Vapour cloud explosion blasts - Multi-Energy method

Energy available (E):		J MJ GJ
Ambient pressure (po) :		Pa bar psi
Explosion strenght:		(1 - 10)
Distance from the explosion center (r) :		m

Combustion energy-scaled distance (r') :
Scaled peak side-on overpressure (Ps')
Scaled peak dynamic overpressure (pdyn')
Scaled positive phase duration (tp')
Peak overpressure (Ps) :	Pa
Positive phase duration (tp) :	s
Positive impulse (is) :	Pa.s
Peak dynamic pressure (pdyn) :	Pa

---

This calculator predicts the maximum overpressure, positive pulse duration, positive phase impulse and dynamic
overpressure at a specified distance from a defined gas explosion source. The formulas used are parametrizations
of the published Multi-Energy method (for ref. see below).

Note that the calculated pressure is a side-on pressure. If the pressure wave hits any target in its way, the
measured pressure will typically be greater than the one estimated with ME method. Click here to learn more.

The multi-energy method (van den Berg, 1985) is a more sophisticated method than the TNT-equivalence method.
It can estimate the blast from gas explosions with variable strength. The method is based on numerical simulation
of a blast wave from a centrally ignited spherical cloud with constant velocity flames. By varying the flame velocity,
a set of curves for different explosion strengths (i.e. explosion pressure inside the cloud) have been produced.
Next figure shows the two of three dimensionless curves that are used in the multi-energy method:


For a detonating cloud, curve 10 can be used. For a deflagration (curves 1 to 9) we see that the pressure profile
inside the cloud is not a shock wave followed by an expansion wave, but it can either be a shock wave followed
by increasing pressure that drops off after the passage of the flame front or a sonic wave (i.e. gradually increasing
pressure) that drops after the flame front.
However, as a blast propagates away from the centre of the explosion, the gradient at the front will steepen
and eventually become a shock wave, like the blast from a TNT charge.

The difficult part of a multi-energy method analysis is to choose:

• The explosion pressure within the exploding gas cloud (i.e. the charge strength)
• The combustion energy, E, given the size of the gas cloud contributing to the blast (i.e. the charge size).

The multi-energy method does not give any information about which explosion pressure (charge strength) to choose
in a blast analysis. That information has to be found separately by using numerical simulations, experimental data
or make a conservative assumption. The combustion energy, E, is also a parameter that is not straightforward to
estimate.

The first thing the calculator does is to calculate the scaled distance r' which is the distance r of the location
under consideration to the centre of the explosion divided by the energy available E and the ambient pressure p_o:

r' = r /(E/p_o)^1/3

Then the scaled peak side-on overpressure P_s', the scaled peak dynamic pressure p_dyn' and the
scaled positive phase duration t_p' is read off the charts depending on assumed explosion strength.

So the peak overpressure P_s, the positive phase duration t_p, the peak dynamic pressure p_dyn
and the positive impulse i_s is calculated:

P_s = P_s' • p_o

t_p = t_p' • (E/p_o)^1/3/c_o

p_dyn = p_dyn' • p_o

i_s =1/2 • P_s • t_p

References: Bjerketvedt, D., Bakke, J.R. and Wingerden, K. van (1993)" Gas explosion handbook" Version1.2
"Methods for the calculation of physical effects. 'Yellow book'. CPR 14E (Part 2)"