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Transient premixed hydrogen/air flames contracting through inhomogeneous fueldistributions and subjected to stretch and pressure oscillations areinvestigated numerically using an implicit method which couples the fullycompressible flow to the realistic chemistry and multicomponent transportproperties. The impact of increasing {\em negative} stretch is investigatedthrough the use of planar, cylindrical and spherical geometries, and acomparison with the results from {\em positively} stretched expanding H2/airflames (MALIK2010) and CH4/air flames (MALIK2012a) is made. A flame relaxationnumber $n_R=\tau_R/\tau_L$ ($\tau_R$ is the time that the flame takes to returnto the mean equilibrium conditions after initial disturbance; $\tau_L$ is aflame time scale) decreases by 10\% with increasing {\em negative} stretch, incontrast to the two expanding flames where $n_R$ decreased by 40\% withincreasing {\em positive} stretch. $n_R$ appears to much more sensitive tovariations in positive/negative curvature than to the thermo-chemistry ofdifferent flame types. $n_R$ may thus be a useful indicator of the strength offlame-curvature coupling. The spectra of pressure fluctuations $E_p(\omega)$scale close to $\sim\omega^{-3}$, which is steeper than in the expanding H2/airflames where $E_p(\omega)\sim\omega^{-2}$. Rapid transport ('flapping') of theflame front by the largest convective velocities induced by the random pressurefluctuations is prominent because of the lack of gas velocity ahead of theflame, $u_g=0$. 'Memory effects' between fuel consumption and the rate of heatrelease is obscured by the flapping, although the contracting flames displayshort time-lags in the mean.

A numerical study of the the response of transient inhomogeneous flames  to pressure fluctuations and negative stretch in contracting hydrogen/air  flames