## 3 Results and Discussion
### Turbulent Flow Models  
Figure 6 shows the vorticity contours for drive ratio of 0.83% obtained using two turbulence models: k-\(\omega\) and k-\(\varepsilon\). These are best discussed in comparison with Figure 5. The vorticity between the plates predicted by the k-\(\omega\) model exhibits weaker vortex structures compared to the results obtained from the laminar model. However, there is still a suspect \"blob\" of vorticity that travels within the channel that is not seen in the experiment. On the other hand, the k-\(\varepsilon\) model produces much more realistic vorticity contours. However, when comparing experimental and CFD results for phases \(\phi 1\), \(\phi 3\), \(\phi 11\) and \(\phi 13\) in Figures 5a and 6b, it is clear that the secondary shear layer (closer to the centre of the channel) is rather under-predicted by the CFD model. The results in Figures 5 and 6 suggest that the disturbances leading to the creation of the elongated vorticity regions referred to as secondary shear layers and the \"blobs\" of vorticity described above originate from the open area at the end of plates. Therefore, a further investigation into the vortex structures at the end of the plates was conducted to help choose turbulence models that best describe the flow, as illustrated in Figures 7-9. Figure 7, based on experimental results at drive ratio 0.83%, shows that the flow enters the left end of the heat exchanger assembly at phase \(\phi 1\) and reaches the maximum amplitude at \(\phi 5\). During these phases, a weak vortex structure from the open area next to the left end of the HHX moves into the channel. The vortex structure at the right end of the heat exchanger assembly elongates as the velocity increases, but stays attached to the plate ends until the maximum velocity is reached at \(\phi 5\). When the flow decelerates, the vortex structures at the right end of the plates start shedding, as seen at \(\phi 8\). Similar  
Figure 5: Comparison between vorticity contour from (**a**) experiment and (**b**) CFD laminar model. 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.  
behaviour is observed for the second half of the cycle as the flow reverses (phases \(\phi\)11 to \(\phi\)20), although differences in the flow patterns exist due to the asymmetry of the temperature profile (cf. Figure 2). Figure 8 shows vorticity contours at the ends of the heat exchanger assembly for drive ratio of 0.83% calculated using the k-\(\varepsilon\) model. The vortex pattern is very different form the experimental one: vortex structures at the right end of the plate for \(\phi\)3 appear more stable. The pair of vortex structures at the end of plates elongates until the flow reaches maximum velocity at \(\phi\)5. In the experiment, vortex structures start to \"wiggle\" in this phase, which the k-\(\varepsilon\) model does not seem to predict. As the flow decelerates, the elongated structures predicted by the k-\(\varepsilon\) model retain their shapes, but start to lose their strength, which reduces considerably by the time the flow reverses at \(\phi\)11. The weak vortex structures are re-entrained by the channel flow to create the elongated secondary vortex structures (secondary shear layers). In the second half of the cycle, similar stable vortex structures are observed on the left end of the plates. Importantly, the discrete vortex shedding phenomena are not seen in the results obtained from the k-\(\varepsilon\) turbulence model. Figure 9 shows vorticity contours at the left and right ends of the heat exchanger assembly calculated for the drive ratio of 0.83% using the k-\(\omega\) model. The vortex structures have a closer resemblance to the experimental result than those from the k-\(\varepsilon\) model. The vortex shedding process starts at the right end at \(\phi\)1 and the left end at \(\phi\)11.