Study on Optimum Body Shape of Minimum Drag in 2-Dimensional Oseen Flow.

本文研究了用最小粘性阻力获得机身外形的反问题。在此之前的第一年，作者将共同研究人员Bessho教授开发的阻力最小化逆过程应用于二维Osen流动，得到了关于原点的对称最优剖面。第二年，将该方法推广到了几种约束条件下阻力最小的前后部非对称剖面。给出了数值结果，并对最优剖面进行了讨论。寻找最佳剖面的过程是迭代方法。首先利用Osee核函数由积分方程组确定给定剖面的流量，然后用面元方法进行数值求解。然后确定最优变形，以使阻力最小，其中控制方程也用一组积分方程组表示，并以与前一步相同的方式得到解。然后对人体轮廓进行变形以获得新的轮廓。迭代这个过程，直到达到收敛。这样得到的最佳剖面与第一年的剖面完全一致。在给定轮廓线中心和长度的情况下，得到了一种新的前、后不对称形状的最佳轮廓线。

The present study deals with an inverse problem for obtaining body profiles with minimum viscous drag. In the preceeding first year, the authors applied an inverse procedure for drag minimization developed by the co-investigator, Prof. Bessho, to two-dimensional Oseen flow, and obtained symmetric optimum profiles about the origin. This second year, the method has veen extended to fore-aft asymmetric profiles with minimum drag under several restriction conditions. Numerical results and discussions on the optimum profiles are made.The procedure to find optimum profiles is an iterative method. The flow quantities for a given profile are firstly determined by integral equations using Oseen's kernel functions, and are numerically solved by a panel method. Then the optimum deformation is determined so that the drag is minimized, in which the governing equation is also expressed by a set of integral equations and the solution is obtained in the same way as the former step. Then the body profiles is deformed to obtain a new profile. This procedure is iterated until a convergence is reached.The optimum profiles thus obtaind are entirely coincide with those in the first year. For the case of center of profile and length prescribed, a new optimum profile of fore-aft asymmetric shape is obtained.