6.4 Turbulence modeling in multiphase flows

Turbulence modeling in multiphase flows is a complex yet crucial aspect of fluid dynamics. It involves predicting how different phases interact and affect turbulent structures, which is essential for optimizing industrial processes and designing efficient systems.

Various approaches exist for modeling multiphase turbulence, from RANS models to LES and DNS. Each method offers unique insights and trade-offs between accuracy and computational cost, helping engineers better understand and control multiphase flow systems.

Turbulence in multiphase flows

• Turbulence plays a crucial role in multiphase flow systems, influencing mixing, heat and mass transfer, and particle interactions
• Modeling turbulence in the presence of multiple phases presents unique challenges due to the complex interactions between phases and the modified turbulence structures
• Accurate prediction of turbulence in multiphase flows is essential for designing and optimizing industrial processes, such as chemical reactors, combustion systems, and multiphase pipelines

RANS models for multiphase turbulence

k-ε model extensions

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• The standard k-ε model has been adapted for multiphase flows by incorporating additional terms to account for the presence of dispersed phases
• Extensions include the mixture k-ε model, which treats the multiphase mixture as a single fluid with modified properties
• The dispersed k-ε model considers separate transport equations for the turbulence quantities of each phase, allowing for phase-specific turbulence modeling
• Interfacial momentum transfer terms are added to the equations to capture the exchange of turbulence energy between phases

k-ω model adaptations

• The k-ω model, known for its improved performance in near-wall regions, has also been extended to multiphase flows
• Adaptations include the mixture k-ω model, which employs a similar approach to the mixture k-ε model
• The dispersed k-ω model considers separate transport equations for the turbulence quantities of each phase
• Modifications to the model constants and additional terms for interfacial turbulence transfer are introduced to capture multiphase effects

Reynolds stress models

• Reynolds stress models (RSMs) provide a higher level of turbulence modeling by solving transport equations for the individual components of the Reynolds stress tensor
• RSMs offer the potential for more accurate predictions of turbulence anisotropy and complex flow features in multiphase systems
• Multiphase RSMs account for the presence of dispersed phases by including additional terms in the stress transport equations
• Challenges in multiphase RSMs include the increased computational cost and the need for robust numerical schemes to handle the complex equations

Large eddy simulation (LES) for multiphase flows

Subgrid-scale modeling approaches

• LES resolves the large-scale turbulent structures while modeling the subgrid-scale (SGS) effects
• In multiphase flows, SGS models need to account for the presence of dispersed phases and their interactions with the resolved scales
• Approaches include the mixture SGS model, which treats the multiphase mixture as a single fluid with modified SGS properties
• The dispersed SGS model considers separate SGS models for each phase, allowing for phase-specific subgrid-scale modeling

Implicit LES vs explicit LES

• Implicit LES (ILES) relies on the numerical dissipation inherent in the discretization schemes to model the SGS effects
• ILES is computationally efficient but may lack control over the SGS modeling
• Explicit LES employs explicit SGS models, such as the Smagorinsky model or dynamic models, to represent the subgrid-scale turbulence
• Explicit LES offers more control over the SGS modeling but requires careful selection and tuning of the model parameters

Challenges of LES in multiphase systems

• LES of multiphase flows faces challenges related to the complex interactions between phases and the wide range of scales involved
• Resolving the interface dynamics and capturing the interfacial momentum transfer requires high spatial and temporal resolution
• Subgrid-scale models need to accurately represent the SGS effects in the presence of multiple phases
• Computational cost can be high, especially for systems with a large number of dispersed particles or droplets

Direct numerical simulation (DNS) of multiphase turbulence

DNS requirements and limitations

• DNS resolves all scales of turbulence without any modeling assumptions, providing the most accurate representation of multiphase turbulence
• DNS requires extremely fine spatial and temporal resolution to capture the smallest scales of turbulence (Kolmogorov scales)
• The computational cost of DNS scales with the Reynolds number, making it prohibitively expensive for high Reynolds number flows
• DNS is limited to relatively simple geometries and low Reynolds numbers due to the computational demands

Insights from multiphase DNS studies

• Despite the limitations, DNS studies have provided valuable insights into the fundamental mechanisms of multiphase turbulence
• DNS has revealed the complex interactions between turbulence and dispersed phases, such as particle clustering and preferential concentration
• Detailed information on turbulence modulation by particles, droplet breakup, and coalescence has been obtained through DNS
• DNS data serves as a benchmark for validating and improving lower-fidelity models, such as RANS and LES

Turbulence modulation by particles

Particle-laden turbulent flows

• Particle-laden turbulent flows are characterized by the presence of dispersed particles in a turbulent carrier fluid
• Particles can be solid particles, droplets, or bubbles, depending on the specific application (gas-solid flows, liquid-liquid dispersions, bubbly flows)
• The presence of particles modifies the turbulence structure and dynamics, leading to turbulence modulation

Turbulence modification mechanisms

• Particles can modify turbulence through various mechanisms, including turbulence attenuation, augmentation, and redistribution
• Turbulence attenuation occurs when particles extract energy from the turbulent fluctuations, reducing the turbulence intensity
• Turbulence augmentation happens when particles enhance the production of turbulence kinetic energy through wake shedding or vortex shedding
• Particles can also redistribute turbulence energy across different length scales through particle-induced velocity fluctuations

Effects of particle size, shape, and concentration

• The extent and nature of turbulence modulation depend on particle properties, such as size, shape, and concentration
• Particle size relative to the turbulence length scales (Kolmogorov scale, integral scale) determines the dominant modulation mechanism
• Non-spherical particles can introduce additional complexity due to their orientation dynamics and anisotropic drag
• Particle concentration plays a crucial role, with higher concentrations leading to stronger modulation effects and potential inter-particle interactions

Turbulent mixing and dispersion

Scalar transport in multiphase turbulence

• Turbulent mixing of scalar quantities, such as temperature, species concentration, or chemical composition, is influenced by the presence of multiple phases
• Dispersed phases can enhance or inhibit scalar mixing depending on their properties and interactions with the turbulent flow
• Scalar transport equations need to account for the exchange of scalar quantities between phases and the modified turbulent diffusivity

Particle dispersion models

• Particle dispersion models aim to predict the spatial distribution of particles in turbulent multiphase flows
• Lagrangian particle tracking is a common approach, where individual particles are tracked as they are transported by the turbulent flow
• Eulerian models, such as the two-fluid model or the mixture model, treat the dispersed phase as a continuum and solve transport equations for particle concentration
• Dispersion models need to account for the effects of turbulence on particle motion, such as turbulent dispersion, preferential concentration, and particle-particle interactions

Mixing enhancement strategies

• Turbulent mixing can be enhanced in multiphase systems through various strategies
• Increasing the turbulence intensity, for example, by introducing flow obstructions or using active mixing devices, can promote mixing
• Optimizing the particle size distribution and concentration can lead to improved mixing performance
• Exploiting the interactions between phases, such as using particles to break up fluid interfaces or induce secondary flows, can enhance mixing

Turbulence-induced particle collisions

Collision frequency and outcomes

• Turbulence plays a significant role in inducing particle collisions in multiphase flows
• The collision frequency depends on factors such as particle size, concentration, and turbulence intensity
• Collision outcomes can include particle coalescence (merging of particles), bouncing (particles rebound after collision), or fragmentation (breakup of particles)
• The outcome of a collision is determined by the particle properties, impact velocity, and surface forces

Effects on particle size distribution

• Particle collisions can lead to changes in the particle size distribution over time
• Coalescence events result in the formation of larger particles, shifting the size distribution towards larger sizes
• Fragmentation events break up particles into smaller ones, increasing the number of small particles in the distribution
• The interplay between coalescence and fragmentation determines the evolution of the particle size distribution in turbulent multiphase flows

Modeling approaches for collisions

• Modeling particle collisions in turbulent flows requires capturing the collision frequency and the post-collision outcomes
• Kinetic theory-based models, such as the granular temperature model, treat particles as a granular medium and solve transport equations for the particle velocity fluctuations
• Direct simulation Monte Carlo (DSMC) methods track individual particle trajectories and model collisions based on probabilistic rules
• Eulerian-Lagrangian models couple Eulerian fluid equations with Lagrangian particle tracking, incorporating collision models based on local particle properties and turbulence characteristics

Validation and benchmarking

Experimental techniques for multiphase turbulence

• Experimental techniques play a crucial role in validating and benchmarking multiphase turbulence models
• Particle image velocimetry (PIV) and laser Doppler anemometry (LDA) provide non-intrusive measurements of fluid and particle velocities
• Phase Doppler anemometry (PDA) allows simultaneous measurement of particle size and velocity
• Tomographic techniques, such as X-ray computed tomography (CT) or electrical capacitance tomography (ECT), enable visualization of phase distributions and interfaces

Numerical benchmarks and test cases

• Numerical benchmarks and test cases serve as reference solutions for validating multiphase turbulence models
• Benchmark cases include canonical flows, such as particle-laden channel flows, jet flows, or bubble columns
• Experimental data from well-characterized systems can be used as validation targets for numerical models
• Collaborative efforts, such as the International Workshop on Multiphase Flow (IWMF), provide standardized test cases and promote model comparison and improvement

Best practices for model validation

• Model validation should follow best practices to ensure the reliability and credibility of the results
• Validation should be performed against high-quality experimental data or well-established numerical benchmarks
• Uncertainty quantification techniques should be employed to assess the sensitivity of the model predictions to input parameters and numerical settings
• Validation metrics, such as mean velocity profiles, turbulence statistics, or phase distribution characteristics, should be carefully selected based on the flow system and the quantities of interest
• Iterative validation and model refinement should be carried out to improve the predictive capabilities of multiphase turbulence models