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I have designed a nozzle for the following input parameters

  • $p_{combustion}=p_c=200*10e5 Pa$
  • $T_{combustion}=T_c=2800 K$
  • $F=70 kN$
  • $\kappa=1,2$
  • $R = 330 J/kgK$
  • I assume that all my gas properties stay constant for this calculation.

The nozzle shall be working ideal at

  • $p_{exit}=p_{ambient}=54048 Pa$

For having no losses this gives me $$v_e=\sqrt{\frac{2\kappa}{\kappa-1} R T_c (1-\frac{p_{exit}}{p_{c}})^{\frac{\kappa-1}{\kappa} } } = 2636 \frac{m}{s}$$

Since I know my thrust for ideal expansion this gives me the mass flow $$\dot{m}=F/v_e=26.55 \frac{kg}{s}$$

For the throat temperature I use: $$T_t=\frac{2T_{c} }{\kappa+1}=2545 K$$ And throat pressure: $$p_t=p_c*(2/(\kappa+1))^{\frac{\kappa}{\kappa-1}}=1.1289*10^7 Pa$$

And density: $$\rho_t=\frac{p_t}{R T_t} = 13.44 kg/m^3$$

So my throat area will be $$A_t=\frac{\dot{m}}{\rho_t \sqrt{\kappa R T_t}}=0.00196777 m^2$$

I hope I haven't done any mistake. Now I freeze my nozzle's geometry for Off-Design calculation.

  1. When I use now my nozzle @SeaLevel Pressure , does my exit velocity $v_e$ change? To my mind not, because my backpressure of $p_{ambient}=101325 Pa$ is still so much lower than my combustion pressure (critical pressure ratio p_ambient/p_c=0.005< 0.53 is still valid)

  2. As long as my nozzle geometry is fixed and the flow choked, then $v_e$ $A_e$ and $p_e$ don't change. Can I just use $$ F = \dot{m} v_e + A_e (p_e - p_{ambient} )$$

In this case, my thrust will be ruduced since $p_{ambient} > p_e $.

Is this correct?

Thank you very much for your help guys!

Best regards Lucas

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  • $\begingroup$ I dont care to find sources so Im writing a comment instead of an answer: yes, with a frozen nozzle geometry, you can use that equation (the rocket equation) to compute off-design thrust. $\endgroup$
    – A McKelvy
    Mar 15, 2023 at 3:49

1 Answer 1

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To a first approximation, exit velocity does not change with changes in ambient pressure, only with throttle setting.

For a worked-out example of thrust vs altitude, see https://space.stackexchange.com/a/46548/6944

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