Flame speed datasets

Table 6.1: Salient characteristics of various experimental S_T data sets.

Flame Burner

configuration

Mixture φ Pressure Measurement

location

Source

V–shape Rod stabiliser at nozzle exit

CH₄–Air 0.75–1.0 Ambient c = 1/τ Smith &

Gouldin (1978) Planar

Taylor-Couette apparatus

CH₄–Air 0.8–1.5 Ambient Leading edge Aldredge et al.

(1998)

Conical Nozzle burner in high pressure

CH4–Air 0.9 0.1–3.0 MPa c = 0.5 Kobayashi et al. (1996)

Planar Diverging duct

CH₄–Air 0.75–0.95 Ambient c = 0.5 Savarianandam

& Lawn (2006) Right Cone Parallel plates

at square channel exit

City gas–Air - Ambient Leading edge Il’yashenko &

Talantov (1966)

The configuration and conditions of various experimental data sets considered in the present study are listed in Table 6.1. As one can see, these experiments

6.4 Comparisons with experimental data

correspond to a variety of flame configurations and burner geometry. The relevant attributes of these flames are given in Table 6.2.

Table 6.2: Attributes of various experimental ST data.

Source s^o_L (m/s) δ_L^o (mm) u⁰ (m/s) Λ (mm) Re Da Smith &

Gouldin (1978)

0.25–0.40 0.45–0.67 0.095–1.13 0.69–1.49 3–75 3-39

Aldredge et al.

(1998)

0.17–0.48 0.37–0.92 0.2–1.06 5.5 50–265 5-219

Kobayashi et al. (1996)

0.06–0.34 0.095–0.5 0.053–0.83 1.0–1.5 7–830 6-97

Savarianandam

& Lawn (2006)

0.19–0.32 0.51–0.79 0.01–0.26 3–36 7-497 142-4535

Il’yashenko &

Talantov (1966)

0.2 0.7 0.22–10.5 6.8–11.2 114–3230 1.2-92

The study of Smith & Gouldin (1978) considered V–shaped rod stabilised methane–air flames of three equivalence ratios: φ = 0.75, 0.85 and 1. They measured the orientation of the T = 2 T_u isotherm, which corresponds to the c = 1/τ iso–surface in the flame brush. This surface is not strictly the flame brush leading edge and this is to be noted while comparing the turbulent flame speed. Smith & Gouldin (1978) reported the component of local mean velocity normal to the above iso–surface as the turbulent flame speed for each φ and three different values of turbulence integral length scale, Λ: 0.69, 0.95 and 1.49mm. As established in Section 6.3, this normal mean velocity corresponds to the turbulent flame speed. Smith & Gouldin (1978) identify that S_T varies locally on the iso–

surface and they clearly note the importance of correlating measurements of S_T at a location where u⁰ and Λ are also measured.

Aldredge et al. (1998) measured both laminar and turbulent flame speeds of methane–air mixtures with equivalence ratio ranging from 0.8 to 1.5, varied in

6.4 Comparisons with experimental data

steps of 0.1, in a Taylor–Couette (TC) apparatus. This apparatus consisted of two vertical concentric counter–rotating cylinders with an annular gap of 1.1cm.

The planar flame, ignited at the open end, propagates into the nearly stationary turbulent mixture in the annulus. The rate of displacement of the propagating flame, which was calculated from video record, was reported as the flame speed.

Clearly, this speed is the turbulent flame speed, S_T.

Kobayashi et al. (1996) measured the turbulent flame speed for lean methane–

air mixture with φ = 0.9 at pressures ranging from 0.1 to 3 MPa. The turbulence measurements under these conditions were reported in another study (Kobayashi et al., 1997). A Hydrogen pilot flame was used to stabilise the turbulent flame at the exit of a nozzle in high pressure environment. Unlike the combustion bombs and SI engines in which the pressure change is unsteady and brief, the apparatus of Kobayashi et al. (1996) was designed to maintain high pressures for long durations. From instantaneous tomographic images of flame, the mean flame cone was identified and the flame speed was calculated as the component of the mean flow velocity normal to the mean flame cone, which corresponds to S_T as noted in sub–section 6.3.2.

Savarianandam & Lawn (2006) focussed on the weakly wrinkled flame regime (u⁰/s^o_L < 1) where the Darrieus–Landau (DL) instabilities have dominant influ-ence on S_T. While the analysis of Damköhler suggests that S_T/s^o_L should be relatively closer to unity in this regime, other studies (Cambray & Joulin, 1992;

Paul & Bray, 1996) indicate that Darrieus-Landau hydrodynamic instabilities result in ST/s^o_L value significantly greater than unity. Flame speeds of nearly planar flames stabilised in a wide angled diffuser at very low turbulence intensi-ties, reported by Savarianandam & Lawn (2006), provide evidence for this. Three methane–air mixtures of φ = 0.75, 0.85 and 0.95 were used and values of u⁰/s^o_L ranged from 0.05 to 1.37. The flame speed was estimated to be the mean flow velocity at the mean flame height location. As noted by Savarianandam & Lawn (2006), this velocity is the leading edge displacement velocity S_T.

Il’yashenko & Talantov (1966) measured turbulent flame speeds in a flame configuration which was obtained in the region confined between two parallel plates, at the exit of a square channel. Ignition flames were used on two opposite sides of the channel exit and the other two sides were extended as walls. This

6.4 Comparisons with experimental data

resulted in a symmetric configuration of two flame surfaces at an angle to the flow and intersecting at a downstream location. The experiments were done with both a smooth channel and a channel with turbulising grid at the exit, which allowed very high turbulence level to be achieved. They used city gas (a mixture of natural gas and coke gas) as the fuel and measured flame speeds up to u⁰/s^o_L∼ 50. The flame speed was estimated from the mean flow velocity and inclination angle of the flame surfaces. As established in Section 6.3.2, this normal velocity corresponds to the turbulent flame speed S_T.

0.1 1 10 100 1000

Figure 6.4: Turbulent combustion regime diagram (Peters, 2000) with attributes of various experimental flames: ∗ Smith & Gouldin (1978); ¨ Aldredge et al.

(1998); M Kobayashi et al. (1996); O Savarianandam & Lawn (2006); ◦, • Il’yashenko & Talantov (1966).

Figure 6.4 shows the above five data sets in the combustion regime diagram, which is adapted from Peters (2000). Although most of the experimental flames are within the corrugated and the wrinkled flamelets regimes, there are some cases spanning the thin reaction zones regime. More experimental data in this

6.4 Comparisons with experimental data

regime would be very useful for model validation. Comparisons between Eq. (6.3) and the above data sets are discussed next.