ARCHIVE LOG

Nozzle Design

AUTHORDhruv Kakade

TIMESTAMP2026.09.28

Define the parameters from openMotor for the fuel.

Parameters to know: $F, P_0, P_e, O/F, T_0, k \text{ and } R$

Here I will choose KNSB:

\implies R = \frac{8.31446}{0.0399}=208.3824561404 J/kg\cdot K

Take Properties, $()_0 \approx ()_1$

Conical

Throat temperature, $T^* = \frac{2 \cdot T_1}{k+1}$

Throat Pressure,

P^* = P_1 \left(1+ \frac{\gamma -1 }{2}\right)^{-\frac{\gamma}{\gamma-1}}

Ideal thrust Coefficient,

C_{f,ideal} = \sqrt{\frac{2\gamma^2}{\gamma - 1} \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{\gamma - 1}} \left[ 1 - \left(\frac{P_e}{P_c}\right)^{\frac{\gamma - 1}{\gamma}} \right]}

Actual thrust coefficient,

\lambda = \frac{1 + \cos(\alpha^\circ)}{2} \\C_{f,\text{actual}} = \lambda \cdot C_f

Throat area, derived using m*=rhoAv*=rhoAa

A_t = \frac{\dot{m} \sqrt{R T_c}}{P_c \sqrt{\gamma \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{\gamma - 1}}}}

From area find D_t

P_e /P_optimum,

P_{optimum} = \frac23 (P_{low} - P_{high})

Exit mach no,

M_e = \sqrt{\frac{2}{\gamma - 1} \left[ \left(\frac{P_c}{P_e}\right)^{\frac{\gamma - 1}{\gamma}} - 1 \right]}

Expansion ratio,

\epsilon = \frac{A_e}{A_t} = \frac{1}{M_e} \left[ \frac{2}{\gamma + 1} \left( 1 + \frac{\gamma - 1}{2} M_e^2 \right) \right]^{\frac{\gamma + 1}{2(\gamma - 1)}}

From A_e find exit diameter

Find diverging length,

L_d = \frac{r_e - r_t}{ \tan(\alpha^\circ)}

Throat Velocity, $a=\sqrt{kRT}$

Exit Velocity,

v = \sqrt{\frac{2k}{k-1} R T_0 \left[ 1 - \left(\frac{p_2}{p_0}\right)^{\frac{k-1}{k}} \right]}

For the contour nozzle see Huzel & Huang page 76.

[3] Rocket Propulsion Elements, George P. Sutton and Oscar Biblarz.

[4] Modern Engineering for Design of Liquid-Propellant Rocket Engines, Huzel & Huang