FLOW AROUND A CYLINDER - istiarto

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� � b � c ��G �� 1 V �� k �� P P �� b S �c �� 2 V �� k �� P �� P �� S b P – 4.20 – the last term of which will join the coefficient a P . First derivative source terms ��1 �P (4.47) The source term containing first derivatives, b 1D , is found in the pressure gradient of the momentum equation and in the velocity gradient of the energy production for the k-� equations. Following the method described in Sect. 4.3.3, the source terms containing first derivatives in the x-, y-, and z-directions are evaluated as follows (the terms within brackets are generally predominant): b 1D � � � x �� b 1D � � � y �� b 1D � � � z �� dV � �(� V ��x �� e x ) dV � � V �� e x � dS S � � � cf �� Sx cf�ewnstb � � � � � � �� e Se,x � �w Sw,x�� n Sw,x � �s Ss,x � �t St,x � �b Sb,x � �� dV � �(� V ��y�� e y) dV � � V �� e y � dS S � � n � � � cf �� Sy cf�ewnstb � � � � � � � Sn,y � �s Ss,y�� t St,y � �b Sb,y � �e Se,y � �w Sw,y � �� dV � �(� V ��z �� e z ) dV � � V �� e z � dS S � � cf �� Sz cf�ewnstb � � � � � � �� t St,z � �b Sb,z�� e Se,z � �w Sw,z � �n Sw,z � �s Ss,z Second derivative source terms � (4.48a) (4.48b) (4.48c) The source term containing second derivatives, b 2D , is found in the momentum equation. These are due to the non-orthogonal terms of the stresses (see Eqs. 4.6 to 4.8) and the explicit parts of the diffusion terms (see Eq. 4.43). An example is given below for the evaluation of the source terms containing second derivatives in the u-momentum equation.
2D � � � x �� b 2D � � � y �� b 2D � � � z �� V �� V t � �x � �� u�� t dV �x �� t cf �� u�� t e �x �� x � dS S � ��t �e �� t�s �� e � �� u�� u�� Se,x �� t� �� w �x ��x �� s � – 4.21 – � �u�� e �x �� x �� dV � �u�� S �x �� x�� cf � � n Sw, x � �t �� w ��u�� u�� u�� Ss,x �� t� S �� t t,x � ��t � �x �� b �x ��x � �y � �� v�� t �x �� t � �� dV � � � V �� V t � �� t cf �� v�� t e �x �� y � dS S � ��t �n ��t�b �� n � �� v�� v�� Sn,y � �� t� �� s �x ��x �� b � ��v�� v�� Sb,y � �� t� �� e �x ��x � �z � �� w�� t �x �� v�� e �x �� y�� dV � �v�� S �x�� y�� cf � � t Ss, y � �t �� s � � � s Se, y � �t �� e �� dV � � � V �� V t � �� t cf �� w�� t e �x �� z � dS S � ��t �t �� t�w �� t � �� w�� w�� St,z � ��t � �� b �x ��x � ��w �� x � � � n Sw, z � �t �� w ��u�� Sn,x � ��x �� n � � Sb,x �� b ��v�� St,y � ��x �� t � ��v �� x � �w�� e �x �� z �� dV � �w�� S �x �� z �� cf � � e Sb, z � �t �� b �� n � � Sw,y �� w ��w�� Se,z � ��x �� e � ��w �� w �� Sn,z � ��t � �� s �x ��x � Ss,z �� s (4.49a) (4.49b) (4.49c) The last four terms on the right-hand side are due to the grid non-orthogonality; they vanish for orthogonal cells. The cell face values of the velocity gradients are obtained by linear interpolation (see Sect. 4.3.3 and Eq. 4.21). 4.3.9 Assembly of the coefficients After evaluating all terms of the convection, diffusion, and sources over the entire computational domain and rearranging the coefficients, the discretized transport equation
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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.
Page 93 and 94: Flow in the plane � = 45° and 90
Page 95 and 96: - 3.13 - Fig. 3.4 Contours of the m
Page 97 and 98: 3.2.4 Vertical velocity (downward f
Page 99 and 100: - 3.17 - flow may undergo a rotatin
Page 101 and 102: - 3.19 - Fig. 3.7 Cont’d.
Page 103 and 104: - 3.21 - A similar observation, in
Page 105 and 106: - 3.23 - Fig. 3.9 Measured turbulen
Page 107 and 108: The following is to be observed: -
Page 109 and 110: - 3.27 - Fig. 3.10 Cont’d.
Page 111 and 112: - 3.29 - 3.4 Bed shear-stresses alo
Page 113 and 114: x [cm] - 3.31 - Table 3.1 Estimated
Page 115 and 116: - 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: 4.3.8 Source terms - 4.19 - The sou
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 and 168: k and � equations - 4.43 - � se
Page 169 and 170: �� z-momentum: - 4.45 - ��1
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
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- 5.11 - Fig. 5.4 Model test result
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- 5.13 - within a greater number of
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- 5.15 - Fig. 5.6 Computational his
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- 5.17 - 5.5 Simulation of flow aro
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- 5.19 - Fig. 5.9 Definition sketch
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- 5.21 - Fig. 5.10 Computed (lines)
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- 5.23 - Fig. 5.11 Computed and mea
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- 5.25 - 1.2U ∞ of the measuremen
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Water-surface profile - 5.27 - The
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- 5.29 - using a Joukowski transfor
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- 5.31 - 5.6.3 Results of the simul
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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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