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Lecture 20: Laminar Non-premixed Flames – Introduction, Non-reacting Jets, Simplified Description of Laminar Non- premixed Flames Yi versus f Experimental.

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Presentation on theme: "Lecture 20: Laminar Non-premixed Flames – Introduction, Non-reacting Jets, Simplified Description of Laminar Non- premixed Flames Yi versus f Experimental."— Presentation transcript:

1 Lecture 20: Laminar Non-premixed Flames – Introduction, Non-reacting Jets, Simplified Description of Laminar Non- premixed Flames Yi versus f Experimental Data Qualitative characteristics of laminar non-premixed or diffusion (of fuel and oxidizer) flames. Review of conserved scalar concept. Role of the momentum equation in deflagration regime: Non-reacting jet mixing solution. Simplified theoretical description of a laminar non- premixed (or diffusion) flame.

2 Opposed jet nonpremixed flame Stagnation point flow non- premixed flame Air Fuel Swirling flow flame with cross fuel injection Spherical stagnation pt. flame Vertical wall fire Horizontal wall fire Inclined wall fire Upward flame spread Downward flame spread Corner fire Beam, column fires Pool fires Forest fires Platform fire Combination fires Non premixed Flame Configurations

3 Laminar Jet Diffusion Flames (Non-premixed Jet Flames)

4 Fuel (F) and oxidizer (O) are stored apart. When combustion is desired, F and O must come together at the molecular level. How many molecules of each decides interim and final products and their temperature. Staged pre or post reaction mixing and rich and lean reactions all lead to different products. Specific strategies such as R-Quench-L, Lean Direct Injection, Direct Injection-Spark Ignition have emerged. Learning the non-premixed flame regime is important. Learning about equipment for specific strategies is critical Nonpremixed flames

5 Concept of a conserved scalar is very useful for nonpremixed flames. A conserved scalar is a quantity defined such that there are no sink or source terms in the conservation equation for that quantity. (Sink and source terms result from reactions, heat transfer, and work transfer) Quantification of how non- (pre)mixed and when Total Energy is a conserved scalar in the absence of net heat loss to or work done on boundaries. Elemental Mass Fractions, Fraction of Mass that originated in the fuel stream(s) and Fraction of Mass that originated in the oxidizer stream(s) are all conserved scalars. Mixture Fraction, Mixedness, Progress Variables, Reaction Fraction, and Reactedness

6 In nonpremixed flames species mass fractions very continuously as mixing at the molecular level and chemical reaction occurs. Definition of mixture fraction f: Fuel Mass + Mass in products that came from fuel Independent of the progress of reaction. That means CH 4 +O 2 have the same mixture fraction as CO+H 2 O+H 2 Both are f=16/(16+32)=(12+2+2)/( ) =16/48= 1/3 f stoich = 16/16+64= 16/80=0.2 Review of Conserved Scalar, Definition of Mixture Fraction

7 Consider the three-"species" reaction: For this system the mixture fraction will be: Review of Conserved Scalar, Definition of Mixture Fraction

8 Assume all species diffuse at the same rate: Conservation equation for the mixture fraction.

9 Divide the product species conservation equation by and add to the fuel species conservation equation: Substituting for the mixture fraction we obtain: Review of Conserved Scalar, Definition of Mixture Fraction

10 When kinetic energy is neglected (along with potential energy, thermal radiation, viscous dissipation, differential diffusion) we can write a similar equation for the absolute enthalpy: These conserved scalar equations, in cylindrical coordinates, will be very useful for our study of laminar non-premixed flames. Review of Conserved Scalar, Definition of Mixture Fraction

11 Consider first the case of a laminar jet of fuel issuing into air with no chemical reaction. Assuming the air and fuel have the same density, there is an analytical solution for the flow field away from the potential core region of the jet. Solution for a Non-reacting, Constant Density Laminar Jet

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13 - MW(jet fluid) = MW(air), ideal gases. - Constant P, T, and  throughout the flow field. - Steady state. - Fick's law applies. - Equal species and momentum diffusivities, Sc = / D = 1. - Neglect axial diffusion of momentum and species. - Solution applies downstream of the jet core region. 14/36 Assumptions: Non-reacting, Constant Density Laminar Jet

14 Axial Momentum Mass Conservation Equations: Non-reacting, =C Laminar Jet Species

15 Along the jet centerline: Far from the jet: Boundary Conditions for a Non-reacting, =C Laminar Jet At the jet exit plane, r ≤ R: At the jet exit plane, r > R:

16 The solution to this problem can be found in Schlichting Boundary Layer Theory for the region of the flow beyond the jet core where the flow is similar. The solution is given by: Solution for a Non-reacting Constant Density Laminar Jet

17 Axial velocity distribution: Fuel mass fraction distribution (assuming Sc = n/D = 1):

18 Law, Combustion Physics, 2006 Finite-rate Kinetics Infinitely Fast Kinetics Infinitesimal Flame Sheet Approximation for Nonpremixed Flames

19 Assume: 1. Laminar, steady, axisymmetric flow 2. Three "species": fuel, product, oxidizer 3. Flame (reaction) sheet assumption, infinitely fast chemical kinetics 4. Equal species diffusivities 5. Le = 1 6. No radiation transport 7. Axial diffusion is neglected 8. Vertical flame axis Simplified Theoretical Description of Laminar Jet Diffusion Flame

20 Conservation of Mass Conservation of Axial Momentum Conservation Equations: Cylindrical Coordinates, Thin Flame Conservation of Fuel Mass Fraction (Inside the Flame Sheet) Conservation of O 2 Mass Fraction (Outside the flame sheet) Conservation of Product Mass Fraction (Everywhere)

21 Conservation of Species Mass Fraction Simplified Theoretical Description of Laminar Jet Diffusion Flame

22 Conserved Scalar Equations for Laminar Jet Flame Boundary Conditions At the jet exit plane

23 A dimensionless enthalpy is defined: Non-dimensional Laminar Jet Diffusion Flame The non-dimensional conservation equations and boundary conditions for h* and f are identical, and therefore h* = f.

24 Inside the flame sheet Assume that the reaction kinetics are described by a single-step, three-species reaction: Description of Global Fast Chemistry Outside the flame sheet

25 Assume constant heat capacities, and that for the jet fluid and oxidizer far from the jet, T = 298 K. Inside the flame sheet: State Relationship for Temperature: Fuel Side Oxidizer = air Solve the h* = f equation for T :

26 State Relationship for Temperature: Oxidizer Side

27 Experimental Support for State Relationships for Major Species


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