New Finite Difference Scheme for Solving Inverse Proposition of Streamline Curvature Method

doi:10.7652/xjtuxb201503002

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New Finite Difference Scheme for Solving Inverse Proposition of Streamline Curvature Method

更新时间：2025-07-09

- New Finite Difference Scheme for Solving Inverse Proposition of Streamline Curvature Method
- Vol. 49, Issue 3, Pages: 11-13+49(2015)
- 作者机构：
  
  西安交通大学能源与动力工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201503002
  CLC： TH452
- Online First：10 March 2015，
  
  Published：2015
- 稿件说明：
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New Finite Difference Scheme for Solving Inverse Proposition of Streamline Curvature Method[J]. 2015, 49(3): 11-13+49.
DOI：

New Finite Difference Scheme for Solving Inverse Proposition of Streamline Curvature Method[J]. 2015, 49(3): 11-13+49. DOI： 10.7652/xjtuxb201503002.

摘要

针对全三元离心叶轮流线曲率法反命题设计

提出了一种求解S2m流面速度梯度方程的新型有限差分解法。该方法将相对速度沿准正交线的方向导数采用前向差分格式

将相对速度沿流线的方向导数分解为两项

一项采用前向差分

另一项采用后向差分格式

其他各参量沿准正交线或流线的方向导数统一采用前向差分格式。这样便解决了简单采用前向差分格式或后向差分格式难以保证求解速度场的矩阵主对角线元素占优问题

使求解格式具有较强的稳定性和收敛性。新型有限差分求解方法应用于Krain叶轮的改型设计

经计算流体动力学(CFD)分析得

改型叶轮效率提高约0.3%

压比提高约0.2

表明利用新型有限差分法求解S2m流面速度梯度方程是可行的。

Abstract

For the streamline curvature inverse proposition design of a full three-dimensional centrifugal impeller

a new finite difference method is put forward to solve the S2m stream surface velocity gradient equation. In the difference scheme

forward difference is chosen for the relative velocity derivative along the quasi orthogonal curve; that along the streamline direction is decomposed into two items

forward difference is used for first item

backward difference for another

and forward difference for all other parameter derivatives. The scheme solves the difficulty to guarantee the matrix main diagonal elements being dominant in solving velocity field with simple forward difference or backward difference scheme

and has higher stability and convergence. The new finite difference scheme is taken to redesign Krain impeller. The CFD analysis shows that modified impeller efficiency is increased by 0.3%

and compression ratio is heightened 0.2.

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references

杨小贺, 单鹏. 风扇与轴流离心压气机一体化通流设计方法 [J]. 航空动力学报, 2010, 25(2): 443-450.

YANG Xiaohe, SHAN Peng. Integrative design method of fan and axial-centrifugal compressor [J]. Journal of Aerospace Power, 2010, 25(2): 443-450.

弓升. 基于S2流面的涡轮叶片设计方法研究 [D]. 南京: 南京航空航天大学, 2008.

李园园. 面向透平压缩机气动设计的可压缩流动数值计算方法 [D]. 西安: 西安交通大学, 2012.

CASEY M V, ROBINSON C. A new streamline curvature throughflow method for radial turbomachinery [J]. ASME Journal of Turbomachinery, 2010, 132(3): 031021.

王尚锦. 离心压缩机三元流动理论与应用 [M]. 西安: 西安交通大学出版社, 1991.

KRAIN H. Swirling impeller flow [J]. ASME Journal of Turbomachinery, 1988, 110(1): 122-128.

KRAIN H, HOFFMANN W. Verification of an impeller design by laser measurements and 3D-visous flow calculations, ASME 89-GT-159 [R]. New York, USA, ASME, 1989.

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