. The ambient density gradient is expressed by a buoyancy frequency TV, defined in section 2.2.4.  Figure A . 3 A definition sketch o f a buoyant jet in a linearly stratified fluid  The dimensionless characteristic length l l l \ measures the relative importance o f the u  source momentum, buoyancy and the ambient density stratification.  - M  b  v  u  B  (A.1) J  150  where M, B, N are defined in section 2.2. If £M I £'b > 1, the buoyant jet behaves like a momentum jet.  If £M I £'b < 1 , a buoyant jet behaves like a plume until the ambient  stratification plays a significant role in the jet trajectory (Wallace & Wright, 1984; Wong, 1984; Jirka and Doneker,  1991). The experimental  conditions examined here  are  0.59 < £ M I £'b < 1.21, which covers a small range o f buoyancy-dominant jets but mostly momentum-dominant jets.  A.2.1 Maximum height of rise and its location The dimensionless maximum height o f rise (Z  m  stagnant ambient fluids is plotted against £  M  I £'b) o f a buoyant jet in linearly stratified I' £'  b  in Figure A . 4 . Z l£' m  b  is relatively  constant with an average o f 0.98 for £M I £'b > 1 , whereas it tends to decrease for the buoyancy-dominant region, £ M I £'b < 1. This observation is similar to experimental results of horizontal buoyant jets observed by Wong (1984). However, the numerical results o f G u and Stefan (1988a) give higher values than those o f the present study and Wong (1984). Therefore, it is rather difficult to identify the effect o f the 3° downward discharge angle on the maximum rise height at this stage.  Figure A . 5 shows the dimensionless location o f the maximum height o f rise ( X / ^ ) o f m  a buoyant jet. To facilitate comparison with previous research, X £ /£ M  N  instead o f £M I£'b.  m  /£  The results indicate that the location X  stratified fluid is independent o f £ / £ M  N  m  N  N  is plotted against / ^  N  in a linearly  and is constant at 4.8. Roberts (1987) estimated  the location o f jet collapse o f non-buoyant jets to be 2.1 - 3.6, with an average value o f 2.8, and subsequent experiments (Roberts, 2001) give an average value o f 3.5. This large difference is probably due to the initial downward-inclined momentum, which allows jets to take a longer path until reaches the maximum rise height. Thus, for a buoyant jet with large source momentum discharged downward, the location o f the maximum rise height is  151  further downstream compared to that under horizontal discharge.  3.0  0.0  1.0  2.0  3.0  4.0  5.0  6.0  7.0  8.0  LM/IV  •  present study  o  Wong(1984, horizontal)  —""Gu&Stefan(1988)numerical result horizotaljet  Figure A . 4 Dimensionless maximum rise height Z /£' m  b  i n linearly stratified  ambient fluid  0.0  1.0  2.0  3.0  4.0 L  M  5.0  6.0  7.0  8.0  /LN  Figure A . 5 Dimensionless location o f maximum rise height i n linearly stratified fluid  152  A.2.2 Top of spreading layer The dimensionless top o f the spreading layer after jet collapse (Z /£ ) t  as £  M  I£  N  tends to decrease  N  increases, regardless o f the discharge angle shown in Figure A . 6 . A l s o , as the  discharge angle decreases, Z /£ t  decreases. Jirka and Doneker (1991) suggested an  N  equation relating the top o f the spreading layer to the discharge angle:  where £' is a characteristic length defined in section 2.2.4, 9 a discharge angle and a a b  coefficient o f or = 2 . 0 ± 0 . 5 . For 3° downward discharge angle and £  M  I£  N  >1.5, Z , I£  N  for the present study is higher than that estimated using E q . (A.2). O n the other hand, 3° downward discharge results in a lower top o f the spreading layer than that o f the horizontal jet investigated by W o n g (1984).  A.2.3 Spreading layer thickness Figure A . 7 also shows that  T j£' f  b  increases with £ / £ ' . In addition, buoyant jets with a M  b  horizontal (Wong, 1984) resulted in a slightly larger spreading layer thickness than 3° downward discharge. It is because for the same source momentum the vertical momentum of downward jets is smaller than that o f horizontal jets, causing slightly smaller entrainment in the vertical direction.  153  • o o •  present study -3 degree Jirka and Doneker (1991) -3 degree, a=2.5 Wong (1984)-horizontal jet Jirka and Doneker (1991) -3 degree, a=1.5 Power (Jirka and Doneker (1991) -3 degree, a=2.5) Power (Jirka and Doneker (1991) -3 degree, a=1.5)  Figure A . 6 Dimensionless top o f the spreading layer i n linearly stratified fluid  0.0  1.0  2.0  3.0  4.0  5.0  6.0  7.0  8.0  9.0  L /L ' M  o present study(-3 degree)  b  • Wong (198^) horizontal jet  Figure A . 7 Dimensionless spreading layer thickness in linearly stratified fluid  155  A.3 Summary of fluid jets in linearly stratified fluid  The experiments also suggested that in a linearly stratified ambient fluid, a buoyant jet grew linearly with distance near the jet exit. However, the jet collapsed abruptly as it reached the maximum rise height and advanced as a horizontal gravity current.  The dimensionless maximum rise height (Z /l' ) M  b  was found to be constant at 0.98 for the  momentum-dominant region ( £ / £ ' > \ ) and to decrease for £ / £ ' < \ . M  b  M  the maximum rise height was independent o f £ / £ M  N  b  The location o f  and found to be constant at a value o f  4.8, which is significantly larger than that value o f 3.5 found for non-buoyant horizontal jets by Roberts (2001). £ /£ M  N  The top o f the spreading layer (Z j£' t  increases. The spreading layer thickness (T j£' f  b  b  ) tended to decrease as  ) increased as £ / £ ' M  b  and the  discharge angle increases.  156  Appendix B Particle-laden jets in linearly stratified ambient fluid The gross characteristics o f particle-laden jets in a linearly stratified fluid are analyzed quantitatively using the same methods as in the two-layer system.  B.l Behavior of particle-laden jets The gross flow characteristics o f particle-laden jets in a linearly stratified fluid were found to be similar to that in a two-layer system. The linear density gradient resulted in a symmetric shape o f the spreading layer compared with that in two-layer systems and no apparent maximum rise was observed, as illustrated i n Figure B . l (a). For jets o f low particle concentration, the linear stratification suppressed vertical spreading at the top while constant  individual particle settling occurred. A s the particle concentration  increased, the flow exhibited a U-shaped bottom configuration resulting from group settling at the near field (Figure B.l(b)).  O n the other hand, when a jet plunged down due to its large initial bulk density, it initially behaved like that in a two-layer system (Figure B . l ( c ) ) . A large amount o f particles settled at some distance and the jet started to rise. A s the head o f the flow rose and mixed with heavy ambient fluid, the density o f interstitial fluid increased. However, due to the constant discharge o f buoyant interstitial fluid, the density o f ambient fluid gradually decreased. A s a result, the buoyancy o f newly discharged fluid became smaller than that o f previously discharged fluid. Eventually the individual separate spreading layers were formed at their neutral buoyancy as illustrated in Figure B . 1(d) - this was also observed by Spark et al. (1993). This is the main difference between jet behavior in twolayer systems and linearly stratified ambient fluids.  157  (a)  (c)  (d)  "-.%.S"%"S"S"S'V;.^"\;„;„:,..''  Figure B . l Behavior o f particle-laden jets in linearly stratified fluid (a) fluid jet like behavior, (b) intermediate (c) plunging in the near-field and (d) detrainment of interstitial fluid in the far field  158  B.2 Analysis of gross flow characteristics  The discharge height from the bed ( h ) and a characteristic length scale £'  b  are  appropriate parameters for buoyant jets in linearly stratified fluid defined in section 2.3. These two parameters are combined to give the dimensionless form £' /h b  and plotted  against R . When R < -2.0 the jets plunged down to the bed, while when - 2.0 < R < 0 jets formed a thick intermediate spreading layer but did not plunge.  Figure B . 2 shows the dimensionless maximum rise height, the top o f the spreading layer and the spreading layer thickness o f particle-laden jets in linearly stratified ambient fluid. The parameters were normalized by the discharge height above the bed ( h ) and plotted against £ / £ ' M  b  • The maximum rise height and the top o f the spreading are slightly  influenced by the dimensionless density ( R ) . The results clearly show that Z  m  and Z  t  decrease as the concentration increases and jets o f high concentration (R < - 2 . 0 ) plunged to the bed. A l s o , the spreading layer thickness tends to increase with £  M  I £' . These results b  are compared with fluid jets and previous studies in Chapter 6.  -4.0 Lm/L ' b  + Tf/Lb' O Zm/Lb' X Zt/LN  Figure B . 2 Dimensionless parameters for particle-laden jets in linearly stratified fluid  159  Appendix C  Comparison of fluid jets and particle-laden jets in linearly stratified ambient fluid  C l Gross characteristics of jets  Figure C l presents the comparison of the maximum rise height o f fluid jets and particleladen jets i n linearly stratified ambient fluid. There was no apparent difference i n the maximum rise height for three cases except for the Strong Plunging Regime where the jets plunged down to the bed (PI2 and PI4) like in two-layer systems. The top o f the spreading layer o f particle-laden jets  Zj£  N  is plotted against £ / £ M  N  i n Figure C.2. The present  results are also compared with those o f 3° downward inclined fluid jets o f Jirka and Doneker (1991).  Zj£  N  o f fluid jets from both present study and Jirka and Doneker (1991)  are higher than that o f particle-laden jets.  Figure C.3 shows the comparison o f the dimensionless spreading layer thickness  {T l£' ) f  b  for the two types o f jet. The Strong Plunging Regime is excluded in the figure. It is shown that T I £'b slightly increases with £M I £'b and the thickness o f particle-laden jets tends to F  be slightly larger than fluid jets and increases with the particle-concentration. This is because when particles settle interstitial fluid also descends and entrains heavy ambient fluid whereas linear stratification inhibits the vertical mixing o f interstitial fluid. It also appears that particle-laden jets result in a slightly thinner spreading layer that the horizontal jets but the difference is negligible.  160  • fluid jet  B particle-laden jet  A Wong (1984)-horizontal fluid jet  Figure C . 1 Comparison o f the dimensionless maximum rise height ( Z  m  / £' ) between fluid h  jets (Wong, 1984); present study) and particle-laden jets in linearly stratified fluids  161  1.0  1.5  2.0  2.5  L /L M  • particle-laden jet  x  3.0  3.5  4.0  N  o fluid jet  3° Jirka (1991)  Figure C.2 Comparison o f the dimensionless o f top o f the spreading layer ( Z / ^ ) t  N  between fluid jets (Jirka, 1991; present study) and particle-laden jets 2.5 X  X  2.0  X  _ _o  1.5 H  o 1.0  •  o  A  x  •  0.5 0.0 0.0  1.0  2.0  • particle-laden jet  3.0  O fluid jet  4.0  5.0  6.0  7.0  8.0  x Wong (1984)- horizontal fluid jet  Figure C.3 Comparison o f the dimensionless spreading layer thickness ( T I l' ) between f  h  fluid jets and particle-laden jets in linearly stratified fluids  162  C.2 Conclusions  C.2.1 Buoyant fluid jets in linearly stratified fluid Buoyant jets grew linearly near the jet exit as i f in a homogenous ambient fluid. However, as a jet reached the maximum rise height, it collapsed abruptly and proceeded as a horizontal gravity current. The maximum rise height decreased for  £ /£' M  b  <1  and was  relatively constant for the momentum-dominant region ( £ / £ ' > \ ) . The spreading layer M  b  thickness appeared to be sensitive to the downward directed momentum and increased with £ /£' M  b  and the discharge angle.  C.2.2 Particle-laden jets in linearly stratified fluid The gross flow behavior o f particle-laden jets in linearly stratified fluids was found to be similar to that in a two-layer system except for the symmetric shape o f the spreading layer. After substantial particle settling, individual separate spreading layers formed. The ambient stratification had little influence on the flow behavior until a considerable amount o f particles settled out o f the flows. The higher the particle concentration, the lower the maximum rise height and top o f the spreading layer.  163  

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