Quality of ideal Gas approximation?

I know that modeling gases as ideal gases includes two approximations:

• approximating Particles as points regarding the collisions with macroscopic objects
• neglecting inter-particle interactions

The first approximation seems pretty "harmless", it is the quality of the second approximation im interested in.

Under what circumstances can inter-particle interaction be neglected?

Especially: Can aerodynamic calculations be done reliably using the ideal gas approximation?

• What flow regime are you asking about? There's a world of difference between subsonic flows which are essentially perfectly continuous and hypersonic flows with occasional molecules striking surfaces. Oct 1, 2022 at 12:16
• Broadly, we can say that the ideal gas assumption is suitable if the compressibility factor is sufficiently close to 1 for one’s purposes for the relevant pressure and temperature. Oct 1, 2022 at 14:11

Real gases behave as ideal gases at low pressures and high temperatures. The quantitative test is $$Z = \frac{P V}{RT} \approx 1$$ where $$Z$$ is the comprehensibility factor. To a good approximation $$Z$$ can be represented in the form of a universal graph for all gases as a function of reduced pressure ($$P_r=P/P_c$$) and reduced temperature ($$T_r=T/Tc$$), where $$P_c$$, $$T_c$$ are the critical pressure and temperature of the gas:
The gas is essentially ideal if $$Z$$ is close enough to 1.
To determine whether the ideal gas is applicable to aerodynamics, suppose the gas to be nitrogen ($$T_c=126.2$$ K, $$P_c=33.98$$ bar). Then use a typical $$P$$ and $$T$$ in your problem and determine $$Z$$. For example, with at $$T=300$$ K we have $$T_r=2.4$$. As we see from the graph, the isotherm $$T_r=2.4$$ is pretty close to 1 up to fairly high pressures. So, nitrogen at 25 C is pretty close to ideal gas at least up to $$P_r\approx 2$$ or $$P=2 P_c\approx 70$$ bar.