以三維數值模擬探討海嘯湧潮與結構物之交互作用

Three-dimension numerical model for the interaction of tsunami bore and structures

鄭喆宇(Che-yu Cheng)

指導教授 ： 吳祚任

國立中央大學/地球科學學院/水文與海洋科學研究所/碩士(2012年)

摘要

2011年3月11日之東日本海嘯事件使國人重視海嘯之威脅。該事件由海溝型地震所引發，地震矩規模為Mw = 9.0。地震引發高達10公尺之沿岸海嘯入射波。根據日本警察廳之資料顯示，受到海嘯湧潮衝擊全毀與半毀之建築物約有40萬棟。本研究希望藉由數值方法，瞭解海嘯湧潮之行為特性，以達到減災之目的。本研究採用LES-VOF三維數值模式，探討海嘯湧潮與結構物之互制行為。應用本數值模式前，本文先以Arnason（2005）所進行之長潰壩實驗進行驗證與分析。
　　一般情況下，長潰壩蓄水水體以及海嘯湧潮發展與行進階段，所需消耗之網格約為總網格之75%，導致整體模擬既耗資源亦費時。本研究改以線性淺水波方程式之特徵曲線法，先推導水位與流速，並做為LES-VOF模式之入流邊界條件再進行三維模擬。由此組合得到之受力峰值與實驗峰值之誤差約為10%。為減少誤差，本研究另以二維潰壩模擬湧潮之行進，並將水位與流速之結果作為LES-VOF之入流邊界條件。以此方法所取得之受力峰值與速度峰值與實驗結果之誤差皆低於5%。由此可見後者結果較佳，因此後續研究皆以二維耦合三維方式進行多案例之模擬與分析。
　　在結果分析方面，由湧潮衝擊結構物過程中之壓力場變化，發現湧潮撞擊之初，結構物之最大壓力位置位於半湧潮高度處，其後壓力值逐漸移至結構物底部，此說明衝擊初期之結構物受力以動壓為主，後期則轉為靜壓。本文並進行參數敏感分析，所探討之參數結構物之幾何條件及渠寬。模擬結果顯示，受力之變化與柱寬之變化約為等比例，而縱深對於受力之變化影響極小，此結果說明阻滯比為本案例之重要影響參數。另外為瞭解實驗縮尺與真實尺度之結果差異，本研究將實驗尺度放大100倍，以模擬真實尺度下之海嘯湧潮衝擊結構物行為。結果發現，受力主要受福祿數影響，雷諾數則是對於潮身撞擊部分具有較大之影響力。

關鍵字

紊流模式 ； 海嘯湧潮 ； 因次分析 ； 流體體積法

並列摘要

On March 11, 2011, a powerful tsunami occurred off the east Japan that makes people to pay attention to the tsunami threat. The powerful tsunami generated by a trench-type earthquake with Mw= 9.0. The wave height was observed about 10 m offshore. More than 400,000 structures were destroyed reported by National Police Agency in Japan. This paper aimed to understand the characteristic of tsunami bores by means of numerical method, and hopefully, for tsunami hazard mitigation. We use 3D LES-VOF model to simulate the interaction of tsunami bore and a square cylinder. The model is validated with the experimental measurements of the long-flume dam-break done by Dr. Arnason（2005）.
　　Simulating the complete bore propagation before reaching the cylinder is very expensive. The process takes about 75% of the whole computational time. To reduce it, this study implement bore height and velocity obtained from solving the shallow water equation （SWE） as the inflow boundary conditions. The results are compared with the experiment data. The general error is approximated as 10 % in terms for the force acting on the cylinder.
　　In order to reduce the error, we implement the solution from the 2D simulation. In this method, we simulate the same problem with the cylinder removed from the flume by solving 2D LES model. The solution is them used as the inflow boundary condition. We also compare the result with the experiment data, and the error is under 5 %. After the comparison, this 2D coupling method is then utilized for following simulations and analysis.
　　From the pressure distribution on the cylinder while the bore is arriving structure, we notice that the maximum pressure occurs at the elevation of half of the bore height, and then moves to the bottom area. This indicates that when the bore is contacting the cylinder, the dominate force is the hydrodynamic dynamic pressure, and transfers the hydrostatic pressure during the bore body passing through. We also discuss the sensitivity of geometric parameters. The result shows that net force increases with the width of the cylinder. However, the effect from changing the length can be neglected. This indicates that the blockage ratio is an important parameter to the net force.
　　In order to understand the difference between laboratory scale and real scale, this study scales the laboratory setting by magnifying 100 times to simulate the tsunami-structure interaction in the real scale. The result shows that the net force is dominated by Froude number. However, the high frequency disturbance is affected by Reynolds number.

並列關鍵字

Tsunami bore ； Turbulence model ； Dimensional Analysis ； Volume of Fluid

參考文獻

[68] 羅德章，陳力民，吳姿潓， “計算流力在潰壩波與結構物互制之研究”，第33屆海洋工程研討會論文集， 2011。

[2] Arnason, H., “Tsunami Bore Impingement onto a Vertical Column.”, 2009.

[3] Abul-Azm, A. G. “Diffraction through wide submerged breakwaters under oblique waves.” Oc. Engng., 21, 683-706, 1994.

[4] Benz, W., Asphaug, E., “Impact simulations with fracture. I. Methods and tests.” Icarus, 107, 98–116, 1994.

[5] Benz, W., Asphaug E., “Simulations of brittle solids using smooth particle hydrodynamics.” Comput. Phys. Commun. Vol. 87. P. 253–265, 1995.