Simulation of high-viscosity-ratio multicomponent fluid flow using a pseudopotential model based on the nonorthogonal central-moments lattice Boltzmann method

In this research, the development of a pseudopotential multicomponent model with the capability of simulating high-viscosity-ratio flows is discussed and examined. The proposed method is developed based on the non-orthogonal central moments model in the lattice Boltzmann method, and the exact difference model (EDM) is used to apply the intercomponent interaction force. In contrast to the original Shan-Chen model, in which the applying force has the viscosity-dependent error term, the error term of this model does not depend on the viscosity. A GPU parallel cuda code has been developed and is employed to study the proposed method. Different cases are considered to evaluate the ability of the model, including the Laplace test, a static droplet, and a two-component concurrent channel flow. Also, wetting and nonwetting relative permeabilities for flows with dynamic viscosity ratios between 0.0002 and 5000 are predicted. Numerical results are compared with those of available analytical solutions. Very good agreement between these results are observed. The model has the capability of simulating multicomponent flows with very low kinematic viscosities of the order of ${10}^{-5}$ and dynamic viscosity ratios of up to an order of ${10}^4$, which is a much wider range compared with that of existing pseudopotential models. Furthermore, the results showed that the parallel processing on GPU significantly accelerated computations. The present parallel performance evaluation shows that the cuda parallel can achieve about 41 times improvement than the CPU serial implementation. The aforementioned enhancement increases the flexibility of the multicomponent lattice Boltzmann method and its applicability to a broader spectrum of engineering applications.

Figure 1

D2Q9 model.

Figure 2

A schematic view of the geometry of static droplet simulation.

Figure 3

The density contour of the droplet with radius of $R=40$ and dynamic viscosity ratio $M={10}^5$.

Figure 4

The contour of spurious velocity for the droplet with the radius of $R=40$ in the dynamic viscosity ratio of $M={10}^5$.

Figure 5

The pressure difference between the inside of droplet and the surrounding fluid in terms of the inverse of the droplet radius for the surface tensions of 0.21 and 0.1.

Figure 6

Maximum spurious velocity magnitude for different viscosities in the dynamic viscosity ratio of $M=1$.

Figure 7

Maximum spurious velocity for different dynamic viscosity ratios (kinematic viscosity of surrounding fluid is 0.0067).

Figure 8

Interface shape of droplet for different contact angles for $G_s^{\mathrm{droplet}}=(-1.1,-0.8,-0.6,-0.2,0,0.6,1.1)$ for the flattest to the most curved surface.

Figure 9

A view of the geometry of multicomponent fluid flow in the channel.

Figure 10

Normalized average velocity and normalized maximum velocity of the channel flow in terms of grid size.

Figure 11

The density profile of different components in the channel flow for $M=0.0002, a=25$, and $G=2.5$.

Figure 12

The density contour and streamlines of nonwetting fluid in the two-component channel flow for $M=0.0002, a=25$, and $G=2.5$.

Figure 13

The velocity profile perpendicular to the flow direction for the channel flow with the dynamic viscosity ratio of $M=5000$.

Figure 14

The velocity profile perpendicular to the flow direction for the channel flow with the dynamic viscosity ratio of $M=0.0002$.

Figure 15

Relative permeability of wetting and nonwetting fluid for the dynamic viscosity ratio of $M=0.002$.

Figure 16

Relative permeability of wetting and nonwetting fluid for the dynamic viscosity ratio $M=0.0002$.

Figure 17

Relative permeability of nonwetting fluid in the two-component channel flow for the dynamic viscosity ratio of $M=500$.

Figure 18

Relative permeability of wetting fluid in the two-component channel flow for the dynamic viscosity ratio of $M=500$.

Figure 19

Relative permeability of nonwetting fluid in the two-component channel flow for the dynamic viscosity ratio of $M=5000$.

Figure 20

Relative permeability of wetting fluid in the two-component channel flow for the dynamic viscosity ratio of $M=5000$.