回转体局部空泡绕流的非线性分析

基于面元法, 通过在回转体和空泡壁面放置源汇,对回转体定长局部空泡的绕流问题进行了分析和讨论,并提出了求解回转体局部空泡绕流“正问题”的方法。计算结果表明：所给出的方法具有快速收敛的特征,第1次迭代和最终收敛时空泡壁面切向速度的误差不超过5％;随着回转体面元总数N的增加,局部空泡的空泡数σ趋于稳定;通过比较可知,该方法得到的理论估算值与实测值的一致性较好。

A NUMERICAL ANALYSIS OF THE FLOW AROUND A PARTIALLY-CAVITATING AXISYMMETRIC BODY

As the speed of underwater vehicles have become higher, cavitation plays an important role in the unsteady forces and also causes severe noise and vibration problems on the shell of vehicle. In order to control these problems and also to design a vehicle with the sufficient shape, it is necessary to be able to predict the extent and behavior of the cavity on the surface of vehicles with improved accuracy. And recently, a potential-based boundary element method (i.e. one employs the normal dipoles and sources distributed on the body and cavity surfaces) was developed by Kinnas & Fine (J. Fluid Mech., 1993, 254(9)) for the nonlinear analysis of the flow around partially and supercavitating 2-D hydrofoils. In this work, a potential-based panel method is presented for the analysis of a partially-cavitating axisymmetric body. The cavity boundary is determined in the framework of two independent boundary-value problems: in the first, the cavity length is specified and the cavitation number is unknown; and in the second, the cavitation number is known and the cavity length is to be determined. For the first problem, the exact cavity boundary is determined by an iterative process in which the dynamic boundary condition is satisfied on an approximate cavity surface and the kinematic boundary condition is used to update the surface. The iterations terminate when both the kinematic and the dynamic boundary conditions are satisfied on the computed cavity surface. The panel method, which employs sources distributed on the body and cavity surfaces, has been found to converge to the final cavity shape with few iterations. In particular, it has been found that the first step in the iterative method predicts a cavity shape which is very close to the converged nonlinear shape. The rapid convergence characteristics of the potential-based panel method has encouraged the extension of the method to solve the so-called "direct" problem, in which the cavity extent is unknown and the cavitation number is known. Based on Newton-Raphson optimum strategy and building the openness of cavity trailing edge, the formulation of the scheme are presented in detail to solve the cavity extent in the text. It is shown that systematic convergence tests of the present numerical method show fast and stable characteristics; and good correlation are obtained with existing theory and experimental results for partially cavitation flows.