*4.13. Experimental Validation*

In addition to numerical verification, it is strongly suggested that, if at all possible, experimental validation is carried out, due to the complex geometries and complex physics encountered after fluid-based topology optimisation. One thing is that a simulation tool shows that the optimised geometry performs better than a reference design but should preferably be validated experimentally.

Only 12 papers, or 7%, contain some form of experimental investigation of the topology-optimised designs. These cover fixed-geometry fluid diodes [43,68], small scale rotary pumps [62], forced convection heat sinks [116,128,141,146], passive coolers for light-emitting diode lamps [154,155], porous bioreactors [186], particle separators [102], and conformal cooling channels [142].

#### **5. Conclusions**

This review paper provides an overview of the development of topology optimisation for fluid flow and fluid-based problems. Since the seminal paper by Borrvall and Petersson [7] in 2003, 186 papers have been published treating a large variety of phenomena and component design, ranging from creeping flow in pipes and microfluidic mixers to turbulent flow and heat transfer, from steady to time-dependent flows, and from simple academic problems to real-life industrial examples. A wide range of topology optimisation methods have been applied to the field, with most being classified as density-based methods and significantly less using level set methods. This is surprising since the potential strength of level set methods, in combination with surface-capturing discretisation schemes, is to provide a better definition of the interface, which can be necessary for more complicated fluid problems. On the contrary, the limited ability to create a new topology favours the density-based methods.

Recommendations for future research directions are outlined based on the extensive literature review, the quantitative analysis, as well as the authors' personal experience and opinions. The community is encouraged to focus on moving the field to more complicated applications, such as transient, turbulent and compressible flows. Generally, previously published examples should serve only the purpose of benchmarks for verifying a new method or implementation. However, if the new method does not show clear improvements in accuracy and efficiency over the previously published

works, it should not be published. It is suggested that published works in the future only present improvements and extensions to the previous .

**Author Contributions:** The two authors have contributed equally to this work. All authors have read and agreed to the published version of the manuscript.

**Funding:** The second author was partly funded by the InnoTop project through the Villum Foundation.

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

## **References**


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