Abstract
This paper studied the Rayleigh–Bénard convection in binary fluid mixtures with a strong Soret effect (separation ratio ) in a rectangular container heated uniformly from below. We used a high-accuracy compact finite difference method to solve the hydrodynamic equations used to describe the Rayleigh–Bénard convection. A stable traveling-wave convective state with periodic source defects (PSD-TW) is obtained and its properties are discussed in detail. Our numerical results show that the novel PSD-TW state is maintained by the Eckhaus instability and the difference between the creation and annihilation frequencies of convective rolls at the left and right boundaries of the container. In the range of Rayleigh number in which the PSD-TW state is stable, the period of defect occurrence increases first and then decreases with increasing Rayleigh number. At the upper bound of this range, the system transitions from PSD-TW state to another type of traveling-wave state with aperiodic and more dislocated defects. Moreover, we consider the problem with the Prandtl number ranging from 0.1 to 20 and the Lewis number from 0.001 to 1, and discuss the stabilities of the PSD-TW states and present the results as phase diagrams.
Highlights
Thermal convection is a common phenomenon in nature, and has a wide range of engineering applications including nuclear systems, crystal growth and chemical vapor deposition, and industrial cooling
By using the high-order compact finite difference (FD) algorithm to numerically solve the fully coupled hydrodynamic field equations, we studied a traveling wave state with source defects of convection in binary fluid mixtures with a negative separation ratio
We found that the new PSD-traveling waves (TW) state is stable when the reduced Rayleigh number r ranges from 1.426 to 2.245, and the defect always occurs at about x = 5.0, regardless of the Rayleigh number
Summary
Thermal convection is a common phenomenon in nature, and has a wide range of engineering applications including nuclear systems, crystal growth and chemical vapor deposition, and industrial cooling. This study concerns the Rayleigh–Bénard convection in binary fluid mixtures, of which complex time-dependence dynamic states appear in the vicinity of primary instabilities. The flow patterns in binary fluid mixtures are more interesting and complicated than those in one-component fluid because of the Soret coupling between the temperature and concentration fields. The Soret coupling reflects the influence of temperature gradients on concentrations of binary fluids, and its strength is characterized by the separation ratio ψ. With ψ < 0, destabilizing temperature gradients results in a competing concentration distribution, and its impacts on buoyancy force stabilize the flow field. For such a mixture of our Entropy 2020, 22, 283; doi:10.3390/e22030283 www.mdpi.com/journal/entropy
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