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Chapter 5 Y=0 Y=1 Y=4 Y=7 0.003 T 0.002 - £ o.ooi - O I ' tj -0.001 -• 0) «* -0.002 > -0.003 g -0.004 -0.005 -L 0 10 20 30 40 50 60 70 80 90 100 X-coordinate (convection velocity x time) Figure 14. Time-averaged vertical velocity induced below the mid-plane of a moving Rankine vortex over 100 time steps. Q Y = 0 OY=l ffi Y=2 Y = 6 -O Y=9 0.085 T 0.055 3 4 5 6 7 3 9 10 X-coordinate (convection velocity x time) Figure 15. Time-averaged horizontal velocity induced below the mid-plane of a moving Rankine vortex over ten time steps.
Chapter 5 H3 Y=0 Oy=i m Y=2 D-y=3 •D Y=7 O-Y-8 -O Y=9 •«•¥•= 10 Y=6 1234567 X-coordinate (convection velocity x time) Figure 16. Time-averaged vertical velocity induced below the mid-plane of a moving Rankine vortex over 10 timesteps. o O O ft VI — 10 Step average 0 10 20 30 40 50 -6 - ——————— l —————— l —————— 1 —————— l ——————— l — -7 - -9 -- 100 Step average Moving core ^Core trajectory 60 70 80 ^^..WJO— *^» .^ 2-12- .§-13 - •O C -14 -- O *****t*(*x^.f^. X-coordinate (convection velocity x time) Figure 17. Time-averaged and time-dependent trajectories of a particle in a moving Rankine vortex. The trajectories in the time-averaged flows are inclined downwards whereas the time-dependent trajectory follows a near cycloid path.
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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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Page 161 and 162: Chapter 4 ENTRAINED FLOW Figure 1.
Page 163 and 164: Figure 3a-j. The plates show partic
Page 165 and 166: Chapter 4 Percentage occurrence •
Page 167 and 168: Chapter 4 Interval (s) 60 80 100 12
Page 169 and 170: Chapter 4 0.024m Conc=8% Figure 12.
Page 171 and 172: Chapter 4 Figure 16. A cloud of par
Page 173 and 174: 1 INTRODUCTION We use a Rankine vor
Page 175 and 176: effective particle fall speed in th
Page 177 and 178: particle velocity Vx=0. The initial
Page 179 and 180: the vortex axis. Vortex circulation
Page 181 and 182: dimensional fall times T^ for diffe
Page 183 and 184: horizontal component lift force (fi
Page 185 and 186: 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: Chapter 5 Rad = 0.006 Rad=0.003 Rad
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 and 238: CHAPTER 7: RECAPITULATION AND RECOM
Page 239 and 240: were shown to compare well with pre
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
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Spalding (1961). A single formula f
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USA. 1-12
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APPENDIX 1: BOUNDARY LAYER STUDIES
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(1967) used hydrogen bubble visuali
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The burst-sweep dynamics study of U
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Horseshoe vortex Vortex filament Ho
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APPENDIX 2: FAST9003.HR(RW)/NHT - P
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of the vorticity shed into the near
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transport dynamics of multiphase fl
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APPENDIX 3: FUNDAMENTAL NAVIER-STOK
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APPENDIX 4: CLOSURE METHODS 1 ZERO
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where cr k and CD are empirical con
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K = CDe^ 2 p 2 \U2 -U1 \=e 1e 2 c (
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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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