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Register a new userChaotic electro-convection flow states of a dielectric liquid between two parallel electrodes
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The two-dimensional regular and chaotic electro-convective flow states of a dielectric liquid between two infinite parallel planar electrodes are investigated using a two-relaxation-time lattice Boltzmann method. Positive charges injected at the metallic planar electrode located at the bottom of the dielectric liquid layer are transported towards the grounded upper electrode by the synergy of the flow and the electric field. The various flow states can be characterized by a non-dimensional parameter, the electric Rayleigh number. Gradually increasing the electric Rayleigh number, the flow system sequentially evolves via quasi-periodic, periodic, and chaotic flow states with five identified bifurcations. The turbulence kinetic energy spectrum is shown to follow the -3 law as the flow approaches turbulence. The spectrum is found to follow a -5 law when the flow is periodic.
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We present a numerical study of the flow states and reversals of the large-scale circulation (LSC) in a two-dimensional circular Rayleigh-Benard cell. Long-time direct numerical simulations are carried out in the Rayleigh number ($Ra$) range $10^{7} le Ra le 10^{8}$ and Prandtl number ($Pr$) range $2.0 le Pr le 20.0$. We found that a new, long-lived, chaotic flow state exists, in addition to the commonly observed circulation states (the LSC in the clockwise and counterclockwise directions). The circulation states consist of one primary roll in the middle and two secondary rolls near the top and bottom circular walls. The primary roll becomes stronger and larger, while the two secondary rolls diminish, with increasing $Ra$. Our results suggest that the reversal of the LSC is accompanied by the secondary rolls growing, breaking the primary roll and then connecting to form a new primary roll with reversed direction. We mapped out the phase diagram of the existence of the LSC and the reversal in the $Ra$-$Pr$ space, which reveals that the flow is in the circulation states when $Ra$ is large and $Pr$ is small. The reversal of the LSC can only occur in a limited $Pr$ range. The phase diagram can be understood in terms of competition between the thermal and viscous diffusions. We also found that the internal flow states manifested themselves into global properties such as Nusselt and Reynolds numbers.
The study focuses on the 3D electro-hydrodynamic (EHD) instability for flow between to parallel electrodes with unipolar charge injection with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is used to study flow pattern. In the absence of cross-flow, the base-state solution is hydrostatic, and the electric field is one-dimensional. With strong charge injection and high electrical Rayleigh number, the system exhibits electro-convective vortices. Disturbed by different perturbation patterns, such as rolling pattern, square pattern, and hexagon pattern, the flow patterns develop according to the most unstable modes. The growth rate and the unstable modes are examined using dynamic mode decomposition (DMD) of the transient numerical solutions. The interactions between the applied Couette and Poiseuille cross-flows and electroconvective vortices lead to the flow patterns change. When the cross-flow velocity is greater than a threshold value, the spanwise structures are suppressed; however, the cross-flow does not affect the streamwise patterns. The dynamics of the transition is analyzed by DMD. Hysteresis in the 3D to 2D transition is characterized by the non-dimensional parameter Y, a ratio of the coulombic force to viscous term in the momentum equation. The change from 3D to 2D structures enhances the convection marked by a significant increase in the electric Nusselt number.
We analyse the nonlinear dynamics of the large scale flow in Rayleigh-Benard convection in a two-dimensional, rectangular geometry of aspect ratio $Gamma$. We impose periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. As Rayleigh number Ra increases, a large scale zonal flow dominates the dynamics of a moderate Prandtl number fluid. At high Ra, in the turbulent regime, transitions are seen in the probability density function (PDF) of the largest scale mode. For $Gamma = 2$, the PDF first transitions from a Gaussian to a trimodal behaviour, signifying the emergence of reversals of the zonal flow where the flow fluctuates between three distinct turbulent states: two states in which the zonal flow travels in opposite directions and one state with no zonal mean flow. Further increase in Ra leads to a transition from a trimodal to a unimodal PDF which demonstrates the disappearance of the zonal flow reversals. On the other hand, for $Gamma = 1$ the zonal flow reversals are characterised by a bimodal PDF of the largest scale mode, where the flow fluctuates only between two distinct turbulent states with zonal flow travelling in opposite directions.
In this numerical study on two-dimensional Rayleigh-Benard convection we consider $10^7 leq Ra leq 10^{12}$ in aspect ratio $0.23 leq Gamma leq 13$ samples. We focus on several cases. First we consider small aspect ratio cells, where at high Ra number we find a sharp transition from a low Ra number branch towards a high Ra number branch, due to changes in the flow structure. Subsequently, we show that the influence of the aspect ratio on the heat transport decreases with increasing aspect ratio, although even at very large aspect ratio of $Gammaapprox10$ variations up to 2.5% in the heat transport as a function of Gamma are observed. Finally, we observe long-lived transients up to at least $Ra=10^9$, as in certain aspect ratio cells we observe different flow states that are stable for thousands of turnover times.
To understand how internal flow structures manifest themselves in the global heat transfer, we study the correlation between different flow modes and the instantaneous Nusselt number ($Nu$) in a two-dimensional square Rayleigh-Benard convection cell. High-resolution and long-time direct numerical simulations are carried out for Rayleigh numbers between $10^{7}$ and $10^{9}$ and a Prandtl number of 5.3. The investigated Nusselt numbers include the volume-averaged $Nu_{text{vol}}$, the wall-averaged $Nu_{text{wall}}$, the kinetic energy dissipation based $Nu_{text{kinetic}}$, and the thermal energy dissipation based $Nu_{text{thermal}}$. The Fourier mode decomposition and proper orthogonal decomposition are adopted to extract the coherent flow structure. Our results show that the single-roll mode, the horizontally stacked double-roll mode, and the quadrupolar flow mode are more efficient for heat transfer on average. In contrast, the vertically stacked double-roll mode is inefficient for heat transfer on average. The volume-averaged $Nu_{text{vol}}$ and the kinetic energy dissipation based $Nu_{text{kinetic}}$ can better reproduce the correlation of internal flow structures with heat transfer efficiency than that of the wall-averaged $Nu_{text{wall}}$ and the thermal energy dissipation based $Nu_{text{thermal}}$, even though these four Nusselt numbers give consistent time-averaged mean values. The ensemble-averaged time trace of $Nu$ during flow reversal shows that only the volume-averaged $Nu_{text{vol}}$ can reproduce the overshoot phenomena that is observed in the previous experimental study. Our results reveal that the proper choice of $Nu$ is critical to obtain a meaningful interpretation.
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