## 4 Conclusions  
Numerical work presented in this paper builds upon previous experimental investigations [16; 17] of the fluid flow and heat transfer processes in oscillatory flow conditions occurring at the coupled hot and cold plate-type heat exchangers. It presents a series of numerical studies, carried out using the ANSYS FLUENT 13.0 CFD package, aiming to match the experimental results by considering a range of flow models including laminar and four available RANS models: k-\(\varepsilon\), k-\(\omega\), SST-k-\(\omega\) and transition-SST. The key finding of this study is that in order to replicate the experimental flow fields, one would need to assume that the transition to turbulence occurs at much lower drive ratios than commonly accepted in the existing literature. In particular, the need for a turbulence model for the drive ratios as low as 0.45% has been demonstrated. The investigation of the differences observed between the velocity profiles from the experiment and laminar model led to a hypothesis that turbulence may have influence on the flow, despite the commonly-accepted criterion for transition proposed by [PERSON] and [PERSON] [7]. This was concluded to be the effect of the finite length of the channel and the presence of the flow disturbances re-entrained after the vortex shedding cycle. Some validity to this description of the flow has been given by showing that the turbulent model gives a good match (with errors of \(\approx 5\%\)) between the results obtained from the experiment and the simulation, particularly at the drive ratio of 0.83% (the highest investigated). The SST k-\(\omega\) model developed by [PERSON] [26] is shown to best capture the essence of the flow at that drive ratio. The application of turbulence models makes the value of the metric \(\sigma_{met}\), introduced to show the deviation between CFD and experimental velocity profiles, smaller. For instance, at the drive ratio of 0.83%, the metric value drops from 0.305 down to 0.174 as the SST k-\(\omega\) replaces the laminar model. It has been shown that transition may occur at a drive ratio as low as 0.45%, which translated into Stokes' layer-based Reynold numbers corresponds to \(Re_{\delta}=100\). The data shown in Table 1 would then in turn indicate the possible value of critical Reynolds number approximately within: \(70<Re_{\delta}<100\). This finding is important in that it contributes to a new understanding that the turbulent flow features may appear at lower flow amplitudes within structures of thermoacoustic systems. Of course, the nature of turbulence and transition in the oscillatory flows is not the same as in relatively better understood steady flows. It is known that there are quite a few different turbulent flow regimes in oscillatory flows, and these may appear at different parts of the cycle with a possibility of relaminarization. Therefore, in the context of the current study, it may well be necessary to refine any future CFD models from the point of view of the possible turbulence regimes in the oscillatory flows. As expected, viscous dissipation increases with drive ratio. The dissipation is also higher within the hot areas. The results give an illustration of possible heat generation within certain areas of the thermoacoustic system as a result of dissipation. The amount of energy may not be large, but it may have a significant impact on the performance of fluid flow and heat transfer within small channels, such as those within the CHX and HHX. Since dissipation is very much related to the values of velocity, the correct prediction of velocity profiles, especially near the wall, is very important. The heat exchangers are normally placed within the most important parts of thermoacoustic devices. Therefore, any contribution to the energy loses is worth considering. The current study included the calculation of cycle- and space-averaged heat fluxes on the CHX and HHX plates.