High-temperature, high-pressure burning velocities of expanding turbulent premixed flames and their comparison with Bunsen-type flames

This paper reports high-temperature/pressure turbulent burning velocities and their correlation of expanding unity-Lewis-number methane/air turbulent flames, propagating in near-isotropic turbulence in a large dual-chamber, constant-pressure/temperature, fan-stirred 3D cruciform bomb. A novel heating method is used to ensure that the temperature variation in the domain of experimentation is less than 1 °C. Schlieren images of statistically spherical expanding turbulent flames are recorded to evaluate the mean flame radius 〈R(t)〉 and the observed flame speeds, d〈R〉/dt and S_F (the slope of 〈R(t)〉), where S_F is found to be equal to the average value of d〈R〉/dt within 25 mm ≤ 〈R(t)〉 ≤ 45 mm. Results show that the normalized turbulent flame speed scales as a turbulent flame Reynolds number Re_T,flame=(u'/S_L)(〈R〉/δ_L) roughly to the one-half power: (S_L^b)⁻¹d〈R〉/dt ≈ (S_L^b)⁻¹S_F = 0.116Re_T,flame^0.54 at 300 K and 0.168Re_T,flame^0.46 at 423 K, where u′ is the rms turbulent fluctuating velocity, S_L and S_L^b are laminar flame speeds with respect to the unburned and burned gas, and δ_L is the laminar flame thickness. The former at 300 K agrees well with Chaudhuri et al. (2012) [16] except that the present pre-factor of 0.116 and Re_T,flame up to 10,000 are respectively 14% and four-fold higher. But the latter at 423 K shows that values of (S_L^b)⁻¹d〈R〉/dt bend down at larger Re_T,flame. Using the density correction and Bradley's mean progress variable 〈c〉 converting factor for schlieren spherical flames, the turbulent burning velocity at 〈c〉=0.5, S_T,c=0.5≈ (ρ_b/ρ_u)S_F(〈R〉_c=0.1/〈R〉_c=0.5)², can be obtained, where the subscripts b and u indicate the burned and unburned gas. All scattering data at different temperatures for spherical flames can be represented by S_T,c=0.5/S_L=2.9[(u′/S_L)(p/p₀)]^0.38, first proposed by Kobayashi for Bunsen flames. Also, these scattering data can be better represented by (S_T,c=0.5-S_L)/u' = 0.16Da^0.39 with small variations, where the Damköhler number Da = (L_I/u′)(S_L/δ_L) and L_I is the integral length scale.