Question

Can a shock wave develop in the converging section of a converging-diverging nozzle? Explain.

Short answer

Answer: No, a shock wave cannot develop in the converging section of a converging-diverging nozzle. It can only form at the throat or in the diverging section when the flow reaches or exceeds the local speed of sound.

Step-by-step solution

Converging-Diverging Nozzle

A converging-diverging nozzle is a device that is designed to accelerate or decelerate a compressible fluid (such as a gas) by changing its velocity and pressure. It consists of two sections: a converging section and a diverging section. In the converging section, the cross-sectional area decreases, causing the fluid velocity to increase and pressure to decrease. In the diverging section, the cross-sectional area increases, allowing the fluid velocity to further increase (or decrease, depending on the regime) and pressure to decrease even more.

Shock Waves

A shock wave is a region of abrupt change in fluid properties (such as pressure, temperature, and density) within a compressible flow. It usually occurs when the flow velocity exceeds the local speed of sound (i.e., when the flow is supersonic), resulting in a sudden and strong compression of the fluid. This compression leads to a steep increase in pressure and the formation of a shock wave.

Shock Waves in a Converging-Diverging Nozzle

A shock wave can occur in a converging-diverging nozzle when the flow transitions from subsonic to supersonic conditions. This can occur either at the throat, where the nozzle's cross-sectional area is minimum, or in the diverging section, where the area is increasing. When a shock wave occurs at the throat, it is referred to as a "normal shock," while when it takes place in the diverging section, it is referred to as an "oblique shock."

Shock Waves in the Converging Section

In the converging section of a converging-diverging nozzle, the flow is subsonic, and the velocity increases while the pressure decreases as the fluid moves towards the throat's minimum cross-sectional area. The local speed of sound is not reached or exceeded in the converging section itself, so a shock wave does not form in this part of the nozzle. However, it is important to note that a shock wave can still be present in the nozzle if it occurs further down the flow path, either at the throat or in the diverging section. This shock wave may influence fluid properties in the converging section, but the shock itself does not originate within the converging section. In conclusion, a shock wave cannot develop in the converging section of a converging-diverging nozzle. It can only form at the throat or in the diverging section when the flow reaches or exceeds the local speed of sound.