基于解析复势的Joukowski翼型的附加质量
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摘要
附加质量是影响水下运动物体受力的重要参数之一。为了高效准确地计算无限域理想流体中Joukowski翼型的附加质量,在推导出基于势流理论的流场复势解析解后,采用复变函数计算流体动能,并根据流体动能与附加质量的关系求解物体的附加质量。通过计算单个圆柱在无限域理想流体中运动的附加质量,验证了采用此方法的便捷性和准确性。运用这个动能推导公式着重研究了不同形状的Joukowski翼型以任意攻角运动的附加质量,得到翼型厚度参数R/a、弧度参数β及翼型运动方向α与附加质量的关系。计算结果表明:水平运动即(α=0)时,Joukowski翼型的附加质量随着R/a、β的增大而增大;竖直运动即(α=π/2)时,附加质量随着R/a的增大、β的减小而减小;除α=0、α=π/2外,此方法还能计算机翼以任意其他攻角运动时的附加质量,具有很好的适用性。
Added mass is one of the most important parameters affecting the mechanical behaviors of objects moving in fluids. The complex potential is used to calculate the kinetic energy of the fluid with a contour integral around the body,and thereby the added mass of moving Joukowski airfoils is determined. The accuracy and convenience of this method is verified by calculating the added mass for a single cylinder. Then the derived formula is transformed to study the added mass of the Joukowski airfoils at arbitrary attack angle α,from which we find out how the added mass dependson the thickness ratio R/a,the level of camber β,and the direction of motion. In particular,it is shown that at α = 0,the added mass of the Joukowski airfoil increases with R/a,as well as β,while at α = π/2,the added mass increases with R/a or the decrease of β. The added mass at other attack angles can also be readily obtained,which demonstrates the practicality of this analytic approach.
Added mass is one of the most important parameters affecting the mechanical behaviors of objects moving in fluids. The complex potential is used to calculate the kinetic energy of the fluid with a contour integral around the body,and thereby the added mass of moving Joukowski airfoils is determined. The accuracy and convenience of this method is verified by calculating the added mass for a single cylinder. Then the derived formula is transformed to study the added mass of the Joukowski airfoils at arbitrary attack angle α,from which we find out how the added mass dependson the thickness ratio R/a,the level of camber β,and the direction of motion. In particular,it is shown that at α = 0,the added mass of the Joukowski airfoil increases with R/a,as well as β,while at α = π/2,the added mass increases with R/a or the decrease of β. The added mass at other attack angles can also be readily obtained,which demonstrates the practicality of this analytic approach.
引文
[1]LAUDER M A,DABNICHKI P.Estimating propulsive forces—sink or swim?[J].Journal of Biomechanics,2005,38(10):1984-90.
[2]GARDANDO P,DABNICHKI P.On hydrodynamics of drag and lift of the human arm[J].Journal of Biomechanics,2006,39(15):2767-2773.
[3]GARDANO P,DABNICHKI P.Application of Boundary Element Method to modelling of added mass and its effect on hydrodynamic forces[J].CMES Computer Modeling in Engineering&ENCES,2006,15(2):87-98.
[4]DABNICHKI P.Modelling,computing and sport[J].Informatik-Spektrum,2008,31(4):316-322.
[5]LANDWEBER L,YIH C S.Forces,moments,and added masses for Rankine bodies[J].Journal of Fluid Mechanics,2006,1(3):319-336.
[6]LANDAU L D,LIFSHITZ E M.Fluid mechanics[M].Institute of Physical Problems,U.S.S.R:Academy of Sciences,1987:26-30.
[7]邱大洪,朱大同.圆形桩柱列的附加质量[J].海洋工程,1983(2):15-21.
[8]YIN C S.New derivations of Darwin’s theorem[J].Journal Fluid Mech,1985,152:163-172.
[9]许维德,林建国.细长回转体附加质量的数值计算[J].水动力学研究与进展,1986,1(2):70-81.
[10]王基盛,杨庆山.流场环境中结构附加质量的计算[J].北方交通大学学报,2003,27(1):40-43.
[11]黄璇,鲁传敬,李杰.带空泡运动航行体的附加质量研究[J].水动力学研究与进展,2009,24(6):800-806.许维德,林建国.细长回转体附加质量的数值计算[J].水动力学研究与进展,1986,1(2):70-81.
[12]刘丹,王晓亮,单雪雄.平流层飞艇的附加质量及其对飞艇运动的影响[J].计算机仿真,2006,23(6):52-56.
[13]马烨,单雪雄.数值计算复杂外形物体附加质量的新方法[J].计算机仿真,2007,24(5):395-398.
[14]傅慧萍,李杰.附加质量CFD计算方法研究[J].哈尔滨工程大学学报,2011,32(2):148-152.
[15]冯双双,魏晓娟,孙磊,等.流场中沿轴向运动圆柱的附加质量计算[J].计算机辅助工程,2015,24(2):42-46.
[16]MILNE THOMSON L,ROTT N.Theoretical hydrodynamics,fifth edition[J].Journal of Applied Mechanics,1968,35(4):846.
[17]CHRISTOPHER E.BRENNEN.Internet book on the fluid dynamics[DB/OL].[2004-05-11].http://brennen.caltech.edu/fluidbook/index.htm.
[18]CHANG C C.Potential Flow and Forces for Incompressible Viscous Flow[J].Proceedings of the Royal Society of London:series A,1992,437:517-525
[2]GARDANDO P,DABNICHKI P.On hydrodynamics of drag and lift of the human arm[J].Journal of Biomechanics,2006,39(15):2767-2773.
[3]GARDANO P,DABNICHKI P.Application of Boundary Element Method to modelling of added mass and its effect on hydrodynamic forces[J].CMES Computer Modeling in Engineering&ENCES,2006,15(2):87-98.
[4]DABNICHKI P.Modelling,computing and sport[J].Informatik-Spektrum,2008,31(4):316-322.
[5]LANDWEBER L,YIH C S.Forces,moments,and added masses for Rankine bodies[J].Journal of Fluid Mechanics,2006,1(3):319-336.
[6]LANDAU L D,LIFSHITZ E M.Fluid mechanics[M].Institute of Physical Problems,U.S.S.R:Academy of Sciences,1987:26-30.
[7]邱大洪,朱大同.圆形桩柱列的附加质量[J].海洋工程,1983(2):15-21.
[8]YIN C S.New derivations of Darwin’s theorem[J].Journal Fluid Mech,1985,152:163-172.
[9]许维德,林建国.细长回转体附加质量的数值计算[J].水动力学研究与进展,1986,1(2):70-81.
[10]王基盛,杨庆山.流场环境中结构附加质量的计算[J].北方交通大学学报,2003,27(1):40-43.
[11]黄璇,鲁传敬,李杰.带空泡运动航行体的附加质量研究[J].水动力学研究与进展,2009,24(6):800-806.许维德,林建国.细长回转体附加质量的数值计算[J].水动力学研究与进展,1986,1(2):70-81.
[12]刘丹,王晓亮,单雪雄.平流层飞艇的附加质量及其对飞艇运动的影响[J].计算机仿真,2006,23(6):52-56.
[13]马烨,单雪雄.数值计算复杂外形物体附加质量的新方法[J].计算机仿真,2007,24(5):395-398.
[14]傅慧萍,李杰.附加质量CFD计算方法研究[J].哈尔滨工程大学学报,2011,32(2):148-152.
[15]冯双双,魏晓娟,孙磊,等.流场中沿轴向运动圆柱的附加质量计算[J].计算机辅助工程,2015,24(2):42-46.
[16]MILNE THOMSON L,ROTT N.Theoretical hydrodynamics,fifth edition[J].Journal of Applied Mechanics,1968,35(4):846.
[17]CHRISTOPHER E.BRENNEN.Internet book on the fluid dynamics[DB/OL].[2004-05-11].http://brennen.caltech.edu/fluidbook/index.htm.
[18]CHANG C C.Potential Flow and Forces for Incompressible Viscous Flow[J].Proceedings of the Royal Society of London:series A,1992,437:517-525