Supersonic Nozzle Flow

Characteristics of Flow

Based on Mach number, the fluid flow is characterized in different regions and also the speed of the object is identified. It is an important quantity which has no dimension because of the ratio of two velocities with same dimension and it plays an important role in getting the proper idea of the motion of vehicles especially airplanes and rockets moving in an air medium. Mach number is the ratio between the speed of the object in air medium and the speed of sound. The speed of sound is 343 m/s (meter/second) at the temperature of 20 degrees Celsius in the considered medium.

• V = Speed of object

• C = Speed of sound

Mach number is generally represented with M. When an object is flying in the sky, the air particles around them are disturbed by the speed of the object. If the Mach number is greater than the speed of sound, then the air particles are compressed thus the compressibility effects are taken into account. As a result of identifying the Mach number, it is possible to find whether the flow is compressible or not.

Classification of Flow Regions

According to the Mach number (M) variations, the flow is classified in different regimes. If the Mach number remains less than 0.3 then the flow is said to be Incompressible. If it varies from 0.3 to 0.8, then the flow is called Subsonic. The flow is sonic when the Mach number is equal to one. The flow is said to be transonic when the Mach number is greater than 0.8 and till 1.2. If the Mach number is greater than 1.2 then it is called as supersonic. Hypersonic flows are greater than Mach number 5. The different flow regime according to the Mach number is listen in the table 1

If the Mach number is high, then the fluid is considered as compressible and compressibility effects are significant. Incompressible fluid is the constant density flow. Even if the pressure is changed there is not much difference in volume with the constant temperature too. The change in pressure is related to change in volume with very small amount when the temperature is constant and lies within the regime of incompressible flow. From Bernoulli’s principle, the pressure variation is related to velocity change. The flow is said to be compressible when there is a volume change with the respective pressure variation. For aircrafts, the height is also considered for performance and it changes the Mach number. When the aircraft flies at different altitude, the pressure varies and speeds of sound changes. In that particular, the change of height resulting in change of Mach number creates necessity of the aircraft to adjust itself.

The flow variation is closely considered and monitored since the flow dominates and decides the performance of the engine. The converging nozzle is used when the flow is subsonic. Converging nozzle is the duct in which the area is decreased at certain inclination constantly. When the incoming flow is supersonic, pressure and temperature of the incoming flow are high while the velocity and Mach number of the inlet flow are lower. When the subsonic flow is passed through the convergent nozzle, the pressure and temperature gt reduced while the velocity and Mach number get increased. With the same purpose of increasing the exit velocity of the supersonic incoming flow, the divergent nozzle can be used. For the divergent nozzle with the supersonic flow, the pressure and temperature of the fluid get reduced and conversely the velocity and Mach number are increased. For subsonic flow, the divergent nozzle is acted as diffuser to reduce the speed of the flow. In the same way, the convergent nozzle is acted as diffuser for supersonic flow. When the compressibility effects are considered in the nature of the flow, the shock wave problems are also considered.