Natural convection in fluid-saturated porous cavities is a classical problem in the study of nonlinear hydrodynamics. Limited by the early computing capabilities, previous studies mainly focused on the dynamic mechanism of the spatiotemporal evolution of centrosymmetric convection modes, and could not fully describe the dynamic behavior of real-world porous natural convection systems with all convection modes. Therefore, the available results could not be directly applied to practical engineering problems. In this study, two-dimensional natural convection in a porous square cavity heated from below is numerically simulated with complete convection modes based on the Galerkin method and the collocation pseudo-spectral method, and the complete route for natural convection dynamically evolving from onset towards chaos is obtained for the first time. The modeling results reveal that along with Ra increasing from 4π2 to 1 200, the natural convection evolves across 21 different stages (including one steady convection stage, six single-frequency oscillation stages, nine quasiperiodic oscillation stages, two frequency-locked resonance stages, and three aperiodic chaotic oscillation stages). The spatial variation and temporal oscillation of convection modes are the fundamental reasons for the repeated alternation between different convection patterns. Different characteristics of single-frequency, quasiperiodic, frequency-locked, and chaotic oscillations in the calculated heat flow represented by Nu are systematically compared in terms of four graphical methods, viz. time series, power spectrum, phase portrait, and Lorenz mapping. The calculated average heat flow and primary oscillating frequency as functions of Ra can be fitted by simple analytical formulas, approximately obeying the scaling laws given by the classical boundary layer theory in a wide range of Ra values. This provides convenient calculation tools for practical engineering designs and applications under the corresponding conditions.
ZHANG Lianping
,
WANG Shimin
. Dynamic evolution of natural convection in a porous square cavity[J]. Journal of University of Chinese Academy of Sciences, 2024
, 41(5)
: 589
-603
.
DOI: 10.7523/j.ucas.2022.077
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