The global response of a premixed laminar flame to the imposed stretch-rate is often expressed in terms of the stretched-flame-speed. For weakly stretched flames, it has been observed that the stretched-flame-speed varies linearly with respect to the stretch-rate. The corresponding slope is known as the Markstein length. Thus,

(14–26)

In Equation 14–26[110], is the flame-speed, is the Markstein length, is the stretch-rate, and the subscript 0 indicates unstretched condition. Thus, is the freely propagating laminar flame-speed which, for example, can be computed using the Premixed Laminar Flame-Speed calculator from Ansys Chemkin.

The steady-opposed-flow flame is one of main configurations (another example being spherically expanding flames) used in investigation of stretch effects on laminar flames. It can be noted that, in this configuration, the stretch equals the strain since curvature (which generally contributes to the total stretch) is absent. In an opposed-flow flame configuration, several successive simulations may be run wherein the inlet velocity is varied and thus the stretch-response of flames can be computed. The Markstein calculator allows an easy set-up for this and uses continuations on the inlet velocities.

The Markstein length from Equation 14–26 can be stated as with respect to unburned or burned mixture depending on the choice of of and . A consumption speed can be defined and computed as:

(14–27)

In Equation 14–27, and indicate density and mass-fraction, respectively, and is the mass-production rate. The subscript indicates the unburned state whereas the superscript implies fuel. While this quantity can be easily computed in numerical simulations, it cannot be directly measured in the experiments. Nonetheless, a Markstein length based on consumption speed and globally imposed stretch-rate can be unambiguously computed from the simulation data. Besides this, other formulations/definitions of Markstein length warrant extracting data from the velocity profile. Figure 14.4: Typical profiles of (normalized) axial velocity and heat release in an opposed-flow flame (premixed mixture impinging on burned products) shows a typical profile of axial velocity and heat-release in an opposed flow flame wherein premixed mixture impinges against hot combustion products. The imposed stretch-rate can be considered as the one just ahead of the pre-heat zone. The axial velocity at the maximum heat release location may be considered as the burned-gas velocity.

Figure 14.4: Typical profiles of (normalized) axial velocity and heat release in an opposed-flow flame (premixed mixture impinging on burned products)

Based on the axial velocity and its gradient at such locations, the Markstein length can be calculated so that it can correspond to a given/recommended experimental data.