Three-dimensional analysis for explosions of a propane-air mixture in cylindrical vessels

A mathematically simple spatial difference method has been applied for analysing three-dimensionally, and for illustrating graphically, the process of the development of a flame after the propane-air stoichiometric mixture is ignited. The calculated results show that the mathematical simulation can well express the process of mixture explosion in cylindrical vessels, and can evaluate the effects of laminar swirl flow on the flame development. It is concluded that the swirl motion deforms the flame front and accelerates the flame enlargement. Described also is a comparison of swirl flame calculation, with and without the centripetal effect caused by the difference in densities between burnt and unburnt gases.List of symbols A, A_f, A_K, A_W area, flame surface area, flame element area, and wall area - b_e heat penetration coefficient - C_d coefficient - C_p molar specific heat at constant pressure - G mass of gas - H cylinder height - h enthalpy and molar enthalpy - L effective length - M_j molecular weight - n, N normal unit vector and normal vector to flame surface - p pressure - q heat input per unit mass - r_c flame center location - r, R radius and vessel radius - R universal gas constant - Re Reynolds number - s_b, s_u flame speed and burning velocity - t time measured from spark-ignition - U_c inward moving velocity of flame center - u_u compression velocity of the unburnt gas just ahead of the flame front - U(u, v, w) velocity vector - v_i, V_i specific volume and volume of region-i - x_j mole fraction of specie-_j - x mass fraction of burnt gas - X(x, Y, z), X(x, r, ) orthogonal and cylindrical coordinate systems - Y_j mass fraction of specie-_j - Y mass fraction of burnt gas - small amount of change - change from the initial stateSuffixes ij flame element number - i region or state - j chemical species