Thermohydrodynamics of an evaporating droplet studied using a multiphase lattice Boltzmann method

In this paper, the thermohydrodynamics of an evaporating droplet is investigated by using a single-component pseudopotential lattice Boltzmann model. The phase change is applied to the model by adding source terms to the thermal lattice Boltzmann equation in such a way that the macroscopic energy equation of multiphase flows is recovered. In order to gain an exhaustive understanding of the complex hydrodynamics during evaporation, a single droplet is selected as a case study. At first, some tests for a stationary (non-)evaporating droplet are carried out to validate the method. Then the model is used to study the thermohydrodynamics of a falling evaporating droplet. The results show that the model is capable of reproducing the flow dynamics and transport phenomena of a stationary evaporating droplet quite well. Of course, a moving droplet evaporates faster than a stationary one due to the convective transport. Our study shows that our single-component model for simulating a moving evaporating droplet is limited to low Reynolds numbers.

Figure 1

(a) Liquid and vapor density variations with temperature for CS EOS; solid line: analytical solution obtained from Maxwell rule of equal areas; markers: LB simulation results by using the β-scheme force term and the EDM force implementation method; (b) equilibrium density distribution over the domain in $T_r=0.8$ and 0.6.

Figure 2

Spurious velocities at the gas-liquid interface at (a) $T_r=0.8$ and (b) $T_r=0.6$.

Figure 3

Comparison of the spurious Reynolds number $\mathrm{R}{\mathrm{e}}_{spu}$ as function of density ratio obtained from the LBM (with $\beta =1,1.25$) and FV-VOF implementation scheme using openfoam and fluent solvers [56].

Figure 4

(a) Verification of numerical pressure difference for $T_r=0.8$ and 0.6 with the Laplace law (dashed lines) and (b) surface tension versus temperature.

Figure 5

The snapshots and velocity vectors of an evaporating droplet at different times: (a) $t=0.089$, (b) $t=0.133$, and (c) $t=0.177$.

Figure 6

Normalized droplet diameter as a function of time for different heat flux rates.

Figure 7

(a) Density and (b) temperature profiles at different times for a droplet exposed to uniform heating which causes the vaporization.

Figure 8

(a) Pressure and (b) temperature distribution along the symmetric line of the domain at different times when using constant pressure boundary condition.

Figure 9

Comparison between time histories of the numerical results and $D^2$ law for (a) different hot boundary temperature with $h^{lv}=0.1$ and (b) different latent heat at $T_r=0.9$.

Figure 10

Effect of density ratio on variation of velocity of a falling droplet. Here, ${\rho }^{*}=6,15,40$, and 130 are equivalent with $T_r=0.9,0.8,0.7$, and 0.6, respectively.

Figure 11

Effect of streamwise length on terminal velocity of droplet with ${\rho }^{*}=6$.

Figure 12

The time evaluation of density and instantaneous velocity field for moving an evaporating droplet. From left to right: $t=0,t=0.039,t=0.072$, and $t=0.1$. (Note: At $t=0$ the droplet is moving with its terminal velocity; i.e., $U_{t,\mathrm{LB}}=0.06$ in lattice units).

Figure 13

Streamlines and inner circulation regions for the moving evaporating droplet at $t=0.022$. (Note that the velocity vectors, as shown in Fig. 12, are plotted with respect to the fixed coordinate system (i.e., domain reference frame), whereas the true streamlines, as shown in this figure, are plotted by using the relative velocity with respect to the droplet. Here, the streamlines are calculated in the frame of reference fixed to the bottom of the droplet.

Figure 14

The time evaluation of density and instantaneous velocity field for moving an evaporating droplet in a fully periodic domain. From left to right: $t=0,t=0.039,t=0.072$, and $t=0.1$.

Figure 15

(a) The instantaneous velocity and (b) the equivalent spherical diameter of an evaporating falling droplet with various density ratios.