# 火箭发动机喷管

## 喷管气流分析

• 简单起见，燃烧气体假定为理想气体
• 气流是等熵的，无摩擦的，且绝热（有少量或没有热损失）
• 气流在推进剂燃烧过程中稳定。
• 气流从进口到出口沿直线流动。
• 气流可压缩。

${\displaystyle V_{e}={\sqrt {\;{\frac {T\;R}{M}}\cdot {\frac {2\;k}{k-1}}\cdot {\bigg [}1-(P_{e}/P)^{(k-1)/k}{\bigg ]}}}}$
${\displaystyle V_{e}}$ 此处: =  喷管出口排气速度， m/s =  入口气体的热力学温度, K =  通用气体常数 = 8314.5 J/(kmol·K) =  气体分子质量, kg/kmol    (也称分子量) =  ${\displaystyle c_{p}/c_{v}}$  = 绝热指数 =  气体在恒压下的比热 =  气体恒容比热 =  出口气体绝对压力 Pa =  入口气体绝对压力, Pa

## 比冲

${\displaystyle F}$ ${\displaystyle =\,{\dot {m}}\,V_{e}+(P_{e}-P_{o})\,A_{e}}$ ${\displaystyle =\,{\dot {m}}\,{\bigg [}V_{e}+{\bigg (}{\frac {P_{e}-P_{o}}{\dot {m}}}{\bigg )}A_{e}{\bigg ]}}$

${\displaystyle F}$ ${\displaystyle =\,{\dot {m}}\,V_{eq}}$

${\displaystyle I_{sp}=\,{\frac {F}{{\dot {m}}\,g_{o}}}\,=\,{\frac {{\dot {m}}\,V_{eq}}{{\dot {m}}\,g_{o}}}\,=\,{\frac {V_{eq}}{g_{o}}}}$
${\displaystyle F}$ 此处: =   火箭发动机总推力, N =   废气质量量率, kg/s =   废气出口速度, m/s =   废气出口压力, Pa =   外部压力, Pa     （也称自由流压力） =   喷管出口面积, m² =   废气出口有效速度, m/s =   比冲, s =   海平面重力加速度 = 9.807 m/s²

${\displaystyle I_{sp}=\,{\frac {F}{{\dot {m}}\,g_{o}}}\,=\,{\frac {{\dot {m}}\,V_{e}}{{\dot {m}}\,g_{o}}}\,=\,{\frac {V_{e}}{g_{o}}}}$

${\displaystyle I_{sp}(vac)=\,{\frac {V_{e}}{g_{o}}}+{\frac {P_{e}\,A_{e}}{{\dot {m}}\,g_{o}}}}$

${\displaystyle F=I_{sp}(vac)\,g_{o}\,{\dot {m}}-A_{e}P_{o}}$

• 双膨胀
• 双喉部喷管

## 参考

1. Richard Nakka's Equation 12
2. Robert Braeuning's Equation 2.22
3. ^ Sutton, George P. Rocket Propulsion Elements: An Introduction to the Engineering of Rockets 6th Edition. Wiley-Interscience. 1992: 636. ISBN 0471529389.
4. ^ NASA: Rocket thrust
5. ^ NASA: Rocket thrust summary
6. ^ NASA:火箭比冲
7. ^ Huzel, D. K. and Huang, D. H. NASA SP-125, Design of Liquid Propellant Rocket Engines 2nd Edition. NASA. 1971.技术报告
8. ^ PWR Engineering: Nozzle Design 互联网档案馆存檔，存档日期2008-03-16.
9. Sutton, George P. Rocket Propulsion Elements: An Introduction to the Engineering of Rockets 7th Edition. Wiley-Interscience. 2001: 84. ISBN 0471326429.http://books.google.co.uk/books?id=LQbDOxg3XZcC&printsec=frontcover&dq=rocket+propulsion&ei=wlEhScL4EYywkwSVv5SCDw#PPA84,M1--
10. ^ Journal of Propulsion and Power Vol.14 No.5, "Advanced Rocket Nozzles", Hagemann et al.
11. ^