**7. Pressure Loss**

The experiments do not provide local pressure data; therefore, the results are compared with the values of the LES for RIB-1 from Campet et al. [19]. Here, the local friction coefficient *Cf* and the pressure coefficient *PNorm* from Equations (13) and (14) are compared. A derivation of the two coefficients is provided by Campet et al. [19]. *CF* has been validated in the above-mentioned paper using measurement data between the ribs and is defined as follows:

$$\mathcal{C}\_f = \frac{\tau\_\text{x}}{0.5 \cdot \mathcal{U}\_0^2 \cdot \rho} \tag{13}$$

with the bulk velocity *U*<sup>0</sup> and the wall shear stress *τ<sup>x</sup>* in the flow direction. The pressure coefficient *Pnorm* is defined with:

$$P\_{norm} = \frac{P - P\_{ref}}{0.5 \cdot \mathcal{U}\_0^2 \cdot \rho} \tag{14}$$

where *Pref* corresponds to the pressure on the wall at *x*/*e* = 0, so *Pnorm* becomes zero at this point. Figure 15 shows the comparison between the two rib structures for *Cf* in the centre of the interrupted rib. It can be seen that the change of sign of *Cf* takes place where the reattachment point of the flow is located. This is caused by the velocity gradient being directly included in the calculation of *τx*. Furthermore, there is a backflow at RIB-2 shortly before the rib shown in Figure 16, which causes *τ<sup>x</sup>* to obtain a negative value. This swirling is not visible at RIB-1, as can be concluded from the results of Campet et al. [19]. In addition to that, the peak in the simulation of RIB-2 is clearly above the values of RIB-1 and the maximum of the first mentioned geometry is 0.0686 compared to 0.0185, which corresponds to an increase of 370%. It is assumed that the velocity gradient on the rib due to the backflow in front of the rib results in a strong increase in local velocity.

The global *Cf* value used to calculate the pressure drop in the Darcy–Weißbach equation has a value of 0.0167 for RIB-2 and 0.0304 for RIB-1. The pressure drop in the geometry examined here is therefore lower by a factor of 1.82, since the influence of *Cf* is directly linear in the equation for the global pressure loss.

**Figure 15.** Comparison of the values of *Cf* between RIB-1 with values from Campet et al. [19] and RIB-2.

**Figure 16.** Two-dimensional velocity combined with vector arrows in front of the rib to show the backflow that takes place there.

Figure 17 compares the pressure coefficients over the centre of the interrupted rib. The maximum value in the range at x/e = 10, shows that the pressure coefficient is almost identical. The pressure coefficient of RIB-1 is almost always above RIB-2 in the positive range and below RIB-2 in the negative range. While the flow has to pass over continuous rib structure at RIB-1, it is partly redirected through the gaps in the interrupted rib at RIB-2, which explains the differences in the pressure coefficient plot.

**Figure 17.** Comparison of the values of *PNorm* between RIB-1 with values from Campet et al. [19] and RIB-2.

#### **8. Conclusions**

In this article, a numerical flow simulation is successfully validated by measurements. A *y*<sup>+</sup> value of less than 0.2 is maintained in order to be able to represent the thermal boundary layer as well as the flow boundary layer at a Prandtl number of 7. The local velocity profiles and fluctuations of the velocity between the ribs show a good agreement with the measurements. This proves that the method is capable of reproducing the flow correctly. Using the Nusselt number validation, it can be demonstrated that a maximum Nusselt number is reached between the ribs until the flow reattaches to the wall. This effect is described by Mayo [17] using the RIB-1 geometry and was again observed in this study. Overall heat transfer is reduced compared to the continuous rib, which is proven by both experiment and simulation. The analysis of the wall shear stress showed that the detachment of the flow is shifted further backwards by the interruption, in contrast to the continuous rib. As was previously the case for the flow field, a successful validation is performed for the heat transfer. An analysis of the pressure drop was realized with the help of the results of Campet et al. [19], who performed an LES of the RIB-1 geometry; here, the results could be compared with each other. It could be shown that the *Cf* value for RIB-2 is higher on the rib than for RIB-1, due to backflow being formed in front of the rib. The pressure coefficient for RIB-2 is lower in comparison to RIB-1, due to the reduction through the rib geometry being interrupted. The simulation was therefore able to reflect the results of the measurement for both the flow and the heat transfer well. Through the results, it can be shown that it is possible to simulate complex internally structured pipes, even without a continuous structure. Thus, further structures with increased complexity can be simulated and evaluated.

**Author Contributions:** Conceptualization, S.K.; methodology, S.K. and G.O.M.; software, S.K. and G.O.M.; validation, S.K. and P.R.; formal analysis, S.K.; investigation, S.K.; resources, S.K.; data curation, S.K.; writing—original draft preparation, S.K.; writing—review and editing, S.K. and P.R. and T.G.; visualization, S.K.; supervision, P.R. and T.G.; project administration, P.R.; funding acquisition, P.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Federal Ministry of Education and Research of Germany (BMBF) Grant No. 13FH119PX6.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to gratefully acknowledge support by the Steinbuch Center for Computing (SCC) at the Karlsruhe Institute of Technology (KIT) for providing computational resources. Most of the simulations have been performed on the bwUniCluster and the forHLR II cluster, where access has been granted to the authors. The article processing charge was funded by the Baden-Württemberg Ministry of Science, Research and the Arts and the University of Applied Sciences Ulm in the funding programme Open Access Publishing.

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