Question 4.2: An arcjet is a small rocket used for in-orbit spacecraft pro...
An arcjet is a small rocket used for in-orbit spacecraft propulsion. Consider a hydrogen arcjet with a nozzle length of 1 cm and the following spatially averaged values: P= 15,000 N/m², T = 5000 K, u=5 {km}/{s}. For molecular hydrogen (H_2): μ = 1, θ_{vib} = 6345 K.
We can evaluate a characteristic flow time based on the velocity change:
\pmb{\tau_{f}} = \left[\frac{1}{u} \frac{du}{ds}\right]^{-1}\frac{1}{u}=10^{-6} sec (4.46)
For evaluation of the vibrational relaxation time:
A= 1.16 \times 10^{-3} \times 1 \times (6345)^{{4}/{3}} (4.47)
\tau _{vib} = 5\times 10^{-6} sec \gt \tau_{f} \Rightarrow nonequilibrium process (4.48)
Indeed, it is found that vibrational nonequilibrium is an important performance degradation mechanism in arcjets that is known as a frozen flow loss. The energy that remains trapped in the vibrational mode is not available for translation into directed kinetic motion, and thus the thrust generated is lower than that predicted theoretically by equilibrium analysis.