Heat Transfer Enhancement Due to Frequency Doubling and Ruelle–Takens–Newhouse Transition Scenarios in Symmetric Wavy Channels

Heat transfer enhancement characteristics, through a transition scenario of flow bifurcations in symmetric wavy wall channels, are investigated by direct numerical simulations of the mass, momentum, and energy equations using spectral element methods. Flow bifurcations, transition scenarios, and heat transfer characteristics are determined by increasing the Reynolds numbers from a laminar to a transitional flow for the geometrical aspect ratios $r=0.125$ and $r=0.375$⁠. The numerical results demonstrate that the transition scenario to transitional flow regimes depends on the aspect ratio. For $r=0.375$⁠, the transition scenario is characterized by one Hopf flow bifurcation in a frequency-doubling transition scenario, where further increases in the Reynolds number always lead to periodic flows; whereas, for $r=0.125$⁠, the transition scenario is characterized by a first Hopf flow bifurcation from a laminar to a time-dependent periodic flow and a second Hopf flow bifurcation from a periodic to a quasiperiodic flow. For $r=0.125$⁠, the flow bifurcation scenario is similar to the Ruelle–Takens–Newhouse (RTN) transition scenario to Eulerian chaos observed in asymmetric wavy and grooved channels. The periodic and quasiperiodic flows are characterized by fundamental frequencies $ω1$⁠, and $ω1$ and $ω2$⁠, respectively. For the aspect ratio $r=0.375$⁠, the Nusselt number increases slightly as the Reynolds number increases in the laminar regime until it reaches a critical Reynolds number of $Rec≈126$⁠. As the flow becomes periodic, and then quasiperiodic, the Nusselt number continuously increases with respect to the laminar regime, up to a factor of 4, which represents a significant heat transfer enhancement due to a better flow mixing.