چکیده

هیدرودینامیک شناورها توسط پیچیدگی حضور سطح آزاد توصیف می‌گردد. جسمی که در نزدیکی سطح آزاد حرکت می‌نماید باعث اغتشاش در سطح افقی مایع و بوجود آمدن امواج می‌گردد. هدف اصلی از محاسبه پارامترهای امواج سطحی در نزدیکی کشتی‌ها، محاسبه مقاومت موج‌سازی و ضرایب هیدرودینامیکی می‌باشد.از آنجایی که با پیشروی شناور در آب عمیق، ذرات سیال توانایی حرکت آزادانه در اطراف شناور را دارا می‌باشد ولی در آب کم عمق، دامنه حرکت این ذرات محدود می‌شود و در نتیجه خطوط جریان در اطراف این شناور نسبت به آب عمیق تغییر خواهد کرد. این تغییرات می‌تواند به عنوان هدف اصلی این تحقیق به شمار آید. با انتخاب بدنه ویگلی و یک نقطه فشاری به عنوان مدل‌های انتخابی جهت انجام این کار،  به شبکه‌بندی مرز جسم و اعمال شرایط مرزی نفوذناپذیری بستر و بدنه و شرط خطی‌سازی شده سطح آزاد و شرط تابش در معادله مشخصه گرین به مدل‌سازی عددی این مسئله پرداخته شده است. نتایج حاصل از روش عددی  المان مرزی شامل محاسبه ضریب سرعت یک چشمه در آب کم عمق جهت تأیید تابع گرین به کار رفته در معادله مشخصه گرین و سپس امواج سطحی در اطراف و پشت شناور و محاسبه پتانسیل اغتشاش در اطراف بدنه است که برای اعداد فرود عمق مختلف انجام شده است.

کلیدواژه‌ها

عنوان مقاله [English]

Numerical calculation of free-surface flow around moving body at finite depth of water

چکیده [English]

Potential flow around the marine structures based on Greens' Theorem has been developed in ocean engineering problems. The main goal of surface wave parameters definition around body is calculation of wave making resistance and hydrodynamic coefficients. As body moves in deep water, fluid particles can move around hull freely but when it enters shallow water the particles movement is restricted and therefore wave pattern around body changes significantly. Changes mentioned can be considered as an interesting purpose in present study.Laplaceequation in irrotational, inviscid, incompressible control volume of fluid is released as governing equation. The three-dimensional Boundary Element method is accomplished to calculate potential function at any point of computational field. To satisfy Neumann boundary conditions, the image method is employed. The Green function consists three parts. First part relates to the location of the singularity in the domain and its images with respect to the bottom. In The Second part, the free surface disturbance due to the singularity and its images is affected. Radiation condition is applied in third part. Numerical computations are applied to free surface waves generated by Wigley hull and moving pressure disturbance for the steady problem. The characteristic of wash wave such as the wave pattern on the free surface for different depth froude numbers and speed coefficients for pressure point in shallow water are reasonably predicted.

کلیدواژه‌ها [English]

  • Potential Flow
  • Boundary element method
  • Source perturbation
  • shallow water

  1. Newman, J.N., Marine Hydrodynamics, 6th ed., MIT Press. 1989.
  2. Wehausen, J.V., Laitone, E.V., Surface Waves, Online Copyright:University ofCalifornia. 2002.
  3. Katsikadelis, J.T., Boundary Elements: Theory and Applications,Athens.Greece: Elsevier. 2002.
  4. Haberman, R., Elementary Applied Partial Differential Equation, 2nd ed.,New Jersey: Prentice-Hall. 1987.
  5. Dean, R.G., Dalrymple, R.A., Water Wave Mechanics for Engineering and Scientist,New Jersey: Prentice-Hall. 1984.
  6. Sahin,I., Hyman, M., “Numerical Calculation for the Flow of Submerged Bodies under a Free Surface”, J. OceanEng., Vol. 20, No. 3, pp. 339-347, 1993.
    1. Sahin,I., Hyman, M., Nguyen, T.C. “Three Dimensional Flow around a Submerged Body in Finite-Depth Water”, Appl. Math. Modeling, Vol. 18, pp. 611-619, 1994.
    2. Kim. B., Shin. Y.S., “A NURB Panel Method for Three-Dimensional Radiation and Diffraction Problems”, J. Ship Research, Vol. 47, pp. 177-186, 2003.
    3. Kouh, J.S., Ho, and C.H. “A High Order Panel Method Based on Source Distribution and Gaussian Quadrature”. J. Ship Tech. Research, Vol. 43, pp. 38-47, 1996.
    4. Tarafder, Md.S, Suzuki, K. “Numerical Calculation of Free Surface Potential Flow around a Ship Using The Modified Rankin Source Panel Method”, J. OceanEng., Vol. 35pp. 536-544, , 2008.
    5. Bal, S. “Prediction wave Pattern and Wave Resistance of Surface Piercing Bodies by a Boundary Element Method”. Int. J. for Numerical Method in Fluids, Vol. 56, pp. 305-329, 2008.
    6. Tuck. E.O, Scullen. D.C. “A Comparison of Linear and Nonlinear Computations of Waves Made by Slender Submerged Bodies”, J. ofEng.Mathematics, Vol. 42, pp. 255-264, 2002.
    7. Jiankang. W., Lee. T.S., Shu. C. “Numerical Study of Wave Interaction Generated by Two Ships Moving Parallely in Shallow Water”, J. Comput. Methods Appl. Mech. Eng., Vol. 190, pp. 2099-2110, 2001.
    8. Bal S., Kinnas SA. “A BEM for the Prediction of Free Surface Effects on Cavitating Hydrofoils”, J. Comput. Mechanics, Vol. 28, pp.260–274, 2002.
    9.  Bulgarelli. U.P., Lungi. C., Landrini. M. “Numerical Modeling Free Surface Flows in Ship Hydrodynamics”, Int. J. Numer. Meth. Fluids, Vol. 43, pp. 465-481, 2003.
    10. Xie. N., Vassalos. D. “Performance Analysis of 3D Hydrofoil under Free Surface”, J. OceanEng., Vol. 34, pp. 1275-1264, 2006.

Tarafder. Md.S, Suzuki. J. “Numerical Calculation of Free-Surface Potential Flow Around a Ship Using The Modified Rankine Source Panel Method”, J. Ocean Eng., Vol. 35, pp. 536-544, 2008