双调和方程在航空离心泵叶型优化设计的应用

为了减少构建代理模型的计算量，提高优化效率，基于双调和方程模型和混合人工鱼群算法对航空离心泵叶型进行优化改型设计。在Matlab平台下分别采用5点4次Bezier曲线和线性函数控制叶型圆周角分布和积叠变化规律，通过软件UG和Fluent的联合批处理方法对15组设计结果进行内流场数值仿真。在曲面插值获得计算空间边界条件的基础上，采用中心差分格式对双调和偏微分方程进行数值求解，建立超曲面性能代理模型。以效率最高为目标函数基于人工鱼群算法对设计变量进行全局寻优。结果表明:基于双调和方程的超曲面代理模型能够保证试验值与预测值完全一致，而优化后的离心叶轮流动中的尾迹效应被明显减弱，水力效率比原型泵提高5.4%。 

Application of biharmonic equation in optimization design of aero centrifugal pump blade profile

In order to reduce the amount of computation and improve the efficiency of optimization process, the optimization design of aero centrifugal pump blade profile based on the biharmonic equation agent model and hybrid artificial fish-swarm algorithm was studied. Five-point fourth-order Bezier curves and linear function were used to control the distribution of the circumference angles and the stacking of the blade profile under the Matlab platform. The numerical simulation of the 15 design results was carried out by the joint batch processing of softwares UG and Fluent. Then based on surface interpolation, the calculation of spatial boundary conditions was obtained, and biharmonic partial differential equation on central difference scheme was solved to establish the hypersurface agent model. The objective function of maximum efficiency was used to optimize the design variables based on the artificial fish swarm algorithm. Results showed that the artificial fish-swarm optimization method based on biharmonic equation agent model can ensure the test value and the predicted value were exactly the same. Compared with prototype the wake effect in the optimized impeller was weakened, and the hydraulic efficiency increased by 5.4%.