FLOW AROUND A CYLINDER - istiarto

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– 5.48 – � Distribute the surface to get the coordinate of the cell vertices, for example by using a simple relation (see Fig. 5.24c): � t,ne � 1 4 � t,e � � t,n � � t,1 � � t,2 � �. The cost of the proposed approach, compared to the present one, is the additional equation to be solved at each time step. The iterative matrix solver, similar to the existing matrix solver of the present model but written for a 2D case, can be used to solve Eq. 5.6. References Graf, W. H., and Yulistiyanto, B. (1998). “Experiments on flow around a cylinder; the velocity and vorticity fields.” IAHR, J. Hydr. Res., 36(4), 637-653. Hurther, D., Lemmin, U., and Arditi, M. (1996). “Using an annular curved array transducer for bistatic ADVP application.” Rapport Annuel, Laboratoire de recherches hydrauliques, EPFL, 1996, B.201.1-B.201.19. Lhermitte, R., and Lemmin, U. (1994). “Open-channel flow and turbulence measurement by high-resolution Doppler sonar.” J. Atm. Ocean. Tech., 11, 1295-1308. Versteeg, H. K., and Malalasekera, W. (1995). An Introduction to Computational Fluid Dynamics: The Finite Volume Method., Longman Group, Essex, England. Yulistiyanto, B. (1997). Flow around a cylinder installed in a fixed-bed open channel., Doctoral Dissertation, No. 1631, EPFL, Lausanne, Switzerland. Notations anb [m2 /s] variable coefficients of the surface function equation. b [m3 /s] source term of the surface function equation. p anb [m3 /s/Pa] variable coefficients of the pressure-correction equation. b p [m3 /s] source term of the pressure-correction equation. c� [–] k-� model constant. Dp [m] diameter of cylinder. d50 [m] mean diameter of sediment. G [m2 /s3 ] production of turbulent kinetic energy. g [m/s2 ] gravitational acceleration. h, h∞ [m] flow depth, uniform-flow depth. k [m2 /s2 ] turbulent kinetic energy. ks [m] equivalent roughness. n [–] normal direction. p, pc [Pa] pressure, pressure correction. Q [m3 /s] discharge. q [m2 /s] discharge per unit width. Re [–] Reynolds number. r [m] radial direction.
– 5.49 – S [m 2 ] surface area. So, Sw [–] bed and surface slopes. t [–] tangential direction. U, U ∞ [m/s] sectional average velocity, average velocity of uniform flow. u, v, w [m/s] Cartesian velocity components. ur, u� [m/s] cylindrical (radial and tangential) velocity components. u � [m/s] friction velocity. V, V � [m/s] velocity, velocity projection on a plane �. x, y, z [m] Cartesian coordinate directions. � t [m] surface function. � [°] angular direction. � e [–] interpolation factor. � [m 2 /s 3 ] kinetic energy dissipation. � [–] Karman constant. �, �t [m 2 /s] kinematic viscosity, turbulent eddy viscosity. � [1/s] vorticity. � [°] angular direction. � [kg/m 3 ] density of water. ��o [N/m 2 ] shear stress, bed shear-stress.
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FLOW AROUND A CYLINDER IN A SCOURED
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- iii - Flow around a Cylinder in a
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- v - Écoulement à Surface Libre
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- vii - Acknowledgements I wish to
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- ix - Table of Contents Abstract i
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- xi - 4.4 Pressure-velocity coupli
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Chapter 1 - 1.i - 1 Introduction 1.
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1 Introduction 1.1 Flow around a cy
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- 1.3 - pitot tubes. Ahmed and Raja
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Chapter 2 - 2.i - 2 Flow Measuremen
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2 Flow Measurements Abstract - 2.1
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2.1 Measurement design - 2.3 - The
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- 2.5 - The water circuit is a clos
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- 2.7 - Consider a target ―i‖ m
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- 2.9 - Obtaining the velocity comp
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- 2.11 - Fig. 2.4 Cartesian and cyl
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- 2.13 - transducer were used, a fo
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- 2.15 - typically needed for this
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- 2.17 - 2.3.3 Comparison to other
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- 2.19 - Fig. 2.7 Scour hole geomet
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- 2.21 - Fig. 2.8 Distributions of
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u ��u �� u� � Du exp�
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- 2.25 - �o , and accordingly the
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- 2.27 - Measurements in zone A. Th
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- 2.29 - and 0.3 u �� u ��
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- 2.31 - Fig. 2.12b Cont’d.
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- 2.33 - Fig. 2.12d Cont’d.
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2.5.4 Measurements in the plane �
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- 2.37 - Fig. 2.13b Cont’d.
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- 2.39 - Fig. 2.13d Cont’d.
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- 2.41 - the solid boundary of the
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- 2.43 - Fig. 2.14b Cont’d.
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- 2.45 - Fig. 2.14d Cont’d.
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- 2.47 - Turbulence intensities in
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- 2.49 - Fig. 2.15a Vertical distri
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- 2.51 - Fig. 2.15c Cont’d.
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- 2.53 - Reynolds stresses in the p
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- 2.55 - Fig. 2.16c Cont’d.
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2.6 Summary and conclusions - 2.57
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- 2.59 - Rolland, T. (1994). Develo
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Chapter 3 - 3.i - 3 Elaboration of
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- 3.1 - 3 Elaboration of the measur
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3.1 Introduction - 3.3 - Presented
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- 3.5 - Fig. 3.1 Measured velocity
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3.2.2 Flow pattern around the cylin
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- 3.9 - Fig. 3.2 Cont’d.
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Flow in the plane � = 45° and 90
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- 3.13 - Fig. 3.4 Contours of the m
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3.2.4 Vertical velocity (downward f
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- 3.17 - flow may undergo a rotatin
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- 3.19 - Fig. 3.7 Cont’d.
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- 3.21 - A similar observation, in
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- 3.23 - Fig. 3.9 Measured turbulen
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The following is to be observed: -
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- 3.27 - Fig. 3.10 Cont’d.
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- 3.29 - 3.4 Bed shear-stresses alo
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x [cm] - 3.31 - Table 3.1 Estimated
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- 3.33 - Fig. 3.12 Estimated bed sh
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- 3.35 - (see Fig. 3.10 and Fig. 3.
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- 3.37 - Fig. 3.14 Axonometric pres
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- 3.39 - U, U∞ [m/s] sectional av
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Chapter 4 - 4.i - 4 Numerical Model
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- 4.1 - 4 Numerical Model Developme
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�u �t �v �t �w �t �
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- 4.5 - The volume integrals of the
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- 4.7 - Fig. 4.1 Overall iterative
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- 4.9 - increase the computer stora
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- 4.11 - �� 1 ��
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- 4.13 - convective transport throu
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- 4.15 - n,��1 during a time st
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� for 0 � Pe e � q eL PE �
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4.3.8 Source terms - 4.19 - The sou
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2D � � � x �� b 2D �
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- 4.23 - b T � V P �t � n P
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- 4.25 - �� u ��1 � c i
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- 4.27 - Next, we need to define th
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4.5 Boundary conditions 4.5.1 Bound
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- 4.31 - The above relation holds a
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- 4.33 - � extrapolate all variab
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G � � t 2 �V t - 4.35 - 2 �
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with � �� nt,b � ��
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- 4.39 - boundary node B are then a
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- 4.41 - Wall function for the �
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k and � equations - 4.43 - � se
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�� z-momentum: - 4.45 - ��1
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- 4.47 - � reconstruct the mesh,
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- 4.49 - Fig. 4.13 The structure of
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- 4.51 - ��
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4.7 Summary - 4.53 - Development of
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- 4.55 - B, �B [-] constant and w
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Page 185 and 186: 5 Numerical Simulation Abstract - 5
Page 187 and 188: 5.2 Experimental data - 5.3 - 5.2.1
Page 189 and 190: - 5.5 - computational nodes. The ot
Page 191 and 192: - 5.7 - (i) Yulistiyanto data (ii)
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Page 203 and 204: - 5.19 - Fig. 5.9 Definition sketch
Page 205 and 206: - 5.21 - Fig. 5.10 Computed (lines)
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Page 211 and 212: Water-surface profile - 5.27 - The
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Page 217 and 218: Velocity fields around the cylinder
Page 219 and 220: - 5.35 - Fig. 5.18 Computed and mea
Page 221 and 222: - 5.37 - than the measured one. The
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Page 237 and 238: - 6.1 - 6 Summary and Conclusions 6
Page 239 and 240: - 6.3 - The spatial distributions o
Page 241 and 242: - 6.5 - � Laboratory measurements
Page 243 and 244: - 6.7 - Fig. 6.1 Measured and compu
Page 245 and 246: IDENTITE - 7.1 - Curriculum Vitæ N
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Page 249 and 250: - iii - Appendices Appendix A: Expe
Page 251 and 252: A Experimental Data - A.1 - The exp
Page 253 and 254: B Numerical Model B.1 Program struc
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Page 257 and 258: B.2 Input data file - B.5 - The inp
Page 259 and 260: - B.7 - #31 imon1, jmon1, kmon1 thr
Page 261 and 262: BLO for blocked cells, INL for inle
Page 263: FLOW AROUND A CYLINDER IN A SCOURED
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