FLOW AROUND A CYLINDER - istiarto

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– 3.28 – Fig. 3.11 Contour of the measured turbulence kinetic energy around the cylinder. The data are normalized by the total kinetic energy, k �K � k�, where k � 1 2�u �� u �� v �� v �� w ��w �� and K � 1 2 u2 � v 2 � w 2 � �.
– 3.29 – 3.4 Bed shear-stresses along the plane of symmetry Determination of the bed shear-stress, � o , from the experimental data is a rather difficult task. While a direct measurement technique would be most desirable, here we must content ourselves with the estimate values based on available data from the velocity and shear-stress distributions (see Fig. 3.1 and Fig. 3.9). Three alternative methods were used: 1. Based on the velocities, u and w, measured closest to the bed, z ≈ 4 [mm], a velocity parallel to the bed —at a distance of � n — was calculated, V t ; the bed shear-stress was calculated as: ��Vt �� o,1 � � �t ��n �� Vt �� t ��n �� (3.5) where � t �1.3 �10 �5 [m 2 s 2 ] was taken as the measured eddy-viscosity in the approach flow. 2. Based on the measured shear-stress distribution (see Fig. 3.9), a (rather subjective) extrapolation towards the bed was used to obtain the bed shear-stress, or: �o,2 � �� u ��w �� bed cos� (3.6) 3. Based on a relation for the velocity distribution (see Graf and Altinakar, 1998, pp. 73-74) the bed shear-stress was evaluated by: �o,3 � ��u �,3� 2 � � U g C 2 �� 2 � ��0.07 U� 2 (3.7) where U is the local depth-averaged flow velocity and C is Chezy coefficient taken as C = 44 [m 1 2 s] (uniform sand bed with d 50 = 2.1 [mm]). A numerical simulation of the flow around the cylinder has also been performed (see Chapter 5), from which the bed shear-stresses can also be obtained; this is denoted as � o,4 . Its value was obtained with a similar equation as Eq. 3.5, in which the k-� turbulence model-equation and the logarithmic law-of-the-wall were used to get the eddy viscosity, � t , and the velocity gradient, �V t �n, (see Chapter 4, Eq. 4.82). For clarity, the expression used to compute � o,4 is rewritten below: 3 4 1 2 �o,4 � �c � k �V t � � (4.82) � ln E �n where c � = 0.09 is a k-� model constant, k turbulent kinetic-energy, � = 0.4 Karman constant, E roughness coefficient of the bed, � n � � u� � n � dimensionless normal distance from the bed, and � the kinematic viscosity of water. The sign convention of � o,4 is the same as that of the velocity.
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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.
Page 59 and 60: - 2.39 - Fig. 2.13d Cont’d.
Page 61 and 62: - 2.41 - the solid boundary of the
Page 63 and 64: - 2.43 - Fig. 2.14b Cont’d.
Page 65 and 66: - 2.45 - Fig. 2.14d Cont’d.
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
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: - 3.27 - Fig. 3.10 Cont’d.
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 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 �
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with � �� nt,b � ��
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- 4.39 - boundary node B are then a
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- 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
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- 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
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- 5.7 - (i) Yulistiyanto data (ii)
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- 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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