Two-phase flow is a fluid mechanics concept that involves the simultaneous movement of liquid and gas phases in an application like **water and vapor** or **oil and gas** in a pipe. Its usage can cover various areas, from chemical processing to power generation.

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ToggleCorrectly predicting and managing two-phase flow regimes is crucial for designing and operating systems involving heat exchangers, pipelines, and reactors.

An example of a two-phase flow regime made by AI

## Two-phase flow regimes

Two-phase flow regimes describe how liquid and gas phase can find their way and how they interact with each other, thereby creating different flow regimes. Several factors such as **pipe orientation**, **fluid velocities**, and **properties**, can change flow patterns. Understanding different regimes can help enhance heat transfer and reduce pressure drop in systems. Engineers use Computational Fluid Dynamics (CFD) tools to simulate and analyze these regimes in complex systems.

The water boiling process which is created a two-phase flow condition

## Importance of flow regime maps

In flow regime maps, **gas** and **liquid** velocities are used to predict different two-phase flow patterns. Engineers can use these maps to anticipate operational challenges and optimize system performance during the design phase of systems. Plotting gas-liquid flow regimes in horizontal and vertical pipes using tools like the **Taitel-Dukler** and **Mandhane** maps is common. The figure below represents the **Mandhane** map, which can predict flow regimes by superficial velocities of liquid and vapor.

Mandhane model for predicting flow regimes

Link: Emamzadeh M, Issa RI. A model forpredicting the transitionbetween stratified and annular flow in horizontal pipes. Multiph Sci Technol 2013;25:79–100. https://doi.org/10.1615/MultScienTechn.v25.i1.40.

## Two-phase flow regimes in horizontal pipes

Different flow regimes in a horizontal pipe

Link: Rasul G, Qureshi MF, Ferroudji H, Butt S, Hasan R, Hassan I, et al. Analysis of cuttings transport and flow pattern in nearly horizontal extended reach well. J Adv Res Fluid Mech Therm Sci 2020;71:69–86. https://doi.org/10.37934/arfmts.71.2.6986.

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### 1. Bubble Flow

One of the most basic two-phase flow regimes is bubble flow. In this process, tiny bubbles of gas are **dispersed** throughout a **continuous liquid phase**. It is common to observe this regime at low gas flow rates in many industrial processes, such as heat exchangers and chemical reactors. CFD tools like Ansys Fluent or specialized multiphase flow solvers can be utilized to simulate bubble behavior, providing detailed insights into phase interaction and system performance.

The link refers to a CFDLAND product, simulating a bubbly flow regime.

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### 2. Slug Flow

A slug flow occurs when **liquid slugs** separate several large **gas bubbles** (also known as Taylor bubbles). As a result of this flow regime, considerable pressure fluctuations can be observed, which are critical to the design of pipelines and risers in the oil and gas industry. Historically, slug flows have been observed in geothermal and nuclear systems, where multiphase heat transfer plays an important role. With advanced CFD simulations, engineers can predict slug lengths and frequencies, enabling them to design systems that can handle these transient flows without compromising performance.

The link refers to a CFDLAND product, simulating a slug flow regime.

### 3. Plug Flow

Further increases in gas velocity can result in **larger interfacial waves** that can wash to the top of the pipe. This can result in elongated gas bubbles separating liquid plugs in a plug flow condition. Due to the elongated gas bubbles, the liquid phase remains continuous below these elongated bubbles along the bottom of the pipe.

### 4. Annular Flow

Annular flow occurs when a thin layer of liquid phase flows along the wall of a pipe. However, the gas phase flows through the pipe core. This regime observes at high gas velocities, which is the main reason for pushing a **thin liquid film** layer near the wall. The main application of this regime is in vertical pipelines such as nuclear reactors and oil production systems. Annular flow can significantly entrain liquid droplets within the gas core, influencing mass transfer and heat exchange. CFD simulations provide a detailed visualization of this flow pattern, allowing for optimization of phase distribution and enhanced system efficiency.

### 5. Stratified Flow

In this regime, **low liquid and gas phase velocities** result in separating the liquid and gas phases. Thus, the liquid phase always remains at the bottom of the pipe, and the gas phase always ends up at the top of the pipe.

### 6. Wavy Flow

As the gas phase velocity increases in a stratified state, it generates **waves along the boundary** that travel with the flow direction. The height of these waves is influenced by the speed difference between the two phases. Typically, the wave peaks do not extend to the top of the pipe.

### 7. Disperse Flow

Disperse flow is a fluid flow in which particles or droplets are **suspended** in a primary fluid, such as air or water. The random distribution of particles or droplets characterizes this flow type. This flow configuration is observed in all types (gas-liquid, gas-solid, liquid-liquid, and liquid-solid) of two-phase flows.

click to access Mass Transfer CFD

## Two-phase flow Reynolds number

In a two-phase flow, the Reynolds number can be more complex than in a single-phase flow, as it must account for the interactions between the phases. The Reynolds number for each phase is often calculated __separately__ or a __mixture__ Reynolds number model is used. Below are common approaches:

### Reynolds Number for Each Phase (Separate model)

The Reynolds number for each phase can be calculated based on the properties of each phase individually:

In the above equations, and are the densities of phases 1 and 2. and are the velocities of those phases. D is the characteristic length. and are the viscosities of phase 1 and 2.

click to access Fluid Mechanics CFD

### Mixture Reynolds Number (Homogeneous Model)

If you consider the two phases as a mixture, you can compute a mixture Reynolds number:

In this formula, is the mixture density, which is a weighted average of the two phases’ densities based on volume fractions. is the mixture velocity, which can also be an average. is the mixture viscosity, typically calculated using models such as the harmonic mean or weighted average based on volume fractions.

## Slip ratio of two-phase flow

In a two-phase flow, the **slip ratio, or velocity ratio**, is defined as the ratio of vapor phase velocity divided by liquid phase velocity. It is essential to assume the two-phase flow model in the model calculation. For instance, if you choose the homogeneous two-phase flow model, the slip ratio is unity. Nevertheless, when you choose a separate flow model, the below formulation was used:

Here, V is velocity, m/s, is vapor phase determiner, is density of a phase, kg/m3, x is steam quality, and is a void fraction.

The link refers to a CFDLAND product that uses slip velocity for paper validation through ANSYS FLUENT.

## Two-phase flow CFD simulation

By using **ANSYS Fluent**, different flow regimes can be simulated. Choosing an appropriate setup depends on the nature of a physical problem and the interaction between phases. In this section, four primary models which are widely used in academic and industrial approaches were introduced:

### Volume of Fluid (VOF) Model

For flows with sharp transitions between phases, such as __free surface flows, filling processes, or sloshing__, the VOF model is designed. The entire flow field is solved using one set of equations, and the volume fractions of each phase are tracked to determine the location of the interface.

### Mixture Model

This model solves a single set of momentum equations for the mixture and tracks each phase’s volume fraction or mass fraction. Often, this model is used when two phases have a __strong coupling__, but it is not as complex as the Eulerian-Eulerian model.

### Eulerian-Eulerian Model

It is assumed that both phases are continuous. Separate conservation equations are solved for each phase. Source terms are used to model the phases’ interactions to account for momentum, heat, and mass transfer. This model has many applications, including dense two-phase flows, such as __fluidized beds__ or __slurry transport__, that have both phases with substantial volume fractions.

click to access Multiphase CFD

### Eulerian-Lagrangian (Discrete Phase) Model

One phase (usually the continuous phase) is treated as a continuum using an Eulerian framework, while the dispersed phase (e.g., droplets, bubbles, or particles) is treated as discrete entities using a Lagrangian framework. As a result, this model is suitable for dilute two-phase flows in which the dispersed phase occupies a small volume fraction.

**Conclusion**

For industries such as oil and gas, power generation, and chemical processing, it is imperative to understand the various regimes of two-phase flow. A variety of flow regimes, such as bubble flows, slug flows, plug flows, annular flows, and stratified flows, present unique challenges and opportunities for optimizing heat transfer, reducing pressure drops, and ensuring system stability. The use of computational fluid dynamics (CFD) has become an integral part of simulating these complex flows, allowing engineers to predict phase interactions, improve performance, and mitigate operational risks. It is possible to improve system efficiency and safety in real-world applications by using CFD and flow regime maps.

It can be beneficial for students and companies to collaborate with **CFDLAND** experts since they have experience in a wide range of CFD fields and projects. With ANSYS FLUENT software, you will be able to simplify your work and achieve high-quality results. Order CFD projects to CFDLAND.