Effect of lifting force on bed topography and bed-surface sediment size in channel bend

對沈滓運移而言，昇力可以減少沈滓顆粒跟床面的摩擦力，使其更容易被剪力所帶走。在彎道中，由於昇力的不均勻分佈，忽略昇力的作用可能會造成在推估沈滓運移量時，產生相當大的誤差。本研究致力於研究昇力相關的理論及數值模式，並將其應用於彎道床形及床質的探討。 由於昇力和渦度呈正向的相關，本研究使用三維的大渦紊流數值模式，模擬彎道中的渦度場，以瞭解昇力的分佈。結果顯示在彎道中，靠近外岸的昇力大於內岸，而隨著床形的發展，此種現象更為明顯。此外，不同於剪力與沈滓顆粒大小無關，昇力的效應會隨著顆粒粒徑增加而減少。 透過昇力相關理論的分析及推導，結果顯示沈滓顆粒啟動之後的摩擦力 小於臨界狀態的摩擦力 。而在有效剪力的表示式中，利用 取代 ，昇力的效應即可納入用以推估沈滓的運移量。 在數值模式方面，本研究採用一套完整的模式，以非耦合的方式結合水理與輸砂模式，模擬彎道床形及床質。模擬的結果顯示，在考慮昇力的效應之後，誤差降低了大約 。為了提供實際工程的應用，研究中亦發展一套簡化的模式，以減少電腦運算的時間。對於此簡化模式而言，雖然模擬結果誤差增加了約 ，但運算時間卻大幅減少為完整模式的 。 最後，本研究規劃了數組數值試驗，探討水理及渠道無因次參數對彎道床形及床質的影響。其中，經由迴歸分析，可得到彎道完全發展段之逕向坡度、沖刷面積比、最大沖刷深度及最大床面中值粒徑與無因此參數的迴歸方程式。結果顯示密度福祿數（densimetric Froude number）及初始沈滓粒徑級配為影響彎道床形及床質變化最重要的因素。此外，在文中採用了其他的彎道實驗資料與回歸方程式預測的結果作比較。結果發現，預測與實驗的值相當吻合，並且其相關係數皆高於 。因此，本研究歸納之回歸方程式於工程的適用性得以驗證。In sediment transport, the lifting force plays an important role in reducing the friction between sediment particle and bed surface, and thus makes particles easier to be transported by shear force. Non-uniform distribution of lifting force in channel bend may cause serious errors in describing sediment transportation if the lifting force effect is not taken into account. In the present study, relevant theories and numerical models are investigated and employed to study the lifting force effect on the bed topography and sediment gradation in channel bend. Since the lifting force, , is related to vorticity, a 3D numerical model incorporating large eddy simulation is applied to simulate the vorticity field in channel bend. The results of simulation show that is larger around the outer bank and smaller around the inner one in a bend. As bed topography develops in a bend, this phenomenon is enhanced. Unlike the shear stress regarded as being independent of sediment size, the lifting force effect is smaller for a larger sediment particle. Through a series of physical considerations, existing theories are reviewed and modified to find that the friction of particle in motion, , becomes smaller than that at incipient motion, . By replacing with in the expression of effective shear stress, the lifting force effect can be taken into consideration in predicting the sediment transport rate. In this research, a total numerical model composed of the flow model and bed model is employed to simulate the bed topography and bed-surface sediment size in a channel bend. Comparing the simulated results with and without consideration of the lifting force effect, it shows that the errors can be reduced by about with the lifting force effect considered. For practical engineering applications, further efforts are made to develop an approximate model for bed-surface sediment size distribution to shorten the computation time. Although errors inherited in the approximate model increase by about , it consumes only about of the computation times of the total model. Finally, various numerical experiments are conducted under various conditions to study the effects of flow and channel parameters on bed topography and sediment gradation in channel bend. The fully developed transverse bed-slope, ratio of the erosion area to the total channel bed area, maximum erosion depth of the developed bed, and maximum median diameter of bed-surface sediment of the developed bed, are expressed as regression functions composed of non-dimensional parameters. The regressed results show that densimetric Froude number and initial sediment gradation are the major factors affecting the variations of bed topography and bed-surface sediment size. In order to verify the applicability of these regression equations, more experimental data in channel bend are employed to testify their validity. The results show that the predicted values agree quite well with the experimental results and the correlation coefficients are all greater than . This verifies the applicability of these regression equations in practical engineering use.謝 誌.....................................................i CONTENTS.................................................ii 摘 要....................................................iv ABSTRACT.................................................vi LIST OF TABLES.........................................viii LIST OF FIGURES...........................................x CHAPTER 1.INTRODUCTION....................................1 1.1. MOTIVES..............................................1 1.2. LITERATURE SURVEY....................................2 1.3. ORGANIZATIONS........................................5 CHAPTER 2. THERORETICAL CONSIDERATIONS....................7 2.1. FLOW MODEL...........................................7 2.2. BED MODEL...........................................11 2.3. DISTRIBUTION OF VORTICITY IN CHANNEL BEND...........13 2.4. EFFECTS OF SDIMENT NON-UNIFORMITY...................22 CHAPTER 3. SIMULATION OF BED TOPOGRAPHY AND BED-SURFACE SEDIMENT SIZE............................................29 3.1. PROCEDURES OF SIMULATION............................29 3.2. RESULTS OF SIMULATION...............................34 3.3. APPROXIMATE FOR BED-SURFACE SEDIMENT SIZE...........38 3.4. DISCUSSIONS.........................................50 CHAPTER 4. NUMERICAL EXPERIMENTS.........................54 4.1. NON-DIMENSIONAL ANALYSIS............................54 4.2. INFLUENCES OF NON-DIMENSIONAL PARAMETERS............57 4.3. COMPREHENSIVE ANALYSIS..............................63 4.4. VERIFICATION OF REGRESSION EQUATIONS................65 CHAPTER 5. CONCLUSIONS AND SUGGESTIONS...................67 5.1. CONCLUSIONS.........................................67 5.2. SUGGESTIONS.........................................69 REFERENCES...............................................71 APPENDIX A –BASICS FOR 3D FLOW MODEL....................80 APPENDIX B –BASICS FOR BED MODEL........................87 TABLES...................................................95 FIGURES.................................................105 NOMENCLATURE............................................16