## 3 Results and Discussion
### Turbulent Flow Models
A slight disagreement on the strength of the secondary shear layer is still visible during the first few phases that represent the acceleration stages of a flow cycle (\(\phi\)2 to \(\phi\)4 and  
Figure 9: Vorticity contours at the left (**a**) and right (**b**) ends of the heat exchanger assembly calculated using the k-\(\omega\) 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. \(\phi\)12 to \(\phi\)14). This may be related to the uncertainty of the measurement, as well as the two-dimensional assumptions of the numerical model used in a three-dimensional situation. Nevertheless, the SST k-\(\omega\) model has provided the best solution for the drive ratio of 0.83% with the closest match to the experiment. The vorticity contours at the ends of the heat exchanger assembly, calculated using the SST k-\(\omega\) model, are shown in Figure 13. They agree well with the experiment and are similar to the results from the k-\(\omega\) model. This indicates that the vortex structures at the end of the plates are strongly influenced by the processes in the shear layer near the wall of the channel and that a correctly-defined flow condition within the channel leads to a better prediction of flow structures at the end of the plate. Clearly, the SST k-\(\omega\) model with its excellent control parameter has given an improved prediction in both areas of the flow field. Figure 11: Velocity profiles from the SST k-\(\omega\) model (black and grey lines) and experiment (red and black symbols). Plotted for the location 10 mm from the joint, inside the cold channel, for the 0.83% drive ratio. Figure 10: Comparison between velocity profiles from experiments and CFD for the location 10 mm from the joint, in the cold channel, for the drive ratio of 0.83%. SST stands for shear-stress-transport. Following the successful application of the SST k-\(\omega\) model at the drive ratio of 0.83%, it was subsequently applied to the other two drive ratios of 0.45% and 0.65%. The resulting velocity profiles for all 20 phases, together with experimental data, are shown in Figure 14. For the drive ratio of 0.65%, a better match to the experiment is obtained, compared to laminar predictions shown earlier in Figure 4c. The maximum deviation in Figure 4c occurs at \(\phi\)5, where the velocity was numerically over-predicted by 8.9%. With the SST k-\(\omega\) model, the maximum deviation is slightly reduced to 8.3%. The match is not as good as predicted for the drive ratio of 0.83%. For the drive ratio 0.45%, the SST k-\(\omega\) model provides no improvement in the velocity profiles compared to the laminar model. This may indicate that the flow at the drive ratio of 0.45% has not yet reached a state suitable for the application of a turbulence model. However, the laminar model does not provide a satisfactory solution either. Observations of the experimental and numerical results in two extreme conditions of drive ratios of 0.3% and 0.83% suggest the occurrence of transition within this range. Therefore, the four-equation transition model (transition-SST [27]) is used. Figure 15 shows the resulting velocity profiles for drive ratios of 0.45% and 0.65%. The velocity profiles for a drive ratio of 0.65% are slightly better predicted than the profile shown in Figure 14a, with the maximum error of 5.3%. Hence, the transition model seems to be a better model for predicting the flow at this drive ratio. The difference in amplitude of velocity between experimental and numerical results at \(\phi\)5 and \(\phi\)15 may be due to the moderation constant [21; 23; 26; 27] not being varied in this study. Figure 5:0 Comparison between vorticity contours from the experiment (**a**) and the SST k-\(\omega\) model (**b**). The drive ratio is 0.83%. Distance \(x\) is measured from the left end of HHK/CHX assembly; vertical axis, \(y\), is omitted for simplicity; the ratio of \(x\)y is 1:1.