Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPhase-field-based lattice Boltzmann model for immiscible incompressible N-phase flows
128
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we develop an efficient lattice Boltzmann (LB) model for simulating immiscible incompressible $N$-phase flows $(N geq 2)$ based on the Cahn-Hilliard phase field theory. In order to facilitate the design of LB model and reduce the calculation of the gradient term, the governing equations of the $N$-phase system are reformulated, and they satisfy the conservation of mass, momentum and the second law of thermodynamics. In the present model, $(N-1)$ LB equations are employed to capture the interface, and another LB equation is used to solve the Navier-Stokes (N-S) equations, where a new distribution function for the total force is delicately designed to reduce the calculation of the gradient term. The developed model is first validated by two classical benchmark problems, including the tests of static droplets and the spreading of a liquid lens, the simulation results show that the current LB model is accurate and efficient for simulating incompressible $N$-phase fluid flows. To further demonstrate the capability of the LB model, two numerical simulations, including dynamics of droplet collision for four fluid phases and dynamics of droplets and interfaces for five fluid phases, are performed to test the developed model. The results show that the present model can successfully handle complex interactions among $N$ ($N geq 2$) immiscible incompressible flows.
rate research
Read More
In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible multiphase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulation are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic multiphase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.
In this brief report, a thermal lattice-Boltzmann (LB) model is presented for axisymmetric thermal flows in the incompressible limit. The model is based on the double-distribution-function LB method, which has attracted much attention since its emergence for its excellent numerical stability. Compared with the existing axisymmetric thermal LB models, the present model is simpler and retains the inherent features of the standard LB method. Numerical simulations are carried out for the thermally developing laminar flows in circular ducts and the natural convection in an annulus between two coaxial vertical cylinders. The Nusselt number obtained from the simulations agrees well with the analytical solutions and/or the results reported in previous studies.
In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard D2Q9 lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small. Meanwhile, the simple structure and basic advantages of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.
We propose a multi-resolution strategy that is compatible with the lattice Greens function (LGF) technique for solving viscous, incompressible flows on unbounded domains. The LGF method exploits the regularity of a finite-volume scheme on a formally unbounded Cartesian mesh to yield robust and computationally efficient solutions. The original method is spatially adaptive, but challenging to integrate with embedded mesh refinement as the underlying LGF is only defined for a fixed resolution. We present an ansatz for adaptive mesh refinement, where the solutions to the pressure Poisson equation are approximated using the LGF technique on a composite mesh constructed from a series of infinite lattices of differing resolution. To solve the incompressible Navier-Stokes equations, this is further combined with an integrating factor for the viscous terms and an appropriate Runge-Kutta scheme for the resulting differential-algebraic equations. The parallelized algorithm is verified through with numerical simulations of vortex rings, and the collision of vortex rings at high Reynolds number is simulated to demonstrate the reduction in computational cells achievable with both spatial and refinement adaptivity.
In this paper, a multiple-distribution-function lattice Boltzmann method (MDF-LBM) with multiple-relaxation-time model is proposed for incompressible Navier-Stokes equations (NSEs) which are considered as the coupled convection-diffusion equations (CDEs). Through direct Taylor expansion analysis, we show that the Navier-Stokes equations can be recovered correctly from the present MDF-LBM, and additionally, it is also found that the velocity and pressure can be directly computed through the zero and first-order moments of distribution function. Then in the framework of present MDF-LBM, we develop a locally computational scheme for the velocity gradient where the first-order moment of the non-equilibrium distribution is used, this scheme is also extended to calculate the velocity divergence, strain rate tensor, shear stress and vorticity. Finally, we also conduct some simulations to test the MDF-LBM, and find that the numerical results not only agree with some available analytical and numerical solutions, but also have a second-order convergence rate in space.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
