The CFD model from the D6CC commercial SCR system is shown in

Figure 10. The first CFD model used an original urea injector, while the second CFD model used the suggested urea injector [

2]. Various urea injectors were analyzed for the ammonia generation process and NO

_{x} conversion value. The SCR catalyst used for this study was vanadium-catalyzed; this catalyst material can support oxidative C–C and C–O bond cleavage, carbon–carbon bond formation, deoxy-dehydration, hydrogenation, and dehydrogenation [

12].

The quasi-steady evaporation model in this simulation allowed the urea droplet particles to lose mass. The driving force in the evaporation and condensation process can maintain the equilibrium of the liquid–vapor system. The UWS used in this study had 60% water and 40% urea [

14]. The wall temperature assists the urea particle to evaporate; the heat transfer equation calculates the evaporation rate, thereby ensuring the saturation temperature can vapor the urea particle.

where

${X}_{is}$ is the equilibrium mole fraction of transferred the component for urea particle; the Raoult’s law method is used to find the value of

${X}_{is}$:

where

${p}_{sat}^{i}\left({T}_{p}\right)$ is the component saturation pressure that is evaluated at the wall temperature in the SCS system, and

${X}_{ip}$ is the component mole fraction in the urea droplet particle; when the condition in Equation (7) is satisfied, the urea particle vaporize in proportion to their mass fractions. The range urea particle diameter in this simulation used the Rosin–Rammler particle size distribution; this method size distribution is a smooth continuous distribution depending on four parameters: reference size, exponent, minimum size, and maximum size. The exponent was developed to describe the volume distribution of urea particles as a function of their diameter as follows:

The particle size was quantified using a cumulative distribution function, which is

$F\left(D\right)$. The mass parameters are the exponent

$q$, the Rosin–Rammler diameter is

${D}_{ref}$ and the urea particle size

$D$; this form confirmed that the Rosin–Rammler particle size could investigate the urea distribution value based on the cumulative mass, volume, or number distribution, depending on the flow rate specification of the urea injector. When the condition in Equation (6) is satisfied, the volatile components in proportion mass fractions, that is:

where the second condition for a saturated vapor is:

where

${Y}_{ip}$ is the mass fraction of component “

i” with the pressure value and

${Y}_{i}$ is the mass fraction of component of “

i” with free stream value; that equation is the cell containing the urea droplet particle; the index “

i” refers to the mixture of gaseous components;

${\epsilon}_{i}$ is the fractional mass transfer;

${\mathsf{\Sigma}}_{T}$ is the temperature transfer components. Effectively, the transfer number represents the driving force for evaporation, which is a function of thermodynamic conditions for the liquid and vapor. Conductance, on the other hand, represents geometrical and mechanical effects, such as the urea droplet size and velocity distribution. However, the transfer number for saturation vapor can be described with:

where

B is the Spalding transfer number for heat transfer;

$T$ is the temperature;

${T}_{p}$ is the particle temperature;

${c}_{p}$ is the gas specific heat;

${L}_{i}$ is the latent heat component. The urea saturation process will produce ammonia gas and will mix in the system; based on that condition, the multi-component equation gas was used in this study, as follows:

where

${\rho}_{j},{a}_{j}$, and

${v}_{j}$ are the density, volume fraction, and velocity of phase j, respectively;

${Y}_{j,i}$ is the mass fraction of species i in phase

j, that is, the fraction of the total mass of that phase;

${D}_{j}$ are the mass diffusivity numbers with the combining the molecular particle and gas turbulent in the system;

${S}_{j,i}$ is a general mass source;

$\stackrel{\xb4}{{m}_{j,i}}$ is used here to refer specifically to the transfer of species from one phase to another if there is a single phase with

${a}_{j}$ equal to 1 and no interphase mass transfer in the system. The NO

_{x} conversion value for an SCR system is shown in Equation (14), where the NOx gas quantity after the SCR system divides the NO

_{x} gas emission from the engine: