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OptiMISES geometry constraints

The importance of geometry constraints lies not only in practical demands. Their absence can also cause severe troubles for the flow solver, which can be seen from the following pathologic example which happened to us in the early stages of the project:

Now let us turn to the most important geometry constraints that are implemented in OptiMISES.

First of all, there are curvature constraints. They can be put on arbitrary regions of the profiles where uniform or initial-value dependent bounds can be set (to make things more easy, the bounds for all constraints can be set relative to their initial values).

Clearly, the most common curvature constraints are on LE and TE (a quick glance on the above figure should convince everybody).

At the LE one has to be careful not to end the region in the spline segment points, which could lead to profile kinks in the segment points where smoothness may not be of high quality (triple knots!). There is, however, some help in the user interface so that this problem can be easily avoided (details can be found in the OptiMISES documentation).

Another very important issue is the TE thickness. It is, however, not at all obvious, how to define the term thickness. In case of the trailing edge, we found that it makes sense to do that as shown here:

Also very important is the blade area, which is computed as the difference of the integral over upper half and lower half of the profile curve plus/minus the trapezoid area below the open TE points.

The outflow angle can be controlled by heuristic strategies. In OptiMISES, strategies are implemented for both turbine and compressor blades. These strategies work out quite well as is shown in the following example, where the only difference was that the outflow control strategy was turned on in the second case:

Another problem that becomes obvious from the introductory figure is the TE skewness, which we define as follows:

The LE thickness is currently defined as just the distance between the LE segment points. This does not make much sense per se, but in combination with LE curvature and area constraints it may well give the desired results.

The blade length is defined as:

The blade width is just the distance between the profile points with minimal and maximal m'-coordinate:

In addition, a tolerance for the rightmost m'-coordinate can be set.

Also the stagger slope can be constrained, which is often needed in turbine blade design. Furthermore, there are constraints for the metal angle, which is the average TE tangent angle. Stagger angle and metal angle constraints, however, will be out of service in case they are involved in a currently active outflow angle control strategy.

Difference of trailing edge tangent angles or, in other words, the blade opening angle at the trailing edge is another criterion that can help to maintain feasibility.

Finally, a simple q3d blade geometry criterion has been implemented in OptiMISES that should guarantee that a sufficiently smooth blade can be interpolated from the optimized profile family. It is defined via the total variation of curves like the ones shown below: