Three-Dimensional Thick Boundary Layer Calculation Of A Submarine And A Research For Two-Dimensional Free Surface Wave

This paper includes two parts. In the first part,a semi-empirical and semi-theoretical calculation approach is presented for practical engineering application. The boundary layer and wake characteristic parameters,viscous resistance and velocity distribution can be obtained by using this method. In the second part,two-dimensional free surface wave is discussed,and some available results are presented.In the first part,the integral method is adopted by comparing the differential method with integral method of boundary layer equations. The integral method has better computing stability and higher precision with less computer time and capacity. The boundary layer and wake of a submarine are theoretically analyzed and computed. The useful results are prepared for hydrodynamic noises prediction and propeller performance research.The studies of the boundary layer and wake for the submarine are based on the calculation of potential flow. The velocity and pressure information of any point on the body surface can be acquired by the Hess-Smith method of non-lifting potential flow for arbitrary three-dimensional bodies. Using the potential flow computation the effective boundary conditions can be found for solving the boundary layer and wake problem. And then the characteristic parameters and velocity distribution of a section can be predicted. Streamline tracing method is used to find streamline and build the streamline reference frame. The three-dimensional thin boundary layer equations consist of longitudinal,transverse momentum integral equations,entrainment equation,the skin friction relation and the velocity profile family. Here the normal pressure gradient is zero. After considering the normal gradient of the velocity and the pressure,the three-dimensional thick boundary layer equations are formed.The skin friction coefficient is zero in the wake,and the longitudinal velocity profile family is different from the three-dimensional thick boundary layer. Equivalent sources method is used for considering the effect of boundary layer displacement. Equivalent imaginary body method is used for considering the effect of wake displacement. Considering the effect of displacement,the boundary layer and wake of a submarine are calculated again.In the first part,a new turbulent boundary layer method,the Two-Layer Model(TLM) integral method,is discussed for the flat plate turbulent boundary layers. In this method,the law of the wall is used in the inner region ,whereas Clauser's eddy viscosity is used in the outer region under the assumption of quadratic parabola distribution for shear stress. The results are compared with the analytic values of the 1/7 power-law One-Layer Mode(lOLM)and good agreements are shown. The method can be extended to axisymmetric and three-dimensional turbulent boundary layer if the pressure gradient effect is considered.In the second part,four free surface tracing modes are presented to deal with two-dimensional free surface wave problem. For numerical studies the propagation and deformation of a solitary wave in a rectangular channel are analyzed by arbitrary Lagrangian-Eulerian finite element method and compared with each other. It is concluded that mode D (some grid points moving along the outward normal to the free surface and the others moving with the fluid particles on the free surface together) is recommendable for practical computations.