ASYMPTOTIC RATE OF DECAY OF TURBULENCE IN A TUBE FOLLOWING A COMBUSTION-INDUCED STEP IN TEMPERATURE

Combustion in a ceramic tube produces a nearly discontinuous change in temperature of the premixed fuel and air at the flame front, from roo m temperature up to the adiabatic flame temperature (approximately 210 0 K). The upstream Reynolds number for a stable flame in a 9.5-mm tube is in the range of 3000-6000, corresponding to turbulent flow. Owing to property changes that accompany the severe increase in temperature at the flame front, the downstream Reynolds number is reduced below th e transitional value (approximately 2100); consequently the turbulence decays while the velocity profile approaches the parabolic one charac teristic of laminar flow. A previous study of ours revealed that, far downstream from the flame front, the turbulent energy decayed exponent ially with downstream distance. This paper examines the asymptotic beh avior of the k-epsilon model and compares the results to that for two- dimensional (axisymmetric) disturbances in a laminar flow. Both analys es predict exponential decay; however the exponent predicted by the k- epsilon model is substantially larger than the equivalent one for a tw o-dimensional disturbance. Differences in the two exponents highlight differences in the respective mechanisms for decay. The k-epsilon mode l is effective when the turbulence is almost fully developed, but is u nable to predict the rate of decay far downstream where the continuous spectrum of turbulent energy has given way to a discrete one.