*3.3. CFD Results on Optimized Geometry*

Results of CFD analysis are shown in Figures 21–24. The set-up of the analysis is the same described previously. In the images, the variables were set with the same scale as in the baseline simulation, for an easier comparison.

**Figure 21.** Pressure distribution on Port A and P walls, optimized geometry.

**Figure 22.** Pressure distribution on sections of Port A and Port P, optimized geometry.

**Figure 23.** Velocity distribution on sections of Port A and Port P, optimized geometry.

**Figure 24.** Streamlines in the valve, optimized geometry.

#### **4. Discussion**

This project shows how valve design can be virtualized and automated, provided that efficient and reliable software tools are available.

The advantage of this approach is the possibility of studying many different geometry variations, simply defining the parameters that are to be investigated. New geometries are automatically generated by CAESES® and then evaluated by Simerics MP+®. Answers can be obtained in very short time, also with different optimization techniques.

Optimization in this case was based on a two-step strategy. The first one, based on the Sobol design of experiment sequence, provides a geometry that let the valve increase the mass flux by about 7%; the second, a T-Search method optimization, further adjusted the geometry to increase the mass flux by another 2%. The overall process allowed for a 9% improvement in the mass flux. The ports' outer radius turned out to be the parameter that mostly influences the result.

Modifying this parameter allows an increase in the ports' volumes, and consequently a higher mass flux can be obtained.

However, larger ports' dimensions might be risky in terms of decelerating the fluid flowing in the valves. CFD results on the new geometry show that this is not the case, as the fluid velocities are not reduced significantly and are comparable with the baseline geometry velocities. The optimized geometry has also an advantage in terms of fluid behavior. Figure 25 shows a comparison of the velocity vectors distribution on the outlet ports for the baseline and optimized geometries: the vortex at the outlet port of the second geometry is significantly reduced.

**Figure 25.** Comparison of the outlet vortex.

In Figure 26, another advantage of the larger outer radius is shown. Velocity distribution in the outer circumference is smoother in the new geometry and enters with an angle better aligned to the port exit section.

Experimental tests, carried out by Duplomatic MS S.p.A. at the Industrial Engineering Department at the University of Naples Federico II, show that the shape obtained by the optimization process are reliable, as expected from the conducted study.

It is worth noting that the authors conducted different studies on similar spool valves in order to achieve better performances. The Industrial Engineering Department proceeded to optimize the ports geometry with a traditional trial and error approach using laboratory testing and CFD. The results obtained in seven months are aligned to the results obtained with the optimization project performed with CAESES® and SimericsMP+®.

**Figure 26.** Comparison of vortex in the outer circumference.

Although these two different approaches reached the same conclusions, two main points should be noted: First of all, the project timeline; seven months for the trial and error approach, one day for the automated approach.

Secondly, the methodology; the trial and error approach can be highly affected by engineer specific expertise while the automated approach is neutral in this respect and somehow free to investigate even apparently unreasonable solutions.

For both methods, the CFD simulation is an essential tool that helps understanding the behavior of the fluid inside the ports, either to find a new solution or to understand the reason for a solution being the optimal one.

#### **5. Conclusions**

A fast and reliable methodology to optimize the shape of the ports of a spool valve in order to obtain a higher mass flux was described. SimericsMP+® and CAESES® were used for this project.

Through these tools, an optimized geometry was automatically identified in a very short time. The advantage of the approach is that no parametric CAD tool is needed as CAESES® directly handles the automated process, including geometric modifications, simulations set up and run.

Moreover, a fast and reliable CFD simulation software, as Simerics MP+®, is necessary, as it accelerates the process to obtain the best geometry.

The conducted study also gave evidence of the fact that an optimizer is useful to identify the parameters that mostly influence the objective. Meanwhile, coupled with an efficient CFD solver, it allows investigation of the physics of the problem and determination of the sensitivity of the parameters.

**Author Contributions:** Conceptualization, M.O.; data curation, G.M. and P.M.; formal analysis, G.M. and P.M.; methodology, M.O. and E.F.; project administration, M.O. and F.G.M.; resources, G.M.; supervision, F.G.M.; Writing—original draft, M.O.; Writing—review & editing, M.O. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was developed as part of a PhD program supported by the Italian Government and the MIUR (Ministry of Education, Universities and Research).

**Acknowledgments:** We would like to thank Ceyhan Erdem e Mike Saroch at Friendship Systems AG for providing outstanding technical support on this project.

**Conflicts of Interest:** The authors declare no conflict of interest.
