基于伴随方法的离心泵叶轮优化设计  

Blade shape optimization of centrifugal pump impeller with adjoint method

作　　者：张人会[1,2] 郭苗[1] 杨军虎[1,2] 刘宜[1,2] 

机构地区：[1]兰州理工大学能源与动力工程学院,甘肃兰州730050 [2]甘肃省流体机械及系统重点实验室,甘肃兰州730050

出　　处：《排灌机械工程学报》2014年第11期943-947,954,共6页Journal of Drainage and Irrigation Machinery Engineering

基　　金：国家自然科学基金资助项目(51109104);"十二五"国家科技支撑计划项目(2013BAF01B02);甘肃省高校基本科研业务费专项资金资助项目

摘　　要：针对水力机械优化设计过程中存在计算量巨大、叶型的控制及修改不便等问题,提出了基于伴随方法的离心泵叶轮优化设计方法.以某低比转数离心泵叶轮为研究对象,采用泰勒展开法进行离心泵叶片形状的参数化控制.将泵内流动控制方程作为优化问题的约束条件,通过引入伴随变量将约束优化问题变为无约束优化问题,推导了目标函数的变分形式、伴随方程及伴随变量在计算域各边界上的边界条件.根据伴随方法计算目标函数对设计变量的梯度矢量,在任意给定的初始直叶片的基础上沿梯度矢量反方向不断更新叶片形状,直至目标函数达到最小值时即为最优设计.由于在目标函数的变分中不包含流场参数的变分,在一次优化迭代中只需要计算流场及伴随变量场各一次,大大减少了叶轮优化过程的计算量.算例计算结果表明所提出的离心泵叶轮伴随优化方法是可行的.To prevent some drawbacks in hydrodynamics optimization procedure of hydraulic machinery, such as a huge time-consuming and the difficulty in blade shape control and update etc, an adjoint method is proposed to optimize the blade shape of centrifugal pump impellers. At first, the camber line of impeller blade of a low specific centrifugal pump is expressed as a polynomial in terms of dimensionless radius. Secondly, the governing equations of ideal fluid flow in the centrifugal pump impeller are considered as the constraints of the optimization problem; then the constrained optimization problem is transformed into an unconstrained one by introducing four adjoint variables. Finally, the variation formulas of objective function, the adjoint equations and the boundary conditions of the computational do- main for the adjoint variables are deduced. The gradients of the objective function with respect to the control variables are calculated. Accordingly the blade shape is updated continually against the direction of the gradients starting with straight blade until a minimized objective function is achieved. Because the variation of flow variables is not included in the variation of objective function, the flow flied and adjoint variable field need to be simulated once only in one optimization cycle, causing a greatly reduced computing time for the optimization. The results of the case study indicate that the proposed adjoint method is feasible for blade shape optimization of centrifugal impellers.

关 键 词：离心泵 伴随方法 参数化控制 优化设计 

分 类 号：S277.9[农业科学—农业水土工程] TH311[农业科学—农业工程]