Trying to make a program to calculate (liquid) engine size. Can you please help me check for any problems?

Question

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

V_e/v_t = 2.085

equation2

A_t/A_e = 0.274

equation3

A_e/A_t = 3.64

equation4

T_t = 3015.9K

Gas constant = 341,47J/kg K

AddedEquation

Vt = 1109,7 m/s

V_e = 2.085* Vt = 2313.52 m/s

equation5

m_dot = F/c = 0.216 kg/s

equation6

m _{dot ox} = 0.144 kg/s

m _{dot f} = 0.072 kg/s

equation7

A_t = 0.0001772 m2

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

equation8

c* = 1640.64m/s

equation9

I_sp = 235.9s

equation10

V_c = 0.000389 m3

equation11

t_s = 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:

D_c = 6 cm

L_c = 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

Answer 1

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?

Answer 2

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.