NOZZLES J3008/7/1

NOZZLES

OBJECTIVES

General Objective : To understand the mechanism of flow in nozzles

Specific Objectives : At the end of the unit you should be able to :

sketch and differentiate the types and shapes of nozzles

define Critical Pressure Ratio

calculate cross-sectional area, A and the temperature of a throat at entrance and exit

calculate maximum mass flow

define and differentiate the use of nozzles in :- steam turbine- gas turbine- jet engine- flow measurement- rocket propulsion- steam injector- injector

UNIT 7

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7.0 INTRODUCTION

Nozzle A nozzle is a device that increases the velocity of a fluid at the expense of pressure. It is a duct of smoothly varying cross-sectional area in which a steadily flowing fluid can be made to accelerate by a pressure drop along the duct.

There are many applications in practice which require a high-velocity stream of fluid, and the nozzle is the best means of obtaining high-velocity, thus nozzles are used in steam and gas turbines, in jet engines, in rocket motors, in flow measurement, and in many other applications.

When a fluid is decelerated in a duct, causing a rise in pressure along the stream, then the duct is called a diffuser; two applications in practice in which a diffuser is used are the centrifugal compressor and the ram jet.

Nozzles and DiffusersA nozzle is a device that increases the velocity of a fluid at the expense of pressure. A common example would be a nozzle used at the end of a garden hose !

A diffuser is a device that increases the pressure of a fluid by slowing it down. Several types of pumps operate by using shaft work to turn an impeller which will increase the kinetic energy of the fluid, followed by a diffuser that converts some of the kinetic energy to an increased pressure.

Nozzle Diffuser

Figure 7.1 Nozzle & Diffuser

INPUTINPUT

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7.1 Types and shapes of nozzles

Typical nozzle cross-sectional areas of particular interest are shown in Figure 7.2

Figure 7.2

a) Convergent Nozzle

Figure 7.3

The convergent nozzle in which the cross-section converges from the entry area to a minimum area which is the exit.

b) Convergent – divergent nozzle

Figure 7.4

Figure 7.4 shows a convergent-divergent nozzle. It can be seen from the inlet area the nozzle converges to a minimum area

called the throat and then to the outlet area.

inlet throat outlet

Inlet Outlet

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7.2 Critical Pressure Ratio

- It has been stated before, that the velocity at the throat of a correctly designed nozzle is the velocity of sound.

- The flow-up to the throat is sub-sonic while the flow after the throat is supersonic. It should be noted that a sonic or supersonic flow requires a diverging duct to accelerate it.

- In the same way, for a nozzle that is convergent, the fluid will attain sonic velocity at the exit if the pressure drop across the nozzle is large enough.

- The ratio of the pressure at the section where sonic velocity is attained to the inlet pressure of a nozzle is called the critical pressure ratio.

- Critical temperature ratio,

- Critical pressure ratio,

7.3 Maximum Mass Flow

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- Consider a convergent nozzle expanding into space, the pressure of which can be varied, while the inlet pressure remains fixed. The nozzle is shown diagrammatically in the Figure 7.5.

- When the back pressure, pb is equal to p1, then no fluid can flow through the nozzle. As pb is reduced the mass flow through the nozzles increases, since the enthalpy drop, and hence the velocity increases.

- However, when the back pressure reaches the critical value, it is found that no further reduction in back pressure can affect the mass flow.

- When the back pressure is exactly equal to the critical pressure, pc then the velocity at exit is sonic and the mass flow through the nozzle is at a maximum value. The exit pressure remains at pc, and the fluid expands violently outside the nozzle down to the back pressure.

- It can be seen that the maximum mass flow through a convergent nozzle is obtained when the pressure ratio across the nozzle is the critical pressure ratio. Also, for a convergent-divergent nozzle, with sonic velocity at the throat, the cross-sectional area of the throat fixes the mass flow through the nozzle for fixed conditions.

- When a nozzle operates with the maximum mass flow, it is said to be choked. A correctly designed convergent-divergent nozzle is always choked.

7. 4 Cross-sectional area, A and temperature of a throat at entrance and exit

valve

p1 Back press, pb

Figure 7.5

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Consider a stream of fluid at pressure p1, enthalpy h1, and with a low velocity C1. It is required to find the shape of duct which will cause the fluid to accelerate to a high velocity as the pressure falls along the duct. It can be assumed that the heat loss from the duct is negligibly small (adiabatic flow, Q = 0), and it is clear that no work is done on or by the fluid (W = 0). Applying the steady-flow energy equation :

Figure 7.6

Applying the steady-flow energy equation, between section 1 and any other section X-X where pressure , enthalpy , and with low velocity C1. It is required to find the shape of duct which will cause the fluid to accelerate to high velocity as the pressure falls along the duct. Figure 7.6

It can be assumed that the heat loss from the duct is negligibly small, and it is clear no work is done on or by the fluid. Applying the steady-flow energy equation which is :

------------(1)

or can be written like these,------------(2)

------------(3)

(where fluid velocity is C and h is an enthalpy)

X 2A1 A2

h1 h2

C1 C2

X 1 X

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In most practical applications the velocity at the inlet to a nozzle is negligibly small in comparison with the exit velocity. It can be seen from equation (5), that a negligibly small velocity implies a very large area, and most nozzles are in fact shaped at inlet in such a way that the nozzle converges rapidly over the first fraction of its length :

And neglecting C1 this gives,

Since enthalpy is usually expressed in KJ/kg, then an additional constant of 103

will appear within the root sign if C is to be expressed in m/s,

(where 1 kJ=103

Nm)

Hence,

If the area at the section X-X is A, and the specific volume is v :

------------(4)

or

------------(5)

Then substituting for the velocity C, from equation (3),

Example 7.1

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Air at 8.6 bar and 190C expands at the rate of 4.5 kg/s through a convergent-divergent nozzle into a space at 1.03 bar. Assuming that the inlet velocity is negligible, calculate the throat and the exit cross-sectional areas of the nozzle.

The nozzle is shown diagrammatically in figure below. The critical pressure ratio is given by,

1 C 2

8.6 bar 1.03 bar

C1=0 C2

Also,

Then,

And,

To find the area of the throat,

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Using equation for a perfect gas,

Then,

Then to find the exit area,

ACTIVITY 7A

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TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH THE NEXT INPUT…!

7.1 Sketch two types of nozzles

7.2 Define :(a) critical presssure ratio(b) maximum mass flow

7.3 A fluid at 6.9 bar and 93C enters a convergent nozzle with negligible velocity, and expands isentropically into a space at 3.6 bar. Calculate the outlet temperature and mass flow per m2 of exit area.

(a) when the fluids is helium (Cp=5.23 kJ/kgK)(b) when the fluid is ethane (Cp=1.66 kJ/kgK)

Assume that both helium and ethane are perfect gases, and the respective molecular weights as 4 and 30.

FEED BACK ON ACTIVITY 7A

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7.1b) Convergent Nozzle

b) Convergent – divergent nozzle

7.2a) critical presssure ratio

- The ratio of the pressure at the section where sonic velocity is attained to the inlet pressure of a nozzle.

b) maximum mass flow- The flow through a convergent nozzle that can be obtained

when the pressure ratio across the nozzle is the critical pressure ratio.

7.3 Solution :a)

It is necessary first to calculate the critical pressure in order to discover whether the nozzle is choked or not.

inlet throat outlet

Inlet Outlet

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We know that,

Therefore for helium,

Then,

So,

Then using equation for critical pressure ratio,

The actual back pressure is 3.6 bar, hence in this case the fluid does not reach the critical conditions and the nozzle is not choked. The nozzle is shown diagrammatically in the figure below :

1 2

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6.9 bar 3.6 bar

Then,

So,

Also,

So,

b) Using the same prosedure for ethane, we have,

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Therefore for ethane ,

Then,

So,

Then using equation for critical pressure ratio,

The actual back pressure is 3.6 bar, hence in this case the fluid reaches critical conditions at exit and the nozzle is choked. The expansion from the exit pressure of 3.91 bar down to the back pressure of 3.6 bar must take place outside the nozzle. The nozzle is shown diagrammatically in the figure below :

1 2

3.6 bar

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6.9 bar 3.91 bar

Then,

So,

Also,

So,

7.4 The nozzle can be used in the following application :

Steam turbine, gas turbine, jet engine, flow measurement, rocket propulsion, steam injector and an injector itself.

INPUTINPUT

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But do you know that :

All jet engines have a nozzle at the back of the engine. It is the exhaust duct of the engine. The air from the turbine blades and the engine mixes together in the nozzle and makes a big force that blasts out at the back of the engine. It is this power that pushes, or thrust, the airplane forward.

a) Steam Turbine Of all the heat engines and prime movers the steam turbine is the nearest to

the ideal and it is widely used in power plants and in all industries where power and/or heat is needed for processes; such as pulp mills, refineries, petro-chemical plants, food processing plants, desalination plants, refuse incinerating and district heating plants.

Operation principle : In principle, the impulse steam turbine consists of a casing containing stationary steam nozzles and a rotor with moving or rotating buckets. The steam passes through the stationary nozzles and is directed at high velocity against the rotor buckets causing the rotor to rotate at high speed.

The following events take place in the nozzles:

The steam pressure decreases.

The enthalpy of the steam decreases.

The steam velocity increases

The volume of the steam increases.

b) Gas Turbine

A gas turbine has a compressor, combustion chamber, and turbine. The turbine and the compressor are on the same shaft. The compressor raises the pressure of atmospheric air and sends this air to the combustion chamber. Here, a fuel (oil, gas, or pulverized coal) burns, raising the temperature and increasing the heat energy. The hot gas in the turbine expands to develop mechanical energy, as expanding steam does in a steam turbine.

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The basic parts of a turbine are the rotor, which has blades projecting radially from its periphery; and nozzles, through which the gas is expanded and directed. The conversion of kinetic energy to mechanical energy occurs at the blades. The basic distinction between the types of turbines is the manner in which the gas causes the turbine rotor to move.

The main use for the gas turbine in the present day is in the air-craft field, and the large unit of a gas turbine is used for electric power generation and for marine propulsion.

c) Jet Engine

Jet engines move the airplane forward with a great force that is produced by a tremendous thrust and causes the plane to fly very fast.

All jet engines, which are also called gas turbines, work on the same principle. The engine sucks air in at the front with a fan. A compressor raises the pressure of the air. The compressor is made up of fans with many blades and attached to a shaft. The blades compress the air. The compressed air is then sprayed with fuel and an electric spark lights the

Translated from a Korean text :The development of gas turbine

can make us fly in the sky, explore the seven seas and generate electric power that we use

everyday to make life better !

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mixture. The burning gases expand and blast out through the nozzle, at the back of the engine. As the jets of gas shoot backward, the engine and the aircraft are thrust forward as shown in Figure 7.7.

In a jet engine airplane, thrust is a result of hot gases (exhaust) rushing out of the engine's nozzle. The action of the gases rapidly moving backward causes a reaction in the air. The air puts out a force equal to the thrust, but in the opposite direction, moving the airplane forward.

Figure 7.7

d) Flow Measurement A nozzle is used frequently as a flow meter by inserting it into a

pipeline and measuring the pressure drop or the differential between the inlet and the throat. This pressure must be kept small, and is measured by a water or mercury manometer.

A convergent nozzle can be used in a pipeline as shown in the Figure 7.8. The different levels in the manometer is ∆ , where ∆ is the

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pressure difference between section 1 and 2, and is the specific weight of the manometer liquid.

Eddies are set up as the fluid leaves the nozzle and the kinetic energy of the jet is dissipated irreversibly. This means that some of the pressure drop, ∆ , is not recovered, and so the nozzle causes a loss of pressure in the pipeline.

The pressure loss can be reduced by using a convergent-divergent nozzle in the pipeline. The pressure loss can be reduced by using a convergent-divergent nozzle as shown in Figure 7.9. Since the nozzle in Figure 7.9 is far from choked condition, it acts as a venturi meter. The flow is expanded down to the throat at section 2, and diffused from 2 to 3.

In this way, the pressure drops to the throat, ∆ , is almost completely recovered in the diffuser portion, and the pressure loss in the pipeline due to the venturi meter is much smaller than that due to a convergent nozzle.

Figure 7.8 Figure 7.9 Convergent Nozzle Convergent-Divergent Nozzle

e) Rocket Propulsion One very important use of the nozzle is

as a means of propolsion. Since the fluid flowing through the nozzle is accelerated relative to the nozzle, then by Nowton’s third law, it follows that the fluid exerts a trust on the nozzle in the opposite direction to the fluid flow.

In 1926, Robert Goddard tested the first liquid-propellant rocket engine. His

engine used gasoline and liquid oxygen. The basic idea is simple. In

most liquid-propellant rocket

engines, a fuel and an oxidizer (for

example, gasoline and liquid oxygen) are pumped into a

combustion chamber. There

they burn to create a high-pressure and high-velocity stream of hot gases. These gases flow through

a nozzle that accelerates them further (5,000 to 10,000 mph exit velocities being

typical), and then they leave the

engine.

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In the jet aeroplane and the ram-jet the atmospheric air is drawn in, compressed, heated, and allowed to expand through a nozzle, leaving the aircraft at high velocity ; the rate of change of momentum of the air backwards relative to the aircraft gives a reactive forward trust to the aircraft.

In order to achieve jet-propelled flight in space, where there is no atmosphere to be drawn into the vehicle, it is necessary that the fuel plus its oxidant should be carried in the rocket. This is known as the rocket propolsion.

A rocket operating on a chemical fuel consists of tanks containing the chemical propollent, and a rocket motor (or rocket engine) which consists of a combustion chamber and a convergent-divergent nozzle. Some way of introducing the propellant from the tanks to the combustion chamber is also necessary, and this can be done by using a pump or by having an additional tank of compressed nitrogen.

When a pump is used it can be driven by a small turbine using the propellant as fuel. A simple line diagram of a rocket is shown in Figure 7.10.

f) Steam Injector Steam injector is widely used in the steam locomotives and is one of

the components used in the nuclear power plants.

In the steam engine of the steam locomotive, the water supply to the boiler is provided by two live steam injectors, or one live steam and one exhaust injector on larger locomotives. Injectors work because steam under the same pressure and conditions flows from a contracted nozzle at

Figure 7.10Adapted from

www.HowStuffWorks.com

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a much greater velocity than water. The steam cone, or nozzle, regulates the quantity of steam used by the injector. It is both convergent and divergent in order to direct the flow of steam into the combining cone and gives it the maximum possible velocity. (Figure 7.11)

The condensation of the steam jet and the transfer of its energy to the water takes place in the combining cone which receives the steam and water. In condensing, the steam gives up its velocity to the water, which is then further accelerated by the vacuum in the combining cone caused by the reduction in the volume of the steam when condensed by the water.

At the inlet end is a jet consisting of a mixture of steam and water, while the outlet end has a jet of hot water flowing at high velocity but very low in pressure. Steam injectors are very efficient and waste very little heat as the steam used is returned to the boiler as hot water.

Figure 7.11

g) Injector One of an example of an injector is a fuel injector. It is an electronically

controlled valve. It is supplied with pressurized fuel by the fuel pump in your car, and it is capable of opening and closing many times per second. Figure 7.12

When the injector is energized, an electromagnet moves a plunger that opens the valve, allowing the pressurized fuel to squirt out through a tiny

Water

Delivery pipe

Steam

Boiler

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nozzle. The nozzle is designed to atomize the fuel -- to make the fuel as fine a mist as possible so that it can burn easily.

The injectors are mounted in the intake manifold so that they spray fuel directly at the intake valves. A pipe called the fuel rail supplies pressurized fuel to all of the injectors.

Figure 7.12Adapted from www.HowStuffWork.com

ACTIVITY 7B

TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH THE NEXT INPUT…!

A fuel injector firing

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Horizontal :1. The _____________ is widely used in power plants and all industries where power

or heat is needed for processes.3. Marine ___________use the gas turbine to delevop mechanical energy.5. A nozzle is used as a _____________ by inserting it into a pipeline. 6. A differential between the inlet and the _________ of a flow meter is called the

pressure drop.8. In the______aeroplane the atmospheric air is drawn in, compressed, heated, and

allowed to expand through a nozzle.

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10. In the steam engine of steam locomotive, the water supply to the _______ is provided by two live steam injectors.

13. When an injector is energized, an electromagnet moves a pluger that opens the ______,allowing the pressurized fuel to squirt out through a tiny nozzle.

Vertical :2. The basic parts of a turbine are the __________, which has blades projecting

radially from its periphery.4. Jet engines move the airplane forward with a great force that is produced by a

tremendous __________ and causes the plane to fly very fast.7. The ______________ can be reduced by using a convergent-divergent nozzle in

the pipeline.9. A rocket operating on a chemical ________ consists of tanks containing the

chemical propellent.11. The steam ______ or nozzle regulates the quantity of steam used by the injector.

FEEDBACK ON ACTIVITY 7B

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SELF-ASSESSMENT

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You are approaching success. Try all the questions in this self-assessment section and check your answers with those given in the Feedback on Self-Assessment. If you face any problems, discuss it with your lecturer. Good luck.

7.1 Calculate the throat and exit areas of a nozzle to expand air at the rate of 4.5 kg/s from 8.3 bar, 327C into a space at 1.38 bar. Neglect the inlet velocity and assume isentropic flow.

7.2 It is required to produce a stream of helium at the rate of 0.1 kg/s travelling at sonic velocity at a temperature of 15C. Calculate the inlet pressure and temperature required assuming a back pressure of 1.013 bar and negligible inlet velocity. Calculate also the exit area of the nozzle. Assume isentropic flow and helium is a perfect gas of molecular weight = 4 and =1.66.

7.3 Recalculate problem 1 assuming a coefficient of discharge is 0.97 and nozzle efficiency is 0.92.

FEEDBACK ON SELF-ASSESSMENT

Answers :

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7.1 3290 mm2 , 4850 mm2

7.2 2.077 bar, 110C , 592 mm2

7.3 The throat diameter = 20.5 mm & the exit diameter = 34 mm