FLOW AROUND A CYLINDER - istiarto

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Momentum equations – 4.44 – Fig. 4.10 Surface boundary. � set all coefficient related to the boundary node T in Eq. 4.52 to zero: C D C aT � aT ��a P� � a T D � � � b T D � � � b T 2D � � � 0 T �� compute �� e t using Eqs. 4.87 and 4.88 � compute the forces due to the normal stress as source terms: �� x-momentum: ��1 �b � bP uP � � T F � �� n,x �� t �St � �� t�ue n,x � 2v en,y � 2we n,z�e n,x �P �� n � �� n,P �� b y-momentum: � � T � � �� P � � t e n,x e n,x �bP�T ��1 �b � bP uP � � T F � �� n,y �� t � �� t�2 ue n,x � v en,y � 2we n,z�e n,y �St �P � �t en,y en,y � S t �n � �� n,P �� b � � T � � �� P �b P�T � S t ��1 uP ��1 vP (4.95a) (4.95b)
�� z-momentum: – 4.45 – ��1 �b � bP uP � � T F � �� n,z �� t �St � �� t�2 ue n,x � 2 ve n,y � we n,z�e n,z �P k equation� � n � �� n,P �� b � � T � � �� P � � t e n,z e n,z �b P�T � S t � set all coefficient related to the boundary node T in Eq. 4.52 to zero: C D C aT � aT � a P � � � a T D � � � b T D � � � b T 2D � � � 0 T � set the surface kinetic energy at T to zero: k T = 0 � equation� � set all coefficients related to all neighboring cells to zero: a E � a W � a N � a S � a T � a B � 0 � set the coefficient at cell P to unity: a P = 1 ��1 wP � set the source terms by (see Eq. 4.84 and also Krishnappan and Lau, 1986): � � 3 4 m�1 3 2 kP c m�1 � �P � cf � �n,P (4.96) where cf is an empirical constant, which is set to 0.164 Pressure and velocity corrections p � set the coefficient at T in Eq. 4.68 to zero: aT � 0 c c � extrapolate the pressure correction at P to T: pT � pP � correct the pressure and the velocity � extrapolate the velocity at P to T and correct this velocity: VT � Vt,P Surface correction � extrapolate the pressure at P to T by assuming a hydrostatic distribution: �� pT � pP � �gz �zPT (see Fig. 4.11a), with g z the z-component of �� g (generally negative) (4.95c) � compute the surface correction based on the pressure-defect relative to the reference pressure: �h ( p) � �pT � pref� �g z � �
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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
Page 117 and 118: - 3.35 - (see Fig. 3.10 and Fig. 3.
Page 119 and 120: - 3.37 - Fig. 3.14 Axonometric pres
Page 121 and 122: - 3.39 - U, U∞ [m/s] sectional av
Page 123 and 124: Chapter 4 - 4.i - 4 Numerical Model
Page 125 and 126: - 4.1 - 4 Numerical Model Developme
Page 127 and 128: �u �t �v �t �w �t �
Page 129 and 130: - 4.5 - The volume integrals of the
Page 131 and 132: - 4.7 - Fig. 4.1 Overall iterative
Page 133 and 134: - 4.9 - increase the computer stora
Page 135 and 136: - 4.11 - �� 1 ��
Page 137 and 138: - 4.13 - convective transport throu
Page 139 and 140: - 4.15 - n,��1 during a time st
Page 141 and 142: � for 0 � Pe e � q eL PE �
Page 143 and 144: 4.3.8 Source terms - 4.19 - The sou
Page 145 and 146: 2D � � � x �� b 2D �
Page 147 and 148: - 4.23 - b T � V P �t � n P
Page 149 and 150: - 4.25 - �� u ��1 � c i
Page 151 and 152: - 4.27 - Next, we need to define th
Page 153 and 154: 4.5 Boundary conditions 4.5.1 Bound
Page 155 and 156: - 4.31 - The above relation holds a
Page 157 and 158: - 4.33 - � extrapolate all variab
Page 159 and 160: G � � t 2 �V t - 4.35 - 2 �
Page 161 and 162: with � �� nt,b � ��
Page 163 and 164: - 4.39 - boundary node B are then a
Page 165 and 166: - 4.41 - Wall function for the �
Page 167: k and � equations - 4.43 - � se
Page 171 and 172: - 4.47 - � reconstruct the mesh,
Page 173 and 174: - 4.49 - Fig. 4.13 The structure of
Page 175 and 176: - 4.51 - ��
Page 177 and 178: 4.7 Summary - 4.53 - Development of
Page 179 and 180: - 4.55 - B, �B [-] constant and w
Page 181 and 182: - 4.57 - �, � 1 , � p [-] und
Page 183 and 184: Chapter 5 - 5.i - 5 Numerical Simul
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)
Page 193 and 194: - 5.9 - ( p � � 1 [mm]), but th
Page 195 and 196: - 5.11 - Fig. 5.4 Model test result
Page 197 and 198: - 5.13 - within a greater number of
Page 199 and 200: - 5.15 - Fig. 5.6 Computational his
Page 201 and 202: - 5.17 - 5.5 Simulation of flow aro
Page 203 and 204: - 5.19 - Fig. 5.9 Definition sketch
Page 205 and 206: - 5.21 - Fig. 5.10 Computed (lines)
Page 207 and 208: - 5.23 - Fig. 5.11 Computed and mea
Page 209 and 210: - 5.25 - 1.2U ∞ of the measuremen
Page 211 and 212: Water-surface profile - 5.27 - The
Page 213 and 214: - 5.29 - using a Joukowski transfor
Page 215 and 216: - 5.31 - 5.6.3 Results of the simul
Page 217 and 218: Velocity fields around the cylinder
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- 5.35 - Fig. 5.18 Computed and mea
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- 5.37 - than the measured one. The
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- 5.39 - Production and dissipation
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- 5.41 - Production of turbulent ki
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- 5.43 - If the above approach were
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- 5.45 - and surface profiles (see
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- 5.47 - Fig. 5.24 Surface boundary
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- 5.49 - S [m 2 ] surface area. So,
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Chapter 6 - 6.i - 6 Summary and Con
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- 6.1 - 6 Summary and Conclusions 6
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- 6.3 - The spatial distributions o
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- 6.5 - � Laboratory measurements
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- 6.7 - Fig. 6.1 Measured and compu
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IDENTITE - 7.1 - Curriculum Vitæ N
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- iii - Appendices Appendix A: Expe
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A Experimental Data - A.1 - The exp
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B Numerical Model B.1 Program struc
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- B.3 -
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B.2 Input data file - B.5 - The inp
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- B.7 - #31 imon1, jmon1, kmon1 thr
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BLO for blocked cells, INL for inle
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FLOW AROUND A CYLINDER - istiarto

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