Understanding 7 Discrete Phase Model (DPM) drag laws, Now it`s time to focus on the other seven choices provided in ANSYS Fluent for Dense Discrete Phase Model (DDPM) simulations.

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ToggleIn fact, many users find dense discrete phase model a little bit confusing. So, let`s briefly introduce DDPM CFD simulation prior to the drag laws

### What is Dense Discrete Phase Model (DDPM)?

Suppose you’re dealing with a **particle-laden flow** in your problem – In other words, so many particles that they’re actually pushing each other around and affecting the continuous phase. So, whenever the **particle volume fraction is high, typically between 10% and 50%**, DDPM approach is wiser choice than DPM. It extends the standard Discrete Phase Model by accounting for particle-particle interactions and the volume displaced by particles in the continuous phase.

This option is categorized in Hybrid Models group box in Multiphase Model section (see Fig. 1). However, it is a **Eulerian-Lagrangian** **approach**, despite being found in the multiphase tab alongside Eulerian-Eulerian models. Additionally, DDPM is particularly useful in applications such as fluidized beds, pneumatic conveying systems, cyclone separators, and coal combustion in furnaces.

Figure 1: Dense Discrete Phase Model in Multiphase model section of ANSYS Fluent

## Dense Discrete Phase Model (DDPM) Drag Laws

When the Dense Discrete Phase Model (DDPM) is activated in Ansys Fluent, the ‘**averaged-discrete-phase-drag**’ option for the **Drag Coefficient** is automatically selected in the Multiphase Model dialog box. This approach, corresponding to Equation 14-499 in the Fluent Theory Guide, calculates the interaction between discrete and fluid phases using averaged values of fluid drag for all particles passing through a fluid cell. The momentum exchange coefficient, , is computed as:

At each time step, Fluent evaluates the drag __for individual particles__ **based on the user-specified drag law in the Set Injection Properties dialog box** (Fig.2). It then computes an average drag, weighted by each particle’s residence time in the cell.

Figure 2: DDPM drag laws in ANSYS Fluent

### 1) Wen-Yu DDPM Drag Law

Wen-Yu is the first model provided for computing drag force exerted on the particles in Dense Discrete Phase Model (DDPM). The drag coefficient formula used in the Wen-Yu model is an empirical correlation that accounts for the particle Reynolds number. The Wen-Yu formula for the drag coefficient CD is given by:

**Application**: **the Wen and Yu model is specifically applicable for dilute phase flows**. In dilute flows, the volume fraction of the dispersed phase is extremely lower than that of the primary fluid phase. So the dispersed phase has a negligible effect on the overall flow.

### 2) Gidaspow DDPM drag law

The **Gidaspow** drag model combines two well-established drag models, including **Wen**-Yu & **Ergun** equation based on void fraction:

- For dilute flows (void fraction > 0.8), it uses the Wen and Yu model.
- For dense flows (void fraction ≤ 0.8), it employs the Ergun equation.

The Gidaspow formula for the drag coefficient CD is given by:

Where:

Cd is the drag coefficient

αf is the volume fraction of the fluid phase

Res is the particle Reynolds number

**Application**: The Gidaspow model is recommended for ** dense fluidized beds**.

### 3) Huilin-Gidaspow DDPM drag law

As the title says, the Huilin-Gidaspow model is a refined version of the original Gidaspow model. Importantly, this model introduces __improvements__ that address certain limitations of the Gidaspow drag law. Primarily, the enhancement in the Huilin-Gidaspow model is a **better blending function**. This function provides a **smoother transition between the dense packing limit and the dilute flow limit**. To be more specific, the smooth switch functions when the __solid volume fraction is less than 0.2__.

**Application**: The application of Huilin-Gidaspow DDPM drag law is similar to Gidaspow model. It can be used for **Fluidized Beds** where the particle concentration may vary in different regions.

### 4) Syamlal-Obrien DDPM drag law

The Syamlal-O’brien drag model works based on measurements of __terminal velocities of particles__. The fundamentals is not our concern here, however, you need to know that The drag coefficient (CD) in the Syamlal-O’Brien model is given by:

Where:

C_D is the drag coefficient

Re_s is the particle Reynolds number

v_{r,s} is the terminal velocity correlation for the solid phase

As can be seen, CD in this model is a function of the volume fraction and relative Reynolds number. This allows the model to account for the effects of particle concentration and flow conditions on drag.

**Application**: This model is instrumental in simulations involving Gas-solid fluidized beds and any gas-solid system.

**Tip**: Syamlal-O’Brien model often provides __more precise results for gas-solid flows__ compared to simpler drag models such as Gidaspow drag model, especially in systems with different particle concentrations.

### 5) Gibilaro DDPM drag law

The Gibilaro model is another DDPM drag law given by ANSYS Fluent. This model was developed by L.G. Gibilaro and is based on a theoretical framework that accounts for the fluid-particle interactions more dynamically than simpler models.

**Application**: ANSYS Guide recommends the Gibilaro drag law for simulation of **circulating fluidized beds. **

** **

### 6) EMMS DDPM drag law

The EMMS (Energy-Minimization Multi-Scale) drag law is a model mostly used for __gas-solid__ flows. This model is designed for cases where heterogeneous meso-scale flow structures are dominant, and such structures cannot be resolved using fine grid resolution in simulations.

In the EMMS method, the mesoscale structures are broken down into a __cluster phase and a dilute phase__.

The drag coefficient is given by:

The coefficients

α, β, and γ are functions of the gas phase volume fraction. Formulas for calculating α, β and γ over different ranges of gas phase volume fraction are provided in tables within the **Fluent Theory Guide.**

**Application**: As mentioned above, the EMMS drag model is beneficial for **gas-solid flows and monodispersed two-phase granular flows** where drag laws, such as the Wen and Yu model or the Gidaspow model, __tend to over-predict solids flux__. To conclude, the EMMS drag law is __very accurate compared to the traditional models,__ regardless of computational cost.

### 7) Filtered DDPM drag law

The **Filtered** drag law is an advanced approach mostly used for simulation of **gas-particle flows**, **particularly in large-scale fluidized bed systems**. So the question is, when to choose Filtered drag law? In fact, this model is designed to address the challenges related to simulating monodispersed two-phase flows __involving gas and granular phases__ on ** Coarse meshes**. As a common example, it can be the best-fit choice for particles in catalysts in large-scale fluidized beds. These particles typically range from

__20 μm to 100 μm__in size.

We have already discussed the importance of the grid in DPM simulations. Suppose large-scale gas-particle flow, and heterogeneous structures range __from microscale to macroscale__. **Unlike the Filtered drag law model, traditional models require very fine mesh resolutions (on the order of a few particle diameters). **To conclude, the Filtered drag model is a perfect alternative for the simulation of gas-solid flow with heterogeneous structure from microscale to macroscale. ** **

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