Thickness of normal shock zone (e.g. in nozzle)

In summary, when a supersonic flow occurs in a nozzle, it can lead to a "normal shock" where there is a sudden change in pressure and velocity. While videos may show a vertical step in the P and v graphs, in reality there will likely be a transition zone with a gradual slope. The thickness of this shock zone, which is around 200 nm in air, is determined by the properties of the fluid and is similar to the mean free path of gas molecules.
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Swamp Thing
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Under certain conditions, a supersonic flow in a nozzle will result in a "normal shock", an abrupt change in pressure and velocity. In the videos I've looked at, they draw the P and v graphs with a vertical step at that point.

But in practice, I assume there will be a non-zero transition zone with a finite slope in the relevant parameters? And if so, what would determine the thickness of the shock zone, i.e. the slope of the transitions?
 
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https://en.wikipedia.org/wiki/Shock_wave#In_supersonic_flows said:
In a shock wave the properties of the fluid (density, pressure, temperature, flow velocity, Mach number) change almost instantaneously. Measurements of the thickness of shock waves in air have resulted in values around 200 nm (about 10−5 in), which is on the same order of magnitude as the mean free path of gas molecules.
 
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FAQ: Thickness of normal shock zone (e.g. in nozzle)

What is a normal shock zone?

A normal shock zone is a region in a supersonic flow where the flow abruptly transitions to subsonic speeds. This transition involves a sudden increase in pressure, temperature, and density while the flow velocity decreases. The shock wave is perpendicular to the direction of the flow.

How is the thickness of a normal shock zone defined?

The thickness of a normal shock zone is defined as the distance over which the flow variables (pressure, density, temperature, and velocity) change from their upstream supersonic values to their downstream subsonic values. This thickness is typically on the order of a few mean free paths of the gas molecules, making it extremely thin.

What factors influence the thickness of a normal shock zone?

The thickness of a normal shock zone is primarily influenced by the molecular mean free path of the gas, which depends on the gas properties (such as temperature and pressure) and the type of gas. Higher temperatures and lower pressures generally increase the mean free path, thereby increasing the shock thickness. However, in practical applications, the thickness remains very small.

Why is the thickness of the normal shock zone important in nozzle design?

The thickness of the normal shock zone is important in nozzle design because it affects the performance and efficiency of the nozzle. In high-speed flows, especially in supersonic and hypersonic regimes, the presence of a shock wave can lead to significant losses in total pressure and can impact the thrust and overall efficiency of propulsion systems. Understanding the shock thickness helps in optimizing nozzle shapes to minimize these losses.

Can the thickness of a normal shock zone be measured experimentally?

Measuring the thickness of a normal shock zone experimentally is challenging due to its extremely small size. Advanced diagnostic techniques such as laser-induced fluorescence, schlieren photography, and high-speed imaging are often used to visualize and estimate the properties of shock waves. However, direct measurement of the exact thickness is difficult and typically relies on theoretical and computational models.

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