Ignition criterion for turbulent high velocity, combustible gases with pilot-stabilized flames

Summary An ignition criterion has been derived for flowing, high velocity, combustible gases with pilot stabilized flames at low pressure.The behavior of ignition temperatures and induction periods (calculated with the criterion) with ignition compositions and turbulence levels agreed with literature findings.It was also found that the criterion could be used to fully delineate an ignition limit — velocity curve if only lean ignition limit — velocity data were available.Nomenclature D laminar diffusivity, ft²/sec - H _f heat of formation of water (pilot product), Btu/lb mole - H _c heat of combustion of combustible, Btu/lb mole - K fraction of heat of combustion of combustible mixture delivered during induction period - R _t correlation function between a particle velocity component at some time and the velocity component of the particle after a time t - T R _t dt - U cold stream velocity, ft/sec based on empty combustion chamber - U _p pilot gas velocity, ft/sec - C _p mean specific heat of combustible mixture, Btu/lb, mole °F - C _p ^/1 mean specific heat of pilot products Btu/lb, mole °F - f fraction of turbulence, u/U - l ₁ mean eddy diameter, ft (available in references 8 & 9) - r _p radius of pilot port, feet - t induction period, seconds - u ¹ fluctuating velocity, feet/second - y mole fraction combustible in air - , , functions - _i ignition temperature, °F - ₀ cold stream temperature, °F - molar density of combustible-air mixture, lb moles/ft³ - ¹ molar density of pilot products, lb moles/ft³