7. Turbulent Premixed Flames

Transcription

1 7. Turbulent Premixed Flames Background: - Structure of turbulent premixed flames; 7. Turbulent Premixed Flames 1 AER 1304 ÖLG

2 - Instantaneous flame fronts (left) and turbulent flame brush envelope (right). 7. Turbulent Premixed Flames 2 AER 1304 ÖLG

3 Definitions: - Laminar flame thickness: δ L α/ = D/ = ν/ (1) - Above equality implies that we assumed, Schmidt Number: Sc = ν/d =1 Lewis Number: Le = α/d =1 Prandtl Number: Pr = ν/α =1 7. Turbulent Premixed Flames 3 AER 1304 ÖLG

4 - Turbulent Reynolds number Re Λ = u Λ ν (2) where Λ is the integral length scale of turbulence. - Turbulent Damköhler number: ratio of characteristic flow time, τ flow, to the characteristic chemical time, τ c. Da = τ flow (3) τ c 7. Turbulent Premixed Flames 4 AER 1304 ÖLG

5 - Characteristic flow time: τ flow = Λ/u - Characteristic chemical time: τ c = δ L / - Then Damköhler number is: Da = Λ u δ L (3a) - Turbulence length scales: λ: Taylor microscale η: Kolmogorov length scale 7. Turbulent Premixed Flames 5 AER 1304 ÖLG

6 - Karlovitz number: Ka = Λ η 2 = δ Lu λ (4) - Turbulent Reynolds number based on λ: Re λ = u λ/ν (5) - Turbulent Reynolds number based on η: Re η = u η/ν (6) Re Λ Re 2 λ Re 4 η (7) 7. Turbulent Premixed Flames 6 AER 1304 ÖLG

7 Turbulent Burning Velocity: - One of the most important unresolved problems in premixed turbulent combustion is the determination of the turbulent burning velocity. - Above statement assumes that turbulent burning velocity is a well-defined quantity that only depends on local mean properties. - However, there is no consensus in literature whether the turbulent burning velocity is a characteristic quantity that can be defined unambigously for different geometries. 7. Turbulent Premixed Flames 7 AER 1304 ÖLG

8 10 8 Weak Turbulence 10 2 Damkohler Number, Da SI Engine regime u'/ = η /δ L =1 Reaction sheets Λ /δ L =1 Distributed reactions Turbulent Reynolds Number, Re Λ 7. Turbulent Premixed Flames 8 AER 1304 ÖLG

9 - Turbulent premixed flame propagation was first investigated by Damköhler (1940). - He identified two limiting cases based on the magnitude of the scale of turbulence as compared to the thickness of the laminar premixed flame. - For large scale turbulence, Damköhler assumed that the interaction between a turbulent premixed flame (wrinkled flame) front and the turbulent flame front is purely kinematic. 7. Turbulent Premixed Flames 9 AER 1304 ÖLG

10 Laminar flame structure. 7. Turbulent Premixed Flames 10 AER 1304 ÖLG

11 - Damköhler equated the mass flux ṁ through the instantaneous turbulent flame surface area A T with the mass flux through the cross-sectional area A o.heused for mass flux through A T,and S T for mass flux through A. ṁ = ρ u A T = ρ u S T A o (8) S T = A T A o (9) 7. Turbulent Premixed Flames 11 AER 1304 ÖLG

12 - Using geometric approximations, Damköhler proposed that (for large-scale, small-intensity turbulence), In view of Eq.2, A T A o =1+ u (10) S T =1+ u (11) - u, turbulent fluctuating velocity in the unburned gas. 7. Turbulent Premixed Flames 12 AER 1304 ÖLG

13 - Using similar geometric arguments, Schelkin showed that: S T = 1+ 2u 2 1/2 (12) - Relationship proposed by Klimov: S T =3.5 u 0.7 (13) 7. Turbulent Premixed Flames 13 AER 1304 ÖLG

14 - Clavin &Williams: 1/2 1/2 (14) S T = u 2 S 2 L -Gülder: S T = u 1/2 Re 1/4 Λ (15) 7. Turbulent Premixed Flames 14 AER 1304 ÖLG

15 - For small-scale and high-intensity turbulence, Damköhler argued that turbulence only modifies the transport between the reaction zone and the unburned gas. S T / (D T /D) 1/2 (16) Since D T u Λ and D δ L -Thenwehave, S T u Λ δ L 1/2 (17) 7. Turbulent Premixed Flames 15 AER 1304 ÖLG

16 - For small-scale high-intensity turbulence conditions (usually called as distributed reaction regime), there are not many formulations available. In this regime, turbulent mixing is rapid as compared to the chemistry. - For the distributed reaction regime the following semi-empirical model has been proposed, Gülder (1990): 3/4 S T SL =6.4 u (18) 7. Turbulent Premixed Flames 16 AER 1304 ÖLG

17 State-of-the-art: - Definition of turbulent burning velocity is not uniform/universal. - Experimental data scatter is significant between different experimental rigs. - Numerical simulation: - Flamelet model/assumption - Turbulent burning closure - Direct numerical simulation 7. Turbulent Premixed Flames 17 AER 1304 ÖLG

18 Experimental Measurement Methods: - Conical stationary flames on cylindrical nozzles. - Swirling flames. - Constant volume vessels. - Stagnation point flames. - Laser-based diagnostics to study flame structure. - Statistical approaches to estimate the flame front surface area. 7. Turbulent Premixed Flames 18 AER 1304 ÖLG