Sciencemadness Discussion Board

modeling an electric arc

UncleJoe1985 - 22-10-2008 at 22:18

Hi everyone. To continue improving the efficiency of my arc furnace for nitric acid production, which you can see from my recent posts, I plan to do a computer simulation of various arc configurations and air flows. I've already have computed the gas velocities using OpenFOAM. Now I need some way to model arcs:

1. Current drawn from neon sign transformer

It seems this depends on the arc distance because I've noticed the transformer
gets hotter when I don't let the arcs grow upwards on the jacobs ladder. Can I safely measure this with a digital multimeter? It seems OK, but I don't want to waste $30 to find out.

2. Temperature as function of current and other factors?
This would be useful to compute how much NO is formed.

3. Voltage drop across arc as function of current and other factors?
Basically, I want to know what V I combination dissipates the most energy, while also trying to minimize the transformer's load. I've heard the arc voltage drop gets lower as current increases, so that probably means increasing current will result in diminishing power gains and eventually negative gain.

I couldn't find much on Google and Science Direct other than a ball park voltage drop of ~100V, which I don't think makes sense because that means @30mA, the arc is only dissipating 3W power! Any ideas?

[Edited on 23-10-2008 by UncleJoe1985]

not_important - 22-10-2008 at 23:42

1.) Measure the current into the transformer, at mains voltage, and reduce by the turns ratio (voltage step up, current step down). Works as average current, you'd need an oscope to get the actual current due to the non-linear nature of the arc as it initiates.

The arc has negative impedance, once it is struck you're pulling more than 30 ma unless the transformer hard limits current at that value.

dann2 - 23-10-2008 at 02:50


The following is from 'Neon Signs', Samual Miller & Donald G. Fink. 1935
It may be of some use.


[Edited on 23-10-2008 by dann2]

IMG_3940.JPG - 94kB

chief - 23-10-2008 at 03:18

Maybe one day I will try this:
==> since the object is to have a high temp , and to cool the arc fastly, so that the counter-reaction has no time to occur (quenching the reaction-products)
==> maybe something that unloads a big capacitor into the gases could work well, because
--> as long as the discharge is violent enough to cause a serious hydro-dynamics into the after-arc-plasma
--> so that it rapidly mixes with cold surrounding air
-> by whirling it effectively,out of the thermal expansion-energy of the plasma,maybe helped by the arc'sown magnetic forces

Probably that for anything would work better than a straight arc: A straight arc just radially expands ...
but if the arc is shaped, eg. by making it occur around some insulator, there will be introduced some dynamics into it ... alsothe insulator could do someof the cooling.

To me it seems the least profitable thing to do would be to just burn lot's of kWh for only 1 % efficiency ...
I also would try it by corona-discarging, or corona-induced arcing ...

My voltage-supply would look like this: A big capacitor, a heavy weight transformer (welding-type under oil ...), the capacitor-discharge into the welding-secondary,the primary might then deliver any arclength, no problem with the current ...
Also, if insulation-problems still would occur: It doesn't need a lot of windings with capacitor-discharge: Wind your own:Maybe 5 windings primary, and the PVC-insulated cable from a usual standard-cable as a secondary (insulates more than 3 kV alone by the PVC), an ready ...

Maybe the discharge should be made through a bed of insulating material, like eg sand, small glass-spheres etc.: This would cool rapidly.
Maybe this insulating material already could serve as the NO- OR NO2- binding-agent, like eg.CaCO3. The just airflow + an arc every now and then through the stuff, leaching it once in a while to get the Ca(NO3)2 OR Ca(NO2)2 ...
But of course the arc would have to be at least current-containing enough to have a more easy way through the air between the CaCO3-Particles than through the maybe not-too-high resistance of the CaCO3

UncleJoe1985 - 23-10-2008 at 15:42


The following is from 'Neon Signs'. It may be of some use."

An arc dropping half the voltage makes more sense. In that case, my arc would be dissipating ~130W.


Measure the current into the transformer, at mains voltage, and reduce by the turns ratio

Good call. I tried it, but also derated the primary power by 0.82 (wow, is it really this inefficient?) since on the transformer it says rated input current is 2.75A, while the output is 9 KV @30mA. I confirmed that rapidly breaking arcs, caused by using a high volume aquarium pump, causes the current to rise to 3.2A, while the low volume pump results in an average current of 2.4A.

I also devised a way to measure the voltage drop across the arc. I'll build a voltage divider using a 1 and 30 M ohm resistor so that I can measure it with my multimeter.

As for a model of voltage drop across an arc, I've found the Ayrton equation, which says

V = a + b * length + (c + d * length) / current

a, b, c, d are empirical constants

which would mean that power dissipation is proportional to arc length, assuming arc current is relatively constant w.r.t arc length. I think longer arcs also have 2 additional advantages:

1. Less power dissipated in NST, hence longer life.

2. Cooler, more efficient arcs - I'm not sure, but I think short arcs are too hot, > 6000 K? Producing NO should probably be most efficient around < 4000 K, although the yield is higher at higher temperatures, poor cooling will cause the extra yield to revert back to N2 and O2. Therefore, a longer arc that is cooler and has more air contact should be more efficient.

To confirm this, I slightly bent the electrodes to make them more aligned and caused the arcs to rise consistently to the top, where they span 6 cm. I noticed that the gas in my delay chamber got significantly darker.

However, I still think a straight rising arc is inefficient because it will pass through the same air multiple times. I've seen a circular arc which I think could be useful. However, I tried building one, albeit sloppily, but it didn't go in circles. Maybe my ferrite magnet wasn't strong enough. Also, I doubt long arcs, which are more efficient, can be sustained this way.

[Edited on 23-10-2008 by UncleJoe1985]