James S. T'ien

Diffusion flame extinction at small stretch rates: The mechanism of radiative loss☆

Abstract A theoretical analysis of diffusion flame extinction in the stagnation point region of a condensed fuel has been made including radiative heat loss from the fuel surface. In addition to the blowoff limit normally found when flame stretch rate is large, an extinction limit has been identified when the flame stretch rate becomes sufficiently small. This limit occurs as a result of flame temperature reduction when the rate of radiative loss becomes substantial compared with the rate of combustion heat release. A flammability map using oxygen mass fraction and stretch rate as coordinates shows that the extinction boundary consists of a blowoff and a radiative extinction branch. The merging point of the two branches defines a fundamental low oxygen flammability limit.

A theory of flame spread over a solid fuel including finite-rate chemical kinetics

Abstract A theory for the steady-state flame spread over a thermally thin solid fuel is developed in this study. The model considers a laminar diffusion flame in a uniform opposed flow and includes the two-dimensional, elliptic, gas-phase energy, and species equations with one-step overall chemical reaction and second-order, finite-rate Arrhenius kinetics. The unsteady, solid-fuel equations neglect heat conduction ahead of the flame but include transient heating and Arrhenius pyrolysis kinetics and are coupled to the quasisteady gas phase. The equations are solved in the laboratory coordinate system. In this study the two-dimensional distributions of temperature and species are obtained, including the low reactivity zone in the flame region. The solid-fuel surface profiles indicate a region of almost uniform temperature (vaporization temperature) during pyrolysis for some parameter values; however, the value is not universally constant for the fuel and does depend on the ambient parameters (pressure, oxygen mass fraction, and magnitude of opposed velocity). The dependence of the flame-spread rate on the ambient parameters is investigated, and qualitative agreement is obtained with experimental results in the near-extinction-limit region. Quantitative agreement with experimental data depends on the choice of parameter values, especially the gas-phase kinetics model parameters, which are generally unknown. The flame-extinction limits due to increased opposed velocity, reduced pressure, and reduced ambient oxygen mass fraction are all obtained in the results calculated from this theory.

Near-Limit Flame Spread over a Thin Solid Fuel in Microgravity

Diffusion flame spread over a thin solid fuel in quiecent and slowly moving atmospheres is studied in microgravity. The flame behavior is observed to depend strongly on the magnitude of the relative velocity between the flame and the atmosphere. In particular, a low velocity quenching limit is found to exist in low oxygen environments. Using both the microgravity results and previously published data at high opposed-flow velocities, the flame spread behavior is examined over a wide velocity range. A flammability map using molar oxygen percetages and characteristics relative velocities as coordinates is constructed. Trends of flame spread rate are determined and mechanisms for flame extinction are discussed.

Diffusion Flame Stabilization at the Leading Edge of a Fuel Plate

Abstract A theoretical model of a laminar diffusion flame at the leading edge of a fuel plate in a forced convective flow is presented and solved numerically to study the flame stabilization and blowoff phenomena. The system of governing equations consists of the two-dimensional Navier-Stokes momentum, energy and species equations with a one-step overall chemical reaction and second-order, finite rate Arrhenius kinetics. The computation is performed over a wide range of Damkohler numbers. For large Damkohler numbers, envelope flames are found to exist where the computed fuel evaporation rate, the flame stand-off distance and the velocity profiles show certain similitude. As the Damkohler number is lowered, a transition to open-tip flame takes place where the flame becomes stabilized on the sides of the fuel plate. Further decreasing of the Damkohler number pushes the diffusion flame downstream out of the leading edge region. In this paper, the flame structures of the envelope and the open-tip flames are p...

Oscillatory Burning of Solid Propellants including Gas Phase Time Lag

Abstract An analysis has been performed for oscillatory burning of solid propellants including gas phase time lag. The gaseous flame is assumed to be premixed and laminar with a one-step overall chemical reaction. The propellant is assumed to decompose according to the Arrenhius Law, with no condensed phase reaction. With this model, strong gas phase resonance has been found in certain cases at the characteristic gas-phase frequencies, but the peaking of the acoustic admittance is in the direction favoring the damping of pressure waves. At still higher frequencies, moderate wave-amplifying ability was found. The limit of low frequency response obtained previously by Denison and Baum was recovered, and the limitations of the quasi-steady theory were investigated.

Gas-phase radiative effects on the burning and extinction of a solid fuel

Abstract Gas-phase radiative effects on the burning and extinction of a solid fuel in a stagnation-point flow geometry are investigated using a statistical narrow-band model with carbon dioxide and water vapor as the radiative participating media. The model, coupled to other flame conservation equations with a one-step overall gas-phase chemical reaction and Arrhenius solid pyrolysis relation, is solved numerically. Flame temperature, solid burning rate, and heat fluxes are examined as functions of stretch rate. Using ambient oxygen percentage and stretch rate as coordinates, A U-shaped extinction boundary is identified. The extinction behavior at low stretch rates is qualitatively similar to that predicted by earlier theory with only surface radiation loss. However, gas radiation introduces additional heat loss from the system and shrinks the solid flammable domain. In addition, gas radiation can cause a substantial decrease of flame temperature and constitutes a significant portion of the heat feedback to the solid at low stretch rates. In the second part of the paper, a computationally less intensive gray gas radiation model is tested. As with a number of earlier investigations, the use of Planck mean absorption coefficient is found to overpredict net emission and flame radiative loss. By multiplying a correction factor (less than 1) in front of the Planck mean absorption coefficient, it is possible to compute many global flame properties with reasonable accuracy. An empirically determined formula is given to find the value of this correction factor for a given flame. This is offered as an engineering approach for the flame radiation treatment.

Near-limit flame spread over paper samples

Abstract In this study the near-limit characteristics of a spreading flame are considered. Flame spreading rates and temperature profiles are measured as extinction conditions are approached. The flame is extinguished by increasing the heat loss, reducing the total pressure, or reducing the oxygen mole fraction in the environment. The gas phase temperature profiles are obtained with fine-wire thermocouple probes. The flame spreading results show that the power-law correlations of McAlevy and Magee [3] do not remain valid near the extinction limit. In all cases the slope of the Log (flame spread rate) vs. Log (total pressure) curves increase and approach vertical at extinction. Differences in vertical and horizontal flame spreading are discussed. The flame temperature profiles are examined for a near-limit flame, but the total pressure level is the only parameter changed. In the near-limit flame the maximum flame temperature is reduced slightly, but the flame is enlarged in physical size greatly. It is observed that near the pyrolysis front, heat transfer forward in the gas phase and normal to the fuel surface are of the same order of magnitude.

Combustion and extinction in the stagnation-point boundary layer of a condensed fuel

Abstract The combustion and extinction phenomena in the stagnation point boundary layer of a condensed fuel is studied experimentally and theoretically with emphasis on the near-limit flame. The numerical analysis assumes a second-order forward overall chemical reaction in the gas phase, with gas-phase activation energy and modified frequency factor, determined by comparison with the experimental results. The effect of external radiation on the extinction limit is computed using a simplified model. Burning rates and extinction data are determined from measurements taken on polymethylmethacrylate samples in an opposed-jet diffusion flame apparatus. Favorable agreement between experimental extinction data and theoretical predictions is obtained for a gas-phase activation energy of 30 kcal/mole and a modified frequency factor of 5.2 × 107 sec−1.

A model of low-speed concurrent flow flame spread over a thin fuel

Abstract A numerical model is developed to examine steady, laminar flame spread and extinction over a thin solid fuel in low-speed concurrent flow. The model incorporates an elliptic treatment of the upstream flame stabilization zone near the fuel burnout point, and a parabolic treatment of the downstream flame, which has a higher flow Reynolds number. This provides a more precise fluid-mechanical description of the flame than using parabolic equations throughout, and is the first time such an approach has been used in concurrent flame spread modeling. The parabolic and elliptic regions are coupled smoothly by matching boundary conditions. The solid phase consists of an energy equation with surface radiative loss and a surface pyrolysis relation. Calculations (with the flame spread rate being an eigenvalue) are performed for forced flow without gravitational influences in a range of velocities which are lower than those induced in a normal gravity buoyant environment. Steady spread with constant flame and...

A numerical analysis of flame flashback in a premixed laminar system

Abstract The flashback and the structure of premixed laminar flames are investigated theoretically. The mathematical model includes the axisymmetric Navier-Stokes energy and species equations with one-step overall chemical reaction and second-order finite rate Arrhenius kinetics. Flashback is examined as a function of incoming velocity profiles, wall velocity gradients, and tube radius. Flame structure at the flashback limit indicates the intrinsic multidimensional nature of the flashback phenomena. The flame is found to generate a local pressure plateau near the flame front which causes an upstream influence on the incoming flow. The calculated flame velocity is shown to be greater than the one-dimensional premixed flame speed, and this is attributed to the flame-pressure interaction. The limitation of using the quasi-one-dimensional velocity balance concept as a predicting tool for flashback is discussed.