孤立波於雙黏性泥質海床上過直立式圓柱之數值研究

Numerical Study of a Solitary Wave Interacting with a Vertical Cylinder over a Bi-viscous Muddy Seabed

李崧瑋(Sung-Wei Li)

指導教授 ： 羅弘岳

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202203364

摘要

本研究基於OpenFOAM的數值方法，研究孤立波於雙黏性泥質海床上過直立式圓柱，調整黏度值與降伏應力對圓柱所受的水平作用力之影響。首先，本研究先建立三維數值水槽，模擬孤立波於牛頓泥質海床上過直立式圓柱，驗證模型設置與網格的正確性，且指出目前的三維網格尺寸能捕捉大致的物理現象。建立二維數值水槽，利用孤立波於賓漢泥質海床的半解析解驗證本研究的數值方法中所假設雙黏性模型，大部分的時間相位與半解析解吻合良好，並得到擬牛頓黏度為1000倍的賓漢黏度之建議標準。最後進行多組三維孤立波於泥質海床上過直立式圓柱數值實驗，同時考慮泥流為牛頓流體模型與雙黏性模型，黏度值與降伏應力為控制變因，分兩組討論。發現泥流為牛頓泥流的數值實驗組，黏度設置越大導致水體與泥流施加於圓柱的總水平正向力越大；泥流為雙黏性泥流的數值實驗組，降伏應力設置越大導致導致水體與泥流施加於圓柱的總水平正向力越大。泥流運動黏度設置小兩個的數量級，水體對圓柱的水平正向力會大於沒有泥床的數值實驗。本研究為各組數值實驗計算直立圓柱的傾倒力矩，基本上傾倒力矩的趨勢與總水平作用力趨勢相同，但數值模擬沒有考慮泥床效應即會低估傾倒力矩。這些研究成果在一定的程度上，提供了後者於離岸風電與其他海洋工程的規劃參考。

關鍵字

孤立波 ； 直立式圓柱 ； 雙黏性泥床 ； 波浪力 ； OpenFOAM

並列摘要

The study based on the numerical model of OpenFOAM. The influences of a solitary wave passing through a vertical cylinder over a bi-viscous muddy seabed was investigated by changing viscosity and yield stress. First, a 3D numerical wave tank was established to simulate the solitary wave passing through a vertical cylinder over a Newtonian muddy seabed not only to verify the parameters of the model settings and grids but also to point out that the size of grid can capture the physical phenomena. A two-dimensional numerical wave tank was established. Using the semi-analytical solution of a Bingham muddy seabed motions induced by a solitary wave to validate the bi-viscous model of this study. Numerical results agreed well with the semi-analytical solution in most of the phases. The study suggests for the Bingham viscosity with a pseudo-Newtonian viscosity of 1000 times. Finally, numerical experiments of a solitary wave passing through a vertical cylinder over a muddy seabed were carried out. Newtonian fluid model and the bi-viscous model for mud flow were considered. The value of viscosity and the yield stress were the controlling variables, which were discussed in two groups. It is found that the higher viscosity setting results in higher total horizontal forces in the group whose mud flow is a Newtonian mud flow. In addition, higher yield stress results in higher total horizontal forces in the group whose mud flow is a bi-viscous mud flow. The kinematic viscosity of mud flow reaches smaller two orders of magnitude that the horizontal force which the water exerts on the cylinder will be greater than the total force of the experiment without a muddy seabed. In this study, the toppling moment of the vertical cylinder was calculated for experiments. Basically, the trend of the topping moment is the same as the total horizontal force. However, the toppling moment will be underestimated if the numerical experiment doesn’t have a muddy seabed. To a certain extent, these results can provide references for the planning and design of offshore wind farms and other offshore structures.

並列關鍵字

Solitary wave ； Vertical cylinder ； bi-viscous muddy seabed ； Wave forces ； OpenFOAM

參考文獻

Boussinesq, J. (1872). Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond. Journal de mathématiques pures et appliquées, 55-108.

Chan, I. C., Liu, P. L. F. (2009). Responses of Bingham-plastic muddy seabed to a surface solitary wave. Journal of Fluid Mechanics, 618, 155-180.

Coussot, P. (1994). Steady, laminar, flow of concentrated mud suspensions in open channel. Journal of Hydraulic Research, 32(4), 535-559.

De Schryver, R., El Cheikh, K., Lesage, K., Yardimci, M. Y., De Schutter, G. (2021). Numerical Reliability Study Based on Rheological Input for Bingham Paste Pumping Using a Finite Volume Approach in OpenFOAM. Materials, 14(17), 5011.

Faltinsen, O. (1993). Sea loads on ships and offshore structures (Vol. 1). Cambridge university press.