Numerical investigation of steady state laminar natural convection of power-law fluids in side-cooled trapezoidal enclosures heated from the bottom

Laminar, steady-state, natural convection of power-law fluids in 2-D trapezoidal enclosures with a heated bottom wall, adiabatic top wall and cooled inclined sidewalls has been analyzed for the first time based on numerical simulations for a range of different values of nominal Rayleigh number (i.e. (Formula presented.)), power-law index (i.e. (Formula presented.)), nominal Prandtl number (i.e. (Formula presented.)) and sidewall inclination angle (i.e. (Formula presented.)). It has been found that the mean Nusselt number (Formula presented.) increases with increasing nominal Rayleigh number (Formula presented.) (up to a 187% increase for (Formula presented.) and up to 2.3% increase for (Formula presented.) between (Formula presented.) and (Formula presented.)) and decreasing power-law index (Formula presented.) (up to a 4.1% increase for (Formula presented.) and up to 193% increase for (Formula presented.) between (Formula presented.) and 1.8) due to the strengthening of advective transport. Moreover, an increase in the sidewall inclination angle (Formula presented.) leads to a decrease in (Formula presented.) (approximately 44% decrease for (Formula presented.) across values of (Formula presented.) and up to 33% decrease for (Formula presented.) across values of (Formula presented.)) due to an increase in the area for heat loss from the cavity. It has been found that (Formula presented.) does not vary significantly with the values of (Formula presented.) considered in the current study. Furthermore, a new correlation for the mean Nusselt number (Formula presented.) in this configuration has been identified which provides adequate approximation of the corresponding values obtained from the simulations

Flame self-interaction during turbulent boundary layer flashback of hydrogen-rich premixed combustion

A three-dimensional direct numerical simulation database of turbulent boundary layer flashback of a hydrogen-rich premixed flame with an equivalence ratio of 1.5 has been analyzed to investigate flame self-interaction (FSI) events. The nonreacting turbulence characteristics of the channel flow are representative of the friction-velocity-based Reynolds number, Reτ=120. A skeletal chemical mechanism with nine species and twenty reactions is employed for the representation of hydrogen-air combustion. Three definitions of the reaction progress variable, c, based on the mass fractions of H2, O2, and H2O, have been considered to define the progress variable. It is found that the FSI events predominantly occur close to the burned gas side for all definitions of c at all the wall normal distances. No FSI events adjacent to the wall have been identified for the c definition based on O2 and H2O mass fractions, whereas FSI events occur for c based on H2 in the near-wall region. In the regions further away from the wall, all c definitions show that tunnel formation and tunnel closure type FSI events remain predominant, which is consistent with the earlier findings by Griffiths et al. [Proc. Combust. Inst. 35, 1341 (2015)1540-748910.1016/j.proci.2014.08.003] involving hydrogen-air premixed flame under shear flow conditions. In this work for c based on H2 mass fraction, unburned gas pockets have also been identified at all wall normal distances and are a consequence of the hydrogen-rich nature of the flame. The reason for the variations in topologies with the change in the definition of c based on different species and wall normal distance is a consequence of several factors, including the changes in the level of turbulence within the turbulent boundary layer, heat loss to the isothermal wall in the near-wall region, and the differential diffusion induced by the nonunity Lewis number. The results from the current analysis show that the turbulent boundary layer and heat loss at the wall play important roles in determining the FSI topologies. The differences in the qualitative nature and distributions of the FSI events between different definitions of c have important implications on the possible extension of flame-surface-based modeling methodology for hydrogen-rich flames within turbulent boundary layers