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Figure 2. Acarlar & Smith (1987). a-b) Side view comparison between hairpin vortex and turbulent boundary layer patterns visualised by hydrogen bubbles, a) Hairpin vortex x/R=20 b) turbulent boundary layer at Re=2200. c-d) Top view comparison.
APPENDIX 2: FAST9003.HR(RW)/NHT - PROJECT PROPOSAL FLUID-PARTICLE TRANSPORT DYNAMICS OF SANDWAVES A three-year PhD project supervised by: Dr NH Thomas, FAST Team, Birmingham University and Dr RJS Whitehouse, HR Wallingford CONTEXT The Maritime Engineering Department of Hydraulics Research (MEHR below) undertakes a wide range of basic and applied work on practical problems of bed erosion and deposition in estuaries and surfzones. Their internationally recognised expertise resides mainly in field measurements and large-scale laboratory modelling both for fundamental research and with reference to site-specific problems. In addition, they undertake numerical modelling in support of such work, using large computational codes to represent the shear-turbulent flows due to waves, currents and bedforms. The Fluid and Surface Transport Team (FAST below) undertakes fundamental and applicable research associated with industrial and environmental problems. Currently eight full-time research projects are under way on topics such as two-phase and three-phase transport dynamics of bubbly flows and bubble-driven dispersion of particles and of droplet flows. The collaborative project described below will provide an opportunity for MEHR to benefit from the fundamental generic methodologies in which the FAST team specialise and for FAST to expand the current A2-1
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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
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stepping the calculation in VT . Do
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averaged exclusion of the coherent
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C from figure 11 (ie 2.2) then we h
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PflRTICLE DENSITY=1000.000 Kg/n3 LI
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Chapter 5 ft) J k I Figure 4. Varyi
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Chapter 5 Relative Fall Time va Sta
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Chapter 5 Figure 7a. Trajectories o
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Chapter 5 Velocity X —Inertia X L
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Chapter 5 Velocity X —Velocity Y
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Chapter 5 Velocity Y Inertia Y Lift
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Chapter 5 DENSITY PARTICLE=2850.000
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Chapter 5 Rad = 0.006 Rad=0.003 Rad
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Chapter 5 H3 Y=0 Oy=i m Y=2 D-y=3
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CHAPTER 6: NUMERICAL SIMULATION OF
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next. If we now adopt the classical
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st = (4) Where p p was the particle
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3 RESULTS 3.1 Specified 6 and V Fig
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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
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: Horseshoe vortex Vortex filament Ho
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
Page 289 and 290: They then defined a hydrodynamic co
Page 291 and 292: with respect to the rest of the vor
Page 293 and 294: The vorticity equation can be split
Page 295 and 296: around the crest and the motion of
Page 297 and 298: micrometers, with mean of 80 microm
Page 299 and 300: i——COMPARISON WITH PREVIOUS WOR
Page 301 and 302: width speed (metres) ^(cm/s) 11 Fig
Page 303 and 304: U (33) = 1.16ms-' Depth = 2.65 m Fi
Page 305 and 306: APPENDIX 9 : DERIVATION OF FORCES O
Page 307 and 308: APPENDIX 10 : MODEL CODE FOR CALCUL
Page 309 and 310: APPENDIX 11: MODEL CODE FOR GROWING
Page 311: 105 if (scancode .eq. 57) stop GOTO
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