Stationary premixed flames in spherical and cylindrical geometries

Abstract

Stationary source-free spherical flames ("flame balls") in premixed combustible gases were studied by employing low-gravity fog) environments in a drop tower and an aircraft flying parabolic trajectories to diminish the impact of buoyancy-induced convective flow. Flame balls were found in all mixture families tested when 1) the Lewis number Le of the deficient reactant was sufficiently low and 2) the compositions were sufficiently close to the flammability limits. Probably as a consequence of the reduction in buoyant convection, the flammability limits at pg were significantly more dilute than those at Earth gravity; for example, 3.35% HI vs 4.0% HI in lean Hi-air mixtures. By comparison with analytical and computational models, it is inferred that the phenomenon is probably related to diffusive-thermal effects in low-Li mixtures in conjunction with flame-front curvature and radiative heat losses from the combustion products. The chemical reaction mechanism appears to play no qualitative role. In the aircraft experiments, the gravity levels (« 10-2 £o) were found to cause noticeable motion of flame balls due to buoyancy, which in turn influenced the behavior of flame balls. At these g levels, a new type of transient, nearly cylindrical flame structure, termed "flame strings," was observed.Nomenclature D = mass diffusivity E = overall activation energy of chemical reaction Fr = Froude number g = acceleration of gravity go = Earth gravity Le = Lewis number P = pressure R = radius of flame ball (R = gas constant r = radial coordinate T = temperature r ad = adiabatic combustion temperature of homogeneous mixture T b = adiabatic temperature of flame ball T* -temperature at flame ball surface V = drift velocity of flame ball a. = thermal diffusivity (3 = nondimensional activation energy, = E/(RT fjig = microgravity P -gas density </ > = equivalence ratio 4> c = critical equivalence ratio, = Le fu /Le ox

Stability of a spherical flame ball in a porous medium

“…Flame balls can be stabilized by uniform and constant heat losses only in the burnt gases [6] as well as by relatively weak linear heat losses that nevertheless are of leadingorder importance when temperatures are close to an ambient, far-field value [7]. Non-uniform velocity fields can also stabilize flame balls [8], while non-uniform enthalpy and boundary effects can induce some movement in a stable flame ball [9][10][11][12].…”

“…Stable flame balls have been found to arise only when the Lewis number of a lean reactant is less than unity [5][6][7][8][9][10][11][12]. In some sense, the presence of the non-conducting solid can be thought of as adding to the heat capacity of the system, which in turn can be thought of as reducing an effective Lewis number of the two-phase medium as a whole.…”

The structure of lean hydrogen-air flame balls

“…1 and 2 represent the variation with equivalence ratio / ¼ 8Y H 2 1 =Y O 2 1 of the flame-ball radius r f and of the peak temperature T max , with the former plot including also results of experiments [11,12]. To be consistent with the reduced-chemistry results presented below, the value of r f is defined in the numerical computations as the radial location where the temperature takes its crossover value (given approximately by T c ¼ 1000 K at atmospheric pressure, as obtained from Eq.…”

“…as obtained from the seven elementary reactions [11]; solid symbols: [12]), from computations with 21-step chemistry (solid curve) and with one-step chemistry (dashed curve) and from the reaction-sheet analysis (dot-dahed curve).…”

A computational study of the transition from localized ignition to flame ball in lean hydrogen/air mixtures

“…This concept was further developed by Buckmaster et al [7,8], via asymptotic analysis, showing that, in the presence of heat loss in the near field, the solution with the smaller equilibrium radius is unstable to one-dimensional perturbations while that with the larger equilibrium radius is stable. It was thus suggested that the flame balls observed in experiments carried out in microgravity [9,10] were stabilized by heat loss and that flame balls can be observed only when the Lewis number is smaller than unity [11].…”