Research ArticleENGINEERING

Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement

See allHide authors and affiliations

Science Advances  22 May 2020:
Vol. 6, no. 21, eaaz8239
DOI: 10.1126/sciadv.aaz8239
  • Fig. 1 Turbulent thermal vibrational convection.

    (A) Instantaneous flow structures observed under different vibration frequencies with ω = 0 (left), ω = 700 (middle), and ω = 1400 (right). The 3D flow is illustrated by temperature isosurfaces with low (green) and high (brown) temperature, and the opacity is set to be 50% (see supplementary movies). For all the three cases, Ra = 108, Pr = 4.38, and δ = 0.1. Here, δ and ω are the dimensionless vibration amplitude and angular frequency with respect to the cell height H and the free-fall time scale H/αgΔ, respectively. (B and C) Corresponding temperature contours (B) on the horizontal slice at z = δth(ω) and (C) on the vertical slice at y/W = 0.5 near the lower conducing plate. Here, δth(ω) is the thermal boundary layer thickness obtained using δth(ω) = 1/[2Nu(ω)]. Note that the colormap is the same for (B) and (C), but a different one is adopted for (A). In the left panel, the typical flow structures of classical thermal turbulence without any vibration are established. In the middle and right panels, with increasing ω, more and more plumes are generated and erupted due to the destabilization of thermal boundary layers. (D) Heat-transport enhancement expressed as the ratio of Nusselt numbers Nu(ω)/Nu(0) versus ω, where Nu(ω) is the Nusselt number of the vibrated convection measured at ω, and Nu(0) is the Nusselt number of classical thermal turbulence without any vibration. The horizontal dashed line marks Nu(ω)/Nu(0) = 1, and the yellow shaded area corresponds to the Nu-enhancement regime. (E) Normalized area Ap/LW of hot plumes as a function of ω obtained at z = δth(ω) near the lower plate. Inset shows the corresponding heat content Qp/Q0 of hot plumes. Here, Q0 is the energy supplied to the system in one large-scale turnover time. (F) Sketch of the rectangular cell with the coordinate system. The horizontal vibration δcos(ωt) in the x direction is applied to the convection cell.

  • Fig. 2 Heat-transport enhancement due to horizontal vibration.

    (A and B) Ratio Nu(ω)/Nu(0) as a function of vibration frequency ω obtained at various Ra and fixed δ = 0.1 for (A) 3D and (B) 2D simulations. The dashed curves are the best fits of the crossover function y = log [101/4 + (ω/ω*)a/4]4 to the respective data, from which the value of ω* is gained. The fitted values of ω* and a are given and discussed in the Supplementary Materials. (C) Ratio Nu(ω)/Nu(0) as a function of the normalized frequency ω/ω* for the same datasets as those in (A) and (B). Note that we also carried out simulations at different values of δ and plotted the ratio Nu(ω)/Nu(0) as a function of the vibrational Rayleigh number (also called Gershuni number) Rav. The same behaviors are obtained (see figs. S7 to S9).

  • Fig. 3 Heat-transport scaling of the vibrated convection.

    (A and B) Log-log plots of the measured Nusselt number Nu as a function of the Rayleigh number Ra for various values of the vibration frequency ω for (A) 3D and (B) 2D simulations. From bottom to top, the symbols are △ : ω = 0; ☆ : ω = 200; ⊲ : ω = 400; ◊ : ω = 550; □ : ω = 700; ⊳ : ω = 850; ○ : ω = 1000; ▽ : ω = 1400; + : ω = 1700. The solid and dashed lines are eyeguides. (C) Fitted exponent in the power-law NuRaβ as a function of vibration frequency ω. The solid and dashed lines mark the values of 0.5 and 0.3, respectively, for reference. Inset shows the shear Reynolds number Res as a function of ω at Ra = 108. The dash-dotted lines indicate the critical value of 200 taken by Grossmann and Lohse (31, 40) and that of 420 given by Landau and Lifshitz (39).

Supplementary Materials

Stay Connected to Science Advances

Navigate This Article