Converging / Diverging nozzles: How nozzle generates a vacuum?

Summary

When an ejector throws the noncondensable out from the system and generates a vacuum it generates a thrust force according to Newton's 3rd law of motion to expel them out. This thrust force depends on the exit velocity of the gas. A supersonic exit velocity generated by converging / diverging nozzle gives the maximum vacuum

I am sure many of you are familiar with ejector nozzles. You must have observed some ejectors have only a convergent nozzle and some have convergent and divergent nozzles. A convergent nozzle can generate maximum sonic speed, Mach = 1. A convergent-divergent nozzle can generate supersonic speed, Mach >1, Therefore, a convergent-divergent nozzle can produce much more vacuum in a given system than a convergent nozzle.

In many ejectors, convergent/divergent nozzles are used to achieve supersonic velocity to get the maximum vacuum. The profile of the ejector nozzle is the fundamental to vacuum it generates. Just keep an image of an ejector nozzle ( download from the internet) in Infront of you and read the post. This will help understand everything about the design of the nozzle.

With a convergent nozzle, you can reach the maximum velocity at the narrowest point. In this situation, the nozzle is said to be choked. Increasing the nozzle pressure ratio further will not increase the nozzle Mach number above one.?You get sonic velocity and the corresponding vacuum.

In converging/ diverging nozzle the flow speed will increase beyond the narrowest point from sonic to supersonic as the flow expands in the diverging section. As the gas exits the throat, the increase in the area allows for it to undergo a Joule-Thompson expansion wherein the gas expands at supersonic speeds from high to low pressure pushing the velocity of the mass flow beyond sonic speed.

Convergent-divergent [CD] type of nozzles are mostly used for supersonic flows. It is impossible to create supersonic flows, Mach number > 1 in the convergent type of nozzle because of the restriction imposed by the choked flow. In CD type of nozzles, an increase of the flow velocity much higher than sonic velocity can be achieved. The key applications CD type nozzles are in propelling nozzles in jet engines or in air intake for engines working at high rpm, turbines, and vacuum systems.

Let us move step by step

What is a nozzle? A?nozzle is a pipe or tube of varying cross-sectional area used to direct or modify the flow of a fluid. Nozzles can control the rate of flow, speed, direction, mass, shape, and/or the pressure of the stream that emerges from them. In a nozzle, the velocity of fluid increases at the expense of its pressure energy.

What do nozzles do?

Nozzles generate thrust. The objective of a nozzle is to increase the kinetic energy of the flowing medium at the expense of its pressure and internal energy. Nozzles can be described as convergent (narrowing down from a wide diameter to a smaller diameter in the direction of the flow) or divergent (expanding from a smaller diameter to a larger one). A nozzle with a convergent section followed by a divergent section and is often called a convergent-divergent (CD) Nozzle. As said above, nozzles generate thrust. Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that system. The force applied on a surface in a direction perpendicular or normal to the surface is also called thrust. The opposite force working in a perpendicular direction upward gives the lift to the airplane or rocket.

In an aircraft, thrust is the force that moves the aircraft through the air. All thrust is generated through some application of Newton's third law of motion, for every action, there is an equal and opposite reaction. Thrust is generated by the propulsion system of the aircraft. The engine does work on the gas and as the gas is accelerated to the rear, the engine is accelerated in the opposite direction. The acceleration of the engine mass produces a force on the aircraft. How the aircraft responds depends on the balance of forces on the airplane.

Therefore, it is the thrust that drives an aircraft or rocket or turbine. The fundamentals which work behind the scene are Newton’s second and third law of motion. In the second law, it says that the force on an object is equal to its mass times its acceleration. In the third law, it says that when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

Thrust equation

The general thrust equation is then given by:

F = (m dot * V) e - (m dot * V)0 + (pe - p0) * Ae

"m dot" is the mass flow rate, the mass per unit time.

V is the velocity

"e" signifies and "0" signifies the free stream

p signifies the pressure

Across the exit area, we may encounter an additional force term equal to the exit area Ae times the exit pressure minus the free stream pressure.

We see that there are two possible ways to produce high thrust. One way is to make the engine flow rate (m dot) as high as possible. As long as the exit velocity is greater than the free stream, entrance velocity, a high engine flow will produce high thrust. This is the design theory behind propeller aircraft and high-bypass turbofan engines. A large amount of air is processed each second, but the velocity is not changed very much. The other way to produce high thrust is to make the exit velocity very much greater than the incoming velocity. This is the design theory behind pure turbojets and rockets. A moderate amount of flow is accelerated to a high velocity in these engines.

?The nozzle of a turbine engine is usually designed to make the exit pressure equal to the free stream. In that case, the pressure-area term in the general equation above becomes zero. The thrust is then equal to the exit mass flow rate times the exit velocity minus the free stream mass flow rate times the free stream velocity.

F = (m dot * V)e - (m dot * V)0

Therefore, it is all how velocity differences within a device drive the thrust,

Here comes the role of the design of the nozzle.

?Convergent nozzle

Convergent nozzles accelerate subsonic fluids. If the nozzle pressure ratio is high enough, then the flow will reach sonic velocity at the narrowest point (i.e., the nozzle throat). In this situation, the nozzle is said to be choked. Increasing the nozzle pressure ratio further will not increase the throat Mach number above one.?It does not achieve supersonic velocity

Divergent nozzle

Divergent nozzles slow fluids if the flow is subsonic,?

The?third type of nozzle design is

Convergent – Divergent nozzle [CD]

Its operation relies on the different properties of gases flowing at subsonic, sonic, and supersonic speeds. The speed of a subsonic flow of gas will increase if the pipe carrying it narrows because the mass flow rate is constant. The gas flow through a convergent-divergent nozzle is isentropic (gas entropy is nearly constant). In a subsonic flow, the sound will propagate through the gas. At the "throat", where the cross-sectional area is at its minimum, the gas velocity locally becomes sonic (Mach number = 1.0), a condition called choked flow. As the nozzle cross-sectional area increases, the gas begins to expand and the gas flow increases to supersonic velocities (Mach number > 1.0). As the gas exits, the throat the increase in the area allows for it to undergo a Joule-Thompson expansion wherein the gas expands at supersonic speeds from high to low pressure pushing the velocity of the mass flow beyond sonic speed.

Convergent-divergent nozzles can therefore accelerate fluids that have choked in the convergent section to supersonic speeds. This CD process is more efficient than allowing a convergent nozzle to expand supersonically externally.

Finally,

Significance of Mach number

Mach number is an important quantity to compare the speed of any object with the speed of sound. It is a parameter to denote the speed of a flying object in an air medium. In fluid dynamics, it has very vast use. By definition, it is a dimensionless quantity expressing the ratio of the velocity of an object in a medium to speed of sound.

Generally, the Mach number is represented with the symbol ‘M’.

Mach Number=?Speed of object/Speed of sound

M=v/c

Where v= Speed of the object in a medium with respect to some boundary either internal or external.

And c =Speed of sound in the local medium.

Various Types of Flow

According to the variation of Mach number fluid flow is classified.

Subsonic: For this type of flow the Mach number remains below 0. 8.

Sonic: For sonic flow, the Mach number is one. That is for this type of flow the velocity of an object is equal to the velocity of sound in the local medium.

Supersonic: When the object flow with greater velocity than the sound it is said to have supersonic velocity. It has a Mack number greater than one.

Credit: Google

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