基于边界涡量流的二维叶型优化建模与求解  

Optimization Model and Solution of Two-dimensional Compressor Blade Based on Boundary Vorticity Flux

作　　者：杨小娟[1] 刘若阳[1] 佘志坤[1] 

机构地区：[1]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《航空工程进展》2015年第4期405-411,共7页Advances in Aeronautical Science and Engineering

基　　金：国家自然科学基金(11290140)

摘　　要：针对二维叶片整体造型优化问题,提出一种基于边界涡量流的二维叶型优化模型,并对该模型进行求解。建立以含参数的Bezier曲线定义的二维叶型型线为边界、以边界涡量流正峰值的最小化为目标函数的优化模型,通过分析边界涡量流的生成机制,把叶型型线边界信息代入边界涡量流中,将边界涡量流用叶型型线参数和型线上的气动参数表示,进而获得新的目标函数表达式。该目标函数表达式可直接对叶型型线参数求导,仅使用简单的定步长梯度算法即可对优化模型求解。结果表明:优化后的叶型型线上的边界涡量流的正峰值显著降低。Concerning the optimization of two-dimensional compressor blade,an optimization model based on boundary vorticity flux（BVF）is proposed and solved.An optimization model is established with the boundary being two-dimensional compressor blade defined by Bezier curve and the optimization target being the minimize of positive peak of BVF.Through the analysis of the BAV producing mechanism and taking the information of blade curve into BVF a new objective function can be obtained.The new objective function can directly get partial derivatives of the parameters of blade curve,which make the simple gradient arithmetic being used to solve the optimization model.The optimization experiment shows that the positive peak of boundary vorticity flux is effectively decreasing in this process.

关 键 词：二维叶型 边界涡量流 BEZIER曲线 梯度算法 

分 类 号：O224[理学—运筹学与控制论] V231.3[理学—数学]