Evaporation and clustering of ammonia droplets in a hot environment

Recent developments in the transition to zero-carbon fuels show that ammonia is a valid candidate for combustion. However, liquid ammonia combustion is difficult to stabilize due to a large latent heat of evaporation, which generates a strong cooling effect that adversely affects the flame stabilization and combustion efficiency. In addition, the slow burning rate of ammonia enhances the undesired production of ${\mathrm{NO}}_x$ and ${\mathrm{N}}_2\mathrm{O}$. To increase the flame speed, ammonia must be blended with a gaseous fuel having a high burning rate. In this context, a deeper understanding of the droplet dynamics is required to optimize the combustor design. To provide reliable physical insights into diluted ammonia sprays blended with gaseous methane, direct numerical simulations are employed. Three numerical experiments were performed with cold, standard, and hot ambient in nonreactive conditions. The droplet radius and velocity distribution, as well as the mass and heat coupling source terms are compared to study the effects on the evaporation. Since the cooling effect is stronger than the heat convection between the droplet and the environment in each case, ammonia droplets do not experience boiling. On the other hand, the entrainment of dry air into the ammonia-methane mixture moves the saturation level beyond 100% and droplets condense. The aforementioned phenomena are found to strongly affect the droplet evolution. Finally, a three-dimensional Voronoi analysis is performed to characterize the dispersive or clustering behavior of droplets by means of the definition of a clustering index.

Figure 1

Sector of the computational domain displaying the magnitude of the velocity field.

Figure 2

(a) Universal log profile of the cylindrical pipe boundary layer ($U^{+}=f\left(y^{+}\right)$). Black circles: reference DNS; red squares: experimental results of Eggels et al. [28]; green solid line: viscous sublayer profile $U^{+}=y^{+}$; blue solid line: fitting of the log-law for the turbulent boundary layer $U^{+}=k^{-1}ln{y}^{+}+B$, with $k=0.43$ and $B=4.8$. (b) Inverse of the average axial velocity for the three cases. The squares are the DNS data and the solid line is the fitting of linear trend described by $U_0/\langle U\rangle \approx 1/\left(2B\right)(z/R-z_0/R)$. The decaying constants are $B_{T_a=220K}=3.05, B_{T_a=300K}=3.45, B_{T_a=600K}=5.05$, whereas the virtual origins are $z_{0,T_a=220K}/R=0.61, z_{0,T_a=300K}/R=1.11$, and $z_{0,T_a=600K}/R=3.25$. (c) Probability density function of the interdroplet distances inside the pipe (black solid line) and at different stages from the nozzle exit (see legend). The red line represents the collisional threshold criterion $\lambda =2r_d$.

Figure 3

Instantaneous temperature field with droplet distribution represented by black dots. From left to right: case (a) with $T_a=220\mathrm{K}$, case (b) with $T_a=300\mathrm{K}$, and case (c) with $T_a=600\mathrm{K}$.

Figure 4

Isosurfaces colored with the Eulerian averaged droplet radius. Solid line: $T_a=220\mathrm{K}$; dashed line: $T_a=300\mathrm{K}$; and dotted line: $T_a=600\mathrm{K}$. Dark blue: $\langle r_d\rangle /r_{d,0}=0.2$ corresponding to 1% of the initial mass; cyan: $\langle r_d\rangle /r_{d,0}=0.5$; orange: $\langle r_d\rangle /r_{d,0}=0.8$ corresponding to 50% of the initial mass; red: $\langle r_d\rangle /r_{d,0}=1$ corresponding to the initial mass. In (a) the radial and axial distances are normalized by the inflow pipe radius ($R$) and diameter ($d$), respectively, whereas in (b) they are normalized by the half-radius jet width ($R_{50\%r_{d,0}}$) and length ($d_{50\%r_{d,0}}$).

Figure 5

Eulerian average of the droplet temperature $\langle T_d\rangle$ [(a), (c), (e)] and carrier gas phase temperature conditioned on the droplet presence $\langle T_{g,DC}\rangle$ [(b), (d), (f)]. (a) and (b): $T_a=220\mathrm{K}$; (c) and (d): $T_a=300\mathrm{K}$; and (e) and (f): $T_a=600\mathrm{K}$.

Figure 6

Radial profiles of the magnitude of the Eulerian averaged droplet and carrier gas velocity.

Figure 7

Eulerian average of the normalized mass source term $\langle {\dot{m}}_d\rangle /(m_{d,0}/t_0)$ [(a), (c), (e)] and normalized enthalpy source term $\langle {\dot{h}}_d\rangle /(h_{d,0}/t_0)$ [(b), (d), (f)]. (a) and (b): $T_a=220\mathrm{K}$; (c) and (d): $T_a=300\mathrm{K}$; and (e) and (f): $T_a=600\mathrm{K}$.

Figure 8

Probability density functions of droplet radius, mass, and enthalpy source terms at $z/d\approx$ 2, 5, and 10. Blue line: $T_a=220\mathrm{K}$; black line: $T_a=300\mathrm{K}$; and red line: $T_a=600\mathrm{K}$.

Figure 9

Isosurfaces of Eulerian average droplet distribution. Solid line: $T_a=220\mathrm{K}$; dashed line: $T_a=300\mathrm{K}$; and dotted line: $T_a=600\mathrm{K}$. Dark blue: $\langle N\rangle /N_0=0$, light blue: $\langle N\rangle /N_0=1$, red: $\langle N\rangle /N_0=3$. In (a) the radial and axial distances are normalized by the inflow pipe radius ($R$) and diameter ($d$), respectively, whereas in (b) they are normalized by $\langle N\rangle /N_0=1$ jet width ($R_{\langle N\rangle /N_0=1}$) and length ($d_{\langle N\rangle /N_0=1}$).

Figure 10

Eulerian average of the droplet clustering index $K$. (a) $T_a=220\mathrm{K}$, (b) $T_a=300\mathrm{K}$, and (c) $T_a=600\mathrm{K}$.