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UNIT 2 : STEAM NOZZLES AND TURBINES

 

STEAM NOZZLES AND TURBINES

 

Flow of steam through nozzles, shapes of nozzles, effect of friction, critical pressure ratio, supersaturated-flow.  Impulse and reaction principles, compounding, velocity diagrams for simple and multistage turbines, speed regulations-governors and nozzle governors. Numerical Problems.

 

STEAM NOZZLES AND TURBINES

Some Technical Terms :

 

1. Wet steam: The steam which contains some water particles in superposition.

2. Dry steam / dry saturated steam: When whole mass of steam is converted into steam then it is called as dry steam.

3. Super heated steam: When the dry steam is further heated at constant pressure, the temperature increases the above saturation temperature. The steam has obtained is called super heated steam.

4. Degree of super heat: The difference between the temperature of saturated steam and saturated temperature is called degree of superheat.

5. Nozzle:It is a duct of varying cross sectional area in which the velocity increases with the corresponding drop in pressure.

6. Coefficient of nozzle: It is the ratio of actual enthalpy drop to isentropic enthalpy drop.

7. Critical pressure ratio: There is only one value of ratio (P2/P1) which produces maximum discharge from the nozzle . then the ratio is called critical pressure ratio.

 8. Degree of reaction: It is defined as the ratio of isentropic heat drop in the moving blade to isentrpic heat drop in the entire stages of the reaction turbine.

9. Compounding: It is the method of absorbing the jet velocity in stages when the steam flows over moving blades.

(i)Velocity compounding

(ii)Pressure compounding and

(iii) Velocity-pressure compounding

10. Enthalpy: It is the combination of the internal energy and the flow energy.

11. Entropy: It is the function of quantity of heat with respective to the temperature.

12. Convergent nozzle: The cross-sectional area of the duct decreases from inlet to the outlet side then it is called as convergent nozzle.

13.Divergent nozzle: The cross-sectional area of the duct increases from inlet to the outlet then it is called as divergent nozzle.

 

Flow of steam through nozzles:

The flow of steam through nozzles may be regarded as adiabatic expansion. - The steam has a very high velocity at the end of the expansion, and the enthalpy decreases as expansion takes place. - Friction exists between the steam and the sides of the nozzle; heat is produced as the result of the resistance to the flow. - The phenomenon of super saturation occurs in the flow of steam through nozzles. This is due to the time lag in the condensation of the steam during the expansion.

Continuity and steady flow energy equations

Through a certain section of the nozzle:

m.v = A.C

                                   where ,m is the mass flow rate,

 v is the specific volume,

A is the cross-sectional area and

C is the velocity.

For steady flow of steam through a certain apparatus, principle of conservation of energy states:

       h1 + C1 2 /2 + gz1 + q = h2 + C2 2 /2 + gz2 + w

 

For nozzles, changes in potential energies are negligible, w = 0 and q = 0.

h1 + C12 /2 = h2 + C22 /2
which is the expression for the steady state flow energy equation.

 

Types of Nozzles:

1. Convergent Nozzle

2. Divergent Nozzle

3. Convergent-Divergent Nozzle

Convergent Nozzle: A typical convergent nozzle is shown in fig. in a convergent nozzle, the cross sectional area decreases continuously from its entrance to exit. It is used in a case where the back pressure is equal to or greater than the critical pressure ratio.

 

FIGURE.1: CONVERGENT NOZZLE

 

Divergent Nozzle: The cross sectional area of divergent nozzle increases continuously from its entrance to exit. It is used in a case, where the back pressure is less than the critical pressure ratio.

FIGURE.2: DIVERGENT NOZZLE

 

Convergent-Divergent Nozzle: In this case, the cross sectional area first decreases from its entrance to throat, and then increases from throat to exit.it is widely used in many type of steam turbines.

FIGURE.3: CONVERGENT-DIVERGENT NOZZLE

 

Supersaturated flow or Meta stable flow in Nozzles:

As steam expands in the nozzle, its pressure and temperature drop, and it is expected that the steam start condensing when it strikes the saturation line. But this is not always the case. Owing to the high velocities, the residence time of the steam in the nozzle is small, and there may not sufficient time for the necessary heat transfer and the formation of liquid droplets. Consequently, the condensation of steam is delayed for a little while. This phenomenon is known as super saturation, and the steam that exists in the wet region without containing any liquid is known as supersaturated steam. The locus of points where condensation will take place regardless of the initial temperature and pressure at the nozzle entrance is calledthe Wilson line. The Wilson line lies between 4 and 5 percent moisture curves in the saturation region on the h-s diagram for steam, and is often approximated by the 4 percent moisture line. The super saturation phenomenon is shown on the h-s chart below:

                              Figure. The h-s diagram for the expansion of steam in the nozzle

 

 

Effects of Supersaturation:

The following are the effects of supersaturation in a nozzle.

1.            The temperature at which the steam becomes supersaturated will be less than  

            the saturation temperature corresponding to that pressure. Therefore,   

            supersaturated steam will have the density more than that of equilibrium

            condition which results in the increase in the mass of steam discharged.

2.            Supersaturation causes the specific volume and entropy of the steam to increase.

3.            Supersaturation reduces the heat drop. Thus the exit velocity of the steam is

            reduced.

4.            Supersaturation increases the dryness fraction of the steam. 

 

Critical Pressure Ratio: The critical pressure ratio is the pressure ratio which will accelerate the flow to a velocity equal to the local velocity of sound in the fluid.

 Critical flow nozzles are also called sonic chokes. By establishing a shock wave the sonic choke establish a fixed flow rate unaffected by the differential pressure, any fluctuations or changes in downstream pressure. A sonic choke may provide a simple way to regulate a gas flow

 

Effect of Friction on Nozzles:

1.            Entropy is increased.

2.            Velocity of flow at the throat get decreased.

3.            The energy available decreases.

4.            Volume of flowing steam is decreased.

5.            Throat area required to discharge a given mass of steam is increased

 

Most of the friction occurs in the diverging part of a convergent-divergent nozzle as the length of the converging part is very small. The effect of friction is to reduce the available enthalpy drop by about 10 to 15%. The velocity of steam will be then

 

Where, k is the co-efficient which allows for friction loss. It is also known as nozzle efficiency.

Velocity of Steam at Nozzle Exit:

 


 

Points to Remember

Nozzle is a duct by flowing through which the velocity of a fluid increases at the expense of pressure drop. if the fluid is steam, then the nozzle is called as Steam nozzle.

A fluid is said to be compressible if its density changes with the change in pressure brought about by the flow.

If the density does not changes or changes very little, the fluid is said to be incompressible. Usually the gases and vapors are compressible, whereas liquids are incompressible.

 

Effect of Friction on Nozzles:

1.                            Entropy is increased.

2.                            The energy available decreases.

3.                            Velocity of flow at the throat getdecreased.

4.                            Volume of flowing steam is decreased.

5.                            Throat area required to discharge a given mass of steam is increased.

 

                  The momentum equation in the steam turbine is given as:
                                                       v = A.C

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