Results led to the conclusion that a minimum of nine simultaneous design variables must be automatically adjusted to provide the freedom needed for the optimization algorithms to achieve good results. These nine variables included the radial and axial components of the hub contour Bezier control points and the control points of the shroud contour blade angle distribution.
The optimization algorithms chosen included the simulated annealing technique to search the entire design space for the neighborhood of the global optimum followed by the modified method of feasible directions to climb to the global optimum. The combination of these two techniques required about three hundred different streamline curvature runs to find an optimum design. Since the streamline curvature solver runs in a few seconds, the execution of several hundred runs was quite reasonable on a modest computer and in a short time.
In fact, the combination of SLC together with automated optimization has become standard design procedure at Concepts NREC and is also in use at several companies that use the Agile Engineering Design System. The traditional design (or redesign) process for the past decade is to first use a meanline code to select the correct size plus inlet and exit velocity triangles for each blade row. If the meanline work is not done correctly, even the best optimizers and CFD tools will not achieve an acceptable solution. The next step is to optimize a design (either manually or automatically) using quasi-3D solvers like SLC and other through-flow and 2D blade-to-blade solvers. After using quasi-3D methods, it is time to use full 3D computational fluid dynamics (CFD) to fine tune the geometry and maximize efficiency.
In the late 1990s, engineers at Concepts NREC examined their own use of CFD and found the time-consuming combination of preprocessing, solving, and postprocessing limited the number of feasible CFD runs on a typical design to less than ten, and the process added a week or more to design time. To reduce that time, CFD was successfully integrated into the design system so that a typical designer could simply push a button to evaluate a candidate design with 3D CFD. This led to the development of Pushbutton CFD® which is now in use at nearly one hundred companies worldwide.
The next logical step in the improvement of the design process was to combine CFD with automated optimization -- although this posed a difficult challenge because the large number of runs required for optimization, together with the relatively slow run times of CFD, made the process rather impractical. The goal was to achieve a CFD-based optimization system that could produce a reasonable result in an overnight run using a typical high-end PC. An overnight run was set at sixteen hours which assumed an engineer would go home at the end of an 8-hour day and return the next morning to find results. Since five to ten minutes is the typical run time in Pushbutton CFD for a single blade row, an optimized design would be necessary with only one hundred to two hundred executions of the solver.
And there were other complications. When using CFD in the design process, Concepts NREC engineers typically look at other design variables (in addition to contours and blade angles) that might include the axial length, impeller exit width, and blade count, plus the location of the splitter leading edge for designs with splitter blades. In principle, any geometric variable of any axial or radial blade row or set of blade rows can be used in a CFD-based optimization, so it can be expected that more variables will soon be added.
To address the problem of long run times, the optimization experts at Engineous use a technique in iSIGHT called "Design of Experiments" (DOE) to sample the design space with an ordered array of CFD runs. They then examine the sensitivity of the optimization goals to the design variables. The DOE can be executed with significantly fewer CFD runs than a full optimization would require, and its results can be used by iSIGHT to automatically build a response surface model (RSM), which is a mathematical approximation of the design space. The RSM can accurately predict the results of a CFD run for an arbitrary set of inputs without having to actually execute the CFD run. The RSM provides the additional benefit of smoothing out sometimes “noisy” CFD results, making it easier for the optimization algorithms to find the global optimum.
By using DOE technique to build a response surface model based on “live” CFD runs and then applying optimization algorithms, the system can successfully achieve overnight CFD-based optimization. Some of the results from using this CFD-based optimization program are described below.
Centrifugal Compressor Impeller with Splitters
The optimum design was found in six hours. Design-point specification of exit total pressure was met within the –1% to +3% error band, and the design mass flow of 0.331 lb/sec was met within the 1% error band. Since Pushbutton CFD is a pressure-based solver, the mass-flow target was specified as an optimization goal built into the response surface rather than a constraint. Impeller efficiency was improved from 89% to 91%.
Centrifugal compressor impeller with splitters
The optimized design was found in about four hours with impeller efficiency improved by 0.4% for this pump with geometry parameters and optimization goals the same as the compressor. Both the compressor and pump optimizations produced geometry with improved aerodynamic performance while also meeting operating condition requirements for mass flow and total pressure.
The goal of this optimization was to maximize the flow rate without changing the radius. Design variables included blade angles, blade number, passage width, and blade count. The results show a 19% increase in flow rate was achieved.
The optimization goal was to maximize the flow rate within the same radius fan. These results show that mass flow was increased by 3% and efficiency is increased by 0.6%.
 Developments in Agile Engineering for Turbomachinery, 2002 ASME Fluids Engineering Division Summer Meeting, Montreal, Quebec, Canada, July 2002.