The Relationship of the Laminar Flame Width to Flame Speed

Abstract

Abstract The width ( δ ) of a laminar flame is often characterized as a basic property of the flame and is sometimes used in turbulent combustion models to categorize the turbulence scale of the mixture. From computed flame speeds and temperature profiles of C3H8/Oa/Ns (ø=1) flames we have determined widths, using definitions based on ( dT*sol;dx)max, Q (the heat release rate) and r (the characteristic chemical time) and characteristic distances have been determined from the transport properties of the burned (δ b) and unburned (δ u) gases. The flame widths are compared via the transport properties, (A/Cp), of the gas mixtures in the flame where A is the thermal conductivity and Cp is the heat capacity. A derived or approximate transport property for the flame widths is defined by the product of the mass flow rate (Mƒ) and the flame width. The functional dependence of these flame widths is compared by varying the Na fraction and initial mixture temperature. Both the set of Na fractions and mixture temperatures show the same range of flame speeds (40–350 cm/sec), but exhibit very different flame width values and dependence. The values of the derived transport properties from the ( dT/dx) max definition approximate the transport properties of the burned gas mixture (ST∼2*SI,) while those from the characteristic chemical time approximate the transport properties of the unburned gas mixture (δt;∼$). However, the values of the derived transport property based on the half-width of the heat release rate gives physically unreasonable transport properties in excess of either the burned or the unburned gases. These calculated flame widths differ significantly in absolute value and show a non-linear dependence on dilution. Although flame speeds for increasing mixture temperature and for differing dilutions are similar, the flame widths calculated for increasing mixture temperatures decrease only slightly compared to those for decreasing dilutions. These definitions of flame width, although given the same name, do not describe similar flame properties. The flame width definition based on the temperature gradient is proposed to be the proper specification of a laminar length scale because it is based on the physically measurable temperature profile and because it incorporates the effects of both heat release and transport which determine the temperature profile.