臺灣博碩士論文加值系統

　　藉由外力作用產生水面之波動，除了一般直接擾動水面外，尚有自由液面承受不均勻的壓力分佈或是水中物體運動等造波之情形。本文將以明渠流經水中固定物體擾動自由水面之造波現象，討論波流互制機制。若考慮一二維淺水渠道其靜水深為H，水流以瞬時(t>0)流速U通過一浸沒於水中(或水流)之圓柱體時，會使自由液面產生波動，當福祿數( ，g為重力加速度)小於1時，稱之為亞臨界流況，其波動將分向上下游傳遞。本文為簡化分析流況，將固定上游之水深與臨近流速，計算有限時間內無黏性自由液面之波動。求解波浪的問題時，一般多假設不可壓縮非旋性流且滿足Laplace之勢能函數來求解，本研究以流函數模式模擬波流場，使用有限解析法滿足完全的非線性液面條件，並引用複數與代數內插格網生成矩陣疊代計算時間精確解，探討圓柱體與自由液面互制之現象。此方法將作為後續考量黏性旋流之比較參考用。

關鍵字：複數與代數內插格網、波流互制、自由液面、福祿數

　　Water-Wave motion generated by external force can be often set up from direct disturbing the free surface, or applying the uneven pressure distribution on the free surface or the induced flow motion by moving sulmerged bodies near the free surface. In the present study, I attempt to investigate the flow-wave interaction an approaching flow passing through a fixed submerged body in the water channel. Consider in the undisturbed water depth of H a uniform stream of velocity U passing a submerged cincular cylindrical body of on the bottom or in the water to generate waves on the free surface. When the Froude number being(defined as for the gravitational constant g)of flow is less than 1, the waves tends to propagate in both upstream and downstream directions. To simplify formulation for the present problems, I fixed water depth and approaching flow speed at upstream to calculate the inviscid free-surface wave profiles at various Fr’s. As is different from the traditional way by means of a potential function solution under the incompressible and rotational, assumption faplcian formulation, we apply, instead, the stream function modeling which is easier for further extension to the more general viscous rotational flow problems. These are simulations the time-accurate wave-flow field by the Finite analytic discretization, complete satisfication of the nonlinean free-surface boundary conditions, complex function and algebraic interpolation grid and scheme in all with this study of ciscular cylinder and free-surface wave interaction calculation to include the viscous effects in the general motational flow by this method can be research performed as well in the continued.

Keyword: complex function and algebraic interpolation grid, flow-wave interaction, free-surface, Froude number

目錄
中文摘要…………………………………………………………………………I
英文摘要…………………………………………………………………………II
誌謝………………………………………………………………………………III
目錄………………………………………………………………………………IV
表目錄……………………………………………………………………………VI
圖目錄……………………………………………………………………………VII
符號說明…………………………………………………………………………IX
第一章　序論……………………………………………………………………1
1.1 前言…………………………………………………………………………1
1.2 文獻回顧……………………………………………………………………3
1.3 本文概述……………………………………………………………………4
第二章　流場方程式與相關條件………………………………………………6
2.1 控制方程式…………………………………………………………………7
2.2 貼壁坐標……………………………………………………………………8
2.3 邊界條件……………………………………………………………………10
2.3.1.1 自由液面運動條件……………………………………………………10
2.3.1.2 正向動力邊界條件……………………………………………………10
2.3.1.3 開放性邊界條件與底床邊界條件……………………………………12
第三章　數值方法………………………………………………………………14
3.1 格網生成……………………………………………………………………14
3.1.1 代數生成格網……………………………………………………………15
3.1.1 代數生成格網……………………………………………………………15
3.2 有限解析法…………………………………………………………………17
3.3 相關邊界條件之離散處理方式……………………………………………19
3.3.1 自由液面運動邊界條件(FSKC)之差分離散式…………………………19
3.3.2 自由液面動力邊界條件(FSDC)之差分離散式…………………………20
3.3.3 Poisson 方程式之有限解析法離散式與三對角矩陣求解……………22
3.3.3.1 Poisson 方程式之有限解析法離散式………………………………22
3.3.3.2 三對角矩陣求解………………………………………………………22
3.3.4.計算流程…………………………………………………………………25
第四章　結果討論與分析………………………………………………………28
4.1.模式測試……………………………………………………………………28
4.1.1 格網測試…………………………………………………………………28
4.1.1.1 指定收斂值測試………………………………………………………28
4.1.1.2 SOR 值測試……………………………………………………………33
4.1.2 孤立波於等水深渠道傳遞之數值試驗…………………………………34
4.2.　半圓柱位於底床之造波…………………………………………………37
4.2.1 半圓柱半徑0.1 r = 之流況……………………………………………37
4.2.2　半圓柱半徑0.15 r = 之流況…………………………………………43
4.2.3 半圓柱半徑0.2 r = 之流況……………………………………………48
4.2.4　半圓柱半徑0.25 r = 之流況…………………………………………53
4.3 　圓柱浸沒水中造波現象…………………………………………………58
4.4 總結…………………………………………………………………………65
第五章　結論與建議……………………………………………………………66
5.1 結論…………………………………………………………………………66
5.2 建議…………………………………………………………………………67
參考文獻…………………………………………………………………………69
附錄………………………………………………………………………………71
附錄A 解析幾何常數之推導……………………………………………………71
附錄B 柱體上流函數之推導……………………………………………………72
自述………………………………………………………………………………73

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