Laminar Diffusion Flames

laminar diffusion flame algorithm and prediction of laminar jet diffusion flame sizes
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Published Date:23-07-2017
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Laminar Diffusion Flames CEFRC Combustion Summer School 2014 Prof. Dr.-Ing. Heinz Pitsch Copyright ©2014 by Heinz Pitsch. This material is not to be sold, reproduced or distributed without prior written permission of the owner, Heinz Pitsch. Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass balances of combustion systems • Introduction • Thermodynamics, flame • Counterflow diffusion flame temperature, and equilibrium • Flamelet structure of diffusion flames • Governing equations • FlameMaster flame calculator • Laminar premixed flames: Kinematics and Burning Velocity • Single droplet combustion • Laminar premixed flames: Flame structure • Laminar diffusion flames 2 Laminar diffusion flames • Seperate feeding of fuel and oxidizer into the combustion chamber  Diesel engine  Jet engine • In the combustion chamber:  Mixing Injection and  Subsequently combustion combustion in a • Mixing: Convection and diffusion diesel engine  On a molecular level  (locally) stoichiometric mixture • Simple example for a diffusion flame: Candle flame  Paraffin vaporizes at the wick → diffuses into the surrounding air • Simultaneously: Air flows towards the flame due to free convection and forms a mixture with the vaporized paraffin 3 Candle flame yellow region (soot particles) dark region with thin blue layer (chemiluminescence) vaporized paraffin air air • In a first approximation, combustion takes place at locations, where the concentrations of oxygen and fuel prevail in stoichiometric conditions. 4 Comparison of laminar premixed and diffusion flames Temperature Fuel Fuel Oxidizer Reaction rate Reaction rate Temperature Oxidizer Structure of a diffusion flame (schematic) Structure of a premixed flame (schematic) 5 Soot in candle flames • Soot particles  Formation in fuel rich regions of the flame  Transported to lean regions through the surface of stoichiometric mixture  In the oxygen containing ambient: Combustion of the soot particles • Sooting flame: Residence time of the soot particles in the region of oxidizing ambient and high temperatures too short to burn all particles 6 Timescales • Considering the relative times required for  Convection and diffusion  Proceeding reactions • For technical combustion processes in diffusion flames:  Characteristic times of convection and diffusion are approximately of same order of magnitude  Characteristic times of chemical reactions much smaller • Limit of fast chemical reactions  Mixing is the slowest and therefore rate determining process → “mixed = burnt” 7 The mixture fraction • Mixture fraction: • Stoichiometric mixture fraction: • Relation with equivalence ratio  Pure oxidizer (f = 0): Z = 0  Pure fuel (f = ∞): Z = 1 8 Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass balances of combustion systems • Introduction • Thermodynamics, flame • Counterflow diffusion flame temperature, and equilibrium • Flamelet structure of diffusion flames • Governing equations • FlameMaster flame calculator • Laminar premixed flames: Kinematics and Burning Velocity • Single droplet combustion • Laminar premixed flames: Flame structure • Laminar diffusion flames 9 Counterflow Diffusion flame • One-dimensional similarity solution • Strain appears as parameter  Da • Used for  Studying flame structure  Studying chemistry in diffusion flames  Study interaction of flow and chemistry 10 Counterflow diffusion flame: Governing Equations • Continuity • X – Momentum • Energy 11 Counterflow diffusion flame: Similarity solution • Three assumptions reduce systems of equation to 1D 1. Similarity assumption for velocity 2. Similarity assumption 3. Mass fractions and temperature have no radial dependence close to centerline 12 Counterflow diffusion flame: Similarity solution • This results in • with boundary conditions 13 Counterflow diffusion flame: Similarity solution • Alternatively, potential flow boundary conditions can be used at y  ±∞ instead of nozzles • With definition of strain rate the similarity coordinate h the non-dimensional stream function f defined by and the Chapman-Rubesin parameter the 1D similarity solution can be derived 14 Counterflow diffusion flame: Similarity solution • Potential flow similarity solution • With Dirichlet boundary conditions for mass fractions and temperature and where the velocities are obtained from 15 Structure of non-premixed laminar flames Temperature for methane/air counterflow diffusion flames Structure of non-premixed laminar flames Maximum flame temperature for methane/air counterflow diffusion flames Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass balances of combustion systems • Introduction • Thermodynamics, flame • Counterflow diffusion flame temperature, and equilibrium • Flamelet structure of diffusion flames • Governing equations • FlameMaster flame calculator • Laminar premixed flames: Kinematics and Burning Velocity • Single droplet combustion • Laminar premixed flames: Flame structure • Laminar diffusion flames 18 Theoretical description of diffusion flames • Assumption of fast chemical reactions  Without details of the chemical kinetics  Global properties, e.g. flame length • If characteristic timescales of the flow and the reaction are of same order of magnitude:  Chemical reaction processes have to be considered explicitly  Liftoff and extinction of diffusion flames  Formation of pollutants • Flamelet formulation for non-premixed combustion • Mixture fraction as independent coordinate for all reacting scalars, • Asymptotic approximation in the limit of sufficiently fast chemistry to one- dimensional equations for reaction zone 19 Flamelet structure of a diffusion flame • Assumptions: Equal diffusivities of chemical species and temperature • The balance equation for mixture fraction, temperature and species read • Low Mach number limit • Zero spatial pressure gradients • Temporal pressure change is retained 20