FLOW AROUND A CYLINDER - istiarto

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– 5.16 – Fig. 5.7 Computational history of some selected variables during the iterative computation of the model. Test C: developing flow with Q B� 0.125 [m 2 s], h ∞ = 18.3 [cm], L = 38 [m], a uniform velocity distribution is maintained at the inlet boundary, u(z) = Q/B/h, and the water surface is not necessarily updated at every time step.
– 5.17 – 5.5 Simulation of flow around a cylinder on a flat channel bed 5.5.1 Computational domain The computational domain covers a longitudinal section of 4 [m] with the cylinder at its center. The grid was generated in two steps. Firstly, the Joukowski conformal mapping was used to generate an orthogonal horizontal (xy plane) grid. Finer grids are concentrated around the cylinder. Secondly, the horizontal grid was repeated in the z direction according to a pre-determined interval to cover the entire flow depth. This is known as a “sigma stretching” method. The number of cells in the x, y and z directions is 99 � 49 � 22 (see Fig. 5.8). The cylinder is represented as a 31 �1� 22 -cell out-blocked region. There are thus 106,040 computational nodes, 16,834 boundary nodes, and 750 dummy nodes. The z distribution of the grid is identical to that of Test A (uniform flow simulation) to enable the use of the computed velocity and turbulence profiles of that test run as the inflow boundary conditions of this simulation. In presenting the results of the simulation and the comparison to the experimental data, cylindrical and Cartesian coordinate systems are frequently used together. The origin of both coordinates is defined at the center of the cylinder, at the original bed level (see Fig. 5.9). 5.5.2 Boundary and initial conditions The boundary conditions are as follows: � Upstream inflow: Q = 0.250 [m 3 /s] and prescribed distributions of u,v,w, k, � which are taken from the results of Test A. � Downstream outflow: h ∞ = 18.3 [cm]. � Left and right channel (glass) walls: wall boundary with k s = 0 [mm] (hydraulically smooth). � Channel (metal) bed and cylinder (PVC) boundaries: wall boundary with k s = 0.22 [mm] (u �k s � �6.6, hydraulically smooth solid boundaries). � Top boundary: water surface. The initial conditions over the computational domain are uniform flow depth corresponding to the known downstream depth, h∞ = 18.3 [cm], hydrostatic pressure, p � ��gz �zsurface � z� [Pa], velocity and k-� according to the known distributions at the inlet section. At early time steps, the water surface was kept constant until the flow field was more or less stable. The simulation was then restarted by letting the water surface move according to the surface boundary treatment. A similar method of surface updating as of Test C in the preceding test run was used. There are two different criteria for the pressure computation, namely the one for terminating the pressure computation in the �- c c iteration ( pmax � 10 [Pa], which is equivalent to pmax � ≤ 1 [mm]) and the other for c c updating the surface boundary ( pmax � 0.01 [Pa] or pmax � ≤ 0.001 [mm]).
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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
Page 149 and 150: - 4.25 - �� u ��1 � c i
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Page 153 and 154: 4.5 Boundary conditions 4.5.1 Bound
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Page 159 and 160: G � � t 2 �V t - 4.35 - 2 �
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Page 163 and 164: - 4.39 - boundary node B are then a
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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
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Page 177 and 178: 4.7 Summary - 4.53 - Development of
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Page 181 and 182: - 4.57 - �, � 1 , � p [-] und
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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
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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
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Page 233 and 234: - 5.49 - S [m 2 ] surface area. So,
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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
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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 IN A SCOURED
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