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So as the title says I am trying to write code to calculate engine size and some other parameters.

For the equations, I used mostly :

Sutton's Rocket Propulsion Elements 8th Edition, and for the starting parameters, the CEA (Chemical Equilibrium Applications) program and with some help from fellow StackExchangers, I managed to get through most of the questions.

Before I give you the procedures, here are the starting parameter, used just so it helps me get through the equations:

Fuel: 96% Ethanol (dissolved in water) - about room temperature
Oxyidiser: Liquid Oxygen
O/F ratio: 2

Chamber pressure: 20 Bar = 2 000 000 Pa
Outside pressure: 1 Bar = 100 000 Pa(I know that's not the totally correct outside pressure)
Chamber temperature: 3310.9K
Molecular mass: 24.347 g/mol = 0.024347 kg/mol
Gamma (ratio of specific heats): 1.1961
Characteristic chamber length L*: 2.2m
(Starting/desired) thrust: 500N
V1: 0.565 m3 /kg

Here are the equations that I used and the actual calculations right after it. The equations are all from the Sutton:

equation1

Ve/vt = 2.085

equation2

At/Ae = 0.274

equation3

Ae/At = 3.64

equation4

Tt = 3015.9K

Gas constant = 341,47J/kg K

AddedEquation

Vt = 1109,7 m/s

Ve = 2.085* Vt = 2313.52 m/s

equation5

mdot = F/c = 0.216 kg/s

equation6

m dot ox = 0.144 kg/s

m dot f = 0.072 kg/s

equation7

At = 0.0001772 m2

Ae = At * 3.643(calculated above) = 0.0006455 m2

equation8

c* = 1640.64m/s

equation9

Isp = 235.9s

equation10

Vc = 0.000389 m3

equation11

ts = 0.00319s

these are all the equations I got. Now for the last part, the length and diameter of the chamber. I know that the diameter should be 3 to 5 times the diameter of the throat.

So I put 2*, 3*, 4*, and 5* diameters of the throat for the chamber diameter, and the 3* was the best.

I concluded that the 4* option looked good so i chose:

Dc = 6 cm

Lc = 11 cm

There were 5 options but the aspect ratios were a bit weirder.

I know this is just the first part of the process of designing a rocket engine but I just want to be sure before I go any further with it. So if you took/take the time, thank you. Also, I apologize for bad formating, still learning that too. Any tips (for the rocket and formating) are always welcome!

Thank you

Edit:

Subscript e or 2 is for nozzle exit

Subscript 1 or c is for chamber

Subscript t is for throat

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    $\begingroup$ Can you explain what your subscripts mean? You didn't use same ones as Sutton. What station is "2"? In other places you used "e" and "t", I can guess at those, but I don't know what "2" is. $\endgroup$ – Organic Marble Sep 13 '20 at 14:03
  • $\begingroup$ @OrganicMarble sorry about that. I edited it so there are no "2" subscripts. Still added the explanations for most that aren't guessable just to make sure. $\endgroup$ – StarshipGood Sep 13 '20 at 18:27
  • $\begingroup$ Please show how you got the gas constant (units?) and what your value of velocity at the throat is. $\endgroup$ – Organic Marble Sep 13 '20 at 19:30
  • $\begingroup$ @Organic it was a typo. I took the eq. from Gas constant and and wrote the result from throat velocity. $\endgroup$ – StarshipGood Sep 14 '20 at 7:17
  • $\begingroup$ Thanks for the edit. I hope to be able to look at this later today. $\endgroup$ – Organic Marble Sep 14 '20 at 16:33
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After the edits, I check your numbers down until the stay time. When you changed the L*, did the $V_1$ change from the number you give at the beginning?

For $V_c / (\dot m V_1)$ I used 0.000389/(0.216 * 0.565) = 0.0032

You give 0.00283

I quit when I found this difference, I can continue once we resolve it.

Here's a table of properties by station that I checked so far.

         Chamber  Throat     Exit_Plane 
P  (bar)  20       11.3        1
T  (K)    3311     3016        not calc'd
V  (m/s)  0        1110        2314
A  (m^2)  ?        1.77x10^-4  6.46x10^-4 
AR (--)            1.0         3.64
VR (--)            1.0         2.085               

One thing to consider / I found questionable is that your design altitude is sea level. That's going to result in massive underexpansion during flight starting at liftoff. Suggest you consider a more expanded nozzle. It's OK for calculation fun but would be terrible for a real engine. See why do under-expanded engines have less than ideal thrust?

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    $\begingroup$ I corrected some stuff and from the @WHG 's answer I changed the L* to 2.2m i believe it doesn't change any of previous calculations. The link for the equations should work now. And for the under-expansion.. I am aware of that, thank you. These are just dummy calculations so it makes it easier for me to go through the equations and in the future write a code (and compare it to these results) $\endgroup$ – StarshipGood Sep 15 '20 at 14:03
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    $\begingroup$ I had it wrong. It is corrected now and the V1 did not change for me. It is as you calculated, about 0.0032s. Sorry for the late response. I wasn't really checking this thread or anything else for sometime now. $\endgroup$ – StarshipGood Oct 26 '20 at 13:15
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Good thing that you asked for help. As people work in a field, they develop an idea of the magnitude calculated quantities should be. Your exhaust velocity looks reasonable but the propellant flow is way too low. You say .216 kg/s, so for say 150 s burn time, about 30 kg, less than the weight of an adult and the thrust is enough for a first stage orbital rocket. Does not make sense. You chose F = 500 kN, so 500 000 N. $m_{dot} = F/V_e = 5\cdot10^5N/2313.5m/s=267 kg/s$.

I checked your exhaust velocity with Sutton's eq 3-16 and it agrees.

The equation for throat area did not go to a picture of the equation so I used Sutton's 3-24. Chamber pressure of 20 bar (not an SI unit) is $2\cdot 10^6 Pa$. If you use the SI units (and the equation is formulated correctly) the result will be in the SI unit. I calculated .17738 $m^2$, so diameter of .4752 m or 18.7 inches.

Thrust of 500 kN is about 11200 lb. Compare with page 269 of Sutton which shows a cutaway of an early version of engine used on Thor and Atlas, he says original thrust of 120 000 lbf and throat diameter of about 15 inches. Chamber pressure not specified but these numbers are in agreement.

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  • $\begingroup$ sorry, but I used thrust of 500N and not 500 000N. Maybe I wrote it somewhere wrong. Can you point it to me so I can fix it, please? Also for BARs, I added the conversion to Pascals, and when calculating I used Pascals. $\endgroup$ – StarshipGood Sep 14 '20 at 18:36
  • $\begingroup$ "(Starting/desired) thrust: 500N" $\endgroup$ – Organic Marble Sep 14 '20 at 19:03
  • $\begingroup$ Mia culpa. For some reason I thought you were calculating for 500 kN. Okay, your flow rate is right. Your throat area is a factor of gamma=1.1961 larger than mine. I get .00017736 $m^2$. Sutton 1st edition suggests L* of 4 to 10 feet for LOx alcohol. $\endgroup$ – W H G Sep 14 '20 at 20:20
  • $\begingroup$ @WHG thanks for the L*. I now changed it to 2.2m. $\endgroup$ – StarshipGood Sep 15 '20 at 14:06

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