2023/08/22 by Yuhan Jiang, Yongling Zhao, Jiang, Yuhan +7
Engineering · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Thin Films #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis
paper · pdf · doi:10.48550/arxiv.2308.11409
openalex publication_date 2023/08/22 · openalex created_date 2023/08/24 · openalex updated_date 2026/07/28
The transition route and bifurcations of the buoyant flow developing on a heated circular horizontal surface are elaborated using direct numerical simulations and direct stability analysis. A series of bifurcations, as a function of Rayleigh numbers (Ra) ranging from 101 to 6×107, are found on the route to the chaos of the flow at Pr=7. When Ra<1.0×103, the buoyant flow above the heated horizontal surface is dominated by conduction, because of which distinct thermal boundary layer and plume are not present. At Ra=1.1×106, a Hopf bifurcation occurs, resulting in the flow transition from a steady state to a periodic puffing state. As Ra increases further, the flow enters a periodic rotating state at Ra=1.9×106, which is a unique state that was rarely discussed in the literature. These critical transitions, leaving from a steady state and subsequently entering a series of periodic states (puffing, rotating, flapping and doubling) and finally leading to chaos, are diagnosed using spectral analysis and two-dimensional Fourier Transform (2DFT). Moreover, direct stability analysis is conducted by introducing random numerical perturbations into the boundary condition of the surface heating. We find that when the state of a flow is in the vicinity of bifurcation points (e.g., Ra=2.0×106), the flow is conditionally unstable to perturbations, and it can bifurcate from the rotating state to the flapping state in advance. However, for relatively stable flow states, such as at Ra=1.5×106, the flow remains its periodic puffing state even though it is being perturbed.