Onset of temporal aperiodicity in high Prandtl number liquid bridge under terrestrial conditions

Abstract

The paper presents a three-dimensional numerical study of the bifurcations and onset of chaotic regime for the thermoconvective oscillatory flow in cylindrical liquid bridge. Three-dimensional Navier–Stokes equations in Boussinesq approximation are solved numerically by finite volume method. Silicone oil 1cSt, with rather large Prandtl number, Pr=18.8, is chosen as test liquid. The simulations are done at normal gravity conditions and unit aspect ratio. The dependence of viscosity of the fluid upon temperature allows us to be close to the real phenomenon. Both spatial and temporal changes occurring in the system are analyzed. The results are compared to the experimental data. A following sequence of well-defined dynamic regimes was detected when temperature difference between the supporting disks is increasing: steady, periodic, quasiperiodic, periodic, and chaotic. The observed succession of bifurcations on the way to chaos is similar to the one coming from experiments. Except for these dynamic bifurcations the system exhibits numerous transitions in spatial organization of the flow. Two-dimensional steady-state flow undergoes standing wave (SW) with azimuthal wave number m=1 as a result of supercritical Hopf bifurcation. Moving above the critical point the following succession of flow states has been numerically found: SW(m=1)→TW (m=1)→SW(m=1+2)→TW(m=1+2). The transition to chaos occurs while the flow pattern represents a traveling wave (TW) with a mixed mode m=1+2, while the m=2 is dominant. Particular attention is paid to the analysis of special properties of the flow: entropy, net azimuthal flow, frequency skips, splitting of maxima, and related phenomena.