FLOW AROUND A CYLINDER - istiarto

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– 2.20 – throughout the flow depth. The velocity was measured at a frequency of 20.8 [Hz] during 150 [s]; this produces a total number of instantaneous velocities of 3140 at each data point. The measurement data are presented in the form of vertical distributions of the time-averaged velocity, of the turbulence intensity, and of the Reynolds stress. The Cartesian coordinate system is used. 2.4.2 Vertical distribution of the (time-averaged) velocity Fig. 2.8 shows the vertical distributions of the time-averaged velocities measured at the six stations. For writing simplicity the term ―velocity‖, otherwise explicitly stated, will be used to describe the time-averaged velocity. In uniform flows, the vertical distribution of the longitudinal velocity, u(z), can be described by the universal law-of-the-wall, for the so-called inner region, z h � 0.2 , and by the Coles law-of-the-wake for the entire flow depth, except within the viscous layer, 0.1 � z h � 1. Assuming the flow is hydraulically rough, the law-of-the-wall reads (Graf and Altinakar, 1998, p. 56): u�z� � u� 1 � �� z �� ln �� BR �� k s (2.20) where u � is the friction velocity, ks is the equivalent standard roughness of the bed ( k s � d 50 � 2.1[mm]), BR is a constant of integration, and � is the Karman constant (� = 0.4). The origin of the vertical distance, z = 0, is defined at a level 0.2ks below the peaks of the bed roughness. By using the best fit method of Eq. 2.20 to the logarithmic plot of the measured longitudinal velocity data for z ≤ 0.2h (see Fig. 2.8a), the friction velocity, u � , and the constant of integration, B R , can be obtained and are presented in Table 2.3 The average values from the six measurements are u � � 2.7 [cm s] and B R � 8.75 [�]. The average value of BR falls in the range of values reported in the literature, i.e. 8.5 ± 15% (see Graf and Altinakar, 1998, p. 56). Using the friction velocity, u � � 2.7 [cm s], and taking the viscosity of water, � �10 �6 [m 2 s], the Reynolds number computed based on the bed standard-roughness is found as Rek s � u� ks � � 57. This value, being less than 70, suggests that the bed is not completely rough. The vertical distribution of the velocity can be expressed by the Coles law-of-the-wake which is valid for the inner and outer regions (except within the viscous layer). For the hydraulically rough uniform flow, the Coles equation can be written in the following form (see Song et al., 1994): u�z� � u� 1 � �� z �� ln �� BR � �� 2� � sin2 ��z �� 2h�� k s (2.21)
– 2.21 – Fig. 2.8 Distributions of the longitudinal velocity, u(z), of the approach flow: (a) in the inner region according to the law-of-the-wall, and (b) in the inner- and outerregions according to the Coles law-of-the-wake.
Page 1 and 2: FLOW AROUND A CYLINDER IN A SCOURED
Page 3 and 4: - iii - Flow around a Cylinder in a
Page 5 and 6: - v - Écoulement à Surface Libre
Page 7 and 8: - vii - Acknowledgements I wish to
Page 9 and 10: - ix - Table of Contents Abstract i
Page 11 and 12: - xi - 4.4 Pressure-velocity coupli
Page 13 and 14: Chapter 1 - 1.i - 1 Introduction 1.
Page 15 and 16: 1 Introduction 1.1 Flow around a cy
Page 17 and 18: - 1.3 - pitot tubes. Ahmed and Raja
Page 19 and 20: Chapter 2 - 2.i - 2 Flow Measuremen
Page 21 and 22: 2 Flow Measurements Abstract - 2.1
Page 23 and 24: 2.1 Measurement design - 2.3 - The
Page 25 and 26: - 2.5 - The water circuit is a clos
Page 27 and 28: - 2.7 - Consider a target ―i‖ m
Page 29 and 30: - 2.9 - Obtaining the velocity comp
Page 31 and 32: - 2.11 - Fig. 2.4 Cartesian and cyl
Page 33 and 34: - 2.13 - transducer were used, a fo
Page 35 and 36: - 2.15 - typically needed for this
Page 37 and 38: - 2.17 - 2.3.3 Comparison to other
Page 39: - 2.19 - Fig. 2.7 Scour hole geomet
Page 43 and 44: u ��u �� u� � Du exp�
Page 45 and 46: - 2.25 - �o , and accordingly the
Page 47 and 48: - 2.27 - Measurements in zone A. Th
Page 49 and 50: - 2.29 - and 0.3 u �� u ��
Page 51 and 52: - 2.31 - Fig. 2.12b Cont’d.
Page 53 and 54: - 2.33 - Fig. 2.12d Cont’d.
Page 55 and 56: 2.5.4 Measurements in the plane �
Page 61 and 62: - 2.41 - the solid boundary of the
Page 67 and 68: - 2.47 - Turbulence intensities in
Page 69 and 70: - 2.49 - Fig. 2.15a Vertical distri
Page 71 and 72: - 2.51 - Fig. 2.15c Cont’d.
Page 73 and 74: - 2.53 - Reynolds stresses in the p
Page 75 and 76: - 2.55 - Fig. 2.16c Cont’d.
Page 77 and 78: 2.6 Summary and conclusions - 2.57
Page 79 and 80: - 2.59 - Rolland, T. (1994). Develo
Page 81 and 82: Chapter 3 - 3.i - 3 Elaboration of
Page 83 and 84: - 3.1 - 3 Elaboration of the measur
Page 85 and 86: 3.1 Introduction - 3.3 - Presented
Page 87 and 88: - 3.5 - Fig. 3.1 Measured velocity
Page 89 and 90: 3.2.2 Flow pattern around the cylin
Page 91 and 92:
- 3.9 - Fig. 3.2 Cont’d.
Page 93 and 94:
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: -
Page 109 and 110:
- 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
Page 131 and 132:
- 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 �
Page 147 and 148:
- 4.23 - b T � V P �t � n P
Page 149 and 150:
- 4.25 - �� u ��1 � c i
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- 4.27 - Next, we need to define th
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4.5 Boundary conditions 4.5.1 Bound
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- 4.31 - The above relation holds a
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- 4.33 - � extrapolate all variab
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G � � t 2 �V t - 4.35 - 2 �
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with � �� nt,b � ��
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- 4.39 - boundary node B are then a
Page 165 and 166:
- 4.41 - Wall function for the �
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k and � equations - 4.43 - � se
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�� z-momentum: - 4.45 - ��1
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- 4.47 - � reconstruct the mesh,
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- 4.49 - Fig. 4.13 The structure of
Page 175 and 176:
- 4.51 - ��
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4.7 Summary - 4.53 - Development of
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- 4.55 - B, �B [-] constant and w
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- 4.57 - �, � 1 , � p [-] und
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Chapter 5 - 5.i - 5 Numerical Simul
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5 Numerical Simulation Abstract - 5
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5.2 Experimental data - 5.3 - 5.2.1
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- 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
Page 197 and 198:
- 5.13 - within a greater number of
Page 199 and 200:
- 5.15 - Fig. 5.6 Computational his
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- 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
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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
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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
Page 231 and 232:
- 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
Page 241 and 242:
- 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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FLOW AROUND A CYLINDER IN A SCOURED
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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 IN A SCOURED
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