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 . The authors assume incompressible fluid with a Prandtl number Pr = 7.1 (water) and with a Rayleigh number Ra = 1.0×10 4 or 4. can observe the optimum frequency where the amplitude of attains the maximum, each η. And, for both Ra's, becomes the minimum at η = 1.5 -2.0. Especially for Ra = 4.0×10 4 , is affected by the initial conditions. For both Ra's, the maximum of the amplitude uniquely exists at each η, when η < 1.5. On the other hand, we can observe not single but plural peak frequencies with locally-maximum '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 = 4.0×10 4 , this relation is also affected by the initial conditions. In addition, the details of a new flow structure S8 is reported.

On <i>g</i>-jitter effects on three-dimensional laminar thermal convection in low gravity

“…Because, we have confirmed in advance that they are strictly periodic. We have already confirmed the numerical accuracies in both non-forced-oscillation and forced-oscillation cases in the terrestrial-gravity environment (Hirata et al, 2006;Tanigawa et al, 2009;Hirata et al, 2013). On the other hand, there might exist unknown factors concerning the numerical accuracy in forced-oscillation cases in low gravity environments.…”

“…5(g), it is interesting to observe another peak with smaller K at ω  400, in addition to the maximum peak at ω  (= 70). In our previous study (Hirata et al 2013) under a constant gravity instead of the present zero gravity, we have also reported plural peak frequencies with locally-maximum K 's at ω  . This will be discussed later in Fig.…”

“…The governing equations (1) -(3) are solved by a finite difference method based on the MAC scheme for velocity-pressure coupling using a staggered computational grid, as well as Hirata et al (2006), Tanigawa et al (2009) and Hirata et al (2013). Concerning the mesh size, we adopt 81 3 for the main computations.…”

“…The full Navier-Stokes equations in three-dimensional Cartesian coordinates are simplified by introducing the Boussinesq approximation. Then, these simplified equations are solved by using the finite difference method (Hirata et al, 2006;Tanigawa et al, 2009;Hirata et al, 2013). We especially focus upon the influences of both Ra η and ω.…”

Dynamics of a binary mixture subjected to a temperature gradient and oscillatory forcing

“…On the theoretical side, to date, there is a continuing interest in understanding the organisation of mean flow and its stability in fluids with (Higuera et al 2014) and without (Hirata et al 1995) interfaces and in porous media (Bardan, Razi & Mojtabi 2004). The evolution of convective patterns in mixtures is much richer than that in single fluids, especially when the Soret effect is taken into account.…”