Calculations for thrust etc?

[pulsejetter]

Hi all, as you may know i have built a Lockwood Hiller pulsejet and posted pics of it completed and some info.
I was wondering if there are any calculations to predict the thrust from the size of the combustion chamber or anything like that?
Also are there any other calculations which could be used to verify the design, for example any thermodynamic calculations or flow calculations?
I don't mind if they're in depth but it would be great to have some because i built this as a college project and would like to have some calculations to back up the design. I'm hoping that it produces around 40lbs of thrust because it is a 55lbs design.

Thanks for all your help.

[metiz]

For some basic thrust guestimates I think you can use Pyro's recipe for beginners. If you wan't a more acurate acount of what's going on, try either NuDIS or Uflow1D. Nudis has a rather steep learning curve and can not distinguish between random errors created by the buggy excel program or by a poorly designed engine (literally hinges on your system) but if you can get it going it's a very helpfull tool.

I haven't worked with Uflow before so I can't comment on that

[pulsejetter]

For some basic thrust guestimates I think you can use Pyro's recipe for beginners. If you wan't a more acurate acount of what's going on, try either NuDIS or Uflow1D. Nudis has a rather steep learning curve and can not distinguish between random errors created by the buggy excel program or by a poorly designed engine (literally hinges on your system) but if you can get it going it's a very helpfull tool.

I haven't worked with Uflow before so I can't comment on that

Thanks for the reply. I have read through pyrojoes recipe for beginners but i cannot find any thrust gestimate informtion. It's mainly to do with the designs of the various components like the exhaust, combustion chamber and intake etc. And still i find the Caliber measure confusing as to what it means, is it refering to one caliber being the smallest diameter of the exhaust pipe?
I will have a look at the others you mentioned.

Thanks.

[PyroJoe]

My apologies for not providing anything in thrust calculation.

IMO there is a significant grey area between a natural aspirating/breathing engine and one that has been pushed well beyond by pressurized fueling/artificial air entrainment.

Not saying any particular method is right or wrong, just that results vary widely by user, available resources, and design.

Don't become discouraged if you only obtain 50% of published maximum rating.

[Mike Everman]

See recent topic, re: thrust:
viewtopic.php?f=7&t=6134&start=0&st=0&sk=t&sd=d

Using that formula in and of itself is a starting point to illustrate the trend.
From my own tests, a well designed and fueled single intake, straight pipe exhaust should get 65% of that, or use 1.2 lb/in^2 of CC area. This is reliable from 2-3" of CC diameter. Sorry I cannot extrapolate bigger yet, but I do not have data for larger. A thermojet style is considerably under this, but is easier to build and start.

[pulsejetter]

Thanks very much for the info provided so far.
From the kentifield graph system which was in the link, it indicates that for my Lockwood hiller pulsejet the maximum theoretical thrust is around 80lbs yet the engine is listed as a 55lbs design.
Does this calculation/ rule of thumb calculation not work for this type of design?

Thanks again.

[Mike Everman]

Well, tough for me to extrapolate up from my experiments, as I said, though 55/80 is 68% of max. One would expect a much better portion of theoretical in a properly tuned tail. I don't have a max thrust number for the SNECMA Escopette, for instance, just the rated thrust of 24 lb @ 1.8 specific fuel consumption, which we can probably guess is at 80% of max static, so it is reaching 72% of theoretical (according to Kentfield).
While the Lockwood plans floating around are not terrifically great in that respect, they are also not far off of what I'll assume is a really good tuned tail in the Escopette.
One thing to remember, though is there is some augmentation in the Escopette setup, coming from it's recouperator at the intake. The main difference is likely to be fuel consumption, which is better on the Escopette.

[PyroJoe]

pulsejetter,
Did the plans specify a chamber of 237mm cylinder, or a 160mm-178mm cone type chamber? It looks like the cone type, if so that would average to about 169mm. Roughly 34.77 square inch area.
1.2 x 34.77=41.72
maybe 41.72 pounds? That would be 76%

[pulsejetter]

pulsejetter,
Did the plans specify a chamber of 237mm cylinder, or a 160mm-178mm cone type chamber? It looks like the cone type, if so that would average to about 169mm. Roughly 34.77 square inch area.
1.2 x 34.77=41.72
maybe 41.72 pounds? That would be 76%

Yes it's the cone type with one end of the combustion chamber being 178mm and the other being 160mm. To get the area of the combustion chamber wouldn't you have to do 169mm x 345mm which is the average diameter as you say multiplied by the length?

Because i can't workout how you got 34.77 inches squared.

Also how did you get the 76% figure, is that the percentage of the maximum thrust?

Thanks.

[PyroJoe]

Average diameter is 169mm, take that times 0.03937 to get 6.65 inches in diameter.

to find area of 6.65" circle=
pi times radius squared=
3.14*(6.65/2)squared=34.71 area

a few rounding errors, but close yes?

now 1.2 times 34.77= 41.72lbs.

then 41.72lbs divided by 55 lbs rating = .7585
= approx. 76%
i think?

[pulsejetter]

Average diameter is 169mm, take that times 0.03937 to get 6.65 inches in diameter.

to find area of 6.65" circle=
pi times radius squared=
3.14*(6.65/2)squared=34.71 area

a few rounding errors, but close yes?

now 1.2 times 34.77= 41.72lbs.

then 41.72lbs divided by 55 lbs rating = .7585
= approx. 76%
i think?

Ahh thanks for that forgot we were finding the area of the circle.
Would you not need to multiply by the length or is it just the area of the circle and not the whole combustion chamber area needed for that calculation?
But i think you need to divide the 6.65 by 2 to get the radius as you've got the diameter. Then you can do the Pi x radius squared.

Thanks again this will prove a useful calculation for thrust predictions.

EDIT: Just read what you put again and it's all correct. missed the part where you put 6.65/2, sorry.

[PyroJoe]

Using Kentfields graph, a 6.65" CC would yield over 100 lbs.

[Mike Everman]

This is all very much ballpark stuff, of course. The thing I haven't been able to wrap my mind around is the effective diameter, considering the cones at each end of the CC. I was trying to figure that out a long time ago and got stalled. The added complication is how far down the rear cone do you consider as part of the CC? Easy enough to get the average diameter for the length of the CC, head to throat, by calculating volume and dividing by length for average area, then the diameter that suggests.
I'll take a look at my motors and get back with that, even though I know it's not rigorous at all.

[pulsejetter]

I would say that the 1.2lbs per inch squared of combustion chamber diameter sounds about right as many people haven't really achieved the 55lbs of thrust that the design is claiming. So 40lbs sounds more realistic/ the types of figure many are getting.

I would've thought that the combustion chamber includes the cone sections too, but then the combustion takes place sometimes quite far from the combustion chamber.
When i ran mine i noticed the combustion chamber was glowing a cherry red on idle but so was the u- bend.

[PyroJoe]

I used to beat myself up over my little one pounder engines.

Over some time have found solace in that the paltry 1 pound may still be pushing at several hundred miles per hour.