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Index of Figures Fig.4.19: Frame positions and file format of the velocity raw data 86 Fig.4.20: Shifting the measured velocity exceeding the measurement domain back to its correct position 87 Fig.4.21: Geometry of the probe support 88 Fig.4.22: Influence of the sampling time on the time-averaged velocity (in the tangential direction). 89 Fig.4.23: Test protocoles (see also Appendix 2.3) 92 Fig.4.24: Flowchart of the MatLab treatment of the water and bed level data 93 Fig.4.25: Schematic view of the projection of the measured velocity components a, b and c to obtain the final velocity vector v 95 Fig.4.26: Used UVP Software, showing a sample file 96 Fig.4.27: Flowchart of the velocity treatment with MatLab 97 5. Test results 99 Fig.5.1: Evolution of the scour (Thalweg) for the preliminary test without macro-roughness (A1) 103 Fig.5.2: Grain sorting, view across the outer side wall at 45° (test with macro-roughness - A2) 104 Fig.5.3: Macro-roughness arrangement in the straight transition zones in the inlet and outlet reach 111 6. Analysis of the test results 113 Fig.6.1: Absolute (on top) and relative scour depth (bottom) as a function of the discharge (without macro-roughness tests, with Peters tests) 116 Fig.6.2: Relative scour depth as a function of the energy slope Se over the whole channel (without macro-roughness tests, with Peters tests) 116 Fig.6.3: Relative scour depth as a function of the width to depth ratio (without macro-roughness tests, with Peters tests) 117 Fig.6.4: Approximation of the real cross-section profile by a simplified one 118 Fig.6.5: Reduction of the scour depth due to macro-roughness (ed = 20 mm) 119 Fig.6.6: Longitudinal plot over the whole channel; average / min. / max. bed and water levels for S0=0.50%, Q=210 l/s, without ribs (on top) and with a rib spacing of 1° (bottom) 120 Fig.6.7: Volume of the scour holes and depositions on the point bars as a function of the discharge (bottom) and the overall energy slope Se,all (top) (including the tests with macro-roughness, without Peters tests) 122 Fig.6.8: Shape of the scour holes and point bars with and without macro-roughness (S0 = 0.50%, Q = 210 l/s) 123 Fig.6.9: Development of the line bend in the first scour (test B1d on top and B2d at the bottom) 125 Fig.6.10: Scheme of the development of the line bend 125 Fig.6.11: Water surface views for tests C1 to C4 at Q = 210 l/s 126 Fig.6.12: Stationary wave at the end of the bend with surface roller (left) and a common one (right). Picture taken across the outer side wall 126 Fig.6.13: Flow separation behind the point bars (left: at 45°, test C4d, right: at 90°, test C1d) 128 Fig.6.14: Vertical view on the water surface waves; ribs-spacing 4°, test C2c 128 Fig.6.15: Evolution of the water and bed levels along the outer side wall for tests without macroroughness - S0 = 0.70%, Q = 150 (on top) and 180 l/s (bottom) 130 Fig.6.16: Evolution of the water and bed levels along the outer side wall for tests with macro-roughness, spaced every 2° - S0 = 0.70%, Q = 150 (on top) and 180 l/s (bottom) 131 page 220 / November 9, 2002 Wall roughness effects on flow and scouring
Index of Figures Fig.6.17: Evolution of the sediment transport rate Qb at S0 = 0.5%, for 3 measured discharges, without macro-roughness (B1), and with ribs spaced every 4, 2 and 1° (B2 to B4). 132 Fig.6.18: Changes of the average bed level for the preliminary tests (with and without ribs) at a constant sediment transport rate 133 Fig.6.19: Comparison of predicted and computed armoring layer (computed with Gessler, 1965, 1670, 1990) 134 Fig.6.20: Characteristic average grain size diameter for the different test series (average over the 3 discharges) 135 Fig.6.21: Bed surface in the first scour hole (tests B1d and B2d) without (left) and with ribs (right) 137 Fig.6.22: Tangential velocities at 40° without macro-roughness (left) and with ribs spaced every 2° (right); view in the downstream direction (see also Appendix 11.4) 138 Fig.6.23: Top: Main (1) and inner bank (2) secondary cells in the first scour hole at 40° (no MR) Bootom: Main (1) and inner bank (2) secondary cells and outer bank secondary cell (3) protecting the wall of the channel (rib spacing 2°) at 70° 140 Fig.6.24: Flow field after the first point bar for a rib spacing of 1° (at 85°) 146 7. Establishing an empirical formula 149 Fig.7.1: Results of the enhanced equation (eq. 7.5) of Kikkawa (see also Fig. 7.3 for explanations) 156 Fig.7.2: Results of the enhanced equation (eq. 7.6) of Bridge (see Fig. 7.1 and 7.3 for explanations) 158 Fig.7.3: Characteristic points in a cross-section profile at the (upstream) maximum scour location on top: cross-section in the upper scour; bottom right: transversal bed slope as a function of h/r 160 Fig.7.4: Results of the centered polynomial equation (3rd degree) without correction factor (eq. 7.10, ) (see Fig. 7.1 and 7.3 for explanations) 161 Fig.7.5: Results of the uncentered polynomial equation (3rd degree) without correction factor (eq. 7.12, ) (see Fig. 7.1 and 7.3 for explanations) 163 Fig.7.6: Results of the uncentered polynomial equation (3rd degree) with vertical correction and horizontal bed slope at the outer bank, without correction factor (eq. 7.15) (see Fig. 7.1 and 7.3 for explanations) 164 Fig.7.7: Results of the uncentered polynomial equation (3rd degree) with vertical correction and horizontal bed slope at the inner bank, with correction factor (eq. 7.20) (see Fig. 7.1 and 7.3 for explanations) 165 Fig.7.8: Results of the uncentered polynomial equation (3rd degree with additional terms) with vertical correction, with correction factor (eq. 7.22) (see Fig. 7.1 and 7.3 for explanations) 167 Fig.7.9: Results of the uncentered polynomial equation (5th degree), horizontal bed slope at the inner bank, with correction factor (eq. 7.27) (see Fig. 7.1 and 7.3 for explanations) 168 Fig.7.10: Results of the uncentered polynomial equation (5th degree), horizontal bed slope at the outer bank, with correction factor (eq. 7.28) (see Fig. 7.1 and 7.3 for explanations) 169 Fig.7.11: Tangential forces acting on a control volume 172 Fig.7.12: Comparison of maximum relative scour depth computed with equation 7.63 with the complete dataset (R2 = 0.876) (left) and the one without Peter’s tests (right). 181 Fig.7.13: Analysis of parameters influencing the reduction of the maximum scour depth (see also Fig. 6.5!) 182 Fig.7.14: Schematic view of the bank protection elements upstream the Wilerbrücke (right end of the scheme). Element 1 is the vertical side wall equiped with ribs [Kuster et al, 1992, Fig. EPFL Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 221
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WALL ROUGHNESS EFFECTS ON FLOW AND
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Abstract By applying vertical ribs
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Résumé En disposant des nervures
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Zusammenfassung • Ein markanter S
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Acknowledgments page x / November 9
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Table of contents 4. Smart & Jäggi
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Table of contents 7.6 Summary and c
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Chapter 1 - Introduction 1.1 Contex
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Chapter 1 - Introduction page 4 / N
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Chapter 2 - State of the art 2.1 Fl
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Chapter 2 - State of the art 2.2.2
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Chapter 2 - State of the art Theref
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Chapter 2 - State of the art resolu
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Chapter 2 - State of the art comple
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Chapter 2 - State of the art ORLAND
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Chapter 2 - State of the art 2.6 Me
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Chapter 2 - State of the art page 2
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Chapter 3 - Theoretical considerati
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Chapter 4 - Experimental setup and
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Chapter 5 - Test results 5.1 Introd
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Chapter 5 - Test results 5.2 Prelim
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Chapter 5 - Test results with and w
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Chapter 5 - Test results 5.2.2 Test
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Chapter 5 - Test results 5.3 Main t
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Chapter 5 - Test results and 210 l/
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Chapter 5 - Test results 5.5 Tests
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Chapter 6 - Analysis of the test re
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Page 216 and 217: Notations K S [m 1/3 /s] roughness
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Page 224 and 225: References Williams, R. (1899). Flu
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Page 230 and 231: Index of Authors Hoffmanns 13 Hoffm
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