## 3 Results and Discussion
### Turbulent Flow Models
The vortex strengths seem slightly over-predicted, compared to the corresponding structures that appear somewhat weaker in the experimental results. The differences may be related to the consequence of \"stitching\" and \"averaging\" of the experimental results as explained in the original papers by [PERSON] et al. [17] and [PERSON] [4]. It may also be the result of two-dimensional assumptions used in the current turbulence model. Nevertheless, the resemblance of the flow structures to the experimental ones is quite convincing. Figure 6: Comparison between vorticity contours from the (**a**) k-\(\omega\) and (**b**) k-\(\varepsilon\) turbulence models. The drive ratio is 0.83%. Distance \(x\) is measured from the left end of HHX/CHX assembly; vertical axis, \(y\), is omitted for simplicity; the ratio of \(x\):\(y\) is 1:1. Figure 8: Vorticity contours at the left (**a**) and right (**b**) ends of the heat exchanger assembly calculated using the k-\(\varepsilon\) model for the drive ratio of 0.83%. Arbitrary distance \(x\) is measured along the “viewing area”; vertical axis, \(y\), is omitted for simplicity; the ratio of \(x\):\(y\) is 1:1. Figure 7: Vorticity contours at the left (**a**) and right (**b**) ends of the heat exchanger assembly calculated from the experimental results for the drive ratio of 0.83%. Arbitrary distance \(x\) is measured along the “viewing area”; vertical axis, \(y\), is omitted for simplicity; the ratio of \(x\):\(y\) is 1:1. The results show that the flow structures at the end of the plates are best predicted by the k-\(\omega\) turbulence model. The slight disparity with experimental results observed for the vorticity plots within the area bounded by the plates of the heat exchangers may require a more refined investigation. [PERSON] [26] proposed a modified two-equation model called the shear-stress-transport (SST) k-\(\omega\) model. It was proposed based on the observations of the performance of the conventional k-\(\varepsilon\) and k-\(\omega\) models; the k-\(\varepsilon\) model is reported to perform best in the wake and free stream region while the k-\(\omega\) model performs best for flows in bounded areas. Therefore, SST k-\(\omega\) model uses both the k-\(\varepsilon\) and k-\(\omega\) models appropriately, based on a control parameter that applies the correct model depending on the distance to the nearest wall. The model is suggested to cater for flows that involve both inviscid and viscous regions. It was used in this study to obtain better predictions and was first tested for the highest drive ratio of 0.83%. The comparison between velocity profiles from the experimental results and the numerical models tested is shown in Figure 10 for selected phases of the flow cycle at the drive ratio of 0.83%. They are plotted at the location 10 mm away from the joint, above the cold plate. As mentioned earlier, the laminar model over-predicts the profiles especially at locations near the wall. The predictions from the k-\(\varepsilon\) and k-\(\omega\) models miscalculate the magnitude of velocity both near the wall and within the flow \"core\" away from the wall. Taking \(\phi\)10 as an example, the k-\(\varepsilon\) model gives good predictions at the core, but under-predicts the velocity magnitude near the wall. On the other hand, the k-\(\omega\) model gives a better prediction near the wall, but under-predicts the magnitude of the velocity at the core. The profiles are better predicted by the SST k-\(\omega\) model. Figure 11 presents a comparison between experimental and numerical results from the SST k-\(\omega\) model for all 20 phases. A good match, with a maximum error of 4.3%, is found for almost all phases in the flow cycle. Figure 12 gives a similar comparison in terms of vorticity contours: a very good qualitative match is found.