含黏性力最速降线问题的最优化解法及其在ADS设计中的应用

An optimization method of brachistochrone problem with viscous friction and its application in ADS design

为优化加速器驱动次临界系统（ADS）靶件束窗形状设计,该文研究了一类含黏性力的最速降线问题。采用变分法进行分析,最终需数值求解一组非线性积分方程。针对Newton迭代法在高黏性系数情况下难以获得收敛解且无法获得近似解的缺陷,提出一种最优化求解思路。通过数值试验比较了4种启发式最优化算法的计算效率,并选择粒子群算法与Newton迭代法作进一步对比。结果表明：在高黏性系数情况下粒子群算法计算效率优于Newton迭代法,并且粒子群算法在该问题上近似线性收敛。用最速降线取代半椭圆的束窗形状后,流动分离更晚且流道滞止区更小,有利于提升换热效率。

The brachistochrone problem with viscous friction was studied to optimize the beam window （BW） shape of an accelerator driven sub-critical system （ADS） target. A set of nonlinear integral equations was derived using the variational method. The Newton iteration method could not get a convergent solution or an approximate solution for the highly viscous conditions, so an optimization method was developed. The particle swarm optimization （PSO） algorithm was found to be more efficient for the highly viscous conditions than other three heuristic algorithms with approximately linear convergence. The flow separation is later and the stagnation region is smaller for the brachistochrone BW instead of the semiellipticaI BW, which enhances the heat transfer.