FLOW AROUND A CYLINDER - istiarto

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– 4.56 – g x ,g y ,g z [m/s 2 ] Cartesian components of the gravitational acceleration. k [m 2 /s 2 ] turbulent kinetic energy. ks [m] wall roughness height. � ks [–] Reynolds number based on the friction velocity and wall roughness. n [m] normal direction. p, p � , p c [Pa] pressure, estimated pressure, and pressure correction. q [m3 /s] discharge. q � [m3 /s] estimated discharge obtained from (u � , v � ,w � ) . qc ,qRC ,qno [m3 /s] discharge corrections due to the velocity-correction, cell-face interpolation, and non-orthogonal terms. t, �t [s] pseudo-time and pseudo-time step. u,v,w [m/s] Cartesian velocity components. u � , v � ,w � [m/s] Cartesian velocity components obtained with estimated pressures. u ��, v ��, w �� [m/s] fluctuating parts of Cartesian velocity components. u � , v � ,w � [m/s] Cartesian friction-velocity components. � u n [m/s] velocity obtained with estimated pressure. c u n [m/s] pressure corrections. impl RC un ,un , [m/s] no un pressure correction components: implicit, Rhie-and-Chow, non-orthogonal. x, y, z [m] Cartesian coordinate components. Greek characters � [m2/s] diffusion coefficient. � [–] linear interpolation factor. �h [m] surface displacement. �h ( p) [m] surface displacement due to the pressure. �h ( z) [m] surface displacement limitation according to the cell size. �n [m] normal distance. � � n [–] dimensionless normal-distance. � [m2 /s3 ] dissipation of the turbulent kinetic energy. � flow variable, the dimensional unit depends on the variable of which it represents. � matrix of the flow variables. � [–] Karman constant. �� convergence criterion: allowable maximum residue of the solution: [m4 /s2 ] of the momentum equation, [m4 /s2 ] of the k-equation, [m4 /s2 ] of the �-equation, [m3 /s] of the pressure-correction equation. �2 [–] convergence criterion: allowable relative maximum-residue of the solution. �, �t [m 2 /s] kinematic viscosity and turbulent eddy viscosity. � t,wall [m 2 /s] wall eddy-viscosity. � [kg/m 3 ] density of water.
– 4.57 – �, � 1 , � p [–] under-relaxation factors. �k, �� [–] constants of the k-� model.� � [N/m 2 ] Reynolds stress. �� [m] local coordinate directions. Other characters � � total residue: [m 4 /s 2 ] of the momentum equation, [m 4 /s 2 ] of the k-equation, [m 4 /s 2 ] of the �-equation, [m 3 /s] of the pressure-correction equation. �, � [1/s] divergent and gradient nabla operators. Superscripts c corrected value. �� , ��1 m, m+1 iteration level indices. iteration level indices. n, n+1 time level indices. * Subscripts estimated value. P cell center. i, j, k Cartesian component indices. cf = e,w,n,s,t,b cell faces: the east, west, north, south, top, and bottom. �� dependent variable index. n, t normal and tangential direction component indices. nb = E,W,N,S,T,B neighboring cells: the East, West, North, South, Top, and Bottom.
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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 �
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 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: - 4.55 - B, �B [-] constant and w
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
Page 219 and 220: - 5.35 - Fig. 5.18 Computed and mea
Page 221 and 222: - 5.37 - than the measured one. The
Page 223 and 224: - 5.39 - Production and dissipation
Page 225 and 226: - 5.41 - Production of turbulent ki
Page 227 and 228: - 5.43 - If the above approach were
Page 229 and 230: - 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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