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Common design parameters of solid rocket motor

2022-07-01 17:38:00 【Michael. py】

The common design parameters of solid rocket motors are ： mass ratio 、 thrust 、 Jet speed 、 Flow rate 、 Characteristic velocity 、 Thrust coefficient 、 working hours 、 Total impulse and specific impulse . This paper will introduce the theoretical definition function of these parameters .

1. mass ratio

mass ratio = Mass of propellant / Total engine mass

2. thrust

thrust $F= \dot{m}u_{e}+(p_{e}-p_{a})A_{e}$
Equivalent jet velocity $u_{ef}=u_{e}+\left ( \frac{p_{e}-p_{a}}{\dot{m}} \right )A_{e}$
Vacuum thrust $F=\dot{m}u_{e}+p_{e}A_{e}$
among ,F Is the thrust ,N; $\dot{m}$ Is the mass flow rate ,kg/s; $u_{e}$ Is the jet speed ,m/s; $A_{e}$ Is the sectional area of the nozzle , $m^{2}$ ; $p_{e}$ Is the nozzle outlet pressure ,p; $p_{a}$ Is the atmospheric pressure outside ,p

3. Jet speed

Jet speed $u_{e}=\sqrt{\frac{2k}{k-1}\cdot \frac{R_{0}}{m}T_{1}\left [ 1-\left ( \frac{p_{e}}{p_{c}{}} \right )^{\frac{k-1}{k}} \right ]}$
Actual jet speed / Extreme jet speed $u_{e}/u_{L}=\sqrt{1-\left ( \frac{p_{e}}{p_{c}} \right )^{\frac{k-1}{k}}}$
among ,k Is the specific heat ratio ; $R_{0}$ Is the common air coefficient ,8.3144;m Is the average molecular weight ;T Is the combustion temperature ; $p_{e}/p_{c}$ Is the expansion pressure ratio of nozzle ; $u_{e}$ Is the actual jet speed ; $u_{L}$ Extreme jet speed

4. Flow rate

Flow rate $\dot{m}=\Gamma \frac{p_{c}A_{t}}{\sqrt{RT_{1}}}$
Flow rate coefficient $C_{D}=\frac{\Gamma }{\sqrt{RT_{1}}}$
Characteristic velocity $c^{*}=1/C_{D}$
among , $\Gamma$ Is the function of specific heat ratio of gas ; $p_{c}$ Is the nozzle inlet pressure ; $A_{t}$ Is the critical cross-sectional area

5. Thrust coefficient

Thrust coefficient $C_{F}=C_{F}^{0}+\frac{A_{e}}{A_{t}}\left ( \frac{p_{e}-p_{a}}{p_{c}} \right )$
$C_{F}^{0}=\Gamma \sqrt{\frac{2k}{k-1}\left [ 1-\left ( \frac{p_{e}}{p_{c}} \right )^{\frac{k-1}{k}} \right ]}$