Perform a temporo-spatial integration of the internal ballistics of a hybrid rocket engine. Use equation (16-1) for the regression rate. If necessary, you may avoid the singularity near x = 0 by using equation (16.2) in this region.

Parameters

L = 5 m

d = .3 m

D = 1 m

a = .036

A* = .025 m²

rho_p = 920 kg/m³

m dot ox = 20 kg/s

The fuel is HTPB, and the oxidizer is O₂.

Use these curve fits for reference.

O2 / HTPB 3800 3600 3400 3200 Flame Temperature (K) 3000 T = 91.701 (0/F) - 1380.9 (0/F) + 8355.5 (0/F) 2800 -25, 592.0 (0/ F) + 40, 466.0 (0/ F) - 28, 680.0 (O/F) 2600 + 8407.4 2400 2200 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 23 2.4 2.5 2.6 27 28 29 3 3.1 3.2 3.3 3.4 3.5 Mixture Ratio by Mass (mox/mfuel) Fig. B.29. Flame Temperature Versus Mixture Ratio. The fuel is hydroxy terminated poly butadi- ene (HTPB) and the oxidizer is liquid oxygen (02). The equation shows a curve fit of the data.O2 / HTPB 28 26 24 Products at the Chamber (kg/kmol) Molecular Mass of Combustion 22 20 M = 0.3094 (0/F) -4.631 (0/ F) + 28.23 (0/ F) - 89.006 (0/F) + 150.56 (0/F) -121.7 (0/F) 18 + 52.301 16 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 22 2.3 24 25 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 Mixture Ratio by Mass (mox/ mfuel) Fig. B.30. Molecular Mass of Combustion Products Versus Mixture Ratio. The fuel is hydroxy terminated poly butadiene (HTPB) and the oxidizer is liquid oxygen (O2). The equation gives a curve fit of the data.O2 / HTPB 1.31 1.3 1.29 1.28 y = 0.0067 (0/F) -0.0786 (0/F) + 0.3487 (0/ F) 1.27 -0.7034 (0/F) + 1.7683 isentropic Parameter at the Throat (}) 1.26 1.25 1.24 1.23 1.22 1.21 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 22 23 2.4 2.5 2.6 2.7 2.8 29 3 3.1 3.2 3.3 3.4 3.5 Mixture Ratio by Mass (mox/mfuel) Fig. B.31. Isentropic Parameter Versus Mixture Ratio. The fuel is hydroxy terminated poly buta- diene (HTPB) and the oxidizer is liquid oxygen (02).O2 / HTPB 320 315 310 305 300 295 Vacuum Specific Impulse (s) 290 285 280 275 270 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 25 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 Mixture Ratio by Mass (mox/mfuel) Fig. B.32. Vacuum Specific Impulse Versus Mixture Ratio. The fuel is hydroxy terminated poly butadiene (HTPB) and the oxidizer is liquid oxygen (02).GO.8 0.2 i = 0.036 0.23 Pf