Hi Everyone. I am trying to dynamically model the effects of an three phase arc flash to estimate the over-pressure inside a cublicle by using the ISC method. In order to do that, I need the evolution of the total amount of energy released by the arc flash with the time. Can anyone help to find that equation?? I have found some articles modelling the energy release as drop voltage * arcing energy * time, other articles modelling that energy as arcing time ^2 * time, ...

Thanks in advance.

Eugenio

Only published model I'm aware of that does what you are asking for is Lee's model for arc blasts. However, it has a couple major defects. It does not consider the fact that voltage and current do not respond the same as far as development of an arc goes. Second, arc blast physics do not mean that the full amount of energy released goes into an arc blast. During a short interval at the beginning, no substantial arc blast is developed. Then a short period occurs where superheated air is released in a concussive force (arc blast), and then after that point the air pressure is reduced to the point where although heat continues to be released and is transmitted via radiation (the predominant form of energy release for high temperature systems), the arc blast is largely over with. In short, Lee's model doesn't match reality at all. The couple charts that the IEEE/NFPA joint study on arcing faults have released confirm this as well as the fact that the force of the arc blast itself is pretty much a constant over a wide range of voltages and currents.

There is another model on Mersen's web site that has re-evaluated the IEEE 1584 data set with a time-based model that although it still might not be the "right" answer improves substantially on IEEE 1584 (Wilkin's model). It is largely empirically based. Lee's model is the theoretically based one but does a poor job of modelling anything beyond 600 V and low level arc flashes.

Another humble opinion relative to comments on radiated energy. I believe I am correct in stating that since the IEEE arc-in-a-box has been used for PPE testing, the PPE suppliers have found that most of the energy transfer is convected. Prior to the IEEE box, the ASTM rod test did have high radiated energy content, but again, I believe that that was proven wrong once the IEEE box testing started. I believe that is one reason the face shields have become lighter in tint. If I am wrong please point me in a direction that substantiates either side. I think there is a PPE vendor that belongs to this forum, perhaps he could interject.

Much of data on the Mersen web site refers to a variation in the IEEE box testing, that is where they insert a barrier below the bare conductors that starts the arc, they refer to this as the horizontal effect. You can include that condition within Easy Power in the arc flash bus drop down.

Another humble opinion relative to comments on radiated energy. I believe I am correct in stating that since the IEEE arc-in-a-box has been used for PPE testing, the PPE suppliers have found that most of the energy transfer is convected.

No way. Radiative heat is transferred proportional to the 4th power of the temperature delta. Convection is only linear. Almost all industrial heating processes over about 1000 F operate on radiative heat transfer primarily because it is so massively more efficient. Almost all kilns and metallurgical processes operate this way. At the temperatures that an arc produces, it is clearly going to be radiative heat transfer.

Just because it's a relatively crummy reflector though with an emissivity of around 0.95 for painted objects while the paint is still present, dropping down to around 0.6 once it burns off, at the temperatures in question (6000 F is thrown around a lot), and not having the ideal parabolic shape, the box is still going to do a reasonably good job of concentrating the arc energy. From what I've seen, it roughly triples the resulting incident energy.

I don't see where convective heat transfer enters into the equation or would need to. Convective heat transfer at the temperatures in question is going to be easily <10% of the heat transferred, because even in a cement kiln operating in the 2500 F range, convective heat transfer is only about 10% of the total heat transfer.

Face shield tinting has to do with UV and visible light, not heat transfer. They got lighter because the manufacturers switched over to materials which were still opaque in the UV spectrum while allowing more visible light to pass through rather than taking the broad spectrum approach of reducing light transmission at all wavelengths. It's the same trick that makes E-rated glass work (almost opaque at IR wavelengths, but allows almost all visible light to pass through).