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Toyota Motorsports is a high-performance testing and development facility in Cologne, Germany. One of their focus points is chassis and engine design for automotive and motorsports. Being specialized in high-technology developments for motorsport engines, the turbocharger components are already state-of-the-art. To further improve performance, Toyota must rely on something other than traditional trial-and-error procedures and prototypes because turnaround times for those are too long. Numerical optimization enables engineers to explore and evaluate many more design alternatives than what can be achieved manually.
Another reason to turn to numerical optimization is the fact that compressor impellers are already designed to work very close to the structure-mechanical limits of the material they are made of. Most changes in shape immediately lead to an excess of acceptable stress levels. An optimization that only considers aerodynamic behavior does not guarantee that the resulting design is also structurally feasible. Simultaneous optimization that includes both aerodynamic and structural force analysis is needed. In other words: a multi-disciplinary optimization coupling computational fluid dynamics (CFD) with computational structural mechanic (CSM) simulations.
This article will describe the multi-disciplinary CFD-CSM optimization of a centrifugal compressor for an exhaust gas turbocharger. The compressor stage studied consisted of a radial impeller with six main and six splitter blades with a vaneless diffuser. There were two aero-thermodynamic, one structure-mechanical, and two aerodynamic objectives to be achieved:
The CFD and CSM simulations were integrated into one single optimization workflow within Cadence's Fidelity Optimization. Each new design was first checked structurally by the CSM solver, and only those not exceeding the maximum von Mises stresses were included in the more time-consuming CFD process. Structurally unacceptable designs were fed into the learning database to drive the optimizer.
A total of 154 parameters defined impeller, meridional channel, and solid body. However, the parameters defining the impeller's hub shell were kept unchanged from the base design to exclude many structural-mechanically non-feasible designs. And to further reduce the number of free parameters, the thickness distribution along the camber curve was not modified either. Eventually, 33 parameters were to be considered as design variables for the optimization, such as the shape of the hub and shroud, the camber curves, and the meridional and tangential blade position.
A robust mesh generation setup is essential for automated optimization workflows where new designs can significantly differ from the original design depending on the range of modified geometry parameters. Fidelity Automesh was used for the fluid domain. Mesh independence was ensured through a mesh convergence study with three different mesh resolutions: 1, 2, and 3 million points. The 2 million-point structured multi-block mesh came out best. Additionally, a robustness test was performed to ensure the high quality of the whole design space. Hundreds of randomly generated geometries covering the whole range of the design space were meshed automatically. All geometries were a success, and orthogonality was never below 20°.
Four databases were generated in parallel in one day and a half and then combined. Of 292 database designs, 270 samples met all mesh and convergence quality criteria, which is more than adequate to start the optimization.
Each new design created during the optimization was again added to the initial database, enriching it as the expected optimum was getting closer. As the first optimization ran, it became clear that not all objectives could be achieved. They decided to stop the optimization and adapt the priorities of the different goals before starting a new optimization run. This procedure was repeated a couple of times and proved helpful since – a priori – objectives can only be determined vaguely at the start of a project.
Figure 1 below summarizes the results at the best point (OP2) of databases and optimization runs for the isentropic efficiency and the total pressure rise.
Figure 1: Result from Database and Optimization: Isentropic efficiency over total pressure ratio at best point
All designs within the red area show increased total pressure and efficiency. The initial design is in the lower-left corner of this box. The two best designs, D1 yellow and D1 green, were compared with each other and the original design. These two designs both fulfill all optimization goals and show substantial improvements. Besides efficiency increase and total pressure ratios, operating range and structure-mechanical results were considered for the selection.
Figure 2 below shows the geometrical differences between the selected optimal design and the original design.
Figure 2: Comparison of original geometry and selected designs D1 and D2
For both geometries, the complete speed line was simulated (Figure 3). Design D1 showed an increase in total pressure ratio of up to 8.0% relative to the original design with a simultaneous expansion of the stall margin. In addition to the extension of the operating range, the most noteworthy improvement is the positive slope of the speed line close to the stall, which, in contrast to the original design, ensures stable operation even near the surge line. All chosen designs maintain the minimum choke mass flow. Efficiency was increased by 1.1 percent. The highest pressure ratio increase design also provided the highest efficiency gain.
Figure 3: Speed lines of designs D1 (yellow) & D2 (green) compared with original Design (red)
D1 shows an efficiency increase of 1.4 % relative to the. In contrast, D2 has a slightly lower overall pressure ratio and efficiency improvements but features an extended surge limit compared to D1. This is a classical conflict of multi-objective optimization, where different goals can sometimes act in opposite directions. The final decision is up to the user.
The von Mises stresses in design D1 exceed the maximum permitted limits by approximately 3%, which is still within the tolerance limit.
The multidisciplinary CFD-CSM centrifugal compressor optimization was a success, and all aerodynamic targets were fulfilled while structural integrity was ensured. The results of the optimization were very satisfactory:
Cover image courtesy of Toyota Gazoo Racing Europe
Original text by Kathrin Wendl