Turbulent heat transfer enhancement by compliant walls

Abstract

This study investigates the effect of compliant walls on the turbulent heat transfer in channel flows over viscous-hyperelastic walls. We perform Direct Numerical Simulations, fully resolving the mutual fluid-structure interactions between the turbulent flow and the compliant walls, varying the wall elasticity and the thermal diffusivity in a fully turbulent condition. We show that the compliant wall leads to an increase not only of the momentum transfer but also of the heat transfer. Since the compliant wall can dynamically move, in the near-wall region heat flux is mostly transferred via turbulent convection rather than diffusion, as typically found with rigid walls. Thus, the heat flux can be controlled not only by varying the thermal diffusivity, but also by changing the transverse modulus of elasticity which governs the wall-normal velocity fluctuations and consequently the temperature ones. Finally, we show that the physical mechanism controlling these modifications are the sweep and ejection events.

Figures (10)

• Figure 1: (a) Sketch of the computational configuration for the present study. The colored regions are the two compliant walls, bounded by two rigid-walls. (b) Visualizations of the instantaneous temperature on $x$-$y$ planes for varying Prandtl numbers: $Pr=1$ (top), $Pr=4$ (middle), and $Pr=7$ (bottom). The white solid lines represent the interface between fluid and compliant wall regions. The color-contours represent the temperature, $T$, with values ranging from $0$ (blue) to $1$ (red).
• Figure 2: The wall-normal profiles of the flow statistics: (left) mean velocity profiles and (right) Reynolds shear and normal stress components of the fluid. The line style differentiate the cases with different walls: solid line for the compliant wall with $G=0.25\rho U_b^2$ , and dashed line for the rigid wall. The line color in the right panel indicates the different components of the Reynolds stress tensor: $\overline{u^\prime u^\prime}$ (black), $\overline{v^\prime v^\prime}$ (violet), $\overline{w^\prime w^\prime}$ (magenta), and $\overline{u^\prime v^\prime}$ (orange).
• Figure 3: The wall-normal profiles of the thermal statistics: (left) mean temperature profiles and (right) variance of the temperature fluctuations. The line style differentiate the cases with different walls: solid line for the compliant wall with $G=0.25\rho U_b^2$, and dashed line for the rigid wall. The line color indicates the different Prandtl number: $Pr=1$ (orange), $Pr=4$ (magenta), and $Pr=7$ (black). Symbols represent the reference results from the literature: (left) $\triangle$: $Pr=1$ at $Re_\tau=150$NA1999use, and $\bigcirc$: $Pr=7$ at $Re_b=2800$YOUSEFI2021Regimes; (right) $\Box$: $Pr=1$ at $Re_\tau=180$ZHOU2025dns, and $\bigtriangledown$: $Pr=10$ at $Re_\tau=150$NA1999use.
• Figure 4: (left) The integral contribution of the total diffusive $q_{D}$ (magenta) and convective $q_{C}$ (green) heat flux components introduced in Eq. (\ref{['eq: heat flux']}) for different Prandtl numbers. The rigid case is shown with thinner bars and a black hatched fill. (right) The wall-normal profiles of all the heat flux contributions for $Pr=7$, with each term normalized by the local total heat flux. The line color represents the different terms in Eqs. (\ref{['eq: dtdy term']}) and (\ref{['eq: vt term']}): $q_{D_f}$ (dark magenta), $q_{D_s}$ (light magenta), $q_{C_f}$ (dark green), and $q_{C_s}$ (light green). The rigid case is shown with dashed lines for comparison.
• Figure 5: Instantaneous visualization on $x-z$ planes at $y\approx0.05h$ and $0.2h$ of the quadrant events for (a, c) $u^\prime v^\prime$ and (b, d) $T^\prime v^\prime$ at $Pr=7$. The top and bottom panels are for the rigid (a, b) and compliant (c, d) cases. Thin black lines represent the instantaneous iso-contour-lines of wall deformation $\delta/h$: $-0.15$ (dashed) and $0.15$ (solid).