Author Topic: A dynamical arc model v2  (Read 265 times)

Offline Uspring

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A dynamical arc model v2
« on: June 14, 2019, 01:18:38 PM »
While quite a bit of knowhow regarding TCs can be found in the net, quantitative information about TC arcs remains a white region in the maps of knowledge. This is mostly due to the scarcity of measurements available. These are difficult, since arc currents need to be measured between the top load and the breakout point. The first measurement of this kind can be found here: http://web.archive.org/web/20160329212336/http://lod.org/Projects/electrum/techdata/waveforms.htm . Since the Electrum was a huge coil, it was possible that someone could sit in the top load and operate a scope there. Since battery operated scopes are now readily available, other measurements became feasible, like mine: https://4hv.org/e107_plugins/forum/forum_viewtopic.php?153922 and Hydrons: https://highvoltageforum.net/index.php?topic=117.0 .

Starting from the available data at that time I've tried to develop an electrical arc model. That was posted here: https://4hv.org/e107_plugins/forum/forum_viewtopic.php?156391 . An arc simulation can be extremely useful. It can serve as a tool to choose primary and secondary tank parameters, will give a hint at achievable arc lengths, allows a guess at primary currents in a DRSSTC, can answer questions like "Are bigger top loads better than smaller ones", are higher or lower operating frequencies better, is there a choice between long and thin versus short and fat sparks, what is the effect of shorter or longer bursts, how does upper pole perform in comparison to lower pole operation etc.

The model posted 2013 on 4hv was based on my measurements alone. It could reasonably well reproduce the current waveform of an arc at different power levels. So I was very excited by Hydrons data, which he posted about 2 years ago, since it allowed a check of the model at much larger power, i.e. 2m arcs instead of 1m and at a different frequency, i.e. 70Khz instead of 140kHz. Sadly the model failed drastically. It predicted more than twice the currents that Hydron measured. I've now revised the model, so that it can reproduce both my old measurements and Hydrons.

The model is basically a chain of RC circuits as shown below.



The resistors aren't really resistors in this case but are a conductivity models, where the current is calculated from the voltage and and arc temperature based on the energy deposited at that point by the arc. The capacitors are charge buckets, which represent the space charges floating in and around the arc. The top diagram of the arc model is below.



On the left is a simple DRSSTC circuit taken from what I know about Hydrons coil. On the right is a chain of blocks. Along the upper 2 wires the arc current is conducted. The lower 2 wires carry position information. The voltages there are centimeters from the end of the breakout point. This information is necessary for the calculation, since I've noticed, that the field of the toroid has an significant impact on the arc currents. With a meter stick like this, I'm able to calcualte the toroids field at each point of the arc and include this effect. The length of the chain depends on the arc length you expect. Each block is worth about 7cm of arc. The voltage at the end of the chain shouldn't exceed more than 30-40kV, because that is about where the arc ends. You can make the chain longer than necessary, but that will cause LTSpice to run slower.

Below is a schematic of the block.



The block is a short chain of subcircuits. The only reason to have this is to avoid a too long chain in the main diagram. Again, the upper 2 connections conduct the arc current and the lower 2 comprise the meter stick.

The meat of the arc model is in the circuit below. I won't go into the details here, they justify another post. A short description anyway: B2 calulates the power dissipated, B3 the conductivity, G1 the arc current and B4 takes the effect of the top load field into account. The only user supplied values are the parameters RTOR, which is the radius of the toroid measured from the center to the outer rim and LBRP, which is the length of the breakout rod measured from the toroid rim to the rods end.



I've checked the model by applying the measured voltages to the model and comparing predicted and measured currents. I've done this for the 3 power levels of Hydrons measurement and mine. Below are shown simulations and real data. The blue traces are top load voltages and the red the arc currents.

Hydron max power:




Hydron high power:




Hydron medium power:




Generally the simulated current rises faster initially than the measured ones. So the model is far from perfect.

Uspring max power:




Each unit on the left in the lower diagram is to be interpreted as about 90kV.
I've left out my lower power measurements, since I've already shown too many diagrams. The model performs quite well there. Below is a simulation for Hydrons coil at max power. In this case not by using the measured voltages as an input to the model, but a complete simulation with the voltage supplied by the DRSSTC circuitry.



The blue trace is the voltage, current is red. Primary current rises up to about 900A, which is quite a bit larger than Hydrons OCD setting of 750A. I'm not sure, why. It might be because I don't have his primary specs right or because of the too large load my model predicts initially, which brings the coil out of tune.

A zip file for the circuitry is appended. Comments and questions are welcome. A later post will detail the thoughts behind the model.
* arcv2.zip
« Last Edit: June 14, 2019, 01:39:11 PM by Uspring »

Offline Hydron

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Re: A dynamical arc model v2
« Reply #1 on: June 16, 2019, 03:10:15 PM »
Very interesting, I'll certainly be having a play with it.

I'll also hopefully be in the position soon of gathering some more data to help fit the model - I actually got some more data from my big coil (along with some physical and electrical measurements) in January, but there were some issues with it:
- I didn't have time to get such a comprehensive data-set as before
- It being summer (in NZ) stopped me from troubleshooting much on the single night I had to setup and test - getting dark late means a narrow window to make noise before it's unreasonable to neighbours trying to sleep
- I also had breakout from multiple points so not all arc current was captured - this is the main reason why I haven't done much with it, as it probably invalidates most of the measurements.
- I did however get some primary/secondary-base coil measurements to go along with the topload ones, all synced up with a fibre optic trigger.

I plan to have another go with both the original big coil and a small QCW coil that's been (very) slowly worked on here in the UK - I have _just_ got enough room in the latter to put a scope in a special toroid and it can probably also run low power in non-QCW mode. No guarantees as to when though sorry! (I know I have promised this before, and unfortunately been unable to do it in the short times I've had on holiday/vacation back in NZ)

Offline VNTC

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Re: A dynamical arc model v2
« Reply #2 on: June 17, 2019, 04:19:07 AM »

Very interesting! Thanks for sharing  I'll try running it against the simulation. I think i will study a lot from this topic.
Thank you!

Offline Uspring

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Re: A dynamical arc model v2
« Reply #3 on: June 17, 2019, 02:40:06 PM »
@Hydron:
I didn't mention that in the post, but I'm certainly eagerly awaiting new data. Do you have any specifics about your big coils primary tank? My simulations predict a somewhat larger current there as your OCD setting, so I am a bit puzzled. Your new data on primary and secondary base currents would definitely be helpful. The breakout points also play a big role. I've taken the extension of your point from the video. I hope I got that right. (7.6cm?) I believe, the length of the rod plays a significant role wrt to the voltages of the top load.

I'm sorry to hear about the less favorable circumstances of your last measurements. But if you post them, I will surely have a look at them anyway.

Wrt QCW: QCW arcs are pretty much steady state arcs, so they are likely easier to simulate. A big problem with current simulations is now, that the temperature rise of the arc is influenced by both the heat capacitance of the heated air and also by heat conduction losses to the surroundings. The heat capacitance determines, how fast the temperature rises and the heat conduction how far. In a steady state arc, the effect of heat capacitance can be neglected. In my simulation, there is a considerable uncertainty about the speed of heat up.

The arcs temperature plays a big role in the calculation. At higher temperatures, the heat causes ionisation by fast air molecules bumping into each other. That begins at 3000-4000K. But also at lower temperatures, there is an effect, because the air expands, making it thinner and causing breakdown voltages to drop. There is also a time dependency there, since the expansion is not immediate but takes a few us. Short, but possibly not negligible. So to sum up, QCW data would be quite interesting.

Online Mads Barnkob

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Re: A dynamical arc model v2
« Reply #4 on: June 17, 2019, 08:54:41 PM »
Thank you for sharing your model data, looks very promising that you have it fit over 3 datasets, is there however any pitfalls or common causes in all 3 sets?

An arc simulation can be extremely useful. It can serve as a tool to choose primary and secondary tank parameters, will give a hint at achievable arc lengths, allows a guess at primary currents in a DRSSTC, can answer questions like "Are bigger top loads better than smaller ones", are higher or lower operating frequencies better, is there a choice between long and thin versus short and fat sparks, what is the effect of shorter or longer bursts, how does upper pole perform in comparison to lower pole operation etc.

Can the simulation do some calculations as well, depending on maybe some more input data, so it automatically calculates some parameters from the model you set up for a specific spark appearance? I know this sounds a bit the wrong way around, but could be a confirmation of the model.

The arcs temperature plays a big role in the calculation. At higher temperatures, the heat causes ionisation by fast air molecules bumping into each other. That begins at 3000-4000K. But also at lower temperatures, there is an effect, because the air expands, making it thinner and causing breakdown voltages to drop. There is also a time dependency there, since the expansion is not immediate but takes a few us. Short, but possibly not negligible. So to sum up, QCW data would be quite interesting.

This was something we discussed many years ago on 4hv, the differences between Kizmo's 1uF, Dalus' 1.5uF and mine 0.8uF, but only at a surface level of calling it low vs. high impedance and compare spark brightness/thickness. So while the low impedance also have lower losses in the primary circuit, shorter ring up time it might still be the preferable choice due to higher arc temperature from the start? Or is the "few us", more than a few, so a high impedance coil with long on-time gets in the same range anyway?
http://www.kaizerpowerelectronics.dk - Tesla coils, high voltage, pulse power, audio and general electronics

Offline Uspring

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Re: A dynamical arc model v2
« Reply #5 on: June 18, 2019, 11:45:53 AM »
Mads wrote:
Quote
...is there however any pitfalls or common causes in all 3 sets?
I'm not sure, what you mean here. Can you explain?

Quote
Can the simulation do some calculations as well, depending on maybe some more input data, so it automatically calculates some parameters from the model you set up for a specific spark appearance? I know this sounds a bit the wrong way around, but could be a confirmation of the model.

The model is parameter free in the sense, that there are no parameters specific for a particular arc appearance. It just calculates, what happens, when you have a given top load voltage. I've done a lot of parameter fitting to reproduce the measured currents, but there are no specific settings for either top load voltage or TC frequency.

In the lowest level schematic, there is a node N4, which is very rougly proportional to temperature. If you would be looking for a fat or bright spark, you'd need to supply different voltages, frequencies or burst length to the model and maximize the voltage at node N4.

Quote
This was something we discussed many years ago on 4hv, the differences between Kizmo's 1uF, Dalus' 1.5uF and mine 0.8uF, but only at a surface level of calling it low vs. high impedance and compare spark brightness/thickness. So while the low impedance also have lower losses in the primary circuit, shorter ring up time it might still be the preferable choice due to higher arc temperature from the start? Or is the "few us", more than a few, so a high impedance coil with long on-time gets in the same range anyway?

Yes, that can be studied with the model along the lines outlined above. I'm not sure, though, how well it will perform under more exotic circumstances. Very short bursts, e.g. the ones used for high notes in musical TCs, tend to produce more branched arcs. My model uses just a single arc, the branching is taken care of in its internal parametrisation. Maybe good enough to estimate the arc currents, but maybe not good enough to judge the arcs appearance. Steve Ward once asked me, whether my previous arc model could find the requirements for straight QCW arcs. Not yet.
« Last Edit: June 18, 2019, 11:52:11 AM by Uspring »

Online Mads Barnkob

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Re: A dynamical arc model v2
« Reply #6 on: June 19, 2019, 10:43:32 AM »
Mads wrote:
Quote
...is there however any pitfalls or common causes in all 3 sets?
I'm not sure, what you mean here. Can you explain?

I was just wondering if there was something too much in common for the coils, so as the model is limited to coils generating 1-2 meter sparks and everything below and above gets more and more out of alignment with reality. I know you got no clear answer as you have no available data for this, but what is your gut feel about it?

I will take the model for a spin one of the coming evenings :)
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Offline Uspring

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Re: A dynamical arc model v2
« Reply #7 on: June 19, 2019, 01:40:16 PM »
A good question and difficult to answer. I wrote, that my first attempts to reproduce Hydrons measurements with my old model failed pretty badly. The reasons for this were partly a not quite correct way, the old model handled the frequency difference. But mostly it was, because I had completely neglected the effect, that the top load field has on the space charges of the arc. A diferently sized top load and a different length of the breakout rod have a strong effect on breakout and further arc growth. In hindsight a blunder, since most coilers know, that e.g. omitting a breakout point, can cause a DRSSTC to arc not at all. I think, the model is basically sound, as its calculations include much of the physics of the charge carriers involved, although in a quantitatively much simplified way. It definitely needs some fine tuning.
That doesn't really answer your question, but if you try it out and it fails (or not), that will add some guide for refinement.  ;)

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Re: A dynamical arc model v2
« Reply #7 on: June 19, 2019, 01:40:16 PM »

 


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