Experimental evaluation of Markstein-number influence on thermoacoustic instability

Darrieus–landau and Thermo-Acoustic Instabilities in Closed Vessel Explosions

“…This was followed by low intensity primary acoustic oscillations (amplitude about 0.5 kPa) that, as in Kaskan's study, stabilised after an initial growth. This stabilisation created a planar flame propagating at the laminar burning velocity, also reported by Aldredge and Killingsworth (2004). With faster flames, secondary acoustic instability readily developed, with larger pressure amplitudes and more enhanced burning velocities.…”

“…The contrasting behaviour of the rich i-octane flame, shown in Figure 9b, is discussed in the next section. Such reductions in D-L,T-D instability have been observed during flame propagation along tubes by Kaskan (1953), Searby (1992), and Aldredge and Killingsworth (2004). The peak value of u n of 2.19 m=s in Figure 8 occurred at about the peak value of the rate of change of heat release rate of 270 MW=s.…”

“…Here, an important difference is that the tubes exhibited more coherent excitable resonant acoustic frequencies than the spherical bomb. The data from the tube explosions with methane-air of Aldredge and Killingsworth (2004) suggested a ratio of u n =u ' of about 6.4 at / ¼ 0.8 and of about 2.9 at the larger Markstein number when / ¼ 1.2.…”

“…More recently, Aldredge and Killingsworth (2004) have investigated the influence of Markstein number on thermo-acoustic instabilities of methane-air flames in an annular channel, again open to the atmosphere. The more stable flames, with higher Markstein numbers, required greater amplitudes of axial velocity fluctuation to excite the secondary thermo-acoustic instabilities.…”

Flame-Surface Advection in Transient Periodic Flow

“…Hence, in this case the fractional increase in the burning speed of the quasi-planar flame above S L is a result of and equal to the fractional increase in the flame-surface area above A yz caused by the transient, nonuniform advection field U, as described earlier (Williams, 1985). Equation provides for more generally applicable results beyond the case of Huygens propagation (S N = S L ), accounting for variations of the reactant density and local normal propagation speed along the flame (e.g., caused by effects of local flow-field strain and flame-surface curvature) (Aldredge, 2005;Aldredge and Killingsworth, 2004;Aldredge and Williams, 1991;Clavin, 1985;Clavin and Garcia-Ybarra, 1983;Clavin and Williams, 1982;Joulin and Clavin, 1979;Kwon et al, 1992;Law, 1988;Lewis and von Elbe, 1961;Markstein, 1953Markstein, , 1964Markstein and Squire, 1955;Searby and Clavin, 1986;Sivashinsky, 1983;Tseng et al, 1993;Williams, 1985). Consider now the propagation of a wrinkled, quasi-planar surface described by x = f 0 (y, z, t).…”