孔隙介质方腔内自然对流的动力学演化*

doi:10.7523/j.ucas.2022.077

摘要/Abstract

摘要： 流体饱和孔隙介质腔体内的自然对流是非线性流体动力学研究的经典问题。前人研究工作受早期计算条件限制主要侧重于中心对称对流模态的时空演化动力学机制,不能完整刻画实际孔隙自然对流系统中包含全部对流模态的动力学行为,因而已有研究结果无法直接应用于实际工程问题。本文基于伽辽金法和配点伪谱法数值模拟底部加热的孔隙介质方腔内模态完备的二维自然对流,首次得到自然对流从发生到走向混沌的完整动力学演化路径。模拟结果揭示,随着Rayleigh数从4π²单调增加到1 200,自然对流演化历经21个不同阶段（包括1个稳态对流阶段、6个单频振荡阶段、9个准周期振荡阶段、2个锁频共振阶段和3个非周期混沌振荡阶段）。对流模态的空间变化与时间振荡是对流形态反复发生交替的根本原因。采用时间序列、功率谱、相图和洛伦兹映射4种作图方法,系统对比了Nusselt数表征的计算热流作单频、准周期、锁频和混沌振荡的不同特征。计算平均热流和振荡主频随Rayleigh数的变化可由简单的解析公式拟合（在很宽的Rayleigh数区间内近似服从经典边界层标度律）,为相应条件下实际工程设计和应用提供了便捷的计算工具。

关键词: 自然对流, 动力学演化, 孔隙介质, 对流模态, 数值模拟

Abstract: Natural convection in fluid-saturated porous cavities is a classical problem in the study of nonlinear hydrodynamics. Limited by the early computing capability, previous studies mainly focused on the dynamic mechanism of the spatiotemporal evolution of centrosymmetric convection modes, and cannot fully describe the dynamic behavior of real-world porous natural convection systems with all convection modes. Therefore, the available results cannot 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 Rayleigh number increasing from 4π²to 1200, 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 Nusselt number 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 Rayleigh number can be fitted by simple analytical formulas (approximately obeying the scaling laws given by the classical boundary layer theory in a wide range of Rayleigh number), providing convenient calculation tools for practical engineering designs and applications under the corresponding conditions.

Key words: natural convection, dynamic evolution, porous media, convection mode, numerical simulation

中图分类号:

P314

张连平, 王世民. 孔隙介质方腔内自然对流的动力学演化^*[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2022.077.

ZHANG Lianping, WANG Shimin. Dynamic evolution of natural convection in a porous square cavity[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2022.077.

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孔隙介质方腔内自然对流的动力学演化^*

Dynamic evolution of natural convection in a porous square cavity

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