Compressible Flow in Nozzles

 A division of fluid mechanics that deals with fluids in which the fluid density varies with pressure is called compressible flow. The effects of compressibility are considered important if the ratio of flow of velocity to the local speed of sound (Mach number) of the flow exceeds 0.3 or if the fluid undergoes a large pressure. Compressible flow in nozzles describes the behavior of fluids that has large variations in density. For flows in which there is no variation in density, the analysis of behavior of flows can be simplified greatly by assuming a constant density. This leads to the theory of incompressible flow. In case of gases with high velocities and liquids with large pressure, there is a chance for occurrence variations in density and the flow can be analyzed as compressible flow if accurate results have to be obtained.

Effect of compressible flow

Compressible flows have a great role in determining the behavior of nozzles. Subsonic and supersonic flow reacts differently to the changes happening in cross sectional area. Subsonic flow goes through a converging duct that narrows down from a wide diameter to a small diameter in the direction of the flow then there is a chance for increased velocity. If a supersonic flow occurs through a similar duct there will be a decrease in velocity. If the convergence area is greater enough so that sound speed is reached it results in choking. There are chances that the flow rate of fluid entering the pipe is limited or shock waves form in the nozzle in this case. Likewise, subsonic flow through a diverging nozzle will be slowed always and supersonic flow will be accelerated. The Mach number of the flow can be directly related to the area by the following relation:

Here A is the area, M is the Mach number, r is the ratio of specific heats and A^* is the area that cause the flow of velocity to reach a Mach number of 1. Thus if a subsonic flow has to be accelerated to supersonic velocities the nozzle should have a converging section in which the flow is subsonic, a throat at which the flow velocity is the local speed of sound. Also a diverging section will be there with supersonic flow. This arrangement is popularly known as de Laval nozzle. This is mostly used in propulsion systems such as rocket and supersonic jet engines.

Questions:

• Define compressible flow?
• How does compressible flow help in determining the behavior of nozzles?