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## CONGRATULATIONS DEREK

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**LIMITS IN COMBUSTION SYSTEMS**OXFORD, 11th APRIL 2006 CONGRATULATIONSDEREK Professor Derek Bradley, BSc, PhD, FRAE, FRS**LIMITS IN COMBUSTION SYSTEMS**OXFORD, 11th APRIL 2006 THEORETICAL ASPECTS OF THE LIMITS OF COMBUSTIONKen Bray – Cambridge University Questions to be addressed: • How fast can we burn?* • What limits exist, to mixture fraction, turbulence parameters etc, beyond which burning cannot take place? • What is the influence of turbulence, and how can we understand it? *D. Bradley, Proc. Comb. Inst. 24, 247 (1992)**CONTENTS OF TALK**• Upper limit to burning rate • Extinction limit • Consequences of incomplete mixing • Geometry effects • Identify models capable of predicting limits • Conclusions**(1) Upper limit to burning rate**Maximum possible chemically-limited heat release rate corresponds to homogeneous combustion of uniform, near-stoichiometric, high temperature mixture. Only significant influence of turbulenceis then via heat loss to boundaries.**IN MOST REAL SITUATIONS:Chemical heat release must be**used to preheat reactants in order to allow them to react. • Heat and mass transfer is required, from hot products to reactants (and to mix fuel and oxidiser, if not premixed). • Turbulence speeds heat and mass transfer. • But turbulent entrainment produces non-uniform mixture, which can slow global rate of reaction.**TURBULENCE SPEEDS HEAT AND MASS TRANSFER**• Large-scale eddying motion causes entrainment of reactants into products, and increases surface area on which small-scale mixing can occur. • The strain and curvature (stretch) of the mixing surface steepen local composition gradients and speed rate of small-scale mixing. • The scalar dissipation defines time-scale for small-scale mixing rate.**SCALAR DISSIPATION**• Definition: where D is molecular diffusivity and c is a composition variable. • Significance: reciprocal of time-scale for small-scale (molecular) mixing • Mean value is one half of rate of decay of the variance due to molecular mixing. • Key parameter in theoretical descriptions, but difficult to model.**SCALAR DISSIPATION AND RATE OF HEAT RELEASE IN**NONPREMIXED COMBUSTION. Temperature equation in terms of mixture fraction Z Scalar dissipationc is mainly controlled by turbulence in nonpremixed flames far from extinction. Unsteady terms mixing Radiative loss Heat release**SCALAR DISSIPATION AND RATE OF HEAT RELEASE: PREMIXED**MEAN SCALAR DISSIPATION IN PREMIXED FLAMES IS INFLUENCED BY BOTH LAMINAR FLAME AND TURBULENCE PROPERTIES. UNSOLVED PROBLEM. LIMITING VALUE IS: MEAN HEAT RELEASE APPROX. CONST. ~ 0.7 MIXING**MODELLING OF SCALAR DISSIPATION**Classical term Classical (nonreactive) model: Thin flamelet limit (premixed): Eg: Model of Swaminathan and Bray*: * Combust. Flame 143 (2005) 549-565 reaction**(2) EXTINCTION LIMITQUENCHING DUE TO FLAME STRAIN AND**CURVATURE • Flame stretch due to strain and curvature tends to increase local gradients and hence rate of heat transfer away from reaction zone. • If rate of heat loss exceeds chemical rate, reaction zone must cool, and reaction rate will fall, leading to local quenching. • Scalar dissipation is a measure of local composition gradient. • Local quenching occurs at critical value of scalar dissipation. • Influenced by differential diffusion effects and hence by Markstein number.**LOCAL FLAME QUENCHING:Similar process, premixed or**nonpremixed Norbert Peters related nonpremixed flame quench to premixed flame. For nonpremixed case he showed that scalar dissipation is where a is the rate of strain. At quench, for corresponding premixed flame.**“S-curve” describing ignition and extinction**of laminar nonpremixed counterflow flame Heat release Infinitely Fast chemistry extinction ignition to cause local quenching in turbulent flame is similar to this counterflow extinction**Local quenching of nonpremixed flames leads to**triple flames and flame ends. c in the flame gap must be significantlyless than the laminar counterflow c if the gap is to close DNS image of autoignition in segregated mixture due to Vervisch et al**Effects of radiative heat loss on back-to-back premixed**laminar flames: Influence of strain rate and equivalence ratio on peak temperature. Source: Graham Dixon-Lewis. Proc. R. Soc. A (2006) 462 349-370.**LOCAL FLAME QUENCHING NEED NOT LEAD TO GLOBAL**EXTINCTION Global extinction also depends on: Probability density function of flame surface stretch rates, P(s), Details of flame brush geometry.**(3) CONSEQUENCES OF INCOMPLETE MIXING:EFFECTS OF**INCOMPLETE MIXING DUE TO ENTRAINMENT BY TURBULENT MOTION A range of mixtures occurs. The mean reaction rate can be expressed in terms of a probability density function (PDF): Can increase or decrease mean reaction rate, in comparison with rate at mean composition.**LOW UNMIXEDNESS:**Reaction rate PDF Mean PDF can introduce states with reaction rates both slower and faster than that of mean.**HIGH UNMIXEDNESS:**PDF Reaction rate fully burned unburned High probabilities of nonreactive unburned and fully burned mixtures**Influence of incomplete mixing on mean heat release rate:**Three presumed PDF shapes Reference: Bray, Champion, Libby and Swaminathan, submitted**COMPARISON OF PDFs WITH EACHOTHER AND WITH DNS DATA**OF RUTLAND AND CANT Beta DNS Laminar flamelet Double delta PDF Reference: Bray, Champion, Libby and Swaminathan, submitted**HIGH UNMIXEDNESS:**Mean rate is: Mean rate is linear in (1-g) Constant depending on PDF I(beta) = 0.14 I(delta) = 0.5 I(flamelet) = 0.05 Pre-exponential factor: B Note: Errors in predicting scalar dissipation lead to uncertainties in (1-g). Reference: Bray, Champion, Libby and Swaminathan, submitted**(4) GEOMETRY EFFECTS**FLAME BRUSH GEOMETRY AND GLOGAL EXTINCTION: INWARD AND OUTWARD PROPAGATION OF SPHERICAL PREMIXED FLAMES C=1 C=0 C=1 C=0 Can be extinguished due to rapid mixing with cold ambient reactants Unlikely to be extinguished due to rapid mixing with hot products**FLAME BRUSH GEOMETRY AND GLOGAL EXTINCTION:**FORMATION OF A HOLE IN A PREMIXED COUNTER-FLOW FLAME flame Premixed reactants Premixed reactants**FLAME BRUSH GEOMETRY AND GLOGAL EXTINCTION**Blow-off of lifted jet diffusion flame flame flame Quenching at Flame “neck” fuel fuel**TURBULENT BURNING VELOCITY:A MEASURE OF HEAT RELEASE**RATE IN PREMIXED COMBUSTION Two alternative definitions: • Displacement speed: relative propagation speed of a specified iso-surface, on which mean properties are constant, • Consumption speed: related to total consumption of reactants in flame brush. • Burning velocity is influenced by flame brush geometry.**DISPLACEMENT SPEED**Scalar flux Can be defined relative to either Reynolds or Favre averaged mean velocity. Favre version is: Relative speed of surface with specified mean property**CONSUMPTION SPEEDIntegral property: depends on flame brush**curvature Radius of curvature n=0: planar n=1: cylindrical n=2: spherical**RELATIONSHIP BETWEEN BURNING**VELOCITIES:Steady planar flame:Unsteady effect due to increase in mass of unburned gas stored within flame brush. Simple analysis: Planar flame brush, brush thickness grows with time, “similarity” assumption:**(5) IDENTIFY MODELS CAPABLE**OF PREDICTING LIMITS: • Closure problems are similar in RANS and in LES. • Successful model must include detailed chemical kinetics as well as a realistic description of competing effects of turbulent mixing. • Selection of models is a matter of judgement. • Different closure strategies have been developed for premixed and nonpremixed combustion. • Many practical flames are partially premixed.**DNS of Yasuhiro MizobuchiJapan Aerospace Exploration Agency**Simulation of lifted hydrogen jet flame, all scales resolved. Jet nozzle diameter: 2 mm Jet Reynolds number: 13600 Chemical mechanism with 9 species, 17 reactions DNS with up to 400,000,000 nodes.**Global structure of the lifted flame**Diffusion flame islands - Island-like form - Combustion controlled by molecular diffusion Turbulent rich premixed flame - Complex structure which is largely different from the laminar flamelet • Leading edge flame • Triple flame like structure at stable locations- 3-D and unsteady with large time scale • Stabilization mechanism Rich premixed Diffusive Lean premixed Iso-surface of H2 consumption rate at 104mol/sec/m3 Iso-surface of H2 consumption rate at 104mol/sec/m3**REMINDER**• Nonpremixed: Composition gradients (and scalar dissipation) mainly determined by turbulence. • Premixed: Robust flamelet structures influence composition gradients (and scalar dissipation).**IDENTIFY MODELS CAPABLE OF PREDICTING LIMITS:NONPREMIXED**Transported PDF models* • Include detailed description of chemical kinetic mechanism. • Most widely tested against experimental data. • Extensively optimised. • Successfully predicts extent of local quenching, as well as lift-off and blow-off. • How do conditional scalar dissipation models represent combination of premixed and nonpremixed burning? *Ref: Cao and Pope. C&F 143, 450-470 (2005)**MODELS CAPABLE OF PREDICTING LIMITS:**Model of Bradley et al* for premixed combustion Heat release rate in laminar flame progress variable c, stretch s *D. Bradley, P.H.Gaskell, X.J.Gu and A. Sedaghat: C&F 143, 227 – 245 (2005) PDF of progress variable and flame stretch Assumes P(c,s)=P(c)P(s) Heat release rate in unstretched laminar flame Burning rate factor**Model of Bradley et alBurning rate factor Pb**Pbis modelled as a function of: Laminar flame extinction stretch rates under positive and negative stretch, PDF of stretch rates A “stretch factor”, f(s), depending on chemical kinetics, Markstein number and laminar flame instabilities. The model appears to include all the factors that are expected to influence limits of combustion. Scalar dissipation model?**(6) CONCLUSIONSI have tried to:**• Describe some of physical processes by which turbulence influences limits in combustion systems, • Explain how turbulence can speed or slow burning rate and lead to global extinction, • Identify models incorporating physics required to predict these processes, • Draw attention to uncertainties in modelling scalar dissipation, • Point out that the same processes must be described in LES as in RANS simulations.