🔥Advanced Combustion Technologies Unit 5 – Turbulent Combustion Modeling Methods

Fundamentals of Turbulent Combustion

• Turbulent combustion involves the interaction between turbulent fluid flow and chemical reactions, leading to complex and chaotic behavior
• Characterized by high Reynolds numbers, indicating the dominance of inertial forces over viscous forces, resulting in increased mixing and heat transfer
• Involves a wide range of length and time scales, from the smallest Kolmogorov scales to the largest integral scales, making it challenging to model and simulate
• Turbulent flow enhances mixing of reactants and products, leading to increased flame surface area and faster combustion rates compared to laminar flow
• Involves the coupling between fluid dynamics, chemical kinetics, and heat transfer, requiring a multidisciplinary approach to understand and model the phenomena
• Plays a crucial role in various practical applications, such as internal combustion engines, gas turbines, and industrial furnaces, where efficient mixing and combustion are essential
• Presents challenges in experimental measurements and numerical simulations due to the high-speed, unsteady, and three-dimensional nature of turbulent flows

Key Concepts in Turbulence Modeling

• Turbulence modeling aims to develop mathematical models that capture the essential features of turbulent flows without resolving all the details of the turbulent fluctuations
• Reynolds-Averaged Navier-Stokes (RANS) equations are widely used in turbulence modeling, where the flow variables are decomposed into mean and fluctuating components
  • RANS equations introduce additional unknown terms, such as the Reynolds stress tensor, which require closure models to solve the equations
• Turbulence models, such as the $k-\epsilon$ model and the $k-\omega$ model, provide closure for the RANS equations by modeling the turbulent kinetic energy ($k$) and its dissipation rate ($\epsilon$) or specific dissipation rate ($\omega$)
• Large Eddy Simulation (LES) is another approach to turbulence modeling, where the large-scale turbulent motions are directly resolved, while the effects of the small-scale motions are modeled using subgrid-scale (SGS) models
• Direct Numerical Simulation (DNS) resolves all the scales of turbulent motion without any modeling assumptions, but it is computationally expensive and limited to low Reynolds number flows
• Turbulent mixing plays a crucial role in combustion processes, as it influences the local mixture composition, temperature, and reaction rates
• Turbulence-chemistry interaction models are required to accurately capture the effects of turbulent fluctuations on the chemical reactions and heat release in combustion simulations

Overview of Combustion Modeling Approaches

• Combustion modeling involves the mathematical description of the complex physical and chemical processes occurring during combustion
• Chemical kinetics is a fundamental aspect of combustion modeling, describing the rates of chemical reactions and the formation and consumption of species
  • Detailed chemical kinetic mechanisms can involve hundreds or thousands of species and reactions, making them computationally expensive
• Reduced and skeletal mechanisms are often employed to simplify the chemical kinetics while retaining the essential features of the combustion process
• Flamelet models assume that the turbulent flame can be represented as an ensemble of laminar flame structures (flamelets) embedded in the turbulent flow field
  • Flamelet models, such as the Steady Laminar Flamelet Model (SLFM) and the Flamelet Progress Variable (FPV) approach, provide a computationally efficient way to model turbulent combustion
• Probability Density Function (PDF) methods describe the turbulent reacting flow in terms of a joint PDF of the flow variables and species concentrations
  • PDF methods can handle the non-linear coupling between turbulence and chemistry, but they require closure models for the chemical source terms
• Conditional Moment Closure (CMC) is a method that solves transport equations for the conditional averages of the reactive scalars, conditioned on a conserved scalar such as mixture fraction
• Eddy Dissipation Concept (EDC) models assume that the chemical reactions occur in fine structures of the turbulent flow, where the timescales of turbulence and chemistry are comparable

RANS-Based Turbulent Combustion Models

• RANS-based turbulent combustion models combine the RANS equations for the turbulent flow with combustion models to describe the mean chemical reactions and heat release
• Eddy Dissipation Model (EDM) assumes that the chemical reactions are fast compared to the turbulent mixing, and the reaction rate is controlled by the turbulent mixing time scale
  • EDM is computationally efficient but lacks the ability to capture the detailed chemistry and extinction phenomena
• Eddy Break-Up (EBU) model is similar to EDM but uses a different expression for the reaction rate based on the turbulent kinetic energy and its dissipation rate
• Presumed PDF models assume a functional form for the joint PDF of the reactive scalars, such as the beta PDF for the mixture fraction and the delta PDF for the progress variable
  • The mean chemical source terms are then closed by integrating the chemical source terms over the presumed PDF
• Flamelet Generated Manifold (FGM) method pre-computes the chemical reactions and species concentrations in laminar flamelet structures and tabulates them as a function of a few controlling variables, such as mixture fraction and progress variable
  • During the CFD simulation, the mean chemical source terms are retrieved from the pre-generated FGM table, reducing the computational cost
• Transported PDF methods solve transport equations for the joint PDF of the reactive scalars, providing a more accurate description of the turbulence-chemistry interaction
  • The chemical source terms appear in closed form in the PDF transport equations, but the molecular mixing terms require closure models

LES and DNS Methods for Combustion

• Large Eddy Simulation (LES) resolves the large-scale turbulent motions and models the effects of the small-scale motions on the combustion process
  • LES provides a more accurate representation of the turbulent flow compared to RANS, capturing the unsteady and three-dimensional nature of turbulent combustion
• Subgrid-scale (SGS) combustion models are required in LES to account for the effects of the unresolved small-scale turbulent fluctuations on the chemical reactions
  • SGS models, such as the Artificially Thickened Flame (ATF) model and the Partially Stirred Reactor (PaSR) model, aim to capture the subgrid-scale turbulence-chemistry interaction
• Direct Numerical Simulation (DNS) resolves all the scales of turbulent motion and the chemical reactions without any modeling assumptions
  • DNS provides the most accurate description of turbulent combustion but is computationally expensive and limited to simple geometries and low Reynolds number flows
• DNS can be used to generate high-fidelity data for the development and validation of turbulent combustion models for LES and RANS simulations
• LES and DNS of turbulent combustion require high-resolution computational grids and advanced numerical methods, such as high-order finite difference or spectral methods, to capture the wide range of scales involved
• Combustion LES and DNS simulations can provide valuable insights into the fundamental processes of turbulent combustion, such as flame-turbulence interaction, ignition, and extinction phenomena

Chemistry-Turbulence Interactions

• Chemistry-turbulence interactions play a crucial role in turbulent combustion, as the turbulent fluctuations affect the local mixture composition, temperature, and reaction rates
• Turbulent mixing can enhance the chemical reactions by increasing the surface area of the flame and promoting the mixing of reactants and products
  • However, turbulence can also lead to local extinction of the flame if the turbulent strain rate exceeds a critical value
• The Damköhler number ($Da$) is a dimensionless parameter that characterizes the relative importance of turbulent mixing and chemical reactions
  • $Da = \tau_t / \tau_c$, where $\tau_t$ is the turbulent time scale and $\tau_c$ is the chemical time scale
  • For $Da \gg 1$, the chemical reactions are fast compared to the turbulent mixing, and the combustion is mixing-limited
  • For $Da \ll 1$, the turbulent mixing is fast compared to the chemical reactions, and the combustion is chemistry-limited
• The Karlovitz number ($Ka$) is another dimensionless parameter that describes the relative importance of the chemical time scale and the Kolmogorov time scale
  • $Ka = \tau_c / \tau_\eta$, where $\tau_\eta$ is the Kolmogorov time scale
  • For $Ka \ll 1$, the chemical reactions occur at scales much smaller than the Kolmogorov scales, and the flame is considered to be in the flamelet regime
  • For $Ka \gg 1$, the chemical reactions occur at scales comparable to or larger than the Kolmogorov scales, and the flame is considered to be in the distributed reaction regime
• Turbulence-chemistry interaction models, such as the Eddy Dissipation Concept (EDC) and the Partially Stirred Reactor (PaSR) model, aim to capture the effects of turbulent fluctuations on the chemical reactions
• Advanced techniques, such as Conditional Moment Closure (CMC) and transported PDF methods, provide a more accurate description of the chemistry-turbulence interactions by solving transport equations for the conditional averages or joint PDF of the reactive scalars

Practical Applications and Case Studies

• Turbulent combustion modeling is essential for the design and optimization of various practical combustion systems, such as internal combustion engines, gas turbines, and industrial furnaces
• In internal combustion engines, turbulent combustion models are used to predict the fuel-air mixing, ignition, flame propagation, and pollutant formation processes
  • RANS-based models, such as the Eddy Break-Up (EBU) model and the Flamelet Generated Manifold (FGM) method, are commonly used in engine simulations due to their computational efficiency
• Gas turbines rely on turbulent combustion to achieve high power density and efficiency
  • LES and DNS studies of gas turbine combustors provide insights into the complex flow and combustion processes, such as swirl-stabilized flames, lean blowout, and thermoacoustic instabilities
• Industrial furnaces, such as those used in the steel and glass industries, involve turbulent combustion of gaseous or liquid fuels
  • RANS-based models, such as the Eddy Dissipation Model (EDM) and the Presumed PDF approach, are commonly used to simulate the combustion process in industrial furnaces
• Combustion of alternative fuels, such as syngas, biogas, and hydrogen-enriched fuels, presents new challenges for turbulent combustion modeling due to the different chemical kinetics and transport properties compared to conventional fuels
• Multiphase turbulent combustion, involving the presence of liquid fuel droplets or solid fuel particles, adds additional complexity to the modeling process
  • Lagrangian particle tracking methods are often coupled with turbulent combustion models to simulate spray combustion or pulverized coal combustion
• Validation and verification of turbulent combustion models against experimental data are crucial for assessing their accuracy and predictive capabilities
  • Laser diagnostic techniques, such as Particle Image Velocimetry (PIV) and Planar Laser-Induced Fluorescence (PLIF), provide valuable experimental data for model validation

Challenges and Future Directions

• Turbulent combustion modeling faces several challenges due to the complex and multi-scale nature of the problem
• Accurate and efficient chemical kinetic mechanisms are essential for capturing the detailed chemistry in turbulent combustion simulations
  • The development of reduced and skeletal mechanisms that retain the essential features of the combustion process while minimizing the computational cost is an ongoing research area
• Turbulence-chemistry interaction models that can accurately capture the effects of turbulent fluctuations on the chemical reactions across a wide range of combustion regimes (flamelet to distributed reaction) are needed
• The prediction of pollutant formation, such as nitrogen oxides (NOx) and soot, in turbulent combustion systems remains a challenge due to the complex chemical pathways involved
• The extension of turbulent combustion models to high-pressure conditions, such as those encountered in advanced gas turbine and diesel engine combustors, requires the consideration of real-gas effects and pressure-dependent kinetics
• The integration of turbulent combustion models with other physical processes, such as heat transfer, radiation, and multiphase flows, is necessary for the comprehensive modeling of practical combustion systems
• The development of efficient numerical algorithms and high-performance computing techniques is crucial for enabling high-fidelity LES and DNS of turbulent combustion in complex geometries and at realistic operating conditions
• Machine learning and data-driven approaches are emerging as promising tools for turbulent combustion modeling, leveraging the growing availability of experimental and numerical data
  • Data-driven models can be used to develop reduced-order models, optimize combustion system design, and assist in the development and calibration of physics-based models
• The validation and uncertainty quantification of turbulent combustion models using advanced experimental techniques and Bayesian inference methods are essential for assessing their reliability and guiding further model development