科创中国

主要讨论一类Schrfdinger方程的反问题,利用变分同化方法,给出了最速下降的迭代格式,通过已知的观测值对模式的初值和未知点源进行最优修正.文中不仅给出了反问题的收敛格式,还进行了数值计算,其结果与理论结果吻合.

The 3D inverse design method,which methodology is far superior to the conventional design method that based on geometrical description,is gradually applied in pump blade design.However,no complete description about the method is outlined.Also,there are no general rules available to set the two important input parameters,blade loading distribution and stacking condition.In this sense,the basic theory and the mechanism why the design method can suppress the formation of secondary flow are summarized.And also,several typical pump design cases with different specific speeds ranging from centrifugal pump to axial pump are surveyed.The results indicates that,for centrifugal pump and mixed pump or turbine,the ratio of blade loading on the hub to that on the shroud is more than unit in the fore part of the blade,whereas in the aft part,the ratio is decreased to satisfy the same wrap angle for hub and shroud.And the choice of blade loading type depends on the balancing of efficiency and cavitation.If the cavitation is more weighted,the better choice is aft-loaded,otherwise,the fore-loaded or mid-loaded is preferable to improve the efficiency.The stacking condition,which is an auxiliary to suppress the secondary flow,can have great effect on the jet-wake outflow and the operation range for pump.Ultimately,how to link the design method to modern optimization techniques is illustrated.With the know-how design methodology and the know-how systematic optimization approach,the application of optimization design is promising for engineering.This paper summarizes the 3D inverse design method systematically.

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