FLOW AROUND A CYLINDER - istiarto

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F C � � � 0 for all � e � nt,e � 0 � E = � P for � = k and � �� VE � Vt,P �� – 4.42 – The diffusive term in the momentum equations, which is due to the normal stress, is evaluated with the same method as that for the wall function approach. This term is considered as a force per unit mass acting on the plane. Momentum equations � set all coefficients related to the boundary node E in Eq. 4.52 to zero: C D C D aE � aE � a P �� compute �� a E P� � b E D � � � b E 1D � � � b E 2D � � � 0 E e t using Eqs. 4.87 and 4.88; its components are e t,x ,e t,y ,e t,z . � compute the forces due to the normal stress as source terms: �� x-momentum: ��1 �b � bP uP � � E F � �� n,x �� e � �� t�ue n,x � 2v en,y � 2we n,z�e n,x �Se �P � �t en,x en,x �� n � �� n,P �� b y-momentum: � � E � � �� P �b P�E ��1 �b � bP uP � � E F � �� n,y �� e � �� t�2 ue n,x � v en,y � 2we n,z�e n,y �Se �P � �t en,y en,y �� S e �n � �� n,P �� b z-momentum: � � E � � �� P �b P�E ��1 �b � bP uP � � E F � �� n,z �� e � �� t�2 ue n,x � 2 ve n,y � we n,z�e n,z �Se �P � �t en,z en,z � S e � n � �� n,P �� b � � E � � �� P �b P�E � S e ��1 uP ��1 vP ��1 wP (4.94a) (4.94b) (4.94c)
k and � equations – 4.43 – � set all coefficients related to the boundary node E in Eq. 4.52 to zero: C D C D aE � aE � a P � � ��a E P� � b E D � � � b E 1D � � � b E 2D � � � 0 E � extrapolate k and � at P to E: k E � k P and � E � � P Pressure and velocity corrections Since the discharge across the boundary is zero, the coefficients related to the contribution from the boundary node E in the discretized pressure correction equation, p p � 0 and b Eq. 4.68, are set to zero: a E � � e � 0 . The pressure correction gradient, �p c �x i , needed for the velocity correction, Eq. 4.57, is computed by the finite-volume technique, Eq. 4.20, which requires the value of p c � � � p e c � � . This latter is obtained by: p E c � � � p E c � � . The velocity at E has to be P corrected such that it is parallel to the symmetry plane, since the flux across the boundary is zero. This is similar to assuming that the velocity at E is the same as the projection of the velocity vector at P on a plane parallel to the symmetry boundary: V E � Vt,P. 4.5.6 Surface boundary At the (water) surface (see Fig. 4.10) the velocity is parallel to the boundary, the discharge across the (water) surface is zero, and thus there is no convective transport across this boundary. The shear stress along the surface, in addition, is neglected. This allows the specification of the velocity along the surface boundary the same as the projection of the velocity at the cell center. The water surface does not create turbulence; therefore, the kinetic energy along the surface boundary is set to zero. The energy dissipation, �, at cell center is obtained in a similar manner as that at the wall boundary; a correction may be given to reduce the computed value as has been reported in some previous works (Krishnappan and Lau, 1986). For the pressure, a hydrostatic distribution is assumed between the surface and the cell center. The pressure at the surface is supposed to be atmospheric; if it is not the case, the surface is moved according to the pressure defect, relative to a reference pressure, which is prescribed at a particular cell. This reference cell is normally defined at the top-most cell of the outflow boundary. This is similar to prescribe a constant flow-depth condition at the outflow. The surface correction is done at the end of each time step. An underrelaxation factor and a limitation may be imposed to avoid excessive change of the computational domain. The procedures to handle surface boundary are described in the following paragraphs.
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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
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
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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
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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
Page 191 and 192: - 5.7 - (i) Yulistiyanto data (ii)
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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
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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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