FLOW AROUND A CYLINDER - istiarto

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– 4.28 – The pressure gradients encountered in the source terms are computed according to the following relations: �� p � �� n �� e e � �p� �� x �� e �p c �� n �� pc �� x �� p c �� e e � �pc �� x �� e S e,x S e S e,x S e �xPE LPE �� p� �� y �� e �� pc �� y �� e S e,y S e S e,y S e �� pc �� y �� e �� p� �� z �� yPE LPE �� e �� pc �� z �� e S e,z S e S e,z S e �� pc �� z �� e �� zPE LPE �� (4.69) in which the interpolation of the pressure gradients along the Cartesian coordinates is done using Eq. 4.21. 4.4.2 Pressure correction procedure The source term, b p , has pressure correction terms contained in the discharge due to non- no orthogonality of the cells, qe . These terms are evaluated explicitly by a double-step pressure correction procedure as follows: � Solve Eq. 4.68 for pc no by neglecting the non-orthogonal terms, qcf � 0 , and correct the velocities and pressure according to Eqs. 4.55a,b. � Solve again Eq.4.4 with the non-orthogonal terms now available from the first step and correct once again the velocities and pressure. 4.4.3 Under-relaxation factor and time step To avoid instability of the computation, it is a common practice to put an underrelaxation factor to the pressure correction, 0 � � p �1, in updating the pressure: p � p � � � p p c (4.70) As mentioned in Sect. 4.2, the time step plays also as an under-relaxation factor for steady flow cases. This type of application, that is using the transient equations to solve steady flows, is generally known as a pseudo-transient computation. In order to achieve the effects of under-relaxed iterative steady-state computations from a given initial field by means of a pseudo-transient computation starting from the same initial field, the timestep size is taken such that (Fletcher, 1997, p. 365): � p 1 � 1 � E�t with E�t � ˜ a P �t (4.71) V P
4.5 Boundary conditions 4.5.1 Boundary placement – 4.29 – The boundary conditions that can be considered in the model are inflow, outflow, wall, (water) surface, and symmetry boundaries. The spatial discretisation of the computational domain is done in such a way that the boundaries coincide with the cell face (see Fig. 4.5). The cell neighboring the boundary has special characteristics that modify the definition of cell set forth in Sect. 4.3.1; it has more than one node and less than six neighbors. Three types of cell and node are introduced (see Fig. 4.5): � Interior cell (the white cell) is a computational cell where the dependent variable, �, is unknown and is to be computed at the interior node (the solid circle); an interior cell has only one node, the interior node. � Boundary cell (the gray cell) is a boundary neighboring cell whose one or more of its faces coincide with a boundary. A boundary cell has one interior node (the solid circle) at the center of the cell and one boundary node (the gray circle) at the center of each face that coincides with the boundary. The known boundary values of all variables � are to be defined at the boundary node, either given or extrapolated from the interior nodes.� � Dummy cell (hatched cell) and dummy node (white node) are used to denote the domain which is excluded from the computation, for example blocked-regions, cylinders, and corners. These dummy cells and nodes are necessary in order to maintain a continuous ordering of the cell and node indexes. Except of some special cases for the k and � equations, the effect of the boundaries to the computation for the interior node of a boundary cell is additive. In the discretized equation of u, v, w, and p c , the contribution of each boundary node is added to the source term, b, of the interior node of the boundary cell, and the coefficient related to this boundary node is eventually set to zero. The k and � for the interior nodes of boundary cells having wall or free-surface boundaries, however, are defined by a given expression. In the following sections are presented the method of computation for the boundary cells.
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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
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 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: - 4.27 - Next, we need to define th
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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Page 199 and 200: - 5.15 - Fig. 5.6 Computational his
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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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