Droplet evaporation is a key phenomenon in many industrial processes, including spray drying, fuel atomization, and cooling towers. Understanding the rate of evaporation and its impact on the surrounding environment is a determinant.

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ToggleThis tutorial aims to guide engineers, researchers, and CFD practitioners through using DPM Droplet particle type. __While DPM allows for both droplet and multi-component particle types, we will focus on the droplet type here, reserving the multi-component approach for a future discussion__.

## DPM Droplet Evaporation

### DPM Droplet Particle Type Fundamentals

Initially, to model the evaporation of a droplet particle, the **Droplet particle type** must be selected in the first place, accessible from “Set Injection Properties” window (see Fig.1).

**Tip**: Droplet particle usage requires definition of__at least__two species. One for the**droplet material**and the other for**evaporating fraction of the droplet**. Consequently, droplet particle type will be available only if**Species Transport Model**is primarily activated.

Figure 1: Droplet particle evaporation tutorial in ANSYS Fluent

Similar to any other particle type in ANSYS Fluent, the discrete phase particle trajectory is followed by integration of force balance on it, written in Lagrangian framework:

represents the particle’s mass multiplied by its acceleration. is the drag force, where is the fluid velocity, is the particle velocity, and is the particle relaxation time. accounts for the gravitational force and buoyancy, where is the gravitational acceleration, is the particle density, and is the fluid density. represents additional forces that may act on the particle, completely explained in DPM Physical Models

Now, we can swift through the basic concepts of DPM droplet evaporation process in ANSYS Fluent. The **droplet evaporation must be introduced from two distinct aspects: 1) Heat Transfer 2) Mass Transfer**

**Tip:**In ANSYS Fluent, the**condensation of droplet particles**is not included unless the user utilizes a User-defined function.

### Heat Transfer of DPM Droplet Evaporation

Droplet evaporation experiences several stages as it moves through the gas phase (continuous phase) regarding heat transfer. When a droplet is injected into a domain with a different temperature, heat transfer occurs due to the **temperature gradient between the droplet and its surroundings**. Naturally, Heat always transfers from higher to lower temperature regions. Nevertheless, in most cases, droplets are injected into a hot domain, and they experience heating, which leads to temperature increase and eventual __vaporization__. Fig. 2 illustrates the temperature gradient between a droplet and its ambient environment:

Figure 2: DPM Droplet evaporation due to temperature gradient

The figure shows a difference between the droplet surface (T-surface) and the ambient temperature (T-ambient). This gradient drives the heat transfer process, causing the droplet temperature to change over time.

**Tip**: Heat can be transferred via **Convection** and **Radiation** mechanisms.

So, how does ANSYS distinguish the governing equations in this process?

According to the ANSYS Fluent code, __droplets experience 3 distinct periods after injection__, each governed by specific laws and equations (see Fig. 3):

( Definition: p= droplet, vap= vaporization, bp= boiling point)

Figure 3: DPM Droplet evaporation in ANSYS Fluent

#### 1) Inert Heating Law (Law 1):

- Condition:
**Tp < Tvap**

Under these circumstances, the droplet temperature (Tp) increases from the injection temperature to the vaporization temperature (Tvap). (** No Phase Change**)

Temperature of the droplet is calculated as (regarding __radiative and convective__ heat transfer):

#### 2) Droplet Vaporization Law (Law 2)

- Condition:
**Tvap < Tp < Tbp**

This stage begins when the droplet __reaches the vaporization temperature and continues until it reaches the boiling point__ (Tbp). In this period, **vaporization occurs, and the droplet’s mass decreases**. Law 2 governs the process and is initiated the moment Tp=Tvap. In this region, an extra term is added due to the presence of evaporation:

Where:

- is the mass of the droplet
- is the specific heat capacity of the droplet
- is the rate of change of temperature of the droplet
- is the surface area of the droplet
- is the heat transfer coefficient
- is the ambient temperature
- is the temperature of the droplet
- is the evaporation rate
- is the latent heat
- is the emissivity of the droplet
- is the Stefan-Boltzmann constant
- is the radiation temperature

**Tips**: **What if the droplet temperature falls below Tvap**? Once law 2 is initiated, vaporization continues even if the droplet temperature falls below Tvap. It stops only if the droplet temperature falls below the ** dew point.** In this condition, the droplet remains in law 2, but no evaporation takes place.

#### 3) Boiling Law (Law 3)

- Condition:
**Tp >= Tbp**

When the droplet temperature reaches the boiling point, **rapid vaporization occurs**. The software automatically transits Law 2 to Law 3, which predicts the ** boiling rate**. The droplet is assumed to stay at a constant temperature while the boiling rate is applied.

**Tip**: Define appropriate material properties for Droplet particles, including Vaporization Temperature, Latent heat, Boiling point, and Volatile component fraction effective (Fig.4). or latent heat required for phase change from an evaporating liquid droplet. Logically, the volatile component fraction of a droplet is 100%.

Figure 4: Material properties for DPM droplet evaporation in Fluent

In the next section, we discuss the mass transfer aspects of droplet particles, which are closely coupled with the heat transfer processes discussed here.

### Mass Transfer of DPM Droplet Evaporation

The concept of **concentration** is the basis of mass transfer in evaporating droplets. It is the driving force for mass transfer: __Difference in vapor concentration between the droplet surface and its surrounding environment__.

Figure 5: Concentration gradient around an evaporating droplet

On the droplet`s surface, the vapor concentration is equal to the ** saturated vapor concentration**. This can be expressed mathematically as:

Where:

- Ci,s is the vapor concentration at the droplet surface
- psat(Tp) is the saturation vapor pressure at the particle temperature
- R is the universal gas constant
- Tp is the particle temperature

During the vaporization process (Law 2), the vaporization rate is defined by gradient diffusion model. The fundamental equation describing this process is:

Where:

- Ni is the molar flux of vapor (kg mol/m²-s)
- kc is the mass transfer coefficient (m/s)
- Ci,s is the vapor concentration at the droplet surface (kg mol/m³)
- Ci,∞ is the vapor concentration in the bulk gas (kg mol/m³)

Finally, the mass transfer coefficient is calculated using the __Sherwood number correlation__:

Where:

- ShAB is the Sherwood number
- dp is the droplet diameter
- Di,m is the diffusion coefficient of vapor in the bulk
- Red is the Reynolds number based on the droplet diameter
- Sc is the Schmidt number

**Tip**: The fundamentals of evaporating droplets’ mass transfer have proved __that it is not just about heat transfer. Actually, it is the concentration gradient that controls the evaporation process.__ Vaporization/Boiling Model provided in material properties for droplet particle has two predefined models: **Diffusion-controlled and convection/diffusion controlled**. Keep the default model for slowly evaporating droplets. The convection/diffusion-controlled model is the best choice when the evaporation rate is high. To conclude:

- Diffusion Controlled Model (Default): for low evaporation rates.
- Convection/Diffusion Controlled Model: for higher evaporation rates.

Figure 6: Vaporization/Boiling model in DPM

**Tip**: Additional sub-models are offered by ANSYS Fluent to enhance simulation accuracy, such as temperature-dependent latent heat, pressure-dependent boiling, and break-up models. Please visit Discrete Phase Model (DPM) Physical Models for more info.

## DPM droplet evaporation Example

Here are some practical simulations related to DPM droplet evaporation. You can find more products in CFD ِDPM Projects. **Drying grains** for safe storage is essential in agriculture. The humid must be evaporated during the drying process, thus the droplet evaporation model is of high importance.

Figure 7: DDPM-DEM CFD Simulation of Drying of Grains, ANSYS Fluent & Matlab Coupling

The other practical application of DPM droplet evaporation is in **air-cooled chillers**, where water mist spray systems can be used on the condenser coils of air-cooled chillers. Notably, this simulation is conducted to **validate the paper** entitled “**Enhancing COP of an air-cooled chiller with integrating a water mist system to its condenser: Investigating the effect of spray nozzle orientation**” published in the International Journal of Thermal Sciences.

Figure 8: Water Mist Spray Nozzle Considering Evaporation Using 2 CFD-way DPM –Numerical Paper Validation

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