Steam Nozzles and Turbines

STEAM NOZZLES AND TURBINES

 

PREREQUISITE DISCUSSIONS

 

A steam turbine is basically an assembly of nozzles fixed to a stationary casing and rotating blades mounted on the wheels attached on a shaft in a row-wise manner. In 1878, a Swedish engineer, Carl G. P. de Laval developed a simple impulse turbine, using a convergent-divergent (supersonic) nozzle which ran the turbine to a maximum speed of 100,000 rpm. In 1897 he constructed a velocity-compounded impulse turbine (a two-row axial turbine with a row of guide vane stators between them.

 

Auguste Rateau in France started experiments with a de Laval turbine in 1894, and developed the pressure compounded impulse turbine in the year 1900.

 

In the USA , Charles G. Curtis patented the velocity compounded de Lavel turbine in 1896 and transferred his rights to General Electric in 1901.

 

In England , Charles A. Parsons developed a multi-stage axial flow reaction turbine in

1884.

 

Steam turbines are employed as the prime movers together with the electric generators in thermal and nuclear power plants to produce electricity. They are also used to propel large ships, ocean liners, submarines and to drive power absorbing machines like large compressors, blowers, fans and pumps.

 

Turbines can be condensing or non-condensing types depending on whether the back pressure is below or equal to the atmosphere pressure.

 

 

STEAM NOZZLE

 

Introduction

 

A steam turbine converts the energy of high-pressure, high temperature steam produced by a steam generator into shaft work. The energy conversion is brought about in the following ways:

 

1.     The high-pressure, high-temperature steam first expands in the nozzles emanates as a high velocity fluid stream.

 

2.     The high velocity steam coming out of the nozzles impinges on the blades mounted on a wheel. The fluid stream suffers a loss of momentum while flowing past the blades that is absorbed by the rotating wheel entailing production of torque.

 

3.     The moving blades move as a result of the impulse of steam (caused by the change of momentum) and also as a result of expansion and acceleration of the steam relative to them. In other words they also act as the nozzles.

 

 

Flow Through Nozzles

 

Ø A nozzle is a duct that increases the velocity of the flowing fluid at the expense of pressure drop.

 

Ø  A duct which decreases the velocity of a fluid and causes a corresponding increase in pressure is a diffuser .

 

Ø The same duct may be either a nozzle or a diffuser depending upon the end conditions across it. If the cross-section of a duct decreases gradually from inlet to exit, the duct is said to be convergent.

 

Ø Conversely if the cross section increases gradually from the inlet to exit, the duct is said to be divergent.

 

Ø  If the cross-section initially decreases and then increases, the duct is called a convergent-divergent nozzle.

 

Ø The minimum cross-section of such ducts is known as throat.

 

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

 

Ø 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 .

 

Shapes of nozzles

 

1.       At subsonic speeds (Ma<1) a decrease in area increases the speed of flow.

2.     In supersonic flows (Ma>1), the effect of area changes are different.

 

Convergent divergent nozzles

 

SIGNIFICANCE OF STEAM TURBINES

 

Ø Large scale electrical energy production largely depends on the use of turbines. Nearly all of the world's power that is supplied to a major grid is produced by turbines.

 

Ø From steam turbines used at coal-burning electricity plants to liquid water turbines used at hydro-electric plants, turbines are versatile and can be used in a number of applications.

 

Ø There are also gas turbines that combust natural gas or diesel fuel for use in remote locations or where a large backup power supply is required. Most power plants use turbines to produce energy by burning coal or natural gas.

 

Ø The heat produced from combustion is used to heat water in boiler. The liquid water is converted to steam upon heating and is exhausted through a pipe which feeds the steam to the turbine.

 

Ø The pressurized steam flow imparts energy on the blades and shaft of the turbine causing it to rotate.

 

Ø The rotational mechanical energy is then converted to electrical energy using a generator.

 

 

 

STEAM TURBINES

 

Turbines

 

Ø We shall consider steam as the working fluid

Ø Single stage or Multistage

Ø Axial or Radial turbines

Ø Atmospheric discharge or discharge below atmosphere in condenser

Ø Impulse/and Reaction turbine

 

Impulse Turbines

 

Ø Impulse turbines (single-rotor or multirotor) are simple stages of the turbines.

Ø Here the impulse blades are attached to the shaft.

Ø Impulse blades can be recognized by their shape.

Ø The impulse blades are short and have constant cross sections.

 

 

Schematic diagram of an Impulse Trubine

 

 

V₁ and V₂ = Inlet and outlet absolute velocity

V_r1 and V _r2 = Inlet and outlet relative velocity (Velocity relative to the rotor blades.)

U = mean blade speed

= nozzle angle,

= absolute fluid angle at outlet

 

It is to be mentioned that all angles are with respect to the tangential velocity ( in the direction of U )

 

Velocity diagram of an Impulse Turbine

 

 

The Single-Stage Impulse Turbine

 

Ø The single-stage impulse turbine is also called the de Laval turbine after its inventor.

Ø The turbine consists of a single rotor to which impulse blades are attached.

 

Ø The steam is fed through one or several convergent-divergent nozzles which do not extend completely around the circumference of the rotor, so that only part of the blades is impinged upon by the steam at any one time.

Ø The nozzles also allow governing of the turbine by shutting off one or more them.

 

 

Compounding in Impulse Turbine

 

Ø If high velocity of steam is allowed to flow through one row of moving blades, it produces a rotor speed of about 30000 rpm which is too high for practical use.

 

Ø It is essential to incorporate some improvements for practical use and also to achieve high performance.

 

Ø This is called compounding.

 

Ø Two types of compounding can be accomplished: (a) velocity compounding and (b) pressure compounding

 

The Velocity - Compounding of the Impulse Turbine

 

Ø The velocity-compounded impulse turbine was first proposed to solve the problems of a single-stage impulse turbine for use with high pressure and temperature steam.

 

Ø It is composed of one stage of nozzles as the single-stage turbine, followed by two rows of moving blades instead of one.

 

Ø These two rows are separated by one row of fixed blades attached to the turbine stator, which has the function of redirecting the steam leaving the first row of moving blades to the second row of moving blades.

 

 

 

Pressure Compounding or Rateau Staging

 

Ø To alleviate the problem of high blade velocity in the single-stage impulse turbine, the total enthalpy drop through the nozzles of that turbine are simply divided up, essentially in an equal manner, among many single-stage impulse turbines in series,Such a turbine is called a Rateau turbine.

 

Ø The inlet steam velocities to each stage are essentially equal and due to a reduced Δh.

 

 

 

Reaction Turbine

 

Ø A reaction turbine, therefore, is one that is constructed of rows of fixed and rows of moving blades.

 

Ø The fixed blades act as nozzles.

 

Ø The moving blades move as a result of the impulse of steam received (caused by change in momentum) and also as a result of expansion and acceleration of the steam relative to them.

Ø The pressure drops will not be equal.

 

Ø They are greater for the fixed blades and greater for the high-pressure than the low-pressure stages.

 

Ø The absolute steam velocity changes within each stage as shown and repeats from stage to stage.

 

 

APPLICATIONS

 

Ø Locomotives

Ø Power generations

Ø Industrial application for producing steam

 

 

 

Governing of Steam Turbine: The method of maintaining the turbine speed constant irrespective of the load is known as governing of turbines. The device used for governing of turbines is called Governor. There are 3 types of governors in steam turbine,

 

1. Throttle governing

 

2. Nozzle governing

 

3. By-pass governing

 

 

i.Throttle Governing:

 

Let us consider an instant when the load on the turbine increases, as a result the speed of the turbine decreases. The fly balls of the governor will come down. The fly balls bring down the sleeve. The downward movement of the sleeve will raise the control valve rod. The mouth of the pipe AA will open. Now the oil under pressure will rush from the control valve to right side of piston in the rely cylinder through the pipe AA. This will move the piston and spear towards the left which will open more area of nozzle. As a result steam flow rate into the turbine increases, which in turn brings the speed of the turbine to the normal range.

 

ii)Nozzle Governing:

 

 

A dynamic arrangement of nozzle control governing is shown in fig.

 

In this nozzles are grouped in 3 to 5 or more groups and each group of nozzle is supplied steam controlled by valves. The arc of admission is limited to 180º or less. The nozzle controlled governing is restricted to the first stage of the turbine, the nozzle area in other stages remaining constant. It is suitable for the simple turbine and for larger units which have an impulse stage followed by an impulse reaction turbine.

 

Solved Problems:

 

 

1. A convergent divergent adiabatic steam nozzle is supplied with steam at 10 bar and 250°c.the discharge pressure is 1.2 bar.assuming that the nozzle efficiency is 100% and initial velocity of steam is 50 m/s. find the discharge velocity.

 

Given Data:-

 

Initial pressure(p₁)=10bar Initial

 

Temperature(T₁)=250°c

 

Exit pressure(p₂)=1.2 bar

 

 

Nozzle efficiency(η_nozzle)=100%

 

Initial velocity of steam (v₁)=50m/s

 

To Find:-

 

Discharge velocity (v₂)

 

Solution:-

 

From steam table,  For  10 bar, 250°c, h₁=2943 KJ/kg s₁=6.926 KJ/kgk

 

From steam table,  For 1.2 bar,

 

h_f2 =439.3 KJ/kg ;   h_fg2=2244.1 KJ/kg;

 

s_f2=1.3 61 KJ/kg K ;  s_fg2=5.937 KJ/kgK.

 

Since s₁=s_2,

 

S1=sf 2+x2sfg2

 

6.926=1.361+x₂(5.937)

 

X₂=0 .9373

 

We know that,

 

h2=hf2+x2hfg2

 

= 439.3+(0.9373)2244.1

 

h₂ = 2542KJ/Kg

 

Exit velocity   (V2) = Rt[(2000(2943)  2542) + 50²]

 

 

= 896.91m/s.

 

2. Dry saturated steam at 6.5 bar with negligible velocity expands isentropically in a convergent divergent nozzle to 1.4 bar and dryness fraction 0.956. De termine the final velocity of steam from th e nozzle if 13% heat is loss in friction. Find th e % reduction in the final velocity.

 

Given data:

 

Exit pressure (P2) = 1.4 bar

 

Dryness fract ion (X2) = 0.956

 

Heat loss = 13%

 

To Find:

 

The percent reduction in final velocity

 

Solution:

 

From steam table for initial pressure P1 = 6.5bar, take values h₁ =

 

h₁ = 2758.8KJ/Kg

 

Similarly, at 1.4 bar,

 

h_fg2 = 2231.9 KJ/Kg

 

h_f2 = 458.4KJ/Kg

 

h2 = hf2 + X2 hfg2

 

= 458.4 + (0.956) 2231.6

 

h₂ = 2592.1 KJ/Kg

 

 

Final velocit y (V2) = Rt (2000(h1-h2) )

 

V2 = 577.39 m/s

 

 

 

Heat drop is 13%= 0.13

Nozzle efficiency (η) = 1- 0.13 = 0.87

 

 

Velocity of s team by considering the nozzle efficiency,

y (V2) = Rt (2000(h1-h2) ) x η

 

V2  = 538.55 m/s

                = % reductio n in final velocity =  6.72%

 

 

 

3.A  convergent  divergent  nozzle  receives  steam  at  7bar  and  200^oc  and  it  expands  isentropically into a space of 3bar neglecting the inlet velocity calculat e the exit area required for a mass flow of 0.1Kg/sec . when the flow is in equilibrium through all and super saturated with PV^1.3=C.

 

Given Data:

 

Initiall pressure (P₁) = 7bar = 7× 10⁵N/m²

 

Initiall temperature (T₁) = 200^oC

 

Press ure (P₂) = 3bar = 3× 10⁵N/m²

 

Mass flow rate (m) = 0.1Kg/sec

 

PV^1.3 =C

To Find:

Exit area

 

Solution:

 

From st eam table for P1 = 7bar and T1 = 200^oC V₁ =

 

0.2999

h₁ = 2844.2

 S1 = 6.886

 Similarly for P2 = 3bar

 Vf2 = 0.001074 Vg2 = 0.60553 hf2 =

 561.5 hfg2 = 2163.2

 Sf2 = 1.672 Sfg2  = 5.319

We know that, S1 = S2 = St

 S₁ = S_f2 + X₂ S_fg2

6.886 = 1.672 + X₂ (5.319) X₂ =

 

0.98

 

Similarly,

 

h2 = hf2 + X2 hfg2

 

h₂ = 561.5 + 0.98 (2163.2)

 

(i)              Flow is in equilibriu m through all:

 

V₂=569.56

ν₂  = X₂ × ν_g2

 

= 0.98× 0.60553 = 0.5934

 

 

 

 

TECHNICAL TERMS

 

1.Diaphragm -  Partitions b etween pressure stages in a turbine's casing.

 

2. Radial - flow turbine - st eam flows outward from the shaft to the casing.

 

3. Radial clearance - cleara nce at the tips of the rotor and casing.

 

4. Axial clearance - the fore -and-aft clearance, at the sides of the rotor and t he casing.

 

5. balance piston - Instead of piston, seal strips are also used to duplicate a piston's counter force.

 

6. steam rate - The steam rate is the pounds of steam that must be supplied per kilowatt-hour of generator output at the steam turbine inlet.

 

7. extraction  turbine  -  ste am  is  withdrawn  from  one  or  more  stages,  at  one  or  more  pressures, for heating, pl ant process, or feedwater heater needs.

 

8. Wet steam: The steam w hich contains some water particles in superposition.

 

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

 

10. Super heated steam: When the dry steam is further heated at consta nt pressure, the temperature increases the above saturation temperature. The steam has obtained is called super heated stea m.

 

11. Degree of super heat: The difference between the temperature of saturated steam and saturated temperature is c alled degree of superheat.

 

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

 

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

 

14. Critical pressure ratio:  There is only one value of ratio (P2/P1) which produces  maximum discharge fro m the nozzle . then the ratio is called critica l pressure ratio.

 

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

 

16. 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

 

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

 

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

 

19. Convergent nozzle: The crossectional area of the duct decreases from inlet to the outlet side then it is called as convergent nozzle.

 

20. Divergent nozzle: The crossectional area of the duct increases from inlet to the outlet then it is called as divergent nozzle.