Oscillatory Double-Diffusive Convection in a Horizontal Cavity with Soret and Dufour Effects
📝 Abstract
Oscillatory double-diffusive convection in horizontal cavity with Soret and Dufour effects is investigated numerically based on SIMPLE algorithm with QUICK scheme in non-uniform staggered grid system. The results show that double-diffusive convection develops from steady-state convection-dominated, periodic oscillatory, quasi-periodic oscillatory to chaotic flow, and finally return to periodic oscillation as buoyancy ratio increases. Moreover, fundamental frequency and fluctuation amplitude increase with buoyancy ratio. As Rayleigh number increases, transition trendy of oscillatory convection is similar to that of buoyancy ratio. But the return of periodic oscillation from chaos is not obtained as Rayleigh number increases. As aspect ratio decreases, the oscillatory convection evolves from periodic into steady-state. In addition, fundamental frequency increases at first and then decreases while fluctuation amplitude decreases with aspect ratio.
💡 Analysis
Oscillatory double-diffusive convection in horizontal cavity with Soret and Dufour effects is investigated numerically based on SIMPLE algorithm with QUICK scheme in non-uniform staggered grid system. The results show that double-diffusive convection develops from steady-state convection-dominated, periodic oscillatory, quasi-periodic oscillatory to chaotic flow, and finally return to periodic oscillation as buoyancy ratio increases. Moreover, fundamental frequency and fluctuation amplitude increase with buoyancy ratio. As Rayleigh number increases, transition trendy of oscillatory convection is similar to that of buoyancy ratio. But the return of periodic oscillation from chaos is not obtained as Rayleigh number increases. As aspect ratio decreases, the oscillatory convection evolves from periodic into steady-state. In addition, fundamental frequency increases at first and then decreases while fluctuation amplitude decreases with aspect ratio.
📄 Content
1 Oscillatory double-diffusive convection in a horizontal cavity with Soret and Dufour effects Jin Wang1, 2, Mo Yang1, Ya-Ling He3, Yuwen Zhang2, 3 * 1 School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China 2 Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA 3 Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China ABSTRACT Oscillatory double-diffusive convection in horizontal cavity with Soret and Dufour effects is investigated numerically based on SIMPLE algorithm with QUICK scheme in non-uniform staggered grid system. The results show that double-diffusive convection develops from steady- state convection-dominated, periodic oscillatory, quasi-periodic oscillatory to chaotic flow, and finally return to periodic oscillation as buoyancy ratio increases. Moreover, fundamental frequency and fluctuation amplitude increase with buoyancy ratio. As Rayleigh number increases, transition trendy of oscillatory convection is similar to that of buoyancy ratio. But the return of periodic oscillation from chaos is not obtained as Rayleigh number increases. As aspect ratio decreases, the oscillatory convection evolves from periodic into steady-state. In addition, fundamental frequency increases at first and then decreases while fluctuation amplitude decreases with aspect ratio. Keywords: Oscillatory double-diffusive convection; Soret and Dufour effects; Chaos; Heat and mass transfer.
Introduction Since its first appearance as an oceanographical topic [1], double-diffusive convection where heat and solute of different diffusivities affect simultaneously the density and fluid motion has matured into a subject with wide applications in a large variety of fields such as astrophysics [2], manufacturing [3-5] and ventilations [6,7]. Compared with nature convection only driven by thermal buoyancy, double-diffusive convection has marked differences on heat and mass transfer. As thermal and solutal buoyancies play important roles on fluid flow and heat transfer during the double-diffusive convection process, it is necessary to develop effective models and methods to better understand the double-diffusive convective mechanism. During the past several decades, many numerical and experimental studies focused on double-diffusive convection have been carried out [8-13]. As a comprehensive flow and heat transfer problem, double-diffusive convection in a typical configuration is a strong and complex nonlinear problem [10, 13]. Any difference between thermal and solutal buoyancies or diffusivities may induce convective instabilities even if the initial and boundary conditions are gravitationally stable. For several decades, researchers devoted to stationary and oscillatory nonlinear characteristics of double-diffusive convection with different
- Corresponding author. Email: zhangyu@missouri.edu.
2 thermal Rayleigh numbers, Lewis numbers, buoyancy ratios, and aspect ratios. Huppert [14] analyzed transition from conduction state to oscillatory motion followed by transition to a more complicated oscillatory motion with increasing thermal Rayleigh number for double-diffusive convection between two infinite planes. Further transition between oscillatory and steady convection was reported by Costa et al. [15] using a second order nonlinear model for two- dimensional double-diffusive convection. Khadiri et al. [16] investigated double-diffusive convection in a square porous cavity heated and salted from below based on the study of natural convection heating from below [17] and monocellular, bicellular and tricellular flows were presented and discussed in detail. Ghorayeb et al. [18] studied numerically the onset of oscillatory double-diffusive convection in a square cavity and the influence of Lewis number on the transition from steady convective flow to oscillatory flow was carried out. Chen et al. [19] expanded on Bergeon’s [20] work in which only stationary onset of instability for double-diffusive convection in inclined cavity was considered and investigated oscillatory convection using linear stability analysis; the results showed two Hopf bifurcation points were obtained as aspect ratio increased. Nonlinear bifurcation analyses of double-diffusive convection in vertical enclosures were also considered by Xin et al. [21] and Bardan et al. [22]. During the nonlinear double-diffusive convection process driven by thermal and solutal buoyancies, most studies only considered contributions of Fourier conduction and Fickian diffusion to heat and mass transfer. However, some investigations show that the Soret and Dufour effects also play significant roles during the nonlinear process [23-25], especially when the thermal
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