基于Rankine源高阶面元法的船舶航行姿态与兴波阻力计算
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摘要
针对航行船舶的兴波阻力和姿态预报,采用Rankine源高阶面元法求解船舶航行兴波问题。计算时采用叠模线性化自由面条件,对自由面影响系数奇异积分采用源点上置的方法处理,物面奇异积分和立体角则直接求解。就数学船型Wigley、S60和KCS集装箱船的航行兴波阻力与姿态分别进行了数值计算与分析,计算中根据姿态变化重新划分船体湿表面,进行迭代计算,不同航速下的姿态、兴波阻力和船侧波高与试验结果比较,吻合良好,自由面波形真实反映了物理现象,研究表明本文方法能准确地预报船舶航行姿态和兴波阻力,对不同船型和航行速度有着广泛的适用性。
Aiming to predict ship performance such as wave drag, sinkage and trim, the steady ship wave problem is solved based on the high-order Rankine source method. Linearized free-surface condition with respect to double body potential is adopted in the calculation. And the raised panel approach is used to remove the singularity of integral related to influence coefficients on the free surface. Singular integral and solid angle of ship hull is solved directly. The present method is applied to Wigley, S60 and KCS container ships; sinkage, trim, wave drag and wave profile of these ships are calculated. The computation is iterative for ship mean wetted surface, which is regenerated based on the calculation of sinkage and trim. Numerical results and referenced experimental data are in good agreement. Calculated wave pattern agrees with Kelvin wave. It is indicated that present method is robust and suitable to predicting sinkage, trim and wave drag of ships with different hull types and at various speeds.
Aiming to predict ship performance such as wave drag, sinkage and trim, the steady ship wave problem is solved based on the high-order Rankine source method. Linearized free-surface condition with respect to double body potential is adopted in the calculation. And the raised panel approach is used to remove the singularity of integral related to influence coefficients on the free surface. Singular integral and solid angle of ship hull is solved directly. The present method is applied to Wigley, S60 and KCS container ships; sinkage, trim, wave drag and wave profile of these ships are calculated. The computation is iterative for ship mean wetted surface, which is regenerated based on the calculation of sinkage and trim. Numerical results and referenced experimental data are in good agreement. Calculated wave pattern agrees with Kelvin wave. It is indicated that present method is robust and suitable to predicting sinkage, trim and wave drag of ships with different hull types and at various speeds.
引文
[1]SUBRAMANI A K,PATERSON E G,STERN F.CFD calculation of sinkage and trim[J].Journal of Ship Research,2000,44:59-82.
[2]倪崇本,朱仁传,缪国平,等.计及航行姿态变化的高速多体船阻力预报[J].水动力学研究与进展,2011,26(1):101-107.
[3]YAO Caobang,DONG Wencai.Method to calculate resistance of high-speed displacement ship taking the effect of dynamic sinkage and trim and fluid viscosity into account[J].Journal of Shanghai Jiaotong University(Science),2012,17(4):421-426.
[4]YANG Chi,LOHNER R.Calculation of ship sinkage and trim using a finite element method and unstructured grids[J].International Journal of Computational Fluid Dynamics,2001,16(3):217-227.
[5]KARA F,VASSALOS D.Time domain computation of the wave-making resistance of ships[J].Journal of Ship Research,2005,49:144-158.
[6]TARAFDERA M S,KHALIL G M.Calculation of ship sinkage and trim in deep water using a potential based panel method[J].Journal of Applied Mechanics and Engineering,2006,11(2):401-414.
[7]YANG Chi,NOBLESSE F.A practical method for predicting sinkage and trim[C]//Proceeding of The Seventeenth(2007)International Offshore and Polar Engineering Conference.Lisbon,Portugal:2007.
[8]HUANG Fuxin.A practical computational method for steady flow about a ship[D].Washington:George Mason University,2013.
[9]王中,卢晓平,付攀.三体船升沉和纵倾计算及其对兴波阻力的影响[J].上海交通大学学报,2010,44(10):1388-1392.
[10]王中,卢晓平,王玮.考虑升沉和纵倾的方尾船非线性兴波阻力计算[J].水动力学研究与进展A辑,2010,25(3):422-428.
[11]GAO Zhiliang,ZOU Zaojian,WANG Huaming.Numerical solution of the ship wave-making problem in shallow water by using a high order panel method[J].Journal of Ship Mechanics,Ser.B,2008,12(6):858-869.
[12]GAO Gao,MA Ling.A raised panel method based on NURBS for free-surface potential flows with forward speed[J].Journal of Ship Mechanics,Ser.B,2003,(2):112-120.
[13]戴遗山.船舶在波浪中运动的频域与时域势流理论[M].北京:国防工业出版社,1998.
[14]陈曦.FPSO在波浪中的运动响应的时域模拟[D].哈尔滨:哈尔滨工业大学,2013.
[15]SHAO Yuanlin.Numerical potential-flow studies on weakly-nonlinear wave-body interaction with/without small forward speeds[D].Trondheim:Noewegian University of Science and Technolog,2010.
[16]高高.船舶兴波问题面元法的误差分析[J].水动力学研究与进展A辑,1997,12(4):470-477.
[17]Experimental data for the Wigley hull are reported in cooperative experiments on the Wigley parabolic model in Japan[R].prepared for the17th ITTC Resistance Committee,2nd edition,1983.
[18]Experimental data for the Series 60 model are reported in cooperative experiments on the Series 60(Cb=0.6)model[R].prepared for the 18th ITTC Resistance Committee,1986.
[19]ENGER S,PERI?M,PERI?R.Simulation of flow around KCS-hull[C]//A Workshop on CFD in Ship Hydrodynamics.Gothenburg,Sweden:2010.
[20]HE Guanghua,KASHIWAGI M.Time domain simulation of steady ship wave problem by a higher-order boundary element method[C]//Proceedings of the Twenty-second(2012)International Offshore and Polar Engineering Conference.Rhodes,Greece,2012.
[21]TARAFDER M S,SUZUKI K.Numerical calculation of free-surface potential flow around a ship using the modified Rankine source panel method[J].Ocean Engineering,2008,35:536-544.
[2]倪崇本,朱仁传,缪国平,等.计及航行姿态变化的高速多体船阻力预报[J].水动力学研究与进展,2011,26(1):101-107.
[3]YAO Caobang,DONG Wencai.Method to calculate resistance of high-speed displacement ship taking the effect of dynamic sinkage and trim and fluid viscosity into account[J].Journal of Shanghai Jiaotong University(Science),2012,17(4):421-426.
[4]YANG Chi,LOHNER R.Calculation of ship sinkage and trim using a finite element method and unstructured grids[J].International Journal of Computational Fluid Dynamics,2001,16(3):217-227.
[5]KARA F,VASSALOS D.Time domain computation of the wave-making resistance of ships[J].Journal of Ship Research,2005,49:144-158.
[6]TARAFDERA M S,KHALIL G M.Calculation of ship sinkage and trim in deep water using a potential based panel method[J].Journal of Applied Mechanics and Engineering,2006,11(2):401-414.
[7]YANG Chi,NOBLESSE F.A practical method for predicting sinkage and trim[C]//Proceeding of The Seventeenth(2007)International Offshore and Polar Engineering Conference.Lisbon,Portugal:2007.
[8]HUANG Fuxin.A practical computational method for steady flow about a ship[D].Washington:George Mason University,2013.
[9]王中,卢晓平,付攀.三体船升沉和纵倾计算及其对兴波阻力的影响[J].上海交通大学学报,2010,44(10):1388-1392.
[10]王中,卢晓平,王玮.考虑升沉和纵倾的方尾船非线性兴波阻力计算[J].水动力学研究与进展A辑,2010,25(3):422-428.
[11]GAO Zhiliang,ZOU Zaojian,WANG Huaming.Numerical solution of the ship wave-making problem in shallow water by using a high order panel method[J].Journal of Ship Mechanics,Ser.B,2008,12(6):858-869.
[12]GAO Gao,MA Ling.A raised panel method based on NURBS for free-surface potential flows with forward speed[J].Journal of Ship Mechanics,Ser.B,2003,(2):112-120.
[13]戴遗山.船舶在波浪中运动的频域与时域势流理论[M].北京:国防工业出版社,1998.
[14]陈曦.FPSO在波浪中的运动响应的时域模拟[D].哈尔滨:哈尔滨工业大学,2013.
[15]SHAO Yuanlin.Numerical potential-flow studies on weakly-nonlinear wave-body interaction with/without small forward speeds[D].Trondheim:Noewegian University of Science and Technolog,2010.
[16]高高.船舶兴波问题面元法的误差分析[J].水动力学研究与进展A辑,1997,12(4):470-477.
[17]Experimental data for the Wigley hull are reported in cooperative experiments on the Wigley parabolic model in Japan[R].prepared for the17th ITTC Resistance Committee,2nd edition,1983.
[18]Experimental data for the Series 60 model are reported in cooperative experiments on the Series 60(Cb=0.6)model[R].prepared for the 18th ITTC Resistance Committee,1986.
[19]ENGER S,PERI?M,PERI?R.Simulation of flow around KCS-hull[C]//A Workshop on CFD in Ship Hydrodynamics.Gothenburg,Sweden:2010.
[20]HE Guanghua,KASHIWAGI M.Time domain simulation of steady ship wave problem by a higher-order boundary element method[C]//Proceedings of the Twenty-second(2012)International Offshore and Polar Engineering Conference.Rhodes,Greece,2012.
[21]TARAFDER M S,SUZUKI K.Numerical calculation of free-surface potential flow around a ship using the modified Rankine source panel method[J].Ocean Engineering,2008,35:536-544.