Thermal Convection in an Oscillating Cube at Various Frequencies and Amplitudes

Abstract

In this study, the authors numerically investigate the frequency response on the three-dimensional thermal convection in a cubic cavity heated below in the gravitational field, concerning flow characteristics such as flow structure and a global quantity the spatially-averaged kinetic energy K. The authors assume incompressible fluid with a Prandtl number Pr = 7.1 (water) and with a Rayleigh number Ra = 1.0×10⁴ or 4.0×10⁴. The direction of a forced sinusoidal oscillation is parallel to the terrestrial gravity. The authors especially focus upon the influences of both the forced-oscillation amplitude η and frequency ω in non-dimensional forms, whose test ranges are 1.5 ≤ η ≤ 15 and 10 ≤ ω ≤ 10³. The obtained results are as follows. For Ra = 4.0×10⁴, as well as Ra = 1.0×10⁴ (Tanigawa et al., 2009), we can observe the optimum frequency ω_Kmax where the amplitude of K attains the maximum, each η. And, for both Ra's, ω_Kmax becomes the minimum at η = 1.5 - 2.0. Especially for Ra = 4.0×10⁴, ω_Kmax is affected by the initial conditions. For both Ra's, the maximum of the K amplitude uniquely exists at ω= ω_Kmax each η, when η < 1.5. On the other hand, we can observe not single but plural peak frequencies with locally-maximum K's each η, when η ≥ 1.5. It is confirmed that such plural frequencies are related with the appearances of various flow structures such as S1, S2, S4, S5, S6 and S8. Especially for Ra = 4.0×10⁴, this relation is also affected by the initial conditions. In addition, the details of a new flow structure S8 is reported.