Read time: 10 minutes
Target audience: CFD Researchers/ Automobile Engineers/ Thermal-Fluid Industry/ Aero Industry
Written by: Dr Tabish Wahidi
Multiphase flows, where two or more phases (gas, liquid, or solid) coexist and interact, are common in many industrial and environmental applications. From oil extraction in deep-sea environments to chemical reactors and fluidized beds, understanding how these phases interact is critical for process optimization and equipment design. However, simulating multiphase flows using Computational Fluid Dynamics (CFD) presents numerous complexities. The interactions between phases, turbulence, surface tension, and phase transition make modeling multiphase flows a challenging task.
This article covers the complexities, various types of multiphase flows, and different solution approaches in CFD simulation to handle such intricate systems.
Multiphase flow refers to the simultaneous flow of materials with different phases or states of matter such as gas, liquid, and solid within a system. These flows are encountered across various engineering disciplines, including chemical, mechanical, nuclear, and civil engineering. Multiphase flow CFD simulation enables the prediction of how multiple phases interact in complex systems.
Multiphase flows are generally classified based on the nature of the phases and their interactions. Some common types include:
Dispersed Flows: In dispersed flows, one phase is distributed as discrete particles, droplets, or bubbles within another continuous phase. Common examples include:
Gas-Liquid Flows: Bubbly flows where gas bubbles are dispersed in a liquid.
Liquid-Solid Flows: Slurries where solid particles are dispersed in a liquid.
Gas-Solid Flows: Pneumatic conveying systems where solid particles are carried by a gas phase.
Separated Flows: In separated flows, the phases remain distinct and separated by well-defined interfaces, such as stratified flows where liquid and gas flow in separate layers.
Examples: Stratified flow in pipes, annular flow in heat exchangers.
Reacting Multiphase Flows: These involve chemical reactions between the phases, which further complicates the simulation. The reaction kinetics are coupled with the phase interaction models.
Examples: Combustion in fluidized beds, catalytic reactors.
Complex Three-Phase Flows: Three-phase flows involve the interaction of gas, liquid, and solid phases simultaneously. These flows are extremely complex due to the interplay between the three phases.
Examples: Oil-water-gas separation in petroleum production, slurry bubble columns.
4. Solution Modules in Multiphase Flow:
Due to the diverse nature of multiphase flows, various solution techniques and models have been developed to simulate these systems. The choice of method depends on factors like the type of flow, the level of detail required, and the computational resources available.
Euler-Euler Approach:
In the Euler-Euler approach, both phases are treated as interpenetrating continua, and a set of conservation equations (mass, momentum, and energy) is solved for each phase. This approach is most appropriate for systems where both phases are present throughout the computational domain and are highly dispersed.
Advantages: Efficient for large-scale simulations with high dispersed phase fractions.
Disadvantages: Limited in its ability to capture sharp interfaces.
Applications: Fluidized beds, gas-liquid bubble columns, liquid-liquid extraction processes.
Euler-Lagrange Approach:
In this method, the continuous phase (gas or liquid) is modeled as a continuum using the Eulerian approach, while the dispersed phase (particles, droplets, or bubbles) is treated as discrete entities and tracked using a Lagrangian framework. Forces such as drag, lift, and gravity are considered for the individual particles.
Advantages: Accurate for tracking individual particles or droplets and capturing detailed particle-phase interactions.
Disadvantages: Computationally expensive when dealing with many particles.
Applications: Pneumatic conveying, sprays, particle-laden flows.
Volume of Fluid (VOF) Method:
The VOF method is used to capture immiscible multiphase flows with distinct interfaces, such as gas-liquid flows. This method tracks the volume fraction of each phase in every computational cell, and the interface is reconstructed dynamically as the flow evolves.
Advantages: Good at capturing sharp interfaces, making it ideal for free-surface flows and sloshing.
Disadvantages: May become computationally expensive for highly turbulent or dispersed flows.
Applications: Ship hull analysis, droplet dynamics, oil-gas flow in pipelines.
Level Set Method:
The level set method is another interface-capturing approach used to simulate multiphase flows. It represents the interface between phases using a distance function and is particularly useful when dealing with highly complex interfaces that change topology over time (e.g., merging or splitting droplets).
Advantages: Accurate in capturing interfaces with complex shapes.
Disadvantages: Requires significant computational resources, particularly for resolving fine interface details.
Applications: Capillary-driven flows, bubble coalescence, droplet breakup.
Phase Field Method:
In the phase field method, a smooth scalar field is used to describe the phase distribution across the domain. This method is well-suited for simulating flows where phase transitions and interfacial dynamics play a crucial role, such as in the formation of emulsions.
Advantages: Can handle complicated interface dynamics and surface tension effects.
Disadvantages: Requires careful parameter tuning to capture interface dynamics accurately.
Applications: Emulsion formation, droplet coalescence, spinodal decomposition.
5. Complexities and its Solution Approach:
Interfacial Dynamics:
Complexity:
The dynamic interfaces between phases (e.g., gas-liquid or liquid-solid). These interfaces can deform, merge, or break apart, influenced by surface tension, buoyancy, and shear forces.
Phenomena such as droplet coalescence, bubble breakup, or film formation make accurate interface tracking difficult, especially when sharp phase boundaries need to be resolved in turbulent flows.
Solution Approach:
Volume of Fluid (VOF) Method: The VOF method tracks the volume fraction of each phase in every computational cell and reconstructs the interface dynamically. It is ideal for immiscible flows with sharp interfaces, such as liquid-gas interactions.
Level Set Method: This method uses a distance function to capture the phase interface, allowing for complex interface geometries and topological changes (e.g., merging or splitting). It is effective in capturing fine details in interfacial dynamics.
Phase Field Method: This approach smooths out the interface using a continuous scalar field. It is particularly useful for cases with complex interface dynamics like emulsification or droplet breakup but requires careful tuning of parameters.
Phase Interaction:
Complexity:
The interaction between different phases involves the exchange of mass, momentum, and energy. For instance, in gas-liquid flows, drag forces, interfacial tension, and heat transfer need to be accurately modeled.
These interactions can become more complicated when mass transfer occurs between phases (e.g., evaporation or condensation), which alters the flow properties.
Solution Approach:
Euler-Euler Approach: In this method, both phases are treated as interpenetrating continua, and conservation equations are solved for each phase separately. The exchange of mass, momentum, and energy between phases is modeled using source terms.
Euler-Lagrange Approach: The continuous phase (gas or liquid) is treated as a continuum, while the dispersed phase (bubbles, droplets, or particles) is tracked as individual entities. Forces such as drag, lift, and buoyancy are applied to the dispersed phase.
Non-Uniform Phase Distribution:
Complexity:
Phases in multiphase flows are rarely uniformly distributed. For example, bubbles may cluster in gas-liquid flows, or solid particles may settle in liquid-solid flows. The spatial non-uniformity of phases significantly affects the overall flow dynamics, such as pressure drop or heat transfer.
Solution Approach:
Euler-Euler Approach: In highly dispersed flows, the Euler-Euler method models the volume fraction of each phase in every computational cell, allowing for the prediction of non-uniform phase distribution.
Multiphase Discrete Particle Model (DPM): For liquid-solid flows or gas-solid flows, the discrete particle model can track individual particles and account for their clustering or settling behaviour.
Phase Change (Boiling, Condensation)
Complexity:
Phase change phenomena such as boiling or condensation involve complex thermodynamic processes, including latent heat transfer and mass fluxes between phases. These phase transitions can dramatically alter the flow field, creating additional complexity in terms of both energy conservation and mass transfer.
Solution Approach:
VOF Method with Phase Change Models: The VOF method, coupled with phase change models, can simulate boiling and condensation by incorporating latent heat and mass transfer terms.
Euler-Euler Approach with Interphase Mass Transfer Models: This approach can handle the transfer of mass and energy between phases, especially for dispersed flows where evaporation or condensation takes place.
Multiscale Nature of Multiphase Flows
Complexity:
Multiphase flows often exhibit behaviour at multiple scales. For example, in gas-liquid flows, the macroscopic behaviour of the system (such as flow regime transitions) is influenced by the behaviour of small-scale phenomena (such as bubble dynamics). Capturing both small and large-scale dynamics in a single simulation is a challenge.
Solution Approach:
Coupled Euler-Euler and Lagrangian Models: In some cases, a hybrid approach is employed where large-scale behaviour is modeled using the Euler-Euler framework, while small-scale phenomena (such as particle tracking) are modeled using the Lagrangian framework. This approach balances accuracy and computational efficiency.
Adaptive Mesh Refinement (AMR): AMR techniques allow for high-resolution grids in areas where small-scale dynamics are important, such as near phase interfaces or in regions with sharp gradients, while using coarser grids elsewhere to save computational resources.
Computational Cost and Convergence
Complexity:
Simulating multiphase flows with high accuracy often requires a significant amount of computational resources. Complex geometries, turbulence, interfacial dynamics, and phase change phenomena increase the number of grid points and time steps required for an accurate solution.
Slow convergence or divergence issues may arise due to the strong coupling between phases.
Solution Approach:
Segregated Solvers: These solvers solve the conservation equations for each phase sequentially and iteratively update the flow field. While less computationally expensive, they can be slower in strongly coupled flows.
Coupled Solvers: Coupled solvers solve the governing equations for all phases simultaneously, leading to faster convergence in tightly coupled systems but at a higher computational cost.
Multigrid and Parallel Computing: Multigrid techniques, along with parallel computing, can accelerate convergence and reduce computational cost
6. Conclusion:
The complexities of multiphase flow CFD simulations, such as interfacial dynamics, phase interactions, and turbulence, require advanced modeling techniques. Depending on the type of flow and the desired level of detail, different solution approaches, including Euler-Euler, Euler-Lagrange, VOF, and phase field methods, are employed to tackle these challenges. As computational power increases and modeling techniques advance, the ability to accurately simulate multiphase flows will continue to improve, leading to better designs and optimization of multiphase systems across industries.