Diffusion and heat transfer in chemical kinetics

modelling of premixed laminar flames using flamelet-generated manifolds and disadvantage of laminar flow
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Published Date:23-07-2017
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Laminar Premixed Flames: Kinematics and Burning Velocity 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 • Introduction • Fundamentals and mass • Kinematic balance for steady balances of combustion systems oblique flames • Thermodynamics, flame • Laminar burning velocity temperature, and equilibrium • Field equation for the flame • Governing equations position • Laminar premixed flames: • Flame stretch and curvature Kinematics and Burning Velocity • Thermal-diffusive flame instability • Laminar premixed flames: • Hydrodynamic flame instability Flame structure • Laminar diffusion flames 2 Laminar Premixed Flames • Premixed combustion used in combustion devices when high heat release rates are desired  Small devices  Low residence times • Examples:  SI engine  Stationary gas turbines • Advantage  Lean combustion possible  Smoke-free combustion  Low NO x • Disadvantage: Danger of  Explosions  Combustion instabilities  Large-scale industrial furnaces and aircraft engines are typically non-premixed 3 Premixed Flames • Premixed flame: Blue or blue-green by chemiluminescence of excited radicals, o o such as C and CH 2 • Diffusion flames: Yellow due to soot radiation Turbulent Laminar Premixed Flame Bunsen Flame (Dunn et al.) 4 Flame Structure of Premixed Laminar Flames • Fuel and oxidizer are convected from upstream Cut through with the burning velocity s L flame • Fuel and air diffuse into the reaction zone • Mixture heated up by heat conduction from the burnt gases • Fuel consumption, radical production, and oxidation when inner layer temperature is reached • Increase temperature and gradients • Fuel is entirely depleted • Remaining oxygen is convected downstream 5 Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Introduction • Fundamentals and mass • Kinematic balance for steady balances of combustion systems oblique flames • Thermodynamics, flame • Laminar burning velocity temperature, and equilibrium • Field equation for the flame • Governing equations position • Laminar premixed flames: • Flame stretch and curvature Kinematics and Burning Velocity • Thermal-diffusive flame instability • Laminar premixed flames: • Hydrodynamic flame instability Flame structure • Laminar diffusion flames 6 Premixed Flame in a Bunsen Burner • Fuel enters the Bunsen tube with high momentum through a small orifice • High momentum  underpressure  air entrainment into Bunsen tube • Premixing of fuel and air in the Bunsen tube • At tube exit: homogeneous, premixed fuel/air mixture, which can and should() be ignited 7 Kinematic Balance for Steady Oblique Flame • In steady state, flame forms Bunsen cone • Velocity component normal to flame front is locally equal to the propagation velocity of the flame front  Burning velocity 8 Kinematic Balance for Steady Oblique Flame • Laminar burning velocity s : Velocity of L,u the flame normal to the flame front and relative to the unburnt mixture (index ‘u’) • Can principally be experimentally determined with the Bunsen burner • Need to measure - Velocity of mixture at Bunsen tube exit - Bunsen cone angle α 9 Kinematic Balance for Steady Oblique Flame • Splitting of the tube exit velocity in components normal and tangential to the flame • Kinematic balance yields relation unburnt gas velocity and flame propagation velocity • For laminar flows: 10 Kinematic Balance for Steady Oblique Flame • Flame front: • Large temperature increase • Pressure almost constant  Density decreases drastically • Mass balance normal to the flame front: • Normal velocity component increases through flame front • Momentum balance in tangential direction:  Deflection of the streamlines away from the flame Laminar Bunsen flame (Mungal et al.) 11 Burning Velocity at the Flame Tip • Tip of the Bunsen cone - Symmetry line - Burning velocity equal to velocity in unburnt mixture - Here: Burning velocity = normal component, tangential component = 0 Laminar Bunsen flame (Mungal et al.)  Burning velocity at the tip by a factor 1/sin(α) larger than burning velocity through oblique part of the cone 12 Burning velocity at the flame tip • Explanation: Strong curvature of the flame front at the tip  Increased preheating - In addition to heat conduction normal to the flame front preheating by the lateral parts of the flame front Laminar Bunsen flame (Mungal et al.) • Effect of non-unity Lewis numbers  Explanation of difference between lean hydrogen and lean hydrocarbon flames 13 Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Introduction • Fundamentals and mass • Kinematic balance for steady balances of combustion systems oblique flames • Thermodynamics, flame • Laminar burning velocity temperature, and equilibrium • Field equation for the flame • Governing equations position • Laminar premixed flames: • Flame stretch and curvature Kinematics and Burning Velocity • Thermal-diffusive flame instability • Laminar premixed flames: • Hydrodynamic flame instability Flame structure • Laminar diffusion flames 14 Measuring the laminar burning velocity • Spherical constant volume combustion vessel - Flame initiated by a central spark - Spherical propagation of a flame - Measurements of radial flame propagation velocity dr /dt f • Kinematic relation for flame displacement speed • Flame front position and displacement speed are unsteady • Pressure increase negligible as long as volume of burnt mixture small relative to total volume • Influence of curvature 15 Measuring the laminar burning velocity 16 Flame front velocity in a spherical combustion vessel • Velocity relative to flame front is the burning velocity • Different in burnt and unburnt region dr /dt f • From kinematic relation v u • Velocity on the unburnt side (relative to the flame front) • Burnt side of the front • Spherical propagation: Due to symmetry, flow velocity in the burnt gas is zero • Mass balance yields: 17 Flame front velocity in a spherical combustion vessel • From mass balance and kinematic relation follows • Flow velocity on the unburnt side of the front  Flow of the unburnt mixture induced by the expansion of the gases behind the flame front • Measurements of the flame front velocity dr /dt f  Burning velocity s : L,u 18 Relation between s and s L,u L,b • Burning velocity s defined with respect to the unburnt mixture L,u • Another burning velocity s can be defined with respect to the L,b burnt mixture • Continuity yields the relation: • In the following, we will usually consider the burning velocity with respect to the unburnt s = s L L,u 19 Flat Flame Burner and Flame Structure • One-dimensional flame • Stabilization by heat losses to burner • In theory, velocity could be increased until heat losses vanish, then  unstretched  u = s u L • Analysis of flame structure of flat flames - Measurements of temperature and species concentration profiles 20