  Transient premixed hydrogen/air flames contracting through inhomogeneous fuel
distributions and subjected to stretch and pressure oscillations are
investigated numerically using an implicit method which couples the fully
compressible flow to the realistic chemistry and multicomponent transport
properties. The impact of increasing {\em negative} stretch is investigated
through the use of planar, cylindrical and spherical geometries, and a
comparison with the results from {\em positively} stretched expanding H2/air
flames (MALIK2010) and CH4/air flames (MALIK2012a) is made. A flame relaxation
number $n_R=\tau_R/\tau_L$ ($\tau_R$ is the time that the flame takes to return
to the mean equilibrium conditions after initial disturbance; $\tau_L$ is a
flame time scale) decreases by 10\% with increasing {\em negative} stretch, in
contrast to the two expanding flames where $n_R$ decreased by 40\% with
increasing {\em positive} stretch. $n_R$ appears to much more sensitive to
variations in positive/negative curvature than to the thermo-chemistry of
different flame types. $n_R$ may thus be a useful indicator of the strength of
flame-curvature coupling. The spectra of pressure fluctuations $E_p(\omega)$
scale close to $\sim\omega^{-3}$, which is steeper than in the expanding H2/air
flames where $E_p(\omega)\sim\omega^{-2}$. Rapid transport ('flapping') of the
flame front by the largest convective velocities induced by the random pressure
fluctuations is prominent because of the lack of gas velocity ahead of the
flame, $u_g=0$. 'Memory effects' between fuel consumption and the rate of heat
release is obscured by the flapping, although the contracting flames display
short time-lags in the mean.
