We reveal the fundamental and dominant flow structures of thermal convection in a cubic cavity under forced oscillation heated differentially by analysing the flow field with the proper orthogonal decomposition (referred to as POD). The database is made of consequtive series of three-dimensional results obtained by the direct numerical simulation based on the Boussinesq approximation for a forcedly-oscillating cube under the zero-gravity environment, at vibrational Rayleigh number (the Rayleigh number based on the cavity's acceleration amplitude instead of the gravitational acceleration) Ra η = 5.0×10 4 -1.1×10 5 , Plandtl number Pr = 7.1 (water) and non-dimensional forced-oscillating frequency ω = 1.0×10 0 -2.0×10 2 . The direction of the forced sinusoidal oscillation is parallel to the temperature gradient. It appears that the most energetic POD modes, or the first POD eigenfunctions with large eigenvalues, account for the transient process on flow structures during one forcing cycle. The first eigenfunctions correspond to the steady and laminar flow structures which appear inside a non-oscillating cube in the terrestrial environments. The POD expansion coefficient is found to be useful for predicting a consecutive series of the dominant flow structures. structures, the data can often be represented satisfactorily using only a few of the first modes. We expect that the most important modes could reflect the dominating flow structures. It is usually not possible to have sufficiently high time resolution to get several snapshots of the concerning flow. Furthermore, a snapshot of a given flow may contain random fluctuations due to turbulence and may be a superposition of several coherent flow structures. Hence, it is necessary for us to use some kind of statistical analysis of the data to extract flow structures effectively. In contrast to methods like conditional sampling, the POD does not need any assumptions about flow. Thus, the analyses using the POD have previously been applied to various experimental and computational outputs (Mayer et al., 2007).In the present study, we numerically investigate the influence of the forced oscillation upon the three-dimensional thermal convection in a cubic cavity heated from one wall and chilled from its opposite wall in the non-gravitational field with a vibrational Rayleigh number Ra η = 5.0×10 4 -1.1×10 5 , a Plandtl number Pr = 7.1 (water) and non-dimensional forced-oscillation frequency ω = 1.0×10 0 -2.0×10 2 . The direction of a forced sinusoidal oscillation is parallel to the temperature gradient. The full Navier-Stokes equations in three-dimensional Cartesian coordinates are simplified by introducing the Boussinesq approximation. 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 identification of the periodically-fluctuating flow during one forcing cycle by means of the use of POD, in order to educe fundamental and dominant flow structures in tran...
We numerically study the forced-oscillation-frequency responses on the three-dimensional thermal convection in a cubic cavity heated from one wall and chilled from its opposite wall in the non-gravitational field at vibrational Rayleigh number (the Rayleigh number based on the cavity's acceleration amplitude instead of the gravitational acceleration) Ra η = 5.0×10 3 -1.1×10 5 , Plandtl number Pr = 7.1 (water) and non-dimensional forced-oscillation frequency ω = 1.0×10 0 -1.0×10 3 . The direction of the forced sinusoidal oscillation is parallel to the temperature gradient inside the cubic cavity. We especially focus upon the influences of both Ra η and ω. As a result, five kinds of structures S2 (with a single roll), S4 (with a toroidal roll), S5 (with four roll), S6 (with four roll) and S (with six roll) appear in the tested ranges of Ra η and ω. The S consists of a pair of trident currents, namely, three ascending streams and three matching descending streams in the cubic cavity. And, such flow structures are revealed in detail. Whenever it is not conductive but convective for ω < 5.0×10 2 , convective motion always starts with the S4 from the rest at each forcing cycle. We find out the optimum frequency where the amplitude of a spatially-averaged kinetic energy K , which is defined by the difference between the maximum K and the minimum K over one forcing cycle, attains the maximum at each Ra η . At ω = , the flow structure is characterised by the S4. So, this fact suggests that the optimum frequency can be related with the S4. In addition, we show the occurrence condition for convection as a function of Ra η and ω, and the boundary for the quasi-steady approximation which is permissible at ω ≲ 10 0 from a quantitative viewpoint.
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