Kang Luo

Coupled Radiation and Mixed Convection in an Eccentric Annulus Using the Hybrid Strategy of Lattice Boltzmann-Meshless Method

A numerical investigation has been made of the interaction of thermal radiation with laminar mixed convection in an eccentric annulus filled with participating media. As a hybrid approach based on a common multiscale Boltzmann-type model, the combination of lattice Boltzmann and direct collocation meshless methods (LB-DCM) is developed to solve the coupled problem of radiation and convection. Numerical simulations are conducted for different eccentricities, Rayleigh number, Reynolds number, convection-radiation parameter, and optical thickness. Results show that the LB-DCM combination is stable and accurate. In addition, this hybrid approach is easy to implement and has excellent flexibility in dealing with irregular geometries.

Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids.

In this paper, we developed a unified lattice Boltzmann model (LBM) to simulate electroconvection in a dielectric liquid induced by unipolar charge injection. Instead of solving the complex set of coupled Navier-Stokes equations, the charge conservation equation, and the Poisson equation of electric potential, three consistent lattice Boltzmann equations are formulated. Numerical results are presented for both strong and weak injection regimes, and different scenarios for the onset and evolution of instability, bifurcation, and chaos are tracked. All LBM results are found to be highly consistent with the analytical solutions and other numerical work.

Three-dimensional finite amplitude electroconvection in dielectric liquids

Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state ...

Unified Lattice Boltzmann Method for Electric Field–Space Charge Coupled Problems in Complex Geometries and Its Applications to Annular Electroconvection

A lattice Boltzmann method (LBM) is developed to solve the electric field–space charge coupled problems. Instead of solving the macroscopic charge conservation equation and the Poissons equation for electric potential, two discrete lattice Boltzmann equations are formulated and solved. A nonequilibrium extrapolation scheme is used to treat the boundary conditions with complex geometry. Our method is validated with several test cases for which analytical solutions and/or reference numerical results exit. An attractive feature of this methodology lies in its natural coupling with the LBM for the fluid flow. As a demonstration and also an application, the unipolar injection induced electroconvection of dielectric liquids in annular geometries is considered. The different flow patterns of the concentric and eccentric configurations are highlighted.

Coupled Lattice Boltzmann and Meshless Simulation of Natural Convection in the Presence of Volumetric Radiation

In this work, the coupled lattice Boltzmann and direct collocation meshless (LB–DCM) method is introduced to solve the natural convection in the presence of volumetric radiation in irregular geometries. LB–DCM is a hybrid approach based on a common multiscale Boltzmann-type model. Separate particle distribution functions with multirelaxation time (MRT) and lattice Bhatnagar–Gross–Krook (LBGK) models are used to calculate the flow field and the thermal field, respectively. The radiation transfer equation is computed using the meshless method with moving least-squares (MLS) approximation. The LB–DCM code is first validated by the case of coupled convection–radiation flows in a square cavity. Comparisons show that this combined method is accurate and efficient. Then, the coupled convective and radiative heat transfer in two complex geometries are simulated at various parameters, such as eccentricity, Rayleigh number, and convection–radiation parameter. Numerical results show that the LB–DCM combination is a potential technique for the multifield coupling models, especially with the curved boundary.

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diag...

Convection-Radiation Interaction in 3-D Irregular Enclosures Using the Least Squares Finite Element Method

Interaction phenomena between laminar forced convection and thermal radiation in complex 3-D geometries with gray participating medium are studied numerically. The solution scheme is based on the least-squares finite element method (LSFEM) which, to the knowledge of the authors, is applied at the first time to 3-D radiative heat transfer in participating media. Three test cases are examined and compared with other published works to verify this LSFEM method. Comparisons show that the LSFEM method is stable and has a good accuracy. Two cases of coupled convective and radiative heat transfer are simulated at different conduction-radiation parameters and Peclet numbers.

Mesoscopic simulation of electrohydrodynamic effects on laminar natural convection of a dielectric liquid in a cubic cavity

Electro-thermo-hydrodynamic (ETHD) flows induced by simultaneous Coulomb and buoyancy forces in a dielectric medium are studied. Previous results limited to two dimensions are extended to three dimensions. The fully coupled governing equations, including the Navier–Stokes equations, the electrohydrodynamic equations, and the energy equation, are solved using a unified lattice Boltzmann model. Various flow patterns, determined by the balance between the buoyancy-driven mechanism and the Coulomb-driven mechanism, can be observed for different combinations of the governing parameters (the electric Rayleigh number T and the Rayleigh number Ra). It is found that the electrical effect on enhancement of heat transfer becomes significant at a relatively low value of Ra. Besides, an approximately linear relationship is found between the Nusselt number Nu and T. Finally, ETHD flows for different directions of charge injection are investigated, and the results reveal that the heat transfer performance of the system is improved when the injection direction is the same as the direction of the temperature gradient.