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Research Papers: Heat Transfer Enhancement

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

[+] Author and Article Information

Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Casilla 10233 Alameda 3363, Estación Central, Santiago, Chileamador.guzman@usach.cl

Raúl A. Hormazabal, Tania A. Aracena

Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Casilla 10233 Alameda 3363, Estación Central, Santiago, Chile

1

Corresponding author.

J. Heat Transfer 131(9), 091902 (Jun 22, 2009) (8 pages) doi:10.1115/1.3139108 History: Received June 07, 2008; Revised April 07, 2009; Published June 22, 2009

## Abstract

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.

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## Figures

Figure 2

Computational mesh for the reduced domain with 16×8 macro-elements and 8×8 nodal points per macro-element for the aspect ratio r=0.125

Figure 3

Velocity characteristics for extended domain simulations for r=0.125: (a) u-velocity for a laminar flow, (b) u-velocity for a time-dependent flow regime, (c) streamlines for a laminar flow, and (d) streamlines for a time-periodic flow regime

Figure 4

Pressure field and streamlines for the aspect ratio r=0.375: Instantaneous representations during a time period of periodic flow regime for a Reynolds number of Re≈554.

Figure 1

Schematic of the symmetric wavy wall channel: (a) extended domain with 14 furrows and plane inlet and outlet regions, and (b) reduced domain with a spatially periodic length L

Figure 5

Eulerian flow characteristics of a periodic flow for Reynolds number of Re≈554 and aspect ratio r=0.375: (a) temporal evolution of the u- and v-velocities, (b) Fourier power spectra of the u-velocity, and (c) phase-portrait of the u- and v-velocity components

Figure 6

Normalized time period T∗/T versus normalized Reynolds number Re/Re∗ for r=0.375

Figure 7

Temporal evolution of the u- and v-velocities of a quasiperiodic flow for Reynolds number of Re≈356 and aspect ratio r=0.125

Figure 8

Transition scenarios from laminar to transitional flows by flow bifurcations for aspect ratios r=0.125 and r=0.375. Two successive Hopf bifurcations, B1 and B2, for the critical Reynolds numbers Rec1 and Rec2, respectively, developed for r=0.125 leading to a quasiperiodic flow through a RTN transition scenario. For the aspect ratio r=0.375, only one flow bifurcation from laminar to time-periodic flow regime develops at the critical Reynolds number Rec, through a frequency-doubling transition scenario.

Figure 9

Poiseuille plane channel friction factor and symmetric wavy channel friction factors for aspect ratios r=0.125 and r=0.375 for increasing Reynolds numbers

Figure 10

Symmetric wavy channel temperature distribution for r=0.375: (a) laminar flow for Re≈54 and (b) eight instantaneous representations during a time period τ for a periodic flow of Re≈554

Figure 11

Heat transfer parameters: (a) time-averaged mean Nusselt number versus Reynolds number for laminar and transitional flow regimes for the aspect ratio r=0.375 and (b) pumping power versus Nusselt number for laminar and transitional flow regimes

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