5.1. Conservation across a normal shock

● Sudden change in flow properties over a thin region (shock wave) ● Occurs in supersonic flows

A normal shock is a phenomenon in fluid dynamics that occurs when there is a sudden change in flow properties, like density, velocity, and pressure, over a very thin region known as a shock wave. This typically occurs in supersonic flows, which are flows moving faster than the speed of sound. Understanding normal shocks is crucial because they represent the transition from supersonic to subsonic conditions within a fluid flow.

You can think of a normal shock like the sound barrier. When a jet plane travels faster than the speed of sound, it creates a shock wave. Imagine a car speeding down a highway; as it approaches a speed that feels faster than any sound can travel, it experiences a dramatic change in its surroundings—this is similar to what happens in a fluid when a shock wave forms.

● Causes: ○ Decrease in Mach number (to subsonic) ○ Increase in pressure, temperature, and entropy ○ Decrease in stagnation pressure

When a normal shock occurs, it has several important effects on the fluid flow. Firstly, the Mach number drops from supersonic to subsonic, meaning the flow is slower after the shock compared to before it. Secondly, there is an increase in pressure and temperature across the shock, which can be surprising. Additionally, the entropy of the flow increases, signifying that the flow has become less ordered. Lastly, the stagnation pressure—essentially the maximum pressure obtainable in the flow—decreases as a result of the energy losses due to the shock.

Consider a water hose. When you fill it with pressurized water and then partially pinch it off at the nozzle, the flow speed decreases, the pressure upstream builds up, and you might feel the hose get warmer. This is similar to what happens in a normal shock, where the flow properties change rapidly, resulting in different conditions behind the 'pinch' or shock wave.

● Continuity, momentum, and energy equations are applied ● Not isentropic (entropy increases)

The analysis of normal shocks relies on fundamental conservation laws: continuity, momentum, and energy equations. Continuity ensures that mass is conserved through the shock, momentum principles govern how forces change, and energy conservation dictates how energy is distributed across the shock. However, the process is not isentropic, meaning that there is an increase in entropy—a sign that energy is dissipated and not all the energy is conserved in the form we want. This indicates that normal shocks involve irreversible processes, unlike isentropic flows which do not have energy losses.

Imagine a crowded concert where everyone is trying to exit through a single door. The crowd (mass) must go through that door (continuity). As they push through, some people might shove harder than others (momentum), and the ambient noise and excitement level rises (energy and entropy). Once they’re outside, the mixing of sounds and energy indicates a less orderly exit, similar to the increase in entropy we see with normal shocks.

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