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OptiMISES

The S1-streamsurface optimization package OptiMISES, developed in a three years project at the IWR, University of Heidelberg, helps to reduce turnaround times for turbomachinery design. The demand is to optimize performance (e. g. minimize flow loss, maximize efficiency ...) without violating solidness contraints, manufacturing constraints, heat engineering constraints and S2-computation compatibility constraints.

Most of these constraints concern geometry, either directly via lower bounds on blade profile area, upper bounds on curvature at the leading edge, lower bounds on leading and trailing edge thicknesses or indirectly like bounds on the exit flow angle. Follow this link to read more about the implementation of such geometry constraints in OptiMISES.

Direct constraints on flow characteristics of the boundary layer like the kinematic shape parameter can also be imposed in OptiMISES, which is of particular importance for compressor blading. As these constraints have to be imposed via penalty terms in the objective function, they usually require some tuning by the user.

Also, it is necessary that the solutions are valid (and optimal!) for a prescribed working range, e. g. over a variety of inlet flow angles or Mach numbers, which is a so-called multiple setpoint optimization problem.

Furthermore, the optimized profile family must allow the interpolation of a feasible 3D blade, which has to meet certain smoothness conditions. Therefore, the family must be optimized as a whole, which gives rise to another multiple setpoint problem.

All this means that the optimization involves a huge number of cascade flow problems. Given the fact that a number of scenarios will have to be evaluated until one arrives at a practical solution, one can easily see that speed is of the essence. This is where the fast simultaneous optimization approach of our group comes into play.

This approach is a direct attack at the optimality conditions. Taking advantage of every available sensitivity information we find a shortcut path where the flow equations will usually be converged only once: at the optimal solution.

But doesn't that mean that we have to merge the optimization algorithm into the already existing, complex design system, which leads to very high costs for software implementation and support?

The answer is no. The partially reduced SQP (PRSQP) method supports modular implementation in that its optimization step is split into projections towards solution and optimum.

An additional advantage is the fact that the projection steps for the multiple setpoint (working range, blade family) problem can be easily assembled from the individual projections. What is even more, these computationally expensive steps can also be performed in parallel.

Another major problem of optimizing complex simulation and design systems is that the value of the objective function usually is not feasible (or even computable) everywhere due to model restrictions. Typically, there is some a priori knowledge that can be mathematically formulated (which we do!), but this is not sufficient. With a simultaneous approach, where convergence of the forward problem will be reached at the optimal solution only, there is no feasibility information available under way. The PRSQP setup, however, gives access to that information in that additional projections towards the flow solution can be inserted any time the algorithm detects that something may be going wrong. Then, immediate measures such as optimization step relaxation can be taken.

So how is the current state of the project?

The newest version of the software is prepared to find the required working range solutions for whole blade families. It has been fully tested and released at the IWR.

We want to conclude with an example. The following compressor profiles shall illustrate why optimizing the full working range is essential: