In many industrial processes, different fluids or materials flow together. This is called multiphase flow. To understand these complex flows, we use powerful tools in CFD. One of the most common and efficient tools is the Mixture multiphase model.
What is the Mixture Model? The Mixture model is a simplified multiphase model in ANSYS Fluent. It is designed for situations where different phases are mixed and move together, but at different velocities. Think of it like dust particles flowing with air or small bubbles rising in water.
The model works by treating the different phases as if they are interpenetrating. This means it assumes the phases can share the same space at the same time. It solves a single set of equations for the combined mixture instead of separate equations for each phase. This approach makes multiphase flow simulation much faster and less demanding on your computer.
The Mixture Model is best used when you have dispersed phases that follow the main flow closely. This is ideal in the chemical industry for designing bubble columns. Using a Mixture model fluent simulation allows engineers to predict the gas holdup and mixing efficiency, which helps in scaling up the reactor from a small lab design to a large industrial size, saving significant cost and time. To see how these industrial problems are solved, you can explore various multiphase CFD simulation tutorials.
Figure 1: Some examples of Multiphase CFD simulation provided by CFDLAND
Mixture Model vs. Other Multiphase Models
Choosing the correct model is the most important step in a multiphase flow CFD analysis. The Mixture model is one of three main options in Fluent. To help you decide, here is a direct comparison. You can find more details in our complete guide on choosing the right modeling approach.
| Feature | Mixture Model | VOF Model | Eulerian Model |
| Best For | Dispersed or mixed flows (e.g., bubbly flow, slurry). | Flows with a sharp interface (e.g., waves, tank filling). | Any multiphase flow, especially when phases interact strongly. |
| How It Works | Solves one set of equations for the mixture. Calculates a slip velocity between phases. | Tracks the boundary between phases that do not mix. | Solves a complete set of equations for each phase individually. |
| Computer Cost | Medium. It offers a good balance between accuracy and speed. | Low. It is computationally cheap. | High. It is the most computationally expensive model. |
| Key Use Case | You need good results for a mixed flow without the high cost of the Eulerian model. | You need to accurately capture the free surface between two immiscible fluids. | You need the highest accuracy for complex flows where phase interaction is critical. |
Therefore, you should choose the Mixture Model when you have a dispersed multiphase flow and want an efficient, reliable solution. It is more powerful than the VOF model for mixed flows and much faster than the complex ANSYS Fluent Eulerian multiphase model.
Understanding the Mixture Model Fundamentals
To use the Mixture Model correctly in your multiphase flow simulation, you need to understand its core ideas. The model is built on a few smart simplifications that make it both fast and effective. The most important idea is the concept of interpenetrating continua. This means the model assumes that different phases, like gas bubbles and water, can exist in the same place at the same time. Think of a wet sponge: the solid sponge material and the liquid water occupy the same volume together. The Mixture multiphase CFD model treats a flow of dusty air in the same way. In every small computational cell, it calculates a single value for pressure and velocity for the mixture as a whole. This approach is the foundation of the Mixture model fluent and is why it is so computationally efficient.
Figure 2: Illustration of interpenetrating continua: both gas (red) and liquid (blue) phases are treated as being mixed and occupying the same computational cell in the Mixture Model
This model works so well because it uses an assumption called “local equilibrium”. This assumption means that the dispersed phase (the bubbles or particles) responds to the main fluid’s motion almost instantly. Imagine a light feather caught in a gust of wind; it immediately travels at the wind’s speed. The Mixture Model is designed for these “feather-like” situations. This assumption holds true when the particle relaxation time is very short, typically between 0.001 and 0.01 seconds. This is the time it takes for a particle to adjust to a change in the fluid’s velocity. Because this time is so short, we can assume the phases are in equilibrium locally.
So, how do the phases interact in the Mixture Model? Instead of solving for complex forces between phases, the model calculates how fast the phases move relative to each other. This is called the slip velocity. The model first calculates the average velocity of the mixture, u_m, which is a weighted average of the phase velocities. The simple idea is:
Mixture Velocity = (share of phase 1 * its velocity) + (share of phase 2 * its velocity)
Then, it uses an algebraic formula to calculate the slip velocity (u_pq), which is simply the difference between the velocity of the secondary phase (u_p) and the primary phase (u_q). This slip is mainly caused by the drag force. By solving for this relative motion algebraically, the model avoids solving full momentum equations for each phase, saving a huge amount of time. This simplified interaction is the key to the Mixture multiphase CFD example problems like bubble columns and sedimentation, where the phases are well-mixed.
Figure 3: Real-world flow regimes. The Mixture Model is ideal for the well-mixed Bubbly Flow (left), where the local equilibrium assumption is valid. It is less suitable for the Churn Turbulent Flow (right), where phase interaction is more complex
The Mathematics Behind the Mixture Model
Now that we understand the basic ideas of the Mixture Model, let’s look at the simple math it uses. You don’t need to be a math expert to understand this. The model uses three main equations to describe the flow of the mixture.
The first equation is the Continuity Equation. This is a very simple but important rule. It just says that mass is conserved. In other words, the amount of mixture flowing into a small space must be equal to the amount flowing out, unless the density changes. It makes sure that the simulation doesn’t create or destroy fluid.
Next is the Momentum Equation. This is the main equation for movement. It is like Newton’s Second Law (Force = mass × acceleration) but for a fluid. It calculates the velocity of the mixture based on all the forces acting on it, like pressure, gravity, and friction. The Mixture multiphase CFD formula for momentum looks complicated, but the idea is simple:
![\frac{\partial (\rho \vec{u}_m)}{\partial t} + \nabla \cdot (\rho_m \vec{u}_m \vec{u}_m) = -\nabla p + \nabla [\mu_{eff} (\nabla \vec{u}_m + \nabla \vec{u}_m^T)] + \rho_m \vec{g} + \vec{F} + \nabla \sum_{k=1}^{n} \alpha_k \rho_k \vec{u}_k' \vec{u}_k'](https://cfdland.com/wp-content/ql-cache/quicklatex.com-f4abfd80eeaeafcd95eb9bc4284c0308_l3.png "Rendered by QuickLaTeX.com")
Change in Mixture’s Motion = – (Pressure Force) + (Friction Force) + (Gravity) + (Other Forces)
This equation solves for one single velocity for the whole mixture. This is a key reason why the Mixture model fluent is so fast.
The third key equation is the Volume Fraction Transport Equation. This equation keeps track of how much of each phase is present in every part of the flow. For example, it calculates if a cell is 90% water and 10% air, or 50% water and 50% air. As the mixture moves, this equation makes sure the volume fractions of the secondary phases are updated correctly. It is like a bookkeeper for the phases, making sure we always know the exact composition of the mixture everywhere.
Finally, let’s talk about slip velocity and drift velocity. We know the model solves for one mixture velocity. But in reality, light bubbles in water rise faster than the water. The model handles this using a clever trick. The slip velocity is the difference in speed between the secondary phase (e.g., bubbles) and the primary phase (e.g., water). The drift velocity is the velocity of a secondary phase compared to the center-of-mass velocity of the mixture. The relative velocity formulation is the key. The model uses a simple algebraic formula to calculate this slip, mainly based on the drag force. It assumes the slip is caused by the particle’s acceleration and its relaxation time (τ_p).
u_pq ≈ τ_p * a_p
This means the slip velocity (u_pq) depends on how fast the particle responds to forces (τ_p) and the acceleration it feels (a_p). By using this simple formula instead of a full, separate momentum equation, the model can account for phases moving at different speeds while remaining very fast and efficient.
Setting Up the Mixture Model in ANSYS Fluent
Setting up a Mixture multiphase Fluent example is a logical process. This guide will walk you through the most important steps in the ANSYS Fluent interface.
First, you need to open the Multiphase Model window. In the Models tab, you will select Mixture. Right away, you will see a box called Model Parameters. The most important setting here is to enable Slip Velocity. This step is critical because it tells Fluent to calculate the velocity difference between your phases, which is the main advantage of the Mixture model. You also set the Number of Eulerian Phases here, which is usually 2 for simple problems.
Figure 4: The main Multiphase Model window in ANSYS Fluent. Key steps are: (1) Select ‘Mixture’, (2) Enable ‘Slip Velocity’, and (3) Set the ‘Number of Eulerian Phases’
Next, click on the Phases tab. This is where you will choose your primary and secondary phases. The primary phase is usually the main continuous fluid (like water), and the secondary phase is the one dispersed in it (like air bubbles or sand particles). For each secondary phase, you must define its properties. The most important property is the Diameter of the particles or bubbles. You can set a constant value, like the 3mm bubbles. If the secondary phase is a solid particle, you will need to enable the Granular option and define its properties.
After defining the phases, you move to the Phase Interaction tab. Here, under the Forces sub-tab, you will configure your drag models. The drag force describes the friction between the phases. For a simple Mixture multiphase Fluent example with small, round particles, the schiller-naumann model is a good starting point. For other cases, like the bubble column, the Grace drag law is a better choice. Getting the drag and slip velocity correct is essential for accurate results, especially in complex simulations like a two-phase ejector considering slip velocity. Following these steps will allow you to set up a wide variety of multiphase problems, from simple bubbly flows to advanced heat transfer simulations like two-phase nanofluid forced convection or designing a nanofluid minichannel heat sink.
Figure 5: 3 VALIDATION examples showing the correct employment of Mixture multiphase model in ANSYS Fluent
Conclusion
The Mixture Model is a powerful and efficient tool for your multiphase flow simulation toolbox. Its main advantage is offering a perfect balance: it is much faster than the complex Eulerian model but still captures the important effect of slip velocity between phases. This makes the Mixture multiphase CFD approach ideal for a wide range of industrial problems where phases are mixed but move at different speeds, such as bubbly flows, sedimentation, and flows with light particle loading.
As we have seen, setting up the Mixture model fluent is a clear, step-by-step process. By correctly defining your phases, interactions, and turbulence, you can get accurate results without the high computational cost of more complex models. For the right application, it is an excellent choice that saves you time and resources.