3.3 Turbulence Fundamentals and Its Effects on Combustion
4 min read•august 9, 2024
Turbulence is a game-changer in combustion. It mixes fuel and air better, speeds up reactions, and shapes flames in wild ways. Understanding turbulence is key to designing efficient engines and burners.
Turbulence affects everything from flame speed to pollutant formation. We'll look at how to measure and model turbulence, and how it interacts with chemical reactions. This knowledge is crucial for optimizing combustion systems.
Turbulence Characteristics
Reynolds Number and Turbulent Kinetic Energy
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- quantifies the ratio of inertial forces to viscous forces in a fluid flow
- Calculated using the equation where ρ is fluid density, u is velocity, L is characteristic length, and μ is dynamic viscosity
- Higher Reynolds numbers indicate , while lower values suggest laminar flow
- Transition from laminar to turbulent flow typically occurs around Re = 2300 for pipe flows
- represents the mean kinetic energy per unit mass associated with eddies in turbulent flow
- Expressed as where u', v', and w' are velocity fluctuations in x, y, and z directions
- Higher turbulent kinetic energy indicates more intense turbulence and greater mixing
Dissipation Rate and Eddy Viscosity
- measures the rate at which turbulent kinetic energy converts into thermal energy through viscous effects
- Denoted by ε and has units of energy per unit mass per unit time (m²/s³)
- , also known as turbulent viscosity, describes the enhanced mixing and momentum transfer in turbulent flows
- Represented by μt and has the same units as dynamic viscosity (kg/m·s)
- Eddy viscosity relates to turbulent kinetic energy and dissipation rate through the equation where Cμ is a dimensionless constant
- Higher eddy viscosity leads to increased mixing and heat transfer in turbulent flows
Kolmogorov Scales and Turbulence Intensity
- represent the smallest scales in turbulent flow where viscous effects dominate
- Consist of length scale (η), time scale (τ), and velocity scale (v)
- Length scale calculated as where ν is kinematic viscosity
- Time scale determined by
- Velocity scale computed using
- quantifies the level of turbulence in a flow
- Calculated as the ratio of the root-mean-square of velocity fluctuations to the mean flow velocity
- Expressed as a percentage, with higher values indicating more intense turbulence
- Typical turbulence intensity values range from 1% (low turbulence) to 20% (high turbulence)
Turbulence Modeling
RANS Models for Turbulence Simulation
- Reynolds-Averaged Navier-Stokes (RANS) models provide time-averaged solutions to the Navier-Stokes equations
- Widely used in engineering applications due to their computational efficiency
- k-ε model solves transport equations for turbulent kinetic energy (k) and dissipation rate (ε)
- k-ω model focuses on turbulent kinetic energy (k) and specific dissipation rate (ω)
- uses a single transport equation for turbulent viscosity
- (RSM) solves transport equations for individual Reynolds stresses
- struggle with accurately predicting complex flows with large-scale unsteadiness
Large Eddy Simulation (LES) for Detailed Turbulence Analysis
- LES resolves large-scale turbulent motions while modeling smaller scales
- Utilizes spatial filtering to separate large and small scales
- Subgrid-scale (SGS) models account for the effects of unresolved small-scale turbulence
- serves as a common SGS model, relating subgrid-scale stresses to resolved strain rate
- adapts the model coefficient based on local flow conditions
- Wall-Adapting Local Eddy-viscosity (WALE) model improves near-wall behavior
- LES provides more detailed turbulence information than RANS but requires greater computational resources
- Hybrid RANS-LES approaches, such as Detached Eddy Simulation (DES), combine RANS near walls with LES in the free stream
Turbulence-Combustion Interaction
Turbulent Flame Speed and Chemistry Interaction
- represents the propagation rate of a flame front in turbulent flow
- Exceeds laminar flame speed due to increased surface area and enhanced mixing
- (Da) compares chemical reaction time to turbulent mixing time
- High Da indicates fast chemistry relative to turbulent mixing, while low Da suggests slow chemistry
- Turbulence-chemistry interaction affects reaction rates, species concentrations, and heat release
- Eddy Break-Up (EBU) model assumes that reaction rate depends on turbulent mixing rate
- Eddy Dissipation Concept (EDC) model accounts for both mixing and finite-rate chemistry effects
- treat turbulent flames as an ensemble of laminar flamelets embedded in turbulent flow
Flame Stretch and Turbulent Combustion Regimes
- describes the deformation of flame surface due to flow non-uniformities
- (Ka) compares flame thickness to smallest turbulent length scales
- Flame stretch can lead to local extinction or re-ignition of the flame
- classify flame-turbulence interactions based on relative time and length scales
- maps turbulent combustion regimes using non-dimensional numbers (Re, Da, Ka)
- occurs when turbulence intensity is low compared to laminar flame speed
- features stronger turbulence that distorts the flame front
- allows turbulent eddies to penetrate the preheat zone of the flame
- involves intense turbulence that can disrupt the flame structure
- Understanding turbulent combustion regimes helps in selecting appropriate modeling approaches for different combustion systems
Key Terms to Review (30)
Borghi Diagram: The Borghi Diagram is a graphical representation used to illustrate the relationship between fuel composition, combustion efficiency, and emissions in combustion systems. This diagram helps in understanding how varying the fuel characteristics can affect the combustion process, including turbulence levels, which are crucial for efficient burning and reduced pollutant formation.
Broken reaction zone regime: The broken reaction zone regime refers to a combustion behavior where the reaction zones within a flame become disrupted or fragmented, leading to complex interactions and changes in the combustion characteristics. This phenomenon often occurs in turbulent combustion scenarios, where the mixing of fuel and oxidizer is influenced by fluctuations in velocity and pressure, causing deviations from normal flame propagation and stability.
Corrugated flamelet regime: The corrugated flamelet regime is a combustion regime characterized by the presence of wrinkled or corrugated flame fronts due to turbulence. This phenomenon occurs when the turbulence level is sufficiently high to enhance the mixing of reactants and products, leading to complex interactions between the flame and the flow. Understanding this regime is essential because it influences flame stability, combustion efficiency, and pollutant formation.
Damköhler Number: The Damköhler number (Da) is a dimensionless number that compares the rate of chemical reaction to the rate of mass transport in a system. It is essential for understanding how turbulence affects combustion, as it helps identify whether a reaction is limited by the speed of the chemical process or by the mixing of reactants. A high Damköhler number indicates that reaction rates dominate, while a low Damköhler number suggests that mass transport plays a more significant role.
Dissipation rate: Dissipation rate refers to the rate at which turbulent kinetic energy is converted into internal energy through viscous forces in a fluid. This concept is crucial because it helps quantify how turbulence affects flow and combustion processes by determining how energy from large scales of motion is lost to smaller scales. Understanding dissipation rate is essential for predicting the behavior of turbulence and its impact on combustion efficiency and emissions.
Dynamic smagorinsky model: The dynamic smagorinsky model is a mathematical approach used in computational fluid dynamics to simulate turbulence effects in fluid flows, particularly in the context of combustion. This model adjusts the turbulence viscosity based on local flow conditions, which enhances accuracy in predicting turbulent behaviors, making it essential for understanding how turbulence influences combustion processes.
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 model: The eddy dissipation concept model is a mathematical framework used to describe the interaction between turbulence and chemical reactions in combustion processes. It focuses on the energy dissipation due to turbulent eddies and how this energy affects the rate of reaction in a flame, providing a simplified yet effective approach for modeling turbulent combustion systems. This model is particularly useful in understanding how turbulence enhances mixing, leading to more efficient combustion.
Eddy Viscosity: Eddy viscosity is a concept used in fluid dynamics that describes the turbulent transport of momentum within a fluid. It serves as an effective viscosity in turbulent flows, allowing for the modeling of the diffusion of momentum due to eddies or chaotic fluid motion. This concept is crucial for understanding how turbulence influences combustion processes, particularly in enhancing mixing and reaction rates.
Flame stretch: Flame stretch refers to the elongation or distortion of a flame due to the influence of local flow velocities and turbulence. This phenomenon affects how flames propagate, interact with surrounding flow fields, and can significantly impact combustion characteristics, especially in turbulent environments where fluctuations in velocity can stretch or compress the flame front.
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.
K-epsilon model: The k-epsilon model is a widely used mathematical model for simulating turbulence in fluid dynamics, particularly in combustion processes. It relies on two transport equations: one for the turbulent kinetic energy (k) and another for the turbulent dissipation rate (epsilon), which describe how turbulence behaves and evolves over time. This model helps in understanding the effects of turbulence on combustion efficiency, pollutant formation, and flame stability.
K-omega model: The k-omega model is a widely used turbulence model in computational fluid dynamics that helps predict the behavior of turbulent flows. It uses two transport equations: one for the turbulent kinetic energy (k) and another for the specific dissipation rate (omega, \(\omega\)). This model is particularly effective in flows where the effects of near-wall regions are significant, making it valuable for analyzing combustion processes influenced by turbulence.
Karlovitz Number: The Karlovitz Number (Ka) is a dimensionless quantity that characterizes the ratio of turbulent time scales to chemical reaction time scales in a combustion system. It provides insights into the relative importance of turbulence and chemistry, influencing how fuel and oxidizer mix and react during combustion processes. Understanding the Karlovitz Number helps predict the behavior of flames and the efficiency of combustion systems.
Kolmogorov Scales: Kolmogorov scales refer to the smallest scales of turbulence in a fluid flow, defined by the dissipation of kinetic energy and characterized by the size of the eddies formed. These scales are crucial in understanding turbulence because they provide insight into how energy is transferred and dissipated at microscopic levels, which directly affects mixing processes and combustion efficiency in turbulent flows.
Large Eddy Simulation: Large Eddy Simulation (LES) is a computational fluid dynamics technique used to model turbulent flows by resolving the larger turbulent structures while modeling the smaller scales. This approach allows for a more accurate representation of turbulence and its effects on combustion processes, which are critical for optimizing performance and reducing emissions in combustion systems. By focusing on the significant turbulent eddies, LES provides insights into the complex interactions between turbulence and combustion phenomena.
RANS Models: RANS models, or Reynolds-Averaged Navier-Stokes models, are mathematical tools used to analyze turbulent flows by averaging the effects of turbulence over time. These models simplify the complex behavior of turbulence into manageable equations, making them essential for predicting the performance of combustion systems under turbulent conditions. RANS models provide insights into how turbulence influences mixing, reaction rates, and overall combustion efficiency.
Reynolds Number: Reynolds number is a dimensionless quantity used to predict flow patterns in fluid dynamics. It provides insight into whether a flow is laminar or turbulent, which is critical in understanding how these flow regimes affect various phenomena, including combustion processes, heat transfer, and fluid behavior in boundary layers.
Reynolds Stress Model: The Reynolds Stress Model (RSM) is a mathematical approach used to predict turbulent flows by accounting for the effects of turbulence on the mean flow properties. This model describes the transfer of momentum due to turbulent fluctuations, emphasizing how these fluctuations impact the overall behavior of a fluid during combustion processes. Understanding the Reynolds stress is essential in analyzing how turbulence influences mixing, reaction rates, and energy transfer in combustion systems.
Smagorinsky Model: The Smagorinsky Model is a widely used turbulence modeling approach in computational fluid dynamics, particularly for large eddy simulations (LES). It provides a way to parameterize the effects of subgrid-scale turbulence, allowing for the simulation of turbulent flows by incorporating a turbulent viscosity that is dependent on the local strain rate and grid size. This model connects the concepts of turbulence, scale interaction, and energy dissipation in fluid flows, making it crucial for understanding how turbulence affects combustion processes.
Spalart-Allmaras Model: The Spalart-Allmaras model is a one-equation turbulence model primarily used for predicting turbulent flows in various engineering applications, especially in aerodynamics and combustion. It simplifies the complexity of turbulence by providing an efficient means to analyze the transport of a single turbulence quantity, which is the turbulent viscosity. This model is particularly beneficial for its computational efficiency, making it a popular choice in simulations involving turbulent combustion and complex flow geometries.
Subgrid-scale models: Subgrid-scale models are mathematical frameworks used to represent the effects of small-scale turbulence that cannot be directly resolved in computational simulations of fluid flow and combustion processes. These models aim to bridge the gap between the fine details of turbulent flows and the larger scales that are typically modeled in simulations, ensuring that essential physical phenomena are captured without requiring excessive computational resources.
Thin reaction zone regime: The thin reaction zone regime refers to a combustion condition where the reaction zone, where fuel and oxidizer interact, is narrow compared to the dimensions of the system. This regime is characterized by high reaction rates and is influenced heavily by turbulence, which enhances mixing and can significantly impact the stability and efficiency of combustion processes.
Turbulence intensity: Turbulence intensity is a measure of the fluctuation of velocity in a turbulent flow compared to the mean flow velocity, often expressed as a percentage. This concept is crucial because it directly impacts the mixing and combustion processes in various applications, highlighting the role of turbulence in enhancing reaction rates and influencing flame stability.
Turbulent combustion regimes: Turbulent combustion regimes refer to the behavior and characteristics of combustion processes that occur in a turbulent flow environment. This type of combustion is significantly influenced by the chaotic and irregular nature of turbulence, which affects the mixing of fuel and oxidizer, the rate of reaction, and the overall efficiency of the combustion process. Understanding these regimes is essential for optimizing combustion systems and improving energy efficiency while reducing emissions.
Turbulent flame speed: Turbulent flame speed refers to the rate at which a flame propagates through a turbulent flow of fuel and oxidizer, influenced by the mixing characteristics of the flow. This speed is significantly greater than that of a laminar flame due to the chaotic motion and enhanced mixing caused by turbulence, leading to more efficient combustion and higher energy release. Understanding turbulent flame speed is crucial for optimizing combustion processes in various applications.
Turbulent flow: Turbulent flow is a fluid motion characterized by chaotic changes in pressure and flow velocity. In this type of flow, the fluid experiences irregular fluctuations and mixing, which significantly impacts combustion processes. Understanding turbulent flow is crucial for optimizing combustion efficiency, reducing emissions, and enhancing overall performance in various combustion systems.
Turbulent kinetic energy: Turbulent kinetic energy is a measure of the energy contained in the chaotic, irregular motion of fluid particles within a turbulent flow. This energy is significant because it affects mixing, combustion rates, and overall reaction efficiency in processes involving turbulent flows, particularly in combustion systems where fuel and oxidizer need to mix effectively for efficient burning.
Wall-adapting local eddy-viscosity model: The wall-adapting local eddy-viscosity model is a turbulence modeling approach that adjusts the turbulent viscosity based on the proximity to walls in a fluid flow. This model enhances the accuracy of predicting flow characteristics near surfaces, which is essential for understanding how turbulence influences combustion processes. By adapting to the varying conditions near walls, this model effectively captures the effects of boundary layers and provides better insights into turbulent mixing and reaction dynamics.
Wrinkled flamelet regime: The wrinkled flamelet regime is a combustion model that describes the interaction between turbulent flow and the flame structure, where the flame front becomes distorted and wrinkled due to turbulence. This regime represents a transition where the thin reaction zones of the flamelets respond to changes in turbulence intensity, leading to enhanced mixing and altered combustion characteristics compared to laminar or fully turbulent regimes.