| A numerical model is developed to examine steady laminar flame spread and extinction over a thin solid in concurrent flows with flame radiation. The fluid mechanical description in the model includes the elliptic momentum, energy and species equations with a one-step second-order finite rate Arrhenius reaction. The multidimensional nature of radiation field, involving gray absorbing, emitting and nonscattering media (CO{dollar}sb2{dollar} and H{dollar}sb2{dollar}O), is simulated by the S-N discrete ordinates method. A simplified thermally thin solid phase treatment assumes a zeroth-order pyrolysis relation and includes radiative interaction between the surface and gas phase. Computations are performed for purely forced flow in zero gravity using the oxygen percentage and free stream velocity as parameters. Selected results are presented showing the detailed flame profile, flow structure, and flame spread characteristics. A flammability boundary is determined, which consists of two branches. The low-speed quenching branch is due to radiative losses from both the gas phase and solid surface, and the high-speed blowoff branch is due to inadequate flow residence time.; The effect of gas radiation on flame behavior is examined by comparison with results that neglect gas radiation. The results indicate that the influence of gas radiation is important both in the gas phase and at the solid surface. In a low-speed flow, the flame temperature decreases, the flame size shrinks, and the flame spread rate is lowered when gas radiation is included. For high-speed flow, gas-phase radiation cools the flame, but the radiative heat flux feedback is increased in the solid pyrolysis region, increasing the fuel vaporization rate. This in turn results in a higher spread rate for these flames when compared with computed results that neglect gas radiation. With gas radiation, quenching occurs at a higher flow velocity, but the blowoff limit is essentially the same when compared to the model predictions without gas radiation.; The effect of solid emissivity on the flame behavior is also explored. It is found that as the solid emissivity decreases, the flame becomes longer and the flame spread rate increases. However, with gas radiation, the flame spread rate increases more slowly when compared to the model predictions without gas radiation. When gas radiation is included, converged steady state solutions are obtained for any values of solid emissivity.; An examination of the effect of solid thickness shows that when the solid thickness {dollar}tau{dollar} is greater than a threshold value, the flame size and profile are essentially the same and the spread velocity is approximately proportional to 1/{dollar}tau{dollar}. But when the thickness is decreased below this threshold, the flame size shrinks, the flame temperature drops, and the flame spread rate increases more slowly than merely as 1/{dollar}tau{dollar}. When the solid becomes sufficiently thin, the flame goes out due to the lack of sufficient fuel vapor to sustain the chemical reaction. |
