This module computes one-dimentional transport of a particle/droplet by a carrier gas. Mass, momentum and energy exchange between the particle / droplet and carrier gas is included. The module can be applied to estimate the terminal velocity and time required to attain terminal velocity in a carrier gas moving at constant velocity. The module can be applied to examine the heating or cooling of a particle / droplet in a carrier gas. The evaporation of a droplet in a carrier gas can also be computed.

The motion of the particle / droplet is computed by numerically solving the force balance equation (1) for the particle.

(1)

where :-
Mp - is mass of particle ,
Vp - is instantaneous velocity of particle / droplet ,
Fb - is buoyancy force acting on the particle / droplet ,
Fg - is gravitational force acting on the particle / droplet ,
Fd - is drag force .

(2)

where :-
r_g - is gas density ,
V_g - is gas velocity ,
A_p - is area of particle = ( p / 4)*dp² ,
d_p - is diameter of particle ,
Cd is calculated as ,

Figure 1

The particle / droplet can consist of a volatile material that can evaporate into the carrier gas. The heat transfer and mass transfer depend on the instataneous particle / droplet temperature in relation to the vaporization temperature (Tvap) and boiling temperature(Tboil) of the volatile material. If the particle / droplet temperature (Tp) is less than the vaporization temperature (Tvap) of the volatile material then inert heating / cooling of the particle / droplet occurs as follows :-

Where ,
C_p - is particle specific heat ,
T_g - is carrier gas temperature ,
s - is Stefan boltzman constant ,
A_p' - is surface area of particle ,
e - is particle emissivity ,
h - is heat tranfer coefficient, and calculated as follows ,

(3)

Where , P_r is calculated as ,
Where ,
C_pg - is gas specific heat capacity,
K_g - is thermal conductivity ,

If Tvap < Tp < Tboil then ,

(4)

Where : hfg - is latent heat of vaporization of volatile material.

(5)

Where :
Kmt - is calculated using equation (5a) ,
Sc - is calculated using equation (5b) ,
Cis - is vapor concentration on the surface of the particle / droplet , and is calculated using equation (5c) ,
Cig - is vapor concentration (Kmole/m³) in carrier gas and, is calculated using equation (5d).

(5a)

Where : Dim - is diffussivity of volatile vapor in gas ,

(5b)

(5c)

Where :
Psat - is saturation pressure at particle / droplet temperature (Tp). This is computed from the input vapor pressure versus temperature data for the volatile material ,
R – is universal gas constant .

(5d)

Where :
Mwap - is molecular weight of volatile material ,
X_i – is mass fraction of volatile material in gas .

r_g is calculated as ,

Where :
P_op - is operating pressure (gas pressure) ,
M_wg – is gas molecular weight .

If Tp = Tboil then ,
The particle / droplet temperature cannot exceed the boiling temperature of the volatile material until all the volatile material is evaporated.

The carrier gas temperature, velocity, volatile material concentration in gas is all held constant at all times.The particle / droplet velocity, diameter, temperature, volatile concentration particle / droplet are computed at each instant of the particle transport.

The inputs for this module are depicted in Figure 2. The inputs consist of particle / droplet phase properties and carrier gas properties. Inputs also contain vapor pressure and temperature data.

Figure 2: ETBX inputs for Droplet Evaporation.

The results are displayed using standard ETBX output window shown in Figure 3. The outputs are mass of droplet at initial and final conditions, droplet status, time and length required to evaporate.

Figure 3: ETBX Droplet Evaporation module outputs.

The detailed results per every 0.0025 seconds can also be obtained as shown in figure 4.

Figure 4: ETBX Droplet Evaporation detailed outputs.