5.2 Turbulence-Chemistry Interaction Models
3 min read•august 9, 2024
Turbulence-chemistry interaction models are crucial for understanding combustion in real-world systems. These models bridge the gap between simplified assumptions and complex realities, helping engineers predict flame behavior and pollutant formation in turbulent environments.
From basic eddy dissipation to advanced , each model offers unique insights. By balancing accuracy and computational cost, these approaches enable better design of combustion systems and more efficient, cleaner burning processes.
Turbulence-Chemistry Interaction Models
Eddy Dissipation and Break-Up Models
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- assumes turbulent mixing controls reaction rates in fast chemistry
- determined by mixing of reactants and hot products
- Model calculates local based on turbulence properties (k and ε)
- similar to eddy dissipation but uses different constants
- Both models suitable for premixed and non-premixed turbulent flames
- Limitations include inability to predict intermediate species or account for finite-rate chemistry effects
Finite-Rate Chemistry Approach
- Incorporates detailed chemical kinetics into turbulent combustion simulations
- Solves for individual species concentrations
- Reaction rates calculated using
- Accounts for temperature dependence of reaction rates
- Capable of predicting formation of intermediate species and pollutants (, )
- Computationally expensive due to large number of species and reactions
- Often combined with turbulence models through various closure methods
Turbulence-Chemistry Closure Techniques
- Address interaction between turbulent fluctuations and chemical reactions
- extends eddy dissipation model to include finite-rate chemistry
- Assumes reactions occur in small turbulent structures called
- treat turbulent flame as ensemble of laminar flamelets
- methods account for turbulent fluctuations in composition and temperature
- provide closure for both turbulence and chemistry
- Each closure technique has strengths and limitations depending on combustion regime and application
Advanced Turbulence-Chemistry Models
Partially Stirred Reactor Approach
- model bridges gap between perfectly stirred reactor and plug flow reactor
- Divides computational cell into reacting and non-reacting zones
- Incorporates finite-rate chemistry and mixing effects
- Mixing time scale determined from turbulence properties
- calculated from reaction rates
- Model suitable for both premixed and non-premixed combustion
- Provides good balance between accuracy and computational cost
Flame Speed and Conditional Moment Closure
- models propagation of premixed turbulent flames
- Based on correlations between turbulent and laminar flame speeds
- Accounts for effects of turbulence intensity and flame stretch
- separates reactive scalars into conditional means and fluctuations
- Conditioning typically done on for
- CMC equations solved for conditional means of species mass fractions and temperature
- Provides accurate predictions of minor species and pollutants in turbulent flames
- Computational cost higher than simple models but lower than full PDF methods
Transported PDF Methods
- Transport probability density function (PDF) methods most comprehensive approach to turbulence-chemistry interaction
- Solve transport equation for joint PDF of velocity, composition, and enthalpy
- Directly account for effects of turbulent fluctuations on chemical reactions
- No need for additional turbulence-chemistry closure models
- Can handle both premixed and non-premixed combustion
- Accurate predictions of turbulence-chemistry interactions, including extinction and reignition
- often used to solve high-dimensional PDF transport equation
- Computationally intensive, limiting application to complex geometries or large-scale simulations
- Hybrid approaches (e.g., transported composition PDF) reduce computational cost while maintaining accuracy
Key Terms to Review (24)
Arrhenius Expressions: Arrhenius expressions describe the temperature dependence of reaction rates in chemical kinetics, representing how the rate of a reaction increases with temperature. They provide a mathematical formula that incorporates the activation energy, allowing for better understanding and modeling of combustion processes in various systems, particularly under turbulent conditions.
Chemical time scale: The chemical time scale refers to the characteristic time frame over which chemical reactions occur in a combustion process. This time scale is crucial for understanding how quickly reactants convert into products and how this relates to turbulence within a flame or reactive flow. Recognizing the chemical time scale helps in modeling combustion processes, particularly in scenarios where turbulence affects the rate of chemical reactions.
CO: CO, or carbon monoxide, is a colorless, odorless gas that is produced during the incomplete combustion of carbon-containing fuels. It is significant in various combustion processes as it indicates the efficiency of fuel usage and the formation of pollutants. Understanding CO formation mechanisms and its interactions with turbulence and chemistry is crucial for developing cleaner combustion technologies.
Conditional Moment Closure (CMC): Conditional Moment Closure (CMC) is a modeling approach used in turbulent combustion to relate the unclosed moments of the species probability density function (PDF) to known conditional averages. It effectively connects the turbulent flow characteristics and the chemistry of combustion, allowing for a more accurate representation of the interaction between turbulence and chemical reactions, which is crucial for predicting combustion behavior in various applications.
Eddy break-up model: The eddy break-up model is a turbulence-chemistry interaction model used to simulate the effects of turbulence on chemical reactions in combustion systems. This model focuses on the idea that turbulent eddies break up into smaller scales, which enhances mixing and reaction rates within a flame, allowing for more accurate predictions of combustion behavior. By understanding how turbulence interacts with chemical kinetics, this model helps to improve the design and efficiency of combustion systems.
Eddy Dissipation Concept (EDC): The Eddy Dissipation Concept (EDC) is a modeling approach used to describe the interaction between turbulence and chemical reactions in combustion systems. It simplifies the complex processes of turbulence-chemistry interactions by assuming that the rate of reaction is limited by the turbulent mixing and that the chemical reactions occur within the eddies formed in a turbulent flow. This concept is crucial for understanding how turbulence affects combustion efficiency and pollutant formation.
Eddy Dissipation Model: The eddy dissipation model (EDM) is a theoretical framework used to describe the interaction between turbulence and chemical reactions in a flow field. It assumes that the rate of reaction is limited by the turbulent mixing process, leading to a simplified representation of combustion phenomena. This model is particularly useful in computational simulations where capturing fine-scale turbulence-chemistry interactions can be challenging, allowing for efficient modeling of reacting flows in engineering applications.
Fine scales: Fine scales refer to the small, intricate details or structures present in turbulent flows, particularly those that influence chemical reactions and mixing processes. Understanding fine scales is crucial because they can significantly affect how turbulence interacts with chemical species, ultimately impacting combustion efficiency and emissions.
Finite-rate chemistry approach: The finite-rate chemistry approach is a modeling technique used to describe chemical reactions in combustion processes where the rates of reaction are not instantaneous. This approach accounts for the fact that reactants do not convert to products instantaneously, and it emphasizes the importance of reaction kinetics, particularly in the presence of turbulence. By incorporating finite-rate effects, this method provides a more accurate representation of how turbulent flows interact with chemical processes in combustion systems.
Flamelet models: Flamelet models are mathematical representations used to describe the structure of turbulent combustion processes by assuming that the combustion can be represented as a series of thin, infinitely fast burning regions called flamelets. These models simplify the complex interactions between turbulence and chemistry, allowing for more efficient simulations of reacting flows in various combustion systems.
Joint velocity-scalar pdf methods: Joint velocity-scalar probability density function (pdf) methods are computational techniques used to model the interaction between turbulence and chemical reactions by representing the joint distribution of turbulent flow velocities and scalar quantities, such as temperature or species concentration. This approach allows for a detailed analysis of how these scalars are affected by turbulence, enhancing the understanding of combustion processes and improving predictions in turbulent reacting flows.
Mixing time: Mixing time refers to the duration required for a fuel and oxidizer to thoroughly mix at the molecular level in a combustion process. This concept is essential in understanding how turbulence affects chemical reactions, as effective mixing can significantly influence the efficiency and completeness of combustion. The interplay between turbulence and mixing time is crucial for optimizing combustion systems, enhancing performance, and reducing emissions.
Mixture fraction: The mixture fraction is a dimensionless quantity that represents the mass fraction of one component in a mixture relative to the total mass of the mixture. It is essential for describing the composition of fuel-air mixtures in combustion processes and is particularly important in modeling combustion behavior under varying conditions. The mixture fraction helps to simplify the analysis of combustion reactions by allowing for the interaction between turbulence and chemical processes to be more effectively represented.
Monte Carlo Methods: Monte Carlo methods are statistical techniques used to estimate numerical results through random sampling and probabilistic simulations. These methods are widely employed in various fields to solve problems that may be deterministic in nature but are complex enough to make analytical solutions impractical, especially when analyzing interactions between turbulence and chemical reactions.
Non-premixed flames: Non-premixed flames occur when the fuel and oxidizer are introduced separately into the combustion zone, leading to a mixing process before ignition. This type of flame is characterized by the formation of a diffusion flame where the combustion products are formed in the reaction zone, resulting in unique temperature and species distributions compared to premixed flames.
NOx: NOx refers to a group of nitrogen oxides, primarily nitrogen dioxide (NO2) and nitric oxide (NO), which are significant pollutants formed during combustion processes. These gases play a crucial role in the formation of ground-level ozone and contribute to smog, acid rain, and respiratory problems, making their understanding essential in combustion technologies and pollution control strategies.
Partially stirred reactor (pasr): A partially stirred reactor (pasr) is a type of chemical reactor that features both well-stirred and non-stirred zones, allowing for varying degrees of mixing within the reactor. This configuration can significantly affect the reaction rates and product distributions, as it combines elements of complete mixing with areas that maintain concentration gradients, creating a more complex interaction between turbulence and chemistry.
Premixed flames: Premixed flames occur when the fuel and oxidizer are mixed together prior to ignition, creating a homogeneous mixture that ignites uniformly. This type of flame is characterized by its stability and well-defined structure, making it crucial for various combustion processes, especially in industrial applications where precise control of combustion conditions is necessary.
Probability Density Function (pdf): A probability density function (pdf) is a statistical function that describes the likelihood of a continuous random variable taking on a particular value. The pdf indicates the relative likelihood of various outcomes, allowing for the calculation of probabilities over intervals rather than specific values. This concept is particularly important in analyzing the interactions between turbulence and chemical reactions, as it helps model the distribution of reactants and products in fluctuating flow conditions.
Reaction progress: Reaction progress refers to the measure of how far a chemical reaction has proceeded at any given time, often expressed in terms of conversion or extent of reaction. This concept helps in understanding the dynamics of a chemical process, including how different variables such as temperature, pressure, and turbulence can affect reaction rates and outcomes.
Transport equations: Transport equations are mathematical formulations that describe the movement and interaction of physical quantities, such as mass, momentum, and energy, within a fluid system. These equations are essential for modeling complex processes, particularly in turbulent flow scenarios where the interaction between turbulence and chemical reactions must be considered for accurate predictions.
Transported pdf methods: Transported probability density function (pdf) methods are computational techniques used to model the interaction between turbulence and chemical reactions in fluid dynamics. These methods track the evolution of a probability density function for species concentrations within turbulent flows, allowing for a more accurate representation of how turbulence affects chemical processes, especially in combustion systems. By transporting the pdfs through the flow field, these methods can capture the stochastic nature of turbulence and its impact on reaction rates and product formation.
Turbulence-chemistry closure techniques: Turbulence-chemistry closure techniques are methods used in computational fluid dynamics to model the interaction between turbulent flow and chemical reactions. These techniques aim to bridge the gap between the large-scale turbulent motion and the small-scale chemical processes, ensuring accurate predictions of reaction rates and species concentrations in complex flow scenarios. By properly capturing these interactions, these techniques enhance the understanding and prediction of combustion behavior in various applications.
Turbulent flame speed closure: Turbulent flame speed closure refers to a modeling approach that accounts for the interaction between turbulence and combustion in turbulent flames. This concept is crucial for accurately predicting the behavior of flames in turbulent flow, as it integrates both the effects of turbulence on flame propagation and the influence of chemical reactions on turbulence characteristics. It allows for improved understanding and simulation of combustion processes in various engineering applications.