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importance when considering discrete second phase transport. 2 PROJECT METHODS AND RESULTS Our interest has centred around understanding and modelling the dynamical interaction of the shear layer with the sandwave, especially with reference to particle-eddy interactions identified in the project proposal (Thomas, 1990) in connection with field measurements indicative of such interactions (Soulsby & Bettess, 1990) . Below we briefly review wider implications of the findings of our experimental studies and computational modelling. 2.1 Experimental studies We constructed a flume of 0.42m square cross-section and length 6.7m specifically to study the flow and particle dynamics over fixed bedforms. These bedforms represent a good approximation to sandwaves because migration velocity is negligible compared with the flow velocity so bedform deformation timescale is much longer than that for the typical trajectories of bedload sand grains. We selected model particles of quiescent fall speed VT equivalent to typical sand grains and surveyed flow speeds U such that the ratio U/VT varied from 3 to 13. The 2mm squat cylindrical particles were large enough to be visualised videographically and their deposition rate at various sites on the bedform surface 7-2
were shown to compare well with previous sedimentation data for quartz sand grains. Their suitability for optical tracking, possibly using colour labelling to differentiate between particles of differing fall speeds has promising implications which we mention in section 3. a) Concentration peak at crest height. Soulsby & Bettess' (1990) observation of a concentration peak over the bedform trough but elevated at the height of the crest has now been shown to derive from interaction between the jetted bedload and the free shear layer. Chapter 3 showed experimentally that this behaviour is due to extended suspension time (ie hindered settling) in the shear layer as compared to the time spent falling through the relatively quiescent recirculating flow region. Horizontal and cycloidal particle trajectories from the crest demonstrated temporary reductions and even local reversals of the particle fall speed. The results, characterised in terms of parameter U/VT compared well with earlier findings for bubble transport in shear flows (Thomas et al, 1983) and for wave induced sediment suspension (Nielsen, 1984) where vortex capture was found to occur for U/VT greater than 3. b) Modal trajectories. Particles follow the broad classification of trajectories shown in figure 1, travelling from the crest to the downstream lee and stoss slopes. It is tempting to attribute the predominance of these modes to our 7-3
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FLUID-PARTICLE TRANSPORT DYNAMICS O
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SYNOPSIS The local dynamics of sand
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TABLE OF CONTENTS LIST OF FIGURES C
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CHAPTER 3: JETTING EXPERIMENTS Summ
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2 Numerical scheme 6-5 3 Results 6-
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LIST OF FIGURES Chapter 1 Figure 1.
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U=830mm/s. Figure 16. Thomas et al
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in the boundary layer. a) The forma
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Chapter 3 Figure 1. After Alien (19
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at various values of U/V from 2.7 t
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y Coanda-flapping of the free shear
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of a sandwave crest in the estuary
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Figure 7h-i. The temporal fluctuati
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inclined downwards whereas the time
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starting position (X,Y) at zero ini
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d Sand grain diameter (m) Fi Number
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G Vortex core growth rate (tn/s) ki
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1 INTRODUCTION Sand forms the botto
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where U is the depth-averaged veloc
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The wavelengths of dunes primarily
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detached and then confined within a
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The vortex radius rn and apparent w
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Recent work by Nezu & Nakagawa (199
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found in the outer streaks. 4 MODEL
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(1987), for example, modelled gas-s
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Profiles of shear stress and turbul
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6ft v "' ' Re In the limit of large
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that the particle radius was much s
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and travels downstream at speed }*U
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capture by transient large eddies s
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Chapter 1 Figure 3. Alien (1984). L
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Chapter 1 10 8 e 4 I 08 •- 02 Yal
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Chapter 1 bw speed fluid Figure 11.
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Chapter 1 Figure 16. Thomas et al (
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Chapter 1 StCMl STRESS SCALE « K /
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Chapter 1 Haiht Vdodty Figure 22. S
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Chapter 1 Time = 1.2 2.4 ' ' :•
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1 INTRODUCTION AND DESIGN CONSIDERA
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Initial costing for a flume of the
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flanges and a maximum flow rate of
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could be wound above or below the l
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4 EXPERIMENTAL SETUP AND METHODS He
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4.2 Flow visualisation and model pa
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any divergence from the beam and to
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even flow over 0.45m width and up t
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Chapter 2 Opt 1 h(m) 0.01 Max D(m)
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Chapter 2 Part of side section Putt
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Chapter 2 Suction tank Bypass Disch
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Chapter 2 QUncorrectedflow £ Corre
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Chapter 2 60 r 501 40? 30r 20 r lOr
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1_ INTRODUCTION The main features o
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2 EXPERIMENTAL METHODS A detailed d
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the relationship is then simply ^ -
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number about 0.14. They were taken
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along the stoss slope. Figures 8 an
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3.3a) Jetting trajectories when U/V
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errors increase substantially due t
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likely distributions. 4 DISCUSSION
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Our suggestion here is akin to that
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not accommodate the differing migra
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considered by proponents of numeric
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Chapter 3 C,;: Figure 3a-j. The pla
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Q CO 23 Figure 6. Distribution of p
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Chapter 3 X(cm) 1 2 3 4 5 6 7 8 9 1
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Chapter 3 U(m/s) V(m/s) U/V M1+M2 M
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O I r+ 21 CO 2 5 8 11 14 17 20 23 >
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8 11 14 17 20 23 25 + Position Figu
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Chapter 3 U/V= B5.7 Q9.3 BlO.7^12.8
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Chapter 3 Band 1 2 3 4 U(m/s) 0.2 0
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1 INTRODUCTION In chapter 3 we cons
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velocity for a maximum of 40% of th
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layer vortices extending over the d
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2.2 Methods for measuring Coanda-fl
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Section 3.4 considers suspension fr
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This same flow structure has also b
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3.2b) Effect of varying inter-crest
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those with fall speed 0.060m/s for
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3.4 Particle capture from stoss slo
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are discussed in the context of est
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jetted grains settling to the lee s
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Chapter 4 ENTRAINED FLOW Figure 1.
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Figure 3a-j. The plates show partic
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Chapter 4 Percentage occurrence •
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Chapter 4 Interval (s) 60 80 100 12
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Chapter 4 0.024m Conc=8% Figure 12.
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Chapter 4 Figure 16. A cloud of par
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1 INTRODUCTION We use a Rankine vor
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effective particle fall speed in th
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particle velocity Vx=0. The initial
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the vortex axis. Vortex circulation
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dimensional fall times T^ for diffe
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horizontal component lift force (fi
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corresponds to the trajectory trave
Page 187 and 188: stepping the calculation in VT . Do
Page 189 and 190: averaged exclusion of the coherent
Page 191 and 192: C from figure 11 (ie 2.2) then we h
Page 193 and 194: PflRTICLE DENSITY=1000.000 Kg/n3 LI
Page 195 and 196: Chapter 5 ft) J k I Figure 4. Varyi
Page 197 and 198: Chapter 5 Relative Fall Time va Sta
Page 199 and 200: Chapter 5 Figure 7a. Trajectories o
Page 201 and 202: Chapter 5 Velocity X —Inertia X L
Page 203 and 204: Chapter 5 Velocity X —Velocity Y
Page 205 and 206: Chapter 5 Velocity Y Inertia Y Lift
Page 207 and 208: Chapter 5 DENSITY PARTICLE=2850.000
Page 209 and 210: Chapter 5 Rad = 0.006 Rad=0.003 Rad
Page 211 and 212: Chapter 5 H3 Y=0 Oy=i m Y=2 D-y=3
Page 213 and 214: CHAPTER 6: NUMERICAL SIMULATION OF
Page 215 and 216: next. If we now adopt the classical
Page 217 and 218: st = (4) Where p p was the particle
Page 219 and 220: 3 RESULTS 3.1 Specified 6 and V Fig
Page 221 and 222: the blue squares to double loops an
Page 223 and 224: A0fl0 = 1.25V-0.33G-0.005 (7) and f
Page 225 and 226: Conversely, the upper line of the p
Page 227 and 228: equations. Such a discrete vortex m
Page 229 and 230: Figure 1. Schematic of the shear la
Page 231 and 232: Chapter 6 J G H K M Figure 3. Seven
Page 233 and 234: Chapter 6 1 T V=0.161 0.1 -- V41185
Page 235 and 236: Chapter 6 - DataV=0.0335, G=0.01
Page 237: CHAPTER 7: RECAPITULATION AND RECOM
Page 241 and 242: We have shown Coanda-flapping makes
Page 243 and 244: figure 5, was critically dependant
Page 245 and 246: stoss slope suspension studies of c
Page 247 and 248: Figure la-g. The seven trajectory m
Page 249 and 250: Chapter 7
Page 251 and 252: Chapter 7 0.0351 0.03 " 03 0.025 0.
Page 253 and 254: Flow 16 (1) pp 19-34. Bernal LP (19
Page 255 and 256: Mechanics of Sediment Transport. Is
Page 257 and 258: turbulence near a smooth wall in a
Page 259 and 260: moderate Reynolds number shear laye
Page 261 and 262: Spalding (1961). A single formula f
Page 263 and 264: USA. 1-12
Page 265 and 266: APPENDIX 1: BOUNDARY LAYER STUDIES
Page 267 and 268: (1967) used hydrogen bubble visuali
Page 269 and 270: The burst-sweep dynamics study of U
Page 271 and 272: Horseshoe vortex Vortex filament Ho
Page 273 and 274: APPENDIX 2: FAST9003.HR(RW)/NHT - P
Page 275 and 276: of the vorticity shed into the near
Page 277 and 278: transport dynamics of multiphase fl
Page 279 and 280: APPENDIX 3: FUNDAMENTAL NAVIER-STOK
Page 281 and 282: APPENDIX 4: CLOSURE METHODS 1 ZERO
Page 283 and 284: where cr k and CD are empirical con
Page 285 and 286: K = CDe^ 2 p 2 \U2 -U1 \=e 1e 2 c (
Page 287 and 288: APPENDIX 6: K-e MODEL OF JOHNS ET A
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They then defined a hydrodynamic co
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with respect to the rest of the vor
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The vorticity equation can be split
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around the crest and the motion of
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micrometers, with mean of 80 microm
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i——COMPARISON WITH PREVIOUS WOR
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width speed (metres) ^(cm/s) 11 Fig
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U (33) = 1.16ms-' Depth = 2.65 m Fi
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APPENDIX 9 : DERIVATION OF FORCES O
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APPENDIX 10 : MODEL CODE FOR CALCUL
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APPENDIX 11: MODEL CODE FOR GROWING
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105 if (scancode .eq. 57) stop GOTO
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