Variable Geometry for Endwall Con­tour­ing of Turbines and Compressors

In our recent blog post about a para­met­ric stator blade for the CFD-driven shape opti­miza­tion, we men­tioned that we had imple­mented an endwall con­tour­ing approach. The idea of this addi­tional geo­met­ri­cal effort is to be able to modify the hub geometry, e.g. in the leading edge region of the blade, to minimize unde­sired sec­ondary flow losses.

The fol­low­ing picture shows this demo stator model again, along with the 3D contours on the hub:

Endwall Con­tour­ing Approach

Basi­cally, one can think about various modeling approaches to realize such a free-form shape around the blade. We have also used several dif­fer­ent tech­niques in our customer projects. Most of the times the engineer is eager to reduce the number of free vari­ables and hence reduce the com­pu­ta­tional time in CFD-driven opti­miza­tions. In the demo model of this blog post, we created an endwall con­tour­ing on the basis of trigono­met­ric func­tions, i.e. sine and cosine waves. Such a periodic function is typ­i­cally defined for a given axial location. The surface itself is gen­er­ated by con­trol­ling and changing the 2D para­me­ters of such a function while sweeping in axial direc­tion. There are several vari­ables to control the shape of the hub in this demo model, the most impor­tant ones are:

• Ampli­tude
• Axial location of maximum amplitude
• Phase shift at the start
• Phase shift at the end

A Short Demonstration …

The fol­low­ing video gives you a short impres­sion of how the model works. Note that these design vari­ables are changed manually, but they can be con­trolled auto­mat­i­cally by opti­miza­tion strate­gies. The ren­der­ing posi­tions of the hub surface are colored accord­ing to their radial distance, measured from the center. There you go:

More Complex Endwalls

With such an approach, one can of course generate more complex shapes in opti­miza­tion runs. The fol­low­ing picture shows a turbine blade where an endwall con­tour­ing was applied and opti­mized for the hub and shroud. The upper part shows a trigono­met­ric approach as described in this post, while the lower picture shows a spline-based approach where control vertices were varied to find the optimal shape.

More Infor­ma­tion

We have also applied endwall con­tour­ing and other methods (e.g. for removing material from the hub due to stress and inertia con­sid­er­a­tions) to mixed-flow impellers. I.e. the para­met­ric concept of variable hub surfaces is not limited to axial rotating machinery.

Do you also design and optimize gas turbines or com­pres­sors that involve endwall con­tour­ing? Feel free to get in touch with us if you have any ques­tions about this article. We are also fast in creating para­met­ric models like the one above for your indi­vid­ual appli­ca­tion in just a few days.

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