N2O/Ethanol bipropellant rocket engine

[racket]

Hi Richard

LOL, what , you use plexiglass , I use to just keep runnin' after lighting the wick on my home made cannons and rockets , didn't stop till I heard the bang , reconned the sound would have been going slower than the shrapnel :-)

I had to start getting the pencil and paper out once I reached a point where my gas turbine experiments were costing me too much money , figured it'd be cheaper to learn some maths , wasn't easy after being outa school for 30 years .

Cheers
John

[Johansson]

Thanks for the explanation John, I will save this "walkthrough" to my laptop so I can do some calcs on my own later.

I am a litte bit of both, it is fun to throw things together and see if it works but much more rewarding to give it some thought first since it always seem to give better results...

[racket]

Hi Anders

They're only "ball park" figures , but should at least get you somewhere close to where you want to go .

The combustion pressure is a function of how much fuel and oxidiser you pump into the combustion chamber per second , all you'd need would be a pressure port and remote gauge in the combustor then feed in sufficient fuel and oxidiser to bring the pressure up to the desired design point of the rocket's motors nozzle.

Sorta design backwards from the nozzle outlet area that will give you the thrust you require , ............different to a gas turbine where the size of the "hole in the front" determines the power output ...................but with a rocket you determine the power by opening or closing the fuel and oxidiser valves ......................we'll need to check fuel/"air" ratios as this changes temperatures of combustion and along with that, gas expansion , combustor pressure and thrust levels .

Lotsa interesting variables to experiment with :-)

Cheers
John

[Johansson]

I think that we will settle with some ball park figures for this engine and use it to experiment with different chamber pressures to see how the thrust reacts to it. The engine will be quite small so it won´t consume so much nitrous oxide for each run, 50lbs thust or so.

A load cell and a pressure sensor in the CC should be enough to give us some valid data along with high speed video of the exhaust through a welding lens so eventual mach diamonds and the expansion of the jet plume can be seen.

I´ll do some calcs on a 50lbs engine and post the dimentions once I am finished.

[Johansson]

Had time to play with the calculator a bit today, a 50lbs engine at 7000ft/sec would then require a 0.44" throat and a 1.3" exhaust. Sounds fair to me.

Is there a limit to how much the exhaust jet can be expanded? As long as the expansion angle is moderate (<15°) shouldn´t it be theoretically possible to expand it all the way to the speed of a wet fart? I´ve read about over and under expanded nozzles but don´t really understand why there is such a thing as an ideal expansion ratio.

[racket]

Hi Anders

Maybe look at it this way , the expansion angle in the CD nozzle becomes an expansion angle of a conical diffuser once the gases have reached their maximum obtainable velocity at some point along the "divergent" portion of the cD nozzle/diffuser .

The "diffuser cone" will slow gases increasing static pressure , no point having slow gases exiting a rocket :-)

The ideal expansion ratio is one where the gas expansion reaches maximum velocity right at the CD nozzle exit , not before or after .

You may need to redo those calcs for a 50 lb engine , the 500 pounder needs 6.6 sq ins exhaust with 2.2 sq ins throat , divide those by 10 and we get 0.66 sq ins for the exhaust and 0.22 sq ins for the throat , this equates to diameters of 0.92 inches for the exhaust and 0.53 inches for the throat .

Cheers
John

[Johansson]

Hmm, this calculator must be joking with me. I ran the calcs in both metric and imperial values and in halv an hour I came up with 5 different throat diameters.

Three years of high school technic studies down the drain... ;D

[Johansson]

Tell me where I get it wrong:

(50lbs x 32.2)/7000 = 0.23lbs/sec
140 x 0.23 = 32.2cu ft/sec
(32.2 / 7000) x 144 = 0.662 in2
Exit diameter = root(0.662/3.14) x 2 = 0.91in
Throat = 0.91/3 = 0.31in = 0.79cm??

[ernie wrenn]

.91/3= .3031 X 2 = .6062 throat ?

Where did I go wrong?

Ernie

[racket]

Hi Anders

The exit AREA is 3 times the throat AREA , the exit area is where the 7,000 ft/sec occurs , the speed at the throat will be only the local sonic velocity for the temperature at the throat as it is running choked , velocity at the throat maybe only half that at the nozzle exit .

With an exit area of 0.662 square inches and a 3:! AREA ratio between exit and throat , the throat is ~0.22 sq ins , divide the 0.22 by Pi gives 0.0700, then square root the 0.0700 for 0.264 ( the radius of the throat ), and multiply by 2 for a diameter of 0.529 inches

Working back the other way , area = Pi R squared , 3.14 X 0.264 X 0.264 = 0.2188 sq ins

Clear as mud ;-)

Cheers
John

[Johansson]

Aaaaaahh! Then I get it.

[ernie wrenn]

NO>>>> I was closer. Not fair. I would have lower chamber pressure and would have higher flow.

I am still missing something, I will sleep with my calculator tonight... I will force it to give up the right answer. I should not have skipped math classes.

Ernie

[racket]

Hi Anders

If you start off with say 300 psi absolute in the combustion chamber and ambiant is 14.7 psia then you have an overall 20.4 :1 pressure ratio ,........ the critical pressure ratio , where gases will at sonic velocity , is ~1.84:1 , so divide our 20.4 by 1.84 and we get a pressure ratio of 11.09 :1 (163 psia) at the throat of the CD nozzle , that remaining 11.09 pressure ratio is reduced/expanded over the divergent portion of the nozzle as the gases go supersonic after passing thru the throat, the gases cannot go supersonic before the throat .

I know it sounds a bit strange that with an ~11:1 pressure ratio between the throat and exhaust face that there is only a 3:1 area ratio between exhaust and throat , but that's what the text book says is needed ?.......................LOL, and I'm not about to question Professor Zucrow's word :-)

Cheers
John

[Johansson]

Hi John and thanks for the input, I don´t think that we should dive much deeper into the calculations before I have built a test engine to confirm the data with.

I talked it over with my friend today and we will go for a 500N engine, much easier to build a larger nozzle and twice the thrust means twice the fun.

[racket]

Hi Anders

I'll go along with the 500 N , might as well make it a size that can move a man and machine ;-)

Probably be more representative of your future "full sized" one .

Cheers
John