🔥Advanced Combustion Technologies Unit 4 – Laminar and Turbulent Flames

Fundamentals of Combustion

• Combustion is a complex chemical reaction involving fuel, oxidizer (typically air), and heat that produces energy in the form of heat and light
• Requires three essential components: fuel, oxidizer, and an ignition source (fire triangle) to initiate and sustain the reaction
• Governed by the principles of thermodynamics, fluid mechanics, and chemical kinetics which influence the rate, efficiency, and emissions of the combustion process
• Involves a series of elementary reactions that form a chain reaction, including initiation, propagation, branching, and termination steps
• Classified into different modes such as premixed combustion (fuel and oxidizer are mixed before ignition) and non-premixed or diffusion combustion (fuel and oxidizer are initially separate)
  • Premixed combustion examples include spark-ignition engines and gas stoves
  • Non-premixed combustion examples include diesel engines and candles
• Combustion efficiency depends on factors such as fuel-air ratio, temperature, pressure, and mixing quality which affect the completeness of the reaction and the formation of pollutants
• Products of complete combustion include carbon dioxide (CO2), water vapor (H2O), and heat, while incomplete combustion can generate carbon monoxide (CO), unburned hydrocarbons (UHC), and particulate matter (PM)

Types of Flames: Laminar vs. Turbulent

• Flames can be classified as either laminar or turbulent based on the flow characteristics of the reactants and the nature of the combustion process
• Laminar flames exhibit smooth, ordered flow with parallel streamlines and minimal mixing between adjacent fluid layers
  • Characterized by low Reynolds numbers (Re < 2300) indicating the dominance of viscous forces over inertial forces
  • Examples include candle flames, Bunsen burner flames, and some industrial burners
• Turbulent flames feature chaotic, fluctuating flow with enhanced mixing and transport of heat and mass due to the presence of eddies and vortices
  • Associated with high Reynolds numbers (Re > 4000) signifying the dominance of inertial forces and the onset of turbulence
  • Most practical combustion systems such as engines, gas turbines, and furnaces involve turbulent flames
• Transition from laminar to turbulent flames occurs at intermediate Reynolds numbers (2300 < Re < 4000) and is influenced by factors such as geometry, flow velocity, and fluid properties
• Turbulent flames exhibit higher burning rates, increased flame surface area, and improved mixing compared to laminar flames, leading to more intense combustion and shorter flame lengths
• Understanding the differences between laminar and turbulent flames is crucial for designing efficient combustion systems and controlling pollutant formation

Laminar Flame Structure and Propagation

• Laminar flames consist of distinct regions: preheat zone, reaction zone, and post-flame zone, each with specific temperature and species concentration profiles
• Preheat zone is where the unburned reactants are heated by thermal conduction and radiation from the reaction zone, initiating chemical reactions
  • Temperature rises from the initial value to the ignition temperature, typically around 1000 K for hydrocarbon fuels
• Reaction zone is a thin region where most of the chemical reactions and heat release occur, characterized by high temperature gradients and radical concentrations
  • Reactions are governed by the Arrhenius equation, $k = A \exp(-E_a/RT)$, relating the reaction rate constant $k$ to the activation energy $E_a$, pre-exponential factor $A$, and temperature $T$
• Post-flame zone is where the combustion products cool down and reach equilibrium, with minimal chemical reactions taking place
• Laminar flame speed $S_L$ is a fundamental property that quantifies the rate at which the flame propagates into the unburned mixture
  • Depends on fuel type, equivalence ratio $\phi$, pressure, and temperature
  • Typically ranges from 20 to 80 cm/s for hydrocarbon-air mixtures at atmospheric conditions
• Laminar flame thickness $\delta_L$ characterizes the distance over which the temperature and species concentrations change from their unburned to burned values
  • Estimated using the thermal diffusivity $\alpha$ and laminar flame speed as $\delta_L \approx \alpha/S_L$, yielding values on the order of 0.1 to 1 mm for most fuels

Turbulent Flame Characteristics

• Turbulent flames are characterized by the interaction between the turbulent flow field and the chemical reactions, leading to a complex and unsteady flame structure
• Turbulence enhances mixing and transport processes, increasing the effective diffusivity and resulting in higher burning rates compared to laminar flames
• Turbulent flame speed $S_T$ is an important parameter that describes the overall propagation rate of the turbulent flame and depends on the laminar flame speed $S_L$ and the turbulence intensity $u'$
  • Correlations such as $S_T/S_L = 1 + C (u'/S_L)^n$ are used to estimate $S_T$, where $C$ and $n$ are empirical constants
• Turbulent flame thickness $\delta_T$ is larger than the laminar flame thickness due to the broadening effect of turbulent eddies and can be several times the laminar value
• Turbulent flames exhibit a range of length scales, from the integral length scale $l_0$ (largest eddies) to the Kolmogorov length scale $\eta$ (smallest eddies), which affect the flame structure and combustion regime
• Damköhler number $Da = \tau_t/\tau_c$ compares the turbulent time scale $\tau_t$ to the chemical time scale $\tau_c$ and determines the relative importance of turbulence and chemistry
  • For $Da \gg 1$, chemistry is fast relative to turbulence, and the flame is wrinkled or corrugated by the turbulent eddies
  • For $Da \ll 1$, turbulence is fast relative to chemistry, leading to a distributed reaction zone and potential local extinction
• Karlovitz number $Ka = \tau_c/\tau_\eta$ relates the chemical time scale to the Kolmogorov time scale $\tau_\eta$ and characterizes the flame stretch and the potential for flame quenching
  • For $Ka < 1$, the flame is weakly stretched and maintains its laminar structure
  • For $Ka > 1$, the flame is highly stretched and can experience local extinction and reignition events

Flame Stability and Extinction

• Flame stability refers to the ability of a flame to maintain its position and structure in the presence of perturbations such as flow fluctuations, heat losses, and compositional variations
• Stable flames are characterized by a balance between the flame propagation speed and the local flow velocity, ensuring that the flame remains anchored at a fixed location (e.g., burner rim or recirculation zone)
• Unstable flames may exhibit phenomena such as flame lift-off (detachment from the burner), blow-off (complete extinction), or flashback (upstream propagation into the burner)
• Extinction occurs when the heat loss from the flame exceeds the heat generation by chemical reactions, leading to a decrease in temperature and eventual quenching of the flame
• Stretch-induced extinction is a common mechanism in turbulent flames, where the flame experiences high strain rates or curvature that enhance heat and radical losses
  • Characterized by the Karlovitz number $Ka$, with extinction occurring for $Ka > Ka_{ext}$, where $Ka_{ext}$ is a critical value depending on the fuel and mixture properties
• Dilution-induced extinction happens when the addition of inert species (e.g., nitrogen or combustion products) to the reactants reduces the flame temperature below a critical value, inhibiting sustained combustion
• Heat loss-induced extinction is caused by the presence of cold surfaces or regions that act as heat sinks, leading to local flame quenching and potential global extinction
• Stability limits are often represented using diagrams such as the equivalence ratio vs. flow velocity plot, which delineates the regions of stable, unstable, and extinct flames for a given burner configuration
• Strategies for enhancing flame stability include the use of pilot flames, swirl-stabilized burners, bluff-body stabilizers, and staged combustion techniques that create recirculation zones and promote mixing

Modeling and Simulation Techniques

• Modeling and simulation play a crucial role in understanding, predicting, and optimizing combustion processes, complementing experimental investigations
• Computational Fluid Dynamics (CFD) is widely used to simulate turbulent reacting flows by solving the governing equations for mass, momentum, energy, and species transport
  • Reynolds-Averaged Navier-Stokes (RANS) methods solve for the mean flow quantities and model the effects of turbulence using closure models such as $k-\varepsilon$ or $k-\omega$
  • Large Eddy Simulation (LES) resolves the large-scale turbulent motions and models the small-scale eddies using subgrid-scale (SGS) models
  • Direct Numerical Simulation (DNS) resolves all the relevant length and time scales without any turbulence modeling but is computationally expensive and limited to simple geometries and low Reynolds numbers
• Chemical kinetics modeling involves the development and use of detailed or reduced reaction mechanisms that describe the elementary steps and species involved in the combustion process
  • Detailed mechanisms can include hundreds of species and thousands of reactions, while reduced mechanisms seek to simplify the chemistry using techniques such as quasi-steady-state approximations (QSSA) or rate-controlled constrained equilibrium (RCCE)
• Turbulence-chemistry interaction (TCI) models are required to account for the subgrid-scale mixing and reaction processes in turbulent flames
  • Eddy Dissipation Concept (EDC) assumes that reactions occur in fine-scale structures and models the reaction rate based on the turbulent mixing time scale
  • Flamelet models assume that the turbulent flame can be represented as an ensemble of laminar flamelets and use pre-computed flamelet libraries to determine the local flame structure and properties
• Radiation modeling is important for accurate predictions of heat transfer and pollutant formation in combustion systems
  • Discrete Ordinates Method (DOM) solves the radiative transfer equation (RTE) for a finite number of discrete directions and is suitable for participating media
  • Monte Carlo methods simulate the emission, absorption, and scattering of photons using random sampling techniques and are computationally expensive but accurate
• Soot modeling is challenging due to the complex formation, growth, and oxidation processes involved
  • Two-equation models solve for the soot mass fraction and number density using empirical source terms for nucleation, surface growth, and oxidation
  • Sectional methods discretize the soot particle size distribution into a finite number of sections and solve for the evolution of each section
  • Stochastic methods such as the Method of Moments with Interpolative Closure (MOMIC) track the statistical moments of the soot particle population and provide a more detailed description of the size distribution

Experimental Methods and Diagnostics

• Experimental investigations are essential for understanding combustion phenomena, validating numerical models, and developing new combustion technologies
• Flame visualization techniques provide qualitative and quantitative information about the flame structure, shape, and dynamics
  • Schlieren imaging utilizes the variation in refractive index due to density gradients to visualize the flame front and flow field
  • Shadowgraphy captures the shadow cast by density gradients and is sensitive to the second derivative of the refractive index
  • Chemiluminescence imaging detects the natural light emission from excited species (e.g., CH*, OH*, C2*) and provides a measure of the heat release rate and flame location
• Laser-based diagnostics offer non-intrusive, high-resolution measurements of temperature, species concentrations, and velocity fields in combustion systems
  • Laser-Induced Fluorescence (LIF) uses a laser to excite specific species (e.g., OH, CH, NO) and measures the resulting fluorescence signal, providing spatially resolved concentration measurements
  • Raman scattering spectroscopy detects the inelastic scattering of laser light by molecules and allows for the simultaneous measurement of temperature and major species concentrations
  • Coherent Anti-Stokes Raman Scattering (CARS) is a nonlinear optical technique that provides high-resolution temperature and species measurements in harsh environments
  • Particle Image Velocimetry (PIV) uses laser sheet illumination and cross-correlation of particle images to determine the instantaneous velocity field in a plane
• Probe-based techniques involve the insertion of physical probes into the combustion chamber to sample or measure local properties
  • Thermocouples measure the local gas temperature using the Seebeck effect and are widely used for temperature mapping and validation of numerical models
  • Gas sampling probes extract a small amount of the combustion gases for analysis using techniques such as gas chromatography (GC) or mass spectrometry (MS) to determine the species concentrations
  • Hot-wire anemometry measures the local flow velocity by sensing the heat transfer from a thin, electrically heated wire and is suitable for high-frequency velocity fluctuations
• Advanced optical diagnostics combine multiple techniques to provide comprehensive measurements of the combustion process
  • Rayleigh scattering, Raman scattering, and LIF can be used simultaneously to measure the temperature, major species, and minor species concentrations in a single laser shot
  • High-speed laser diagnostics enable the study of transient and unsteady combustion phenomena with temporal resolutions on the order of microseconds to milliseconds
• Experimental data analysis and post-processing are crucial for extracting meaningful information from the raw measurements
  • Statistical methods such as Reynolds decomposition, probability density functions (PDFs), and correlations are used to characterize the turbulent flame structure and dynamics
  • Proper Orthogonal Decomposition (POD) identifies the dominant modes of variation in the data and can be used for data compression and reduced-order modeling
  • Machine learning techniques such as artificial neural networks (ANNs) and support vector machines (SVMs) are increasingly used for pattern recognition, data classification, and model development based on experimental data

Applications in Combustion Systems

• Combustion technologies find widespread applications in various sectors, including transportation, power generation, industrial processes, and residential heating
• Internal combustion engines (ICEs) are the primary power source for vehicles and rely on the controlled combustion of fossil fuels (e.g., gasoline, diesel) to generate mechanical work
  • Spark-ignition (SI) engines use a spark plug to initiate combustion of a premixed fuel-air charge and are commonly used in gasoline-powered vehicles
  • Compression-ignition (CI) engines rely on the autoignition of the fuel-air mixture due to high compression ratios and are used in diesel-powered vehicles and heavy-duty applications
  • Advanced combustion strategies such as homogeneous charge compression ignition (HCCI), reactivity controlled compression ignition (RCCI), and partially premixed combustion (PPC) aim to combine the benefits of SI and CI engines in terms of efficiency and emissions
• Gas turbines are widely used for power generation and propulsion applications, utilizing the Brayton cycle to convert the energy from combustion into mechanical or electrical power
  • Stationary gas turbines operate at a fixed speed and are used for baseload and peak power generation, as well as combined heat and power (CHP) applications
  • Aircraft gas turbines (jet engines) provide propulsive power by accelerating the combustion products through a nozzle and are designed for high power density and reliability
  • Lean premixed combustion is commonly employed in modern gas turbines to reduce NOx emissions by operating at lower flame temperatures and avoiding local hot spots
• Boilers and furnaces are used for industrial process heating, steam generation, and space heating applications, utilizing the heat released from combustion to raise the temperature of a working fluid or material
  • Fluidized bed combustion (FBC) systems suspend the solid fuel particles in an upward flow of air, providing efficient mixing and heat transfer while allowing for the use of low-grade fuels and sorbents for pollutant control
  • Oxy-fuel combustion replaces the air with a mixture of oxygen and recycled flue gases, enabling higher flame temperatures and CO2 capture for carbon sequestration or utilization
• Renewable and alternative fuels are increasingly being used to reduce the environmental impact of combustion and mitigate climate change
  • Biofuels such as ethanol, biodiesel, and biogas are derived from biomass sources and can be used as drop-in replacements or blends with conventional fossil fuels
  • Hydrogen is a clean-burning fuel that