Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation o...Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation of added resistance. Based on the potential flow assumption, the velocity potential is computed using Green＇s formula. The Kochin function is applied to compute added resistance using Maruo＇s far-field method, the body surface is described by a B-spline curve and potentials and normal derivation of potentials are also described by B-spline basis functions and B-spline derivations. A collocation approach is applied for numerical computation, and integral equations are then evaluated by applying Gauss–Legendre quadrature. Computations are performed for a spheroid and different hull forms; results are validated by a comparison with experimental results. All results obtained with the present method show good agreement with experimental results.展开更多
In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increa...In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increasing number of design variables,it becomes difficult to maintain the smoothness on the surface which consequently makes the optimization process progressively complex.In this paper,smoothing methods based on B-spline functions are studied to improve the smoothness and design efficiency.The wavelet smoothing method and the least square smoothing method are developed through coordinate transformation in a linear space constructed by B-spline basis functions.In these two methods,smoothing is achieved by a mapping from the linear space to itself such that the design space remains unchanged.A design example is presented where aerodynamic optimization of a supercritical airfoil is conducted with smoothing methods included in the optimization loop.Affirmative results from the design example confirm that these two smoothing methods can greatly improve quality and efficiency compared with the existing conventional non-smoothing method.展开更多
文摘Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation of added resistance. Based on the potential flow assumption, the velocity potential is computed using Green＇s formula. The Kochin function is applied to compute added resistance using Maruo＇s far-field method, the body surface is described by a B-spline curve and potentials and normal derivation of potentials are also described by B-spline basis functions and B-spline derivations. A collocation approach is applied for numerical computation, and integral equations are then evaluated by applying Gauss–Legendre quadrature. Computations are performed for a spheroid and different hull forms; results are validated by a comparison with experimental results. All results obtained with the present method show good agreement with experimental results.
文摘In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increasing number of design variables,it becomes difficult to maintain the smoothness on the surface which consequently makes the optimization process progressively complex.In this paper,smoothing methods based on B-spline functions are studied to improve the smoothness and design efficiency.The wavelet smoothing method and the least square smoothing method are developed through coordinate transformation in a linear space constructed by B-spline basis functions.In these two methods,smoothing is achieved by a mapping from the linear space to itself such that the design space remains unchanged.A design example is presented where aerodynamic optimization of a supercritical airfoil is conducted with smoothing methods included in the optimization loop.Affirmative results from the design example confirm that these two smoothing methods can greatly improve quality and efficiency compared with the existing conventional non-smoothing method.
