Some aspects of the mathematical modelling of fireballs

Abstract

The development of large-scale reballs is a typical result of explosions associated with accidental fuel releases in the oil and process industries. The two major mechanisms that lead to reball formation are vapour cloud explosions and boiling liquid expanding vapour explosions (BLEVEs). An ability to model reballs is extremely important from the point of view of safety and risk analysis. The present paper provides a state-of-the-art review of the computational techniques available for the mathematical modelling of reballs. The emphasis is placed on computational uid dynamics (CFD) modelling, based on Reynolds-averaged Navier-Stokes (RANS) equations for reactive ow. The results of calculations and estimations of reball hazards are compared with available experimental data. New results are presented for problems that are usually given less attention in reball studies. These concern estimations of air entrainment rates into reballs and potential strategies for reball suppression. Keywords: reball, vapour cloud explosion, computational uid dynamics modelling, suppression NOTATION B m Spalding's mass transfer number C aerosol concentration in the layer surrounding the reball (kg/m 3 ) C D drag coef cient C p speci c heat (J/kg K) C R eddy breakup constant C C aerosol concentration inside the reball (kg/m 3 ) d p droplet diameter (m) D reball diameter (m) Fr Froude number g acceleration due to gravity (m/s 2 ) h height of the reball above the ground (m), speci c enthalpy (J/kg) DH c heat of combustion (J/kg) I radiation intensity (W/m 2 ) I s radiation dose (J/m 2 ) k turbulence kinetic energy (m 2 /s 2 ), thermal conductivity (W/m K) l distance along the radiation ray (m) L latent heat of phase change (J/kg) L * characteristic length scale (m) m p mass of droplet (kg) M mass of fuel (kg) Nu Nusselt number p pressure (Pa) q heat ux (W/m 2 ) Q R heat source due to radiation (W/m 3 ) R radius of the reball (m) Re p particle Reynolds number s soot conversion factor for fuel S pf source term for variable f due to particles S f source term for variable f Sh Sherwood number t time (s) t b burnout time (s) t * characteristic time-scale (s) T temperature (K) U(u, v, w) velocity vector (m/s) X (x, y, z) Cartesian coordinate (m) Y mass fraction a absorption coef cient (m 71 ) G f exchange coef cient for variable f d ij Kronecker's symbol e turbulence kinetic energy dissipation rate (m 2 /s 3 ) m dynamic viscosity (kg/m s) n kinematic viscosity (m 2 /s) The MS was

The boiling liquid expanding vapour explosion (BLEVE): Mechanism, consequence assessment, management

“…As a result of these processes, the whole mass turbulently increases in volume, evolving towards an approximately spherical shape that rises, leaving a wake of variable diameter. Such fireballs can be very large, causing a very strong thermal radiation [29,30].…”

“…They work by destroying the active centers which are necessary to sustain the flame. AFEAs can be generated by the combustion of solid propellants [30,115].…”

Risks of Fire and Explosion Associated With the Increasing Use of Liquefied Petroleum Gas

“…As a result of these processes, the whole mass turbulently increases in volume, evolving toward an approximately spherical shape that rises, leaving a wake of variable diameter. Such fireballs can be very large, causing a very strong thermal radiation [26,27]. The size, the life, and the radiation intensity of a fireball may also depend on the temperature of the liquid lading [28], and whether the loss of confinement of the flammable material had occurred when the pressure inside was still rising [29].…”

Configuration factors for ground level fireballs with shadowing

“…However, fireballs can also be modeled as ground level spherical emitters (Novozhilov, 2003;Stepanov et al, 2011) with its radius just touching the ground throughout its duration (Mannan, 2012). This represents the most conservative case, since the fire is closest to people https://doi.org/10.1016/j.jlp.2017.12.010 Received 25 July 2017; Received in revised form 31 October 2017; Accepted 13 December 2017 and structures, engulfing them.…”

“…Therefore, the shape and size of the fireball and its relative position to the target must be taken into account. When conducting hazard or risk analysis of process vessels or storage tanks that contain flammable liquids or gases, it is important to be able to accurately compute the configuration factor (Makhviladze et al, 1999a,b;Roberts et al, 2000;Novozhilov, 2003;Stepanov et al, 2011).…”