Numerical simulation of sediment transport and morphological evolution

NUMERICAL SIMULATION OF SEDIMENT TRANSPORT AND MORPHOLOGICAL EVOLUTION LIN QUANHONG NATIONAL UNIVERSITY OF SINGAPORE 2009 NUMERICAL SIMULATION OF SEDIMENT TRANSPORT AND MORPHOLOGICAL EVOLUTION LIN QUANHONG (B.Eng. and M.Eng., Tianjin University, China) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2009 To My Parents i Acknowledgements First and foremost, I would like to express my gratitude to my supervisors, Professor Cheong Hin Fatt and Professor Lin Pengzhi, for their guidance, support and encouragement throughout my study at National University of Singapore. Numerous meetings and discussions are the origins of the research ideas and the directions of the way going forward. Their attitude for the research will lead me further in the future career. The time spent with me and the patience allowing me to improve myself should be appreciated. Without them, this thesis would not have been possible. I also like to thank my previous supervisor, Professor Zhang Qinghe at Tianjin University during my study for the Master of Engineering from 2001 to 2004. His knowledge and virtue are always worthy of my respect. I have also benefited from the generosity of many others and special thanks go to the following persons. The numerical model developed in this study is partially based on the PhD thesis of Dr. Yong-Sik Cho at Cornell University. And the program for the turbulence spectrum analysis was generously provided by Dr. Ren-Chieh Lien at the University of Washington, who also gave me valuable guidance in this research field. In addition, analytical solutions of the shock wave for the numerical testing of the morphological evolution equation were kindly provided by Dr. Wen Long at University of Maryland. Their generosity is appreciated. I would like to acknowledge the Research Scholarship provided by National University of Singapore from 2004 to 2008. I am grateful for the financial support from the Research Engineer position provided by Professor Cheong Hin Fatt from 2008 to 2009. ii I am happy to thank Mr. Zhang Dan, Mr. Zhang Wenyu, Dr. Liu Dongming, Mr. Chen Haoliang, Mr. Sun Yabin, Mr. Xu Haihua, Dr. Ma Peifeng, Dr. Anuja Karunarathna, Dr. Pradeep Fernando, Dr. Cheng Yonggang, Mr. Shen Wei, Mr. Chen Zhuo, Mr. Lim Kian Yew, Mr. Satria Negara, Dr. Gu Hanbin, and Dr. Zhang Jinfeng, for their friendship and valuable discussion during the study. Special thanks go to Dr. Wang Zengrong, for his helpful discussion about the signal analysis with me. Thanks are extended to Mr. Krishna and Ms. Norela for their help between office and laboratory and to Mr. Semawi and Mr. Roger for their assistance my experiments at Hydraulics Laboratory. Last but not least, I would like to express the gratitude from my heart to my parents and my sister, who have been giving me the unconditional love in my life. I also like to thank my wife for her care, patience and love. I could not finish my study without the support from all of them iii Table of Contents Acknowledgements ii Table of Contents iv Summary viii List of Tables x List of Figures xi List of Symbols xx Introduction 1.1 Background of Sediment Transport Study …………………………………….1 1.2 Background of Shallow-Water Equations Models …………………………… 1.3 Review on Considerations of Slope Effect on Sediment Transport … .……12 1.4 Objective and Scope of Present Study ………………………………… .……16 Mathematical Formulation of the Numerical Model 2.1 2.2 2.3 20 Shallow-Water Equations …………………………………………………….20 2.1.1 Continuity equation …………………………………………………… 20 2.1.2 Momentum equation ………………………………………………… 22 Depth-Averaged kˆ  ˆ Turbulence Closure ………………………………….26 2.2.1 Three-dimensional k   model ……………………………………… 26 2.2.2 Depth-averaged kˆ  ˆ model ………………………………………… 28 Sediment Transport Model ……………………………………………………30 2.3.1 Some parameters for sediment transport ……………………………… 31 2.3.2 Bed load transport equations ………………………………………… 33 2.3.3 Suspended load transport equation …………………………………… 34 2.3.4 Sediment deposition function ………………………………………… 35 2.3.5 Sediment entrainment function ……………………………………… 36 2.4 Morphological Change Model ………………………………………………38 2.5 Correction for Bed Shear Stress ………………………………………………38 iv 2.6 2.7 2.8 Effect of Bed Slope on Sediment Transport …………………………………44 2.6.1 Effect of bed slope on critical shear stress…………………………… 45 2.6.2 Van Rijn (1989)’s method…………………………………………… 49 2.6.3 Application to some cases…………………………………………… 50 2.6.4 Verification of the slope effect equation……………………………… 51 2.6.5 Modification of sediment transport direction………………………… 53 2.6.6 Procedure of considering the effect of bed slope……………………… 58 Initial and Boundary Conditions ………………………………………………59 2.7.1 Initial conditions ……………………………………………………… 59 2.7.2 Boundary conditions ………………………………………………… 60 Summary of Governing Equations …………………………………………….62 Numerical Implementation 3.1 65 Model Implementation …………….…………………………………….… 65 3.1.1 Sketch of computational domain ……………………………………… 65 3.1.2 Shallow-water equations ……………………………………………… 67 3.1.3 Depth-averaged kˆ  ˆ equations ……………………………………… 71 3.1.4 Suspended load transport equation …………………………………… 74 3.1.5 Morphological evolution equation …………………………………… 76 3.1.6 Computational cycle ………………………………………………… 82 3.2 Stability Analysis ……….……………………………………………….…….82 3.3 Special Numerical Treatments ……………… ……………………………….85 3.3.1 Boundary condition for kˆ  ˆ equations on solid boundary ………… 85 3.3.2 Approximate calculation method for gradually varied beds ………… 86 Numerical Testing 4.1 4.2 88 1D Hydrodynamic Module …………….………………………………….… 88 4.1.1 Solitary wave propagation …………………………………………… 88 4.1.2 Idealized dam-break …………………………………………………… 95 4.1.3 Partial dam-break ……………………………………………………… 99 4.1.4 Hydraulic jump ……………………………………………………… 103 2D Hydrodynamic Module …………….……………………………….… 106 v 4.3 4.4 4.2.1 Sloshing in a tank …………………………………………………… 106 4.2.2 Uniform flow in a straight channel ………………………………… 112 4.2.3 Recirculating flow near a groyne …………………………………… 114 Convection-Diffusion Equation ……….……………………………….…….120 4.3.1 1D Gaussian hump …………………………………………………… 120 4.3.2 2D Gaussian hump …………………………………………………… 123 4.3.3 2D point source …………………………………………………… 127 1D Morphological Equation ……………… ……………………………….131 Sediment Transport in 1D Situations 136 5.1 Introduction ………………………………………………………………….136 5.2 Sediment Transport in a Trench …………………………………………….137 5.3 5.2.1 Experimental setup …………………………………………………….137 5.2.2 Velocity and concentration fields ……………… .………………… 141 5.2.3 Verification of approximate calculation method .………………… 150 5.2.4 Calculations of morphological evolution .……… ………………… 153 5.2.5 Sensitivity analysis .……… ………………………………………… 158 Sediment Transport over a Dune …………………………………………….164 5.3.1 Experimental setup .……… ………………………………………… 164 5.3.2 Experimental results .……… ………………………………………… 166 5.3.3 Numerical simulation and results .……… ………………………… 169 5.3.4 Sensitivity analysis.……… ………………………………………… 172 Turbulent Flows and Morphological Evolution in Channels with Abrupt CrossSection Change 174 6.1 Introduction ………………………………………………………………….174 6.2 Turbulent Flow in a Channel with an Abrupt Expansion ………………….177 6.3 6.2.1 Laboratory experiments ……………………………………………….177 6.2.2 Analysis of experimental data ………………………………………….179 6.2.3 Numerical simulation ………………………………………………….187 6.2.4 Results and discussions ……………………………………………….188 Morphological Evolution in a Channel with an Abrupt Expansion ………….195 6.3.1 Laboratory experiments ……………………………………………….195 vi 6.4 6.5 6.6 6.7 6.3.2 Experimental results ………………………………………………….196 6.3.3 Numerical simulation ………………………………………………….210 6.3.4 Results and discussions ……………………………………………….210 Turbulent Flow in a Channel with an Abrupt Contraction ………………….211 6.4.1 Laboratory experiments ……………………………………………….211 6.4.2 Numerical simulation ………………………………………………….213 6.4.3 Results and discussions ……………………………………………….214 Morphological Evolution in a Channel with an Abrupt Contraction ……….221 6.5.1 Laboratory experiments ……………………………………………….221 6.5.2 Experimental results ………………………………………………….221 6.5.3 Numerical simulation ………………………………………………….228 6.5.4 Results and discussions ……………………………………………….228 Morphological Evolution in a Channel Consisting of a Contraction and an Expansion …………………………………………………………………….234 6.6.1 Laboratory experiments ……………………………………………….234 6.6.2 Numerical simulation ………………………………………………….236 6.6.3 Results and discussions ……………………………………………….237 Summaries ……………………………………………………………………246 Conclusions and Future Work 249 7.1 Conclusions …………………………………………………………………249 7.2 Recommendations for Future Work …………………………………………253 7.2.1 Cohesive sediment transport ………………………………………….253 7.2.2 Bed evolution in channel bends ……………………………………….254 7.2.3 Bed evolution in dam-break problems ……………………………….254 References 256 vii Summary A two-dimensional depth-averaged numerical model has been developed to simulate long-term sediment transport and morphological evolution. Furthermore, considering the fact that the detailed experimental studies on the turbulent flows involving sediment transport and morphological evolution are few, a series of experiments have been conducted in the laboratory flume to provide valuable measured data for purposes of model validation. The numerical model consists of three modules: the hydrodynamic module, the sediment transport module and the morphological evolution module. Firstly, the hydrodynamic conditions are computed by solving the shallow-water equations with the depth-averaged kˆ − εˆ turbulence closure. Based on the flow conditions, the suspended sediment concentration is evaluated by solving the convection-diffusion equation while the bed load transport is predicted from an empirical equation. Finally, the bed evolution is calculated using fifth-order accurate WENO (Weighted Essentially Non-Oscillatory) scheme. In order to improve the prediction, the bed shear stress obtained from the traditional Manning’s formula is corrected according to the secondary flow effect with the assumption of a “triangular model” for the main flow and the cross flow components. To simulate the sediment transport on the sloping bed more realistically, the effect of the bed slope, i.e., the effect of gravity on the sediment particle, is incorporated into the model. Both the critical shear stress for the sediment incipient motion and the sediment transport direction are corrected according to the local bed slope. In addition, utilizing the difference of the stability criteria between flow and sediment transport calculations, an viii slope effect will smooth the bed with relatively high gradient and make the simulation more realistic. In addition, the approximate calculation method proposed for the gradually varied beds has been validated in the trench case. The numerical results have shown that this approximate method will significantly improve the computational efficiency and at the same time keep the results with almost same accuracy. Therefore, it is a very promising method for simulating the gradually varied beds. After the studies of the one-dimensional situations, the studies of the two-dimensional situations covering the turbulent flows, the sediment transport and the morphological evolution in the channels with changed cross-section were carried out. Firstly, the flow field in a channel with an abrupt expansion has been studied in the laboratory flume. Three-dimensional velocity components were measured using MicroADV throughout the whole flow field. Based on the collected velocity data, the three-dimensional mean velocity components and the turbulent kinematic energy were calculated and the dissipation rate of TKE was estimated using the spectrum analysis to find out the Kolmogorov inertial subrange. Furthermore, the turbulent viscosity was calculated according to its definition. After obtaining all these mean and turbulent flow quantities for the whole three-dimensional space in the flow field, their depth-averaged values were calculated based on the data within the measurement depth. From the measurements, it was found that the main flow is in longitudinal direction with much smaller transverse component. Due to the presence of the obstacle corner, a recirculating region forms behind the expansion position and the turbulence has very strong intensity within this region. In addition to the experimental study, the numerical simulation was conducted for the flow filed in the expanded channel using the present model. The numerical results have shown 251 to be very encouraging when compared with the experimental data in terms of both mean flow and turbulent flow fields. Secondly, the bed load transport and morphological evolution in the same expanded channel were investigated experimentally under the same flow conditions. The main phenomenon observed in the expanded channel was the sand deposition due to the slowdown of the flow and a sand hump forming across the flume obliquely. The hump evolved in both longitudinal and transverse directions and the whole procedure which lasted for eight hours has been recorded by profiling the bed elevations hourly. In addition to the laboratory study, the present model was also applied for modeling the morphological evolution in the sudden-expanded channel. The numerical results gave the reasonably good prediction for the evolution trend although the deposited hump height was underestimated. Thirdly, the flow field in a channel with an abrupt contraction has been studied in the laboratory flume. Similarly to the one in the channel with an abrupt expansion, detailed measurements have been carried out in the sudden-contracted channel for the threedimensional velocities from which the mean velocity and the turbulence quantities as well as their depth-averaged values were obtained. The longitudinal component of the flow was found to be retarded by the obstruction on the one side and accelerated on the other side while the transverse one has very small magnitude. The turbulence field has extraordinarily strong intensity in the regions adjacent to the contraction wall in the narrow channel. The numerical results from the present model agree well with the measurements in terms of both mean and turbulent flow fields except some underestimations on those high turbulences. 252 Fourthly, the morphological evolution in the contracted channel was investigated in the laboratory flume. Under the flow condition, the sand bed was scoured due to the sudden contraction of the flume cross-section and a cone-shaped hole formed around the contraction position. In the modeling, the evolution of the scour hole was simulated accurately with the help of the bed shear stress correction. Lastly, the hydrodynamic conditions and the morphological evolution in a channel consisting of a contraction and an expansion were studied numerically using the present model. The available experimental data and the numerical results from 3D model were used for comparisons. The present model gives successful predictions for the water surface depression in the contracted channel and the velocity field. In addition, reasonable agreements have been shown for simulation of the sand bed deformations including both a scour ditch and a dune. 7.2 Recommendations for Future Work 7.2.1 Cohesive sediment transport In the present model, only cohesionless sediment transport has been considered. In the natural environment, fine-grained and cohesive suspended sediment plays a very important role in the water quality and the growth of ocean creatures. In order to increase the model’s applicability, cohesive sediment transport can be included. For the sediment with grain-size less than 63 µ m , a single particle has very low settling velocity and can be suspended in the water for a long time. However, the cohesive properties of the fine sediments can make them flocculate and form large aggregates or flocs which have much larger settling velocity than a single particle. There are many 253 factors affecting the settling velocity of flocs, including sediment particle size, water salinity, turbulence intensity and sediment concentration. On the other hand, after the sediment settles down onto the bed, the consolidation of the bed will occur associated with different time scales. With accurate description of the settling velocity, the processes of the flocculation and aggregation, deposition, consolidation and re-suspension are necessary to be represented in the numerical simulation of the cohesive sediment transport. 7.2.2 Bed evolution in channel bends Flow field and morphological evolution in the straight channels with changed crosssection have been studied in Chapter 6. The situation will become much more complex in channel bends as the water flows along the curve. Flow shows strong spiral characteristic due to the superposition of the secondary flow on the forward movement of the water. Therefore, the sediment transport is determined to be much more complex than in the straight channels. Due to the similarity to the alluvial natural rivers, the morphological evolution in the channel bends is of importance to be studied. Quite abundant experiments with different layout of bend have been carried out to study the bed evolution in channel bends, e.g., Zeng (1982) and Yen (1970). These provide valuable data base for the validation of the numerical model. 7.2.3 Bed evolution in dam-break problems In Chapter 4, some numerical testing for the flows in the ideal dam-break and the laboratory partial dam-break has been conducted using the present model. When the channel bed is movable, large amount of the sediment will be eroded and then transported 254 within a short time and the morphological change will become very significant. Due to the strong interaction between flow and sediment during the dam-break, the present model which is the uncoupled one with simplified governing equations will not be able to make satisfactory prediction for the problem. Therefore, the model coupling flow motion and sediment transport is necessary for the accurate description of the physical phenomenon. 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Methods Fluids, 29(4), 375-387. 266 [...]... morphological evolution resulted from the bed load transport is investigated and the evolution of the bed profiles are recorded Using the present model, the numerical simulation is carried out and good predictions for the trend of the bed evolution are obtained Lastly, the hydrodynamic conditions and the morphological evolution in a channel consisting of a contraction and an expansion are studied numerically... 7 Due to the importance of the experimental study and efficiency of numerical simulation, researchers usually combine both of them to study the sediment transport and morphological evolution For example, when investigating the vegetation effects on the morphological behavior of alluvial channels, Jang and Shimizu (2007) carried out both laboratory experiments and numerical simulations Zhang et al (2007)... earth and the human being Therefore, it is very important to study the sediment transport phenomena and the resulting morphological change Due to the complexity of the sediment transport mechanism, both numerical modeling and experimental investigation are very important methods for studying the sediment transport Compared with the experimental study, numerical simulation is probably a very convenient and. .. Comparisons between numerical results and observed data showed good agreement Duan and Julien (2005) employed a depth-averaged two-dimensional numerical model to study the inception and development of channel meandering processes Both bed load and suspended load were calculated assuming equilibrium sediment transport and the bank erosion consisted of the basal erosion and the bank failure The numerical results... 7.5 and 15 hours between numerical results simulated with and without bed slope effect Solid line: initial bed profile; Circles and triangles: experimental measurements of bed elevation after 7.5 and 15 hours respectively; Dash-dot line and dashed line: numerical results of bed elevation after 7.5 and 15 hours from present model with bed slope effect; Line with plus and with cross: numerical results of. .. solid wall  angle of repose mean quantities xxv Chapter 1 Introduction 1.1 Background of Sediment Transport Study Sediment transport under hydrodynamic conditions plays an essential role in the morphological evolution of rivers, estuaries and coastal areas (Guo and Jin, 1999) From the long-term point of view, it determines, for example, the local scour or deposition in the vicinity of the river structures... …………………………….……… 130 Figure 4.26: Numerical simulation of Gaussian hump evolution up to 10,000 s …… 133 Figure 4.27: Comparisons of the bed elevation between the analytical solution (solid line) and the numerical result (circle) at t=600 s (left), 2000 s (middle) and 6000 s (right) .134 xiii Figure 4.28: Time history of the total volume of the sand bed; the total volume of the sand bed is normalized by its... 7.5 and 15 hours respectively; Dash-dot and dashed lines: present numerical results after 7.5 and 15 hours respectively; Lines with plus and with cross: van Rijn’s numerical results after 7.5 and 15 hours respectively; Dotted line: numerical result of water surface after 15 hours ……………………………………….……………………………… 156 Figure 5.12: Bed elevation comparisons after 7.5 and 15 hours between numerical results and. .. ………………………………………………………………………………… 160 Figure 5.15: Comparisons of bed elevations in Test 3 after 7.5 and 15 hours between numerical results simulated with and without bed slope effect Solid line: initial bed profile; Circles and triangles: experimental measurements of bed elevation after 7.5 and 15 hours respectively; Dash-dot line and dashed line: numerical results of bed elevation after 7.5 and 15 hours from present model with... and with cross: xv numerical results of bed elevation after 7.5 and 15 hours respectively from present model without bed slope effect; Dotted line: numerical result of water surface after 15 hours …………………………………………………………………………………161 Figure 5.16: Comparison of bed elevations after 7.5 and 15 hours in Test 3 predicted using different values of angle of repose Solid line: initial bed profile; Circles and . NUMERICAL SIMULATION OF SEDIMENT TRANSPORT AND MORPHOLOGICAL EVOLUTION LIN QUANHONG NATIONAL UNIVERSITY OF SINGAPORE 2009 NUMERICAL SIMULATION. SIMULATION OF SEDIMENT TRANSPORT AND MORPHOLOGICAL EVOLUTION LIN QUANHONG (B.Eng. and M.Eng., Tianjin University, China) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF. conditions, the morphological evolution resulted from the bed load transport is investigated and the evolution of the bed profiles are recorded. Using the present model, the numerical simulation