RESUMEN
We numerically study turbulent Rayleigh-Bénard (RB) convection under spatial temperature modulation, where the bottom temperature varies sinusoidally around a mean value in space. Both two- and three-dimensional simulations are performed over the Rayleigh number range 10^{7}≤Ra≤10^{10} and the wave number range 1≤k≤120 at fixed Prandtl number Pr=0.7. It is demonstrated that spatial temperature modulation with small wave numbers can enhance the global heat transfer (characterized by the Nusselt number Nu) in the turbulent regime, while Nu is close to that in standard RB convection in the case of large wave numbers. Further, we propose two characteristic modulation length scales: one is the penetration depth δ_{k} above which spatial modulation is negligible, the other is the inversion depth δ_{k2} below which there exists a stable inverse temperature gradient. Based on the relative thickness of the thermal boundary layer (BL) δ_{th} compared with these two length scales, the underlying modulation mechanism is physically explained and three regimes are identified: (1) an unperturbed BL regime (δ_{k}<δ_{th}), in which the modulation effect does not penetrate through the thermal BL and Nu is nearly unchanged; (2) a partially modulated BL regime (δ_{k2}<δ_{th}<δ_{k}), in which hot spots trigger more plume emissions from the thermal BL, resulting in Nu enhancement; and (3) a fully modulated BL regime (δ_{th}<δ_{k2}), in which the stable temperature inversion over the cold phases begins to affect convective flows, which alters the trend of Nu enhancement.
RESUMEN
Thermal turbulence is well known as a potent means to convey heat across space by a moving fluid. The existence of the boundary layers near the plates, however, bottlenecks its heat-exchange capability. Here, we conceptualize a mechanism of thermal vibrational turbulence that breaks through the boundary-layer limitation and achieves massive heat-transport enhancement. When horizontal vibration is applied to the convection cell, a strong shear is induced to the body of fluid near the conducting plates, which destabilizes thermal boundary layers, vigorously triggers the eruptions of thermal plumes, and leads to a heat-transport enhancement by up to 600%. We further reveal that such a vibration-induced shear can very efficiently disrupt the boundary layers. The present findings open a new avenue for research into heat transport and will also bring profound changes in many industrial applications where thermal flux through a fluid is involved and the mechanical vibration is usually inevitable.
RESUMEN
The flow instabilities of Rayleigh-Bénard convection in a cylinder with effect of uniform internal heat source are investigated numerically. The instabilities of the static state and of axisymmetric flows are investigated by linear stability analysis. The convection threshold depends on the strength of internal heat source q and the aspect ratio of the cylinder Γ. The stability of axisymmetric flows is strongly affected by these two parameters, as well as the Prandtl number Pr. Depending on the value of q, three regimes are identified: weak internal heating, moderate internal heating, and strong internal heating regime. In a weak internal heating regime, the instability characteristics are similar to Rayleigh-Bénard convection. In a moderate internal heating regime, intense interaction of buoyancy instability and hydrodynamic instability result in complex instability curves. When q is large enough, the internal heating effect overwhelms the boundary heating effect. Specifically, the influence of Pr on instability is studied at a moderate internal heat strength q=6.4. An extremely multivalued stability curve is observed. At most five critical Rayleigh numbers can be determined for the axisymmetry-breaking instability at a certain Prandtl number. An axisymmetric unsteady instability mode is observed as well. By nonlinear simulation, the oscillatory flow patterns are obtained, and the axisymmetry-breaking bifurcation of the unsteady toroidal flow is studied.
RESUMEN
The instabilities and transitions of flow in an annular container with a heated bottom, a cooled top, and insulated sidewalls are studied numerically. The instabilities of the static diffusive state and of axisymmetric flows are investigated by linear stability analysis. The onset of convection is independent of the Prandtl number but determined by the geometry of the annulus, i.e., the aspect ratio Γ (outer radius to height) and radius ratio δ (inner radius to outer radius). The stability curves for onset of convection are presented for 0.001≤δ≤0.8 at six fixed aspect ratios: Γ=1, 1.2, 1.6, 1.75, 2.5, and 3.2. The instability of convective flow (secondary instability), which depends on both the annular geometry and the Prandtl number, is studied for axisymmetric convection. Two pairs of geometric control parameters are chosen to perform the secondary instability analysis-Γ=1.2, δ=0.08 and Γ=1.6, δ=0.2-and the Prandtl number ranges from 0.02 to 6.7. The secondary instability exhibits some similarities to that for convection in a cylinder. A hysteresis stability loop is found for Γ=1.2, δ=0.08 and frequent changes of critical mode with Prandtl number are found for Γ=1.6, δ=0.2. The three-dimensional flows beyond the axisymmetry-breaking bifurcations are obtained by direct numerical simulation for Γ=1.2, δ=0.08.