Jet Fire - Flame shape

A calm wind situation

Opening diameter: m
Molecular weight of fuel: kmol/kg
Gas specific heat ratio (gamma):
Upstream pressure at the opening: Pa bar psi
Ambient pressure : Pa bar psi
Distance from the orifice to the visible flame tip (L) minus the lift-off distance (s): m

Release type :
Lift-off distance : m
L : m

diameter (m)
axial distance from the orifice (m)
At x : m
flame diameter : m

In practice a fire resulting from a high-pressure gas release will have a shape of a frustum of a cone with an opening angle of 20-25o. In case of large jet fires there may be smoke production from regions of the flame plume, which to certain extent may cover or shield large parts of the flame plume.

The first thing this calculator does is to calculate the effective Mach number, Mef :
γ = isentropic exponent (heat ratio) of the actual gas = cp/cv (-)
pv = upstream pressure at the event orifice (bar)
po = atmospheric pressure (bar)
The lift-off distance, s, is then determined from the following equation by Kent:
ue = exit velocity (m/s)
ua = the average jet velocity (m/s) ≈ 0.4⋅ue
De = the orifice or exit diameter (m)
The effective exit velocity which is the effective exit Mach number,Mef ,times the local sound speed, is given by the following relation:
where Tv is the upstream gas temperature and R is the individual gas constant of the actual gas which can be found by dividing the universal gas constant(=8.314 kJ/kgK) by the molecular weight of the gas.

The well known model of Hawthorne et al., Ref. /6-12/, is then used to predict the distance, L, from the orifice to the visible flame tip:
Ct = mole ratio of fuel to reactants
α = mole ratio of reactants to products (-)
Tad = adiabatic flame temperature (K)
Tv = temperature of the fuel before it is released (K)
M0 = molecular weight of air = 29 (kmol/kg)
Mf = molecular weight of fuel (kmol/kg)

Since α ≈ 1, Ct < 0.1 and Tad/Tv varies between 7 and 9 for most actual fuels, we aproximate the equation above.

McCaffrey et al., Ref. /6-13/, state that for choked releases(i.e. releases with an effective Mach number, Mef,greater than unity) the exit diameter, De, has to be replaced by a hypothetical nozzle(i.e. a convergent-divergent nozzle) which has a diameter, Def, given by the following equation:

The diameter of the jet flame plume (shown in the graph) is determined from the following equation by Baron, Ref. /6-15/:
where x = the axial distance from the orifice (m).
Reference: Scandpower A/S,SINTEF-NBL"Handbook for Fire Calculations and Fire Risk Assessment in the Process Industry" 3rd Edition 1997