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# A Variational Finite Element Method for Solving the Blade-to-Blade Flow in Centrifugal Compressor’s Cascades With Splitter Blades on an Arbitrary Streamsheet of Revolution and a Mathematical Treatment to the Region Behind CascadesPUBLIC ACCESS

[+] Author Affiliations
Chen Yulin, Chen Kangmin, Zhang Dangfang

Shanghai Institute of Mechanical Engineering, Shanghai, China

Paper No. 85-IGT-148, pp. V001T02A051; 6 pages
doi:10.1115/85-IGT-148
From:
• ASME 1985 Beijing International Gas Turbine Symposium and Exposition
• Volume 1: Aircraft Engine; Turbomachinery
• Beijing, People’s Republic of China, September 1–7, 1985
• Conference Sponsors: International Gas Turbine Institute
• ISBN: 978-0-7918-7942-9

## abstract

A variational finite element method for solving the blade-to-blade flow in centrifugal compressor’s cascades with splitter blades on an arbitrary streamsheet of revolution is suggested in this paper. At first, the variational principles Ref.(1) is modified, then the variational principle after modification is discretized by eight node isoparametric finite elements to carry out the system of nonlinear algebraic equations for solving the velocity potential function. Finally, the flow field which agrees with Kutta condition and has an region behind the cascade of enough length has been worked out.

In this paper, it has been discovered that when the region behind cascade L3 spreads too long the system of equations might become unsolvable as a suitable exit angle β2 can't be found. The linear relation between the velocity defference of the two side of the trailing edge and the exit angle β2 has been found, it shows the range of linear variation of β2 decreases with the increasing of the length of the region behind cascades, in addition, the linear variational relation between Display Formula$tan⁡β2$ and L3 has also been obtained.

The iterative computational method for the flow field with different length L3 is used to get the solution of flow field satisfying Kutta condition and with enough length L3.

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