A Numerical Analysis of The Wave Forces on Vertical Cylinders by Boundary Element Method Msc Cao Tan Ngoc Than* ** Graduate School, Cheju National University, Cheju, Korea, 690 756 -Speaker April 18,2009 Contents Giới thiệu Phương Pháp Phần Tử Biên Kết phân tích kiểm tra Kết luận I Introduction Gần có nhiều lọai công trình biển khác xây dựng nhóm cọc cột tròn Vì tương tác sóng nhóm cột tròn cần nghiên cứu cách xác để đánh giá ổn định công trình Có nhiều nhà nghiên cứu công trình nghiên cứu tương tác sóng nhóm cột là:  Chakrabarti (1978) Ohkusu (1974) – phân tích lực sóng lên nhóm cột  Kim Park (2007)- phân tích lực sóng lên cột tròn riêng lẽ phương pháp phần tử biên Research Object  Phương pháp tính lực sóng tác dụng lên nhóm cột sử dụng phương pháp phần tử biên phát triển để giải tượng nhiễu xạ sóng nhóm cột  Mô hình cột, hai cột ba cột sử sụng nghiên cứu  Để kiểm chứng kết quả, kết tính toán lực sóng tác dụng lên cột, hai cột, ba cột nghiên cứu so sánh với kết tính toán MâcCamy and Fuchs (1954), Chakrabảti (1978) va Ohkusu (1974)  Sóng dâng lên (run-up) phân bố chiều cao sóng xung quanh cột (wave height distribution) tính toán nghiên cứu II Boundary Element Analysis Hiện tượng song nhiễu xạ(Diffraction phenomenon)  As an incident wave impinges on the cylinder, a reflected wave moves outward On the sheltered side of the cylinder there will be a “shadow” zone where the wave fronts are bent around the cylinder, the so-called diffracted waves  Khi sóng tới (incident wave) tác dụng lên cột, sóng phản xạ (reflected wave) phản ngược trở lại Phần phía sau cột xuất vùng khuất (shadow zone) Sketch of the incident, diffracted and reflected wave fronts for a vertically placed cylinder Adapted from B Mutlu(1997)  The diffraction effect becomes important when the ratio D / L becomes larger than 0.2(Isaacson, 1979) Different flow regimes in the ( KC , D / L ) plane Adapted from Isaacson (1979) Basic Equations It is assumed that fluid is inviscid, incompressible, and its motion is irrotational Velocity potential can be defined as follows: it  ( x, y , z; t )  Re { ( x, y , z )e } where i   is the imaginary unit Total velocity potential:   I  S Velocity potential of incident wave: I ( x, y , z )  cosh k ( h  z ) cosh kh I , I  e Velocity potential of scattered wave:  S ( x, y , z )  Dispersion relation: cosh k ( h  z ) cosh kh   gk kh S ( x, y ) ik ( x cos   y sin  ) Boundary Conditions Laplace equation  S  in  Free surface condition:  S   S z  on Γ g F Sea bed condition:  S  z on  B Cylinder surface condition:  S n   I n on H ; m  1, , N m Radiation condition: lim R   S R  R   ik  S   on Γ R R  x2  y Definition of two vertical circular cylinders (N=2)  The boundary value is presented by using  S in two dimension ( x, y ) plane as follows: Helmholtz Equation:  S  k S  in  Cylinder surface condition: S  I  n n on S H , m  1, , N m Radiation boundary condition: lim R R{  S R  ik S }  on S  Wave Force 2a incident incident wave wave 2a D Y D X Wave force in x -direction acting on cylinder versus wave number ka incident wave Y X 2a D Wave force in x -direction acting the cylinders in two tandem cylinders versus wave number ka incident wave Y X D 2a Wave force in x -direction acting on the three cylinders in array versus wave number ka triangular Effect of Cylinder Spacing 2a incident wave Y D X Wave force in x -direction acting on cylinder versus ratio   a / D for ka  1.0 incident wave Y X 2a D Wave force in x -direction acting on the cylinder in two tandem cylinders versus ratio   a / D for ka  1.0 incident wave Y X D 2a Wave force in x -direction acting on three cylinders in triangular array versus ratio   a / D for ka  1.0 Effect of Incident Wave Angle  incident wave Y X 2a D Wave force in x -direction acting on the cylinder at various incident wave angle   0 ,30 ,450 ,60 for ka  1.0  incident wave Y X 2a D Wave force in x -direction acting on the cylinder at various incident wave angle   0 ,30 ,450 ,600 for ka  1.0 Run-up incident wave  Y D X  2a Run-up on the outer walls of the cylinders in two transverse cylinders for ka  1.0 incident wave Y  X 2a  D Run-up on the outer walls of the cylinders in two tandem cylinders for ka  1.0 incident wave  D   Run-up on the outer walls of three cylinders in triangular array for ka  1.0 Free-Surface Elevation nt w ide inc ave ent incid a) e wav b) Wave height distribution around two transverse cylinders and two tandem cylinders for ka  1.0 inciden t wave Wave height distribution around three cylinders in triangular array for ka  1.0 IV Conclusions and Remarks  The wave forces acting on two cylinders and three cylinders are computed by using boundary element method The numerical results are in good agreement with those of Chakrabarti (1978) and Ohkusu (1974)  As the wave number ka increases The wave forces on the cylinders oscillate around the wave forces on an isolated cylinder  As the cylinder spacing increases, the wave force on the cylinders not decrease linear to the wave force on an isolated cylinder, however it oscillates around the wave force on an isolated cylinder The amplitude of oscillation is extremely large as the ratio   0.2  Due to the interaction of the cylinders, the run-up profiles of the cylinders are quite different from that of an isolated cylinder  This numerical computation method will be used broadly for analysis of offshore structures to be constructed in coastal zones in the future ... (1974)  As the wave number ka increases The wave forces on the cylinders oscillate around the wave forces on an isolated cylinder  As the cylinder spacing increases, the wave force on the cylinders. .. Remarks  The wave forces acting on two cylinders and three cylinders are computed by using boundary element method The numerical results are in good agreement with those of Chakrabarti (1978) and... xạ(Diffraction phenomenon)  As an incident wave impinges on the cylinder, a reflected wave moves outward On the sheltered side of the cylinder there will be a “shadow” zone where the wave fronts are