Introduction to Eulerian Multiphase Model in ANSYS Fluent

Fluids with different phases are everywhere in engineering. We see them in gas-liquid bubble columns, solid-liquid mixtures, and gas-solid flows. To solve these complex problems, engineers use the Eulerian multiphase model in ANSYS Fluent.

This model is the most powerful tool for multiphase flow simulation. However, it needs a deep understanding of physics. In this first blog of our complete series, we will explain the basic concepts of the Eulerian model. We will learn how it works, its main equations, and how to set up the phases. If you want to practice with real data, you can explore our ready-to-use Multiphase CFD Simulation tutorials.

Introduction to Multiphase Flows

A multiphase flow happens when two or more different states of matter move together in the same space. The most common phases are gas, liquid, and solid.

Based on the materials involved, we can divide multiphase flows into different types:

• Gas-Liquid Flows: Air bubbles rising in water, or water droplets sprayed into a gas stream.
• Gas-Solid Flows: Solid particles carried by air, like smoke or sandstorms.
• Liquid-Solid Flows: Solid particles mixed in a liquid, like mud or a chemical slurry.
• Three-Phase Flows: A mix of gas, liquid, and solid, such as gas bubbles rising in a liquid-solid slurry.

Engineers study multiphase flows to design and improve industrial equipment. The most common industrial applications are bubble columns, fluidized beds, stirred tanks, and cyclone separators.

For example, bubble columns are widely used in chemical processing, distillation, and boiling processes. To design a good bubble column, we must find important hydrodynamic parameters. The most important parameters are the specific gas-liquid interfacial area, the Sauter mean bubble diameter, and the gas holdup.

Without a reliable multiphase flow simulation, it is very hard to predict how these complex systems will behave in the real world.

Figure 1: Real-world applications of the Eulerian multiphase model in ANSYS Fluent, including Particle mixing and fluidized beds, taken from CFDLAND prepared tutorials

What is the Eulerian Model?

When we want to run a multiphase flow simulation, we must choose how the software calculates the phases. In ANSYS Fluent, there are two main ways to model a secondary phase (like bubbles or sand) moving inside a primary continuous phase (like water or air).

These two approaches are the Euler-Lagrangian method and the Eulerian-Eulerian method.

1. The Euler-Lagrangian Method (DPM): In this method, the software solves the main fluid as a continuous space. However, it explicitly tracks the exact path of every single bubble or particle. This is called the Discrete Phase Model (DPM). This method is perfect for dilute flows where you have a small number of particles. If you are interested in this approach, you can learn it practically through our DPM CFD Simulation tutorials. However, if your simulation has millions of particles, tracking each one individually will crash your computer.
2. The Eulerian-Eulerian Method: This is the core of the Eulerian multiphase model. Instead of tracking individual particles, it looks at the flow in a “macroscopic” sense. In the Eulerian approach, both the continuous phase and the dispersed phase are considered to be interpenetrating continua.

What does “interpenetrating continua” mean? It simply means the software assumes that all phases can exist in the same computational cell at the same time, mixing together as a volume. Each phase is treated mathematically as a separate, continuous fluid. Because we do not track individual particles, the Eulerian model ANSYS Fluent can easily handle very dense flows, no matter how many millions of bubbles or particles are in the tank.

Figure 2: Comparing the discrete Euler-Lagrangian particle tracking method with the macroscopic Eulerian multiphase model approach in ANSYS Fluent.

When to Choose the Eulerian Model vs. Other Models?

ANSYS Fluent has several multiphase models. Here is a simple guide on when to use the Eulerian model:

• Use DPM: When the particle volume is very low (less than 10%) and you want to track their exact paths.
• Use VOF (Volume of Fluid): When you have clear, sharp borders between fluids, like a wave on the ocean or water filling a glass.
• Use the Mixture Model: When you have a dense flow, but the particles are very small and move at almost the exact same speed as the main fluid.
• Use the Eulerian Model: When you have complex, dense flows where phases move at very different speeds and interact heavily (like heavy drag and lift forces). The Eulerian model is the most comprehensive and accurate multiphase model, but it also requires the most computer power and memory.

Figure 3: Available multiphase models provided in ANSYS Fluent

Conservation Equations in the Eulerian Model

To perform a successful multiphase flow simulation, the software needs to calculate how each phase moves and interacts. Because the Eulerian multiphase model treats phases as interpenetrating continua, it must solve a separate set of mathematical equations for each phase.

Before we look at the equations, we must understand two fundamental concepts in multiphase flow CFD:

Primary Phase vs. Secondary Phases

• Primary Phase: This is the continuous background fluid (for example, water in a bubble column).
• Secondary Phase: This is the dispersed phase that moves inside the primary fluid (for example, air bubbles or solid particles). You can have multiple secondary phases.

The Volume Fraction Concept

Because we do not track individual bubbles, the software calculates the Volume Fraction (a) of each phase in every computational cell. It tells us how much space a phase occupies. The most important rule of the volume fraction multiphase concept is that the sum of the volume fractions of all phases in a cell must always equal exactly 1.

Now, let’s look at the core governing equations solved for a specific phase (let’s call it phase q ).

Figure 4: The governing continuity and momentum equations solved for each phase in the Eulerian multiphase model.

1. The Continuity Equation (Conservation of Mass)

This equation simply tracks the mass of phase q. It makes sure that mass is neither created nor destroyed out of nowhere. In simple terms:

• Transient Term: How the mass of phase q changes over time.
• Convection Term: How the mass moves across the cell boundaries.
• Mass Transfer: The mass transferred from phase p to phase q (for example, during evaporation or condensation).
• Source Term (Sq): Any external mass added by the user.

2. The Momentum Equation (Conservation of Momentum)

This is the most critical equation in gas-liquid flow CFD and granular flows. It calculates the velocity (mq) of the phase by looking at all the physical forces pushing or pulling it. This looks complicated, but it simply means that the movement of the phase is caused by:

• Pressure Gradient (): Fluids move from high pressure to low pressure.
• Shear Stress (): The internal friction (viscosity) of the fluid.
• Buoyancy/Gravity (): Gravity pulls heavy phases down, causing lighter phases to rise.
• Interphase Forces (): This represents forces like Drag, Lift, Virtual Mass, and Wall Lubrication between the phases.

The success of your Eulerian model ANSYS Fluent simulation highly depends on choosing the correct models for these interphase forces.

3. The Energy Equation

If your simulation includes heating, cooling, or phase change (like boiling), the software will also solve an energy equation for each phase. It tracks the temperature changes by balancing heat transfer between the phases (like the Ranz-Marshall or Gunn models) and the surrounding walls.

Phase Interaction Overview

In the previous section, we saw the mathematical equations for the phases. Because the Eulerian multiphase model assumes both phases exist in the same cell at the same time, they must interact. They push, pull, and transfer energy to each other.

In multiphase flow simulation, we call this Phase Interaction. The most important type of interaction is Interphase Momentum Exchange (transfer of movement). If one phase moves faster than the other, it will pull or push the other phase with it. To calculate this physical behavior, the Eulerian model in ANSYS Fluent uses specific force models. These forces are divided into two main groups:

• Drag forces
• Non-Drag forces.

Drag is the most important force in any Eulerian multiphase setup. You can think of it as hydrodynamic friction. For example, when an air bubble rises in water, the water creates a resistance that tries to slow the bubble down. The software calculates this drag force using a simple governing equation based on the velocity difference between the phases:

• is the momentum exchange coefficient (how strong the friction is).
•  is the “slip velocity” (the difference in speed between the primary phase  and secondary phase ).

For basic simulations, drag might be enough. However, in complex gas-liquid flow CFD (like bubble columns), drag is not the only force. To get accurate results, we must also include Non-Drag Forces:

• Lift Force: When the liquid flow rotates or changes speed (shear flow), it creates a force that pushes bubbles sideways.
• Wall Lubrication Force: This is a special force that prevents bubbles from touching the solid walls of a pipe or tank. It gently pushes them away from the wall.
• Virtual Mass Force: When a light bubble accelerates quickly, it must push the heavy liquid around it out of the way. This liquid acts like extra “virtual” mass attached to the bubble.
• Turbulent Dispersion Force: This force accounts for turbulent eddies (swirls in the water) scattering the bubbles and mixing them evenly.

Figure 5: Eulerian Phase interaction tab window

Why is choosing the correct model critical? If you choose the wrong drag or lift model, your CFD simulation will give completely wrong physical results. Before running your Eulerian model ANSYS Fluent project, you must always evaluate which forces are important for your specific fluid materials and bubble sizes.

Figure 6: Interphase momentum exchange forces in the Eulerian multiphase model, including drag and non-drag forces.

Secondary Phase Settings and Particle Size in Fluent

When you set up an Eulerian multiphase model in ANSYS Fluent, you must carefully define your phases. Usually, the continuous background fluid (like water) is set as the Primary Phase. The dispersed fluid or solid (like air bubbles or sand) is set as the Secondary Phase. For every secondary phase, there is one critical rule: You must assign a phase diameter for each secondary phase.

Figure 7: Diameter specification for secondary phase – ansys panel

The software needs this diameter to calculate the contact area between the phases. Without it, ANSYS Fluent cannot correctly calculate drag forces, heat transfer, or mass transfer in your multiphase flow simulation.

There are three main ways to define the phase diameter in Fluent:

1. Constant Diameter: You enter a single number. You should only use this if you assume every single bubble or particle in your system is exactly the same size.
2. Sauter Mean Diameter: This is used when particles have different sizes, but you want to use a single average value. The Sauter mean diameter keeps the correct volume-to-surface-area ratio for the mixture.
3. User-Defined: You can write your own custom code (UDF) if the diameter changes based on specific rules or locations.

The Importance of Particle Size Distribution (PSD)

In the real world, bubbles and solid particles are never just one size. If you look inside an industrial reactor, you will see a wide Particle Size Distribution (PSD). There are tiny bubbles, medium bubbles, and large bubbles all mixing together. The size of the bubbles directly controls the total interfacial area. The interfacial area is the physical boundary where two phases touch. If you want accurate heat transfer or mass transfer (like a chemical reaction), you must know the exact interfacial area.

If you just guess a “constant diameter,” your multiphase flow simulation will give you completely wrong heat and mass. To solve this problem, engineers use the Population Balance Model (PBM) in ANSYS Fluent. The PBM tracks the exact population of bubbles over time, calculating how they constantly break apart (breakage) and merge together (coalescence).

A perfect example of this is our comprehensive project: A Bubble Column CFD Simulation Using the Fluent Population Balance Model (PBM).

In this project, we simulated a gas-liquid bubble column. If we used a single constant bubble size, the design would fail. Why? Because inside a bubble column, the flow is highly dynamic. Turbulence, buoyancy, and shear forces constantly smash bubbles together (coalescence, using models like the Luo model) and rip them apart (breakage, using models like Lehr or Luo).

Figure 8: Plot showing the volume fraction of a different bubble size group (a “bin”) calculated using the Population Balance Model (PBM) in ANSYS Fluent.

By coupling the Eulerian model ANSYS Fluent with the PBM, this project successfully:

1. Tracked the Bubble Size Distribution (BSD): It calculated exact bubble sizes instead of guessing.
2. Found the “Sweet Spot”: The simulation discovered a “Dominant Sweet Spot” where specific medium bubble diameters (like 0.012 m to 0.03 m) reached high volume fractions. This is the ideal operating range where breakage and coalescence are perfectly balanced.
3. Predicted Interfacial Area Accurately: By knowing the exact size distribution in every cell, the software precisely calculated the gas holdup and interfacial area, which is highly critical for real-world chemical manufacturing.

When you have a dense flow where bubble sizes change rapidly, combining the Eulerian model with the PBM is the most professional and scientifically accurate approach.

Solver Overview and Solution Strategies

After setting up the phases and forces, you must choose how ANSYS Fluent calculates the math. In an Eulerian model ANSYS Fluent simulation, the equations are strongly linked. Drag forces and mass transfer create very large source terms. Therefore, you must use a powerful numerical solver. For the Eulerian model, ANSYS Fluent offers two main algorithms for pressure-velocity coupling:

1. Phase Coupled SIMPLE (PC-SIMPLE): This is a segregated solver. It solves the equations one by one (first momentum, then pressure, then volume fraction). It is a very stable method but can be slow. If you use the PC-SIMPLE solver and convergence is slow, you should reduce the Under-Relaxation Factors (URFs) for the volume fraction and pressure.
2. Full Multiphase Coupled Solver: This is a modern and highly robust method. The Coupled solver calculates the volume fraction, pressure, and momentum all at the exact same time simultaneously.

• For Steady-State Problems: The coupled solver is much faster and more efficient than PC-SIMPLE. It is recommended to use a Courant number around 20 and higher URFs (0.5 to 0.75).
• For Transient Problems: The efficiency of the coupled solver is not as good for very small time steps. If you use it for transient multiphase flow simulation, you should use larger time steps and very high Courant numbers (like 1E7).

No matter which solver you choose, Eulerian simulations can easily crash if you are not careful. Always start your simulation with conservative solution controls. Use first-order discretization schemes at the beginning. Once the flow field stabilizes, you can gradually increase the under-relaxation factors and switch to higher-order schemes (like QUICK) for better accuracy.

Figure 9: Recommended conservative solver settings for pressure-velocity coupling in the Eulerian multiphase model.

Summary & What’s Next

The Eulerian multiphase model is the most powerful tool for solving dense and complex fluid interactions in ANSYS Fluent. In this blog, we explored the absolute basics. We learned how it treats phases as interpenetrating continua, looked at the core conservation equations, and understood why phase interaction forces (like drag) are so critical. We also saw why adding the Population Balance Model (PBM) is essential for capturing the true Particle Size Distribution (PSD).

However, this is only the beginning. Multiphase flows involve many more physical phenomena. In our next blogs in this series, we will explore advanced topics like Phase Change (Evaporation and Condensation), cavitation, and how to apply the Eulerian Granular Model for solid particles.

Stay tuned, and do not forget to check our professional CFD tutorials to practice these concepts in real engineering projects!

 

Frequently Asked Questions (FAQ)

• What is the Eulerian multiphase model in ANSYS Fluent? The Eulerian model is a comprehensive multiphase framework in ANSYS Fluent. It treats all phases (gas, liquid, or solid) as continuous, interpenetrating fluids. It solves separate mass and momentum equations for every phase, making it perfect for dense flow simulations like bubble columns and fluidized beds.
• When should I use the Eulerian model instead of the DPM model? You should use the Discrete Phase Model (DPM) when your secondary phase volume is very low (less than 10%) and you want to track exact particle paths. You must use the Eulerian model when you have a dense flow (high volume fraction) where particles and bubbles heavily interact, collide, and share space.
• What is the most important phase interaction force in the Eulerian model? The drag force is the most critical interaction. It represents the hydrodynamic friction between the phases. Choosing the wrong drag model (like using a spherical drag law for large, cap-shaped bubbles) will result in completely wrong CFD predictions.
• Why is Particle Size Distribution (PSD) important in multiphase CFD? In real flows, bubbles and particles constantly break and merge, creating a wide range of sizes. Because heat transfer, mass transfer, and drag forces depend directly on the contact area between phases, you must know the exact sizes. Guessing a single constant diameter leads to huge errors.
• How do I calculate changing bubble sizes in ANSYS Fluent? To calculate changing sizes, engineers couple the Eulerian model with the Population Balance Model (PBM). The PBM tracks how bubbles break (breakage) and merge (coalescence) over time, feeding the highly accurate Sauter mean diameter back to the Eulerian equations.