P1: Nitrous at Balls in '09


Simulation Analysis

Last Update, 1/1/09 by Stephen Daniel


This sections discusses the simulation of test #10. We show that by adjusting the injector Cd, the fuel regression rate, and the C* efficiency we can get a good fit to the burn time, the chamber pressure trace, and the mass of fuel consumed.

Assuming good data and good simulation models, we believe these derived values represent reasonable approximations to reality.


We don't have a fuel regression model or CPROPEP entry for ABS, so we used PBAN for both.

We manually adjusted C* efficiency, injector Cd, and a fuel regression constant until the average pressure looked good and the run time and fuel mass consumed matched almost exactly.

The shape of the simulated pressure trace is a good match to the measured, with a couple of exceptions. The motor appears to have had some trouble coming up to pressure immediately. This is visible in the video as well. Test 11 starts instantly. I assume that in test 10 the pyro-valve did not immediately break free.

Early in the burn the chamber pressure is higher than expected. The igniters burn during the entire time the pyro-valve is cooking (about 16.8 seconds) and pre-heat the fuel grain. I assume this results in very high initial fuel regression.

The injector Cd that matches the burn time (0.37) is lower than we've been using for our design work. However our design has been guided by very approximate data. Furthermore we chose to design to a high injector Cd, on the theory that we could alwas add more holes in the injector later. I expect we will need to drill out the injector to achieve our target thrust.

The C* efficiency (72%) is much lower than our design goal of 95%. We believe that switching from a straight length of pipe to a fuel grain cast with mixing chambers forward and aft of the actual grain will significantly improve this.

To match the observed fuel consumed I had to cut the fuel regression almost in half (57.5%). Our fuel regression models suffer from a severe lack of data behind them.

Pressure Graph

Test 10 Pressure Graph

Simulation Results

Section 1: Geometry
        Tank Height         0.152 meters
        Tank Volume         1.093 liters
        Ullage Height       0.000 meters
        Grain Length        0.297 meters
        Nozzle Throat       1.000 inches
        Nozzle Exit         1.600 inches
        Nozzle Half Angle   15.0 degrees
        C* Adjustment       0.72
        Cf Adjustment       0.95
        Ambient Pressure    1.0  atm

Section 2: Fill Conditions N2O Supply Pressure 508.0 psi Init Pressure 415.0 psi Init Temp 26 F Init N2O Mass 1.01 kg Init N2O Density 0.92 g/cc N2O Vented to chill 0.08 kg 0.18 lbs Total N2O Consumed 2.40 lbs Fuel PBAN
Section 3: Empty Conditions Final Pressure 256.8 psi Final Temp -5.1 F Ullage N2O Mass 0.05 kg Ullage Percentage 5.0 % Section 4: Chamber Summary Init Final Average Grain Port 3.042 3.162 3.104 inches Grain Mass 0.442 0.332 kg Fuel Consumed 0.110 kg Min Max Average Chamber Pressure 112.15 145.11 130.52 psi O/F Ratio 8.3 9.0 8.7
Section 5: Injector Summary Injector Count 8 Diameter of Injectors 1.78 mm 0.070 inches Cd of Injectors 0.37 Tank/Chamber Pressure Ratio Min Max Average 2.29 2.86 2.60
Section 6: Nozzle Summary Min Max Average Exit Pressure 0.57 0.74 0.67 atm Nozzle CF (un-adj) 1.32 1.32 1.32
Section 7: Performance Summary Init Min Max Average Thrust 139 100 139 122 lbf 616 446 616 541 N Delivered ISP 1298 1223 1298 1269 meters/sec Delivered ISP 132 125 132 129 seconds Burn Time 2.508 seconds Total Impulse 1357 N-seconds Motor Designation K-541 (6%)