# 5.5. PIC05: Evaporation¶

## 5.5.1. Description¶

This case is used to verify the transport equations governing energy and species conservation. The setup consists of a single parcel representing a droplet suspended in a humidified air stream. This reflects the wet bulb phenomenon, where evaporation from the droplet results in a lowered humidified air temperature. The following reaction represents species transfer from the suspended droplet:

(5.9)$H_{2} O (l) \rightarrow H_{2} O (g)$

Fifteen seconds of physical time is simulated to ensure the droplet achieves a steady-state (SS) temperature. The SS temperature should then compare with the theoretical wet-bulb temperature.

## 5.5.2. Setup¶

Table 5.10 PIC-05 Setup, Initial and Boundary Conditions.

Computational/Physical model

3D, Transient

Multiphase

Gravity

Turbulence equations are not solved

Uniform mesh

First order upqind discritization scheme

Geometry

Coordinate system

Cartesian

Grid partitions

x-length

0.01

(m)

1

y-length

0.01

(m)

1

z-length

0.01

(m)

1

Material

Gas density, $$\rho_{g}$$

Ideal gas law

(kg·m-3)

Solids Type

PIC,DEM

Diameter, $$d_{p}$$

0.2

(mm)

Density, $$\rho_{s}$$

958.6

(kg·m-3)

Solids Properties (PIC)

Pressure linear scale factor, $$P_{s}$$

0.0

(Pa)

Exponential scale factor, $$\gamma$$

1.0

(-)

Statistical weight

25

(-)

Solids Properties (DEM)

Coefficient of friction, $$\mu_{pp},\mu_{pw}$$

0.0

(-)

Coefficient of restitution, $$e_{pp},e_{pw}$$

1.0

(-)

Spring constant, $$k_{pp},k_{pw}$$

0.1

(kg·m-1)

Initial Conditions

x-velocity, $$u_{g}$$

3.0

(m·s-1)

y-velocity, $$v_{g}$$

0.0

(m·s-1)

z-velocity, $$w_{g}$$

0.0

(m·s-1)

Gas volume fraction, $$\epsilon_{g}$$

0.999894

(-)

Gas volume fraction at packing, $$\epsilon_{g}^{*}$$

0.4

(-)

Pressure, $$P_{g}$$

101,325

(Pa)

Gas temperature, $$T_{g}$$

303.15

(K)

Solid temperature, $$T_{s}$$

303.15

(K)

Species fraction of air, $$X_{g1}$$

Varied

(-)

Species fraction of water vapor, $$X_{g2}$$

Varied

(-)

Boundary Conditions

West boundary

$$u_{g}$$ Varied

(kg·s-1)

Mass inflow

$$X_{g1},X_{g2}$$ Varied

(-)

East boundary

101,325

(Pa)

Pressure outflow

North and South boundaries

Free-slip walls

Top and Bottom boundaries

Free-slip walls

## 5.5.3. Results¶

MFiX-PIC and MFiX-DEM simulations are performed by varying the relative humidity of surrounding air. Table 5.8 summarizes the different settings of relative humidity and the corresponding wet bulb temperatures. Based on the comparison of the data from  it can be concluded that the predictions from MFiX-PIC simulations are accurate Table 5.8. Also, the results are consistent with the predictions from MFiX-DEM.

 Rel. Humidity (%) $$X_{g1}$$ $$X_{g2}$$ Mass Flow Rate (g/s) Wet Bulb T (°C) 0 1.000000 0.000000 0.349315 10.5 10 0.997390 0.002610 0.348762 13.2 20 0.994771 0.005229 0.348208 15.7 30 0.992144 0.007856 0.347655 18.0 40 0.989509 0.010491 0.347102 20.1 50 0.986865 0.013135 0.346548 22.0 60 0.984212 0.015788 0.345995 23.8 70 0.981552 0.018448 0.345442 25.5 80 0.978882 0.021118 0.344888 27.1 90 0.976204 0.023796 0.344335 28.6 100 0.973518 0.026482 0.343281 30.0 Fig. 5.6 Comparison of wet bulb temperatures between data, MFiX-DEM and MFiX-PIC.