1. Steam Turbines
Module VI

2. Steam turbine
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:
The high-pressure, high-temperature steam first expands in the nozzles emanates as a high velocity fluid stream.
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.
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.

3. Steam turbine system
Nozzle, wheel and steam jet

4. Steam turbine
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.
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.

5. Steam nozzle

6. Converging-diverging nozzle
Rocket with
Converging-diverging nozzle
Converging-diverging nozzle

7. Converging-diverging nozzle

8. Flow Through Nozzles
A nozzle is a duct that increases the velocity of the flowing fluid at the expense of pressure drop.
A duct which decreases the velocity of a fluid and causes a corresponding increase in pressure is a diffuser .
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.
Conversely if the cross section increases gradually from the inlet to exit, the duct is said to be divergent.
If the cross-section initially decreases and then increases, the duct is called a convergent-divergent nozzle.
The minimum cross-section of such ducts is known as throat.
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 .

9. Speed of sound, a
Mach number (M) = V/a
where V is velocity of the source relative to the medium and a is the speed of sound in the medium.
Also, a a2
where p is the pressure and  is the density

10. Steam Nozzle and Steam Turbine
Stagnation, sonic properties and isentropic expansion in nozzle
The stagnation values are useful reference conditions in a compressible flow.
Suppose the properties of a flow (such as T, p, ρ etc.) are known at a point.
The stagnation properties at a point are defined as those which are to be obtained if the local flow were imagined to cease to zero velocity isentropically.
The stagnation values are denoted by a subscript zero.
Thus, the stagnation enthalpy is defined as
For a perfect gas, this yields,
which defines the stagnation temperature. It is meaningful to express the ratio T0/T of in the form
If we know the local temperature (T) and Mach number (Ma), we can fine out the stagnation temperature .

11. Stagnation, sonic properties and isentropic expansion in nozzle
Consequently, isentropic relations can be used to obtain stagnation pressure and stagnation density as,
In general, the stagnation properties can vary throughout the flow field.
However, if the flow is adiabatic, then (h + v2/2) is constant throughout the flow.
It follows that h0 T0 and a0 and are constant throughout an adiabatic flow, even in the presence of friction.
In contrast, the stagnation pressure and density decrease if there is friction.
Here a is the speed of sound and the suffix signifies the stagnation condition.
It is understood that all stagnation properties are constant along an isentropic flow.

12. Stagnation, sonic properties and isentropic expansion in nozzle
If such a flow starts from a large reservoir where the fluid is practically at rest, then the properties in the reservoir are equal to the stagnation properties everywhere in the flow as shown in figure below.

13. Stagnation, sonic properties and isentropic expansion in nozzle…
There is another set of conditions of comparable usefulness where the flow is sonic, Ma=1.0.
These sonic, or critical properties are denoted by asterisks: p* * a* and T*.
These properties are attained if the local fluid is imagined to expand or compress isentropically until it reaches Ma=1.
Like total enthalpy, hence T0 , is conserved so long the process is adiabatic, irrespective of frictional effects.
In contrast, the stagnation pressure and density decrease if there is friction.
From Eq , , we note that
is the relationship between the fluid velocity and local temperature (T), in an adiabatic flow. The flow can attain a maximum velocity of

14. Stagnation, sonic properties and isentropic expansion in nozzle…
The unity Mach number, Ma=1, condition is of special significance in compressible flow, Hence,
For diatomic gases, like air =1.4 , the numerical values are
The fluid velocity and acoustic speed are equal at sonic condition and is
Both stagnation conditions and critical conditions are used as reference conditions in a variety of one dimensional compressible flows.

15. Effect of Area Variation on Flow Properties in Isentropic Flow
In considering the effect of area variation on flow properties in isentropic flow, we shall concern ourselves primarily with the velocity and pressure. We shall determine the effect of change in area, A, on the velocity V, and the pressure p.
From Bernoulli's equation, we can write
…(1)
A convenient differential form of the continuity equation can be obtained
Therefore,
…(2)

16. Effect of Area Variation on Flow Properties in Isentropic Flow
Invoking the relation (a2 = p/ ) for isentropic process, we have
…(3)
We see that for Ma < 1 an area change causes a pressure change of the same sign, i.e. positive dA means positive dp for Ma < 1.
For Ma>1, an area change causes a pressure change of opposite sign.
Using,
we have
…(4)
We see that Ma < 1 an area change causes a velocity change of opposite sign, i.e. positive dA means negative dV for Ma < 1.
For Ma>1, an area change causes a velocity change of same sign.

17. Effect of Area Variation on Flow Properties in Isentropic Flow
These relations lead to the following important conclusions about compressible flows:
At subsonic speeds (Ma < 1) a decrease in area increases the speed of flow. A subsonic nozzle should have a convergent profile and a subsonic diffuser should possess a divergent profile. The flow behaviour in the regime of Ma < 1 is therefore qualitatively the same as in incompressible flows.
In supersonic flows (Ma > 1), the effect of area changes are different. According to Eq. (4), a supersonic nozzle must be built with an increasing area in the flow direction.
A supersonic diffuser must be a converging channel.
Divergent nozzles are used to produce supersonic flow in missiles and launch vehicles.
…(4)

18. Effect of Area Variation on Flow Properties in Isentropic Flow
Suppose a nozzle is used to obtain a supersonic stream staring from low speeds at the inlet. Then the Mach number should increase from Ma=0 near the inlet to Ma>1 at the exit.
It is clear that the nozzle must converge in the subsonic portion and diverge in the supersonic portion. Such a nozzle is called a convergent-divergent nozzle.
A convergent-divergent nozzle is also called a de Laval nozzle, after Carl G.P. de Laval who first used such a configuration in his steam turbines in late nineteenth century.
From Fig. it is clear that the Mach number must be unity at the throat, where the area is neither increasing nor decreasing. This is consistent with Eq. 4 which shows that dV can be non-zero at the throat only if Ma=1.
It also follows that the sonic velocity can be achieved only at the throat of a nozzle or a diffuser.

19. Effect of Area Variation on Flow Properties in Isentropic Flow
The condition, however, does not restrict that Ma must necessarily be unity at the throat,
According to Eq. 4, a situation is possible where Ma  1 at the throat if dV=0 there.
For an example, the flow in a convergent-divergent duct may be subsonic everywhere with Ma increasing in the convergent portion and decreasing in the divergent portion with at the throat (see upper fig.).
The first part of the duct is acting as a nozzle, whereas the second part is acting as a diffuser.
Alternatively, we may have a convergent-divergent duct in which the flow is supersonic everywhere with Ma decreasing in the convergent part and increasing in the divergent part and again Ma  1 at the throat (see Fig. below).
Convergent-divergent duct with Ma  1 at throat
Convergent-divergent duct with Ma  1 at throat

20. Icentropic flow of a vapor or gas through a nozzle
First law of thermodynamics:
where (h1 – h2) is enthalpy drop across the nozzle
For the isentropic flow, dh = νdp

21. Isentropic flow of a vapor or gas through a nozzle
Assuming that the pressure and volume of steam during expansion obey the law pνn = constant, where n is the isentropic index,

22. Isentropic flow of a vapor or gas through a nozzle
Now, mass flow rate
=>
Therefore, the mass flow rate at the exit of the nozzle
The exit pressure, p2 determines ṁ the for a given inlet condition. The mass flow rate is maximum when,

23. Isentropic flow of a vapor or gas through a nozzle
For maximum ṁ,
If we compare this with the results of sonic properties, as described earlier, we shall observe that the critical pressure occurs at the throat for Ma = 1.
The critical pressure ratio is defined as the ratio of pressure at the throat to the inlet pressure, for checked flow when Ma = 1

24. Steam Nozzles Mass flow rate through the nozzle
Supersaturated vapour behaves like supersaturated steam and the index to expansion, n = 1.3

25. Steam Turbines

26. Velocity diagram

27. U = Tangential velocity of blade
V = absolute velocity of fluid
Vr = Relative velocity of fluid wrt blade

28. Steam Turbines Turbines We shall consider steam as the working fluid
Single stage or Multistage
Axial or Radial turbines
Atmospheric discharge or discharge below atmosphere in condenser
Impulse/and Reaction turbine
Impulse Turbines
Impulse turbines (single-rotor or multirotor) are simple stages of the turbines.
Here the impulse blades are attached to the shaft.
Impulse blades can be recognized by their shape. They are usually symmetrical and have entrance and exit angles respectively, around 20 ° .
Because they are usually used in the entrance high-pressure stages of a steam turbine, when the specific volume of steam is low and requires much smaller flow than at lower pressures, the impulse blades are short and have constant cross sections.

29. Steam Turbines The Single-Stage Impulse Turbine
The single-stage impulse turbine is also called the de Laval turbine after its inventor.
The turbine consists of a single rotor to which impulse blades are attached.
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.
The nozzles also allow governing of the turbine by shutting off one or more them.
Impulse turbine are also characterized by the fact that most or all of the enthalpy, and hence the pressure, drop occurs in the nozzles (or fixed blades that act as nozzle) and little or none in the moving blades.
What pressure drop occurs in the moving blade is a result of friction that gives rise to the velocity coefficient (k = Vr2/Vr1 ).

30. Impulse steam turbines
Schematic diagram of an single stage impulse steam turbine

31. Velocity diagram

32. Combined Velocity diagram
Velocity diagram of an Impulse Turbine
V1 and V2 = Inlet and outlet absolute velocity
Vr1 and Vr2 = Inlet and outlet relative velocity (Velocity relative to the rotor blades.)
U = mean blade speed
1 = nozzle angle,
2 = 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 )

33. Blade efficiency Tangential force on a blade, Or,
Work done/time or Power developed =
Blade efficiency or Diagram efficiency or Utilization factor is given by
Or,

34. Stage efficiency

35. Maximum blade efficiency
where, k = Vvr2/Vr1 = friction coefficient

36. Maximum blade efficiency...
1 is of the order of 180 to 220

37. Maximum blade efficiency...
Now,
(For single stage impulse turbine)
 The maximum value of blade efficiency
For equiangular blades,
If the friction over blade surface is neglected

38. Comments on maximum efficiency
For a given steam velocity it is clear that the work done per kg of steam or efficiency would maximum, when cos1 = 1 or 1 = 0.
For zero value of 1 , the axial flow component would be zero.
But it is essential to have an axial flow component to allow the steam to reach the blades and to clear the blades on leaving.
As 1 increases, the work done on the blades reduces, but at the same time surface area of blades reduces, thus there are less frictional losses.
With these conflicting requirements, the blade angle a is generally kept between 150 and 300.

39. Comments on optimum speed ratio

40. Compounding in Impulse Turbine
If high velocity of steam is allowed to flow through one row of moving blades, it produces a rotor speed of about rpm which is too high for practical use.
It is therefore essential to incorporate some improvements for practical use and also to achieve high performance.
This is possible by making use of more than one set of nozzles, and rotors, in a series, keyed to the shaft so that either the steam pressure or the jet velocity is absorbed by the turbine in stages. This is called compounding.
Three types of compounding can be accomplished:
velocity compounding
pressure compounding and
Pressure-velocity compounding
Either of the above methods or both in combination are used to reduce the high rotational speed of the single stage turbine.

41. The Velocity - Compounding of the Impulse Turbine
The velocity-compounded impulse turbine was first proposed by C.G. Curtis to solve the problems of a single-stage impulse turbine for use with high pressure and temperature steam.
The Curtis stage turbine, as it came to be called, is composed of one stage of nozzles as the single-stage turbine, followed by two rows of moving blades instead of one.
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.
A Curtis stage impulse turbine is shown in Fig. with schematic pressure and absolute steam-velocity changes through the stage. In the Curtis stage, the total enthalpy drop and hence pressure drop occur in the nozzles so that the pressure remains constant in all three rows of blades.
Two row velocity compounded impulse

42. Side view
Top view
Three row velocity compounded impulse turbine

43. The Velocity - Compounding of the Impulse Turbine
Velocity is absorbed in two stages.
In fixed (static) blade passage both pressure and velocity remain constant.
Fixed blades are also called guide vanes.
Velocity compounded stage is also called Curtis stage.
The velocity diagram of the velocity-compound Impulse turbine is shown in Figure
The fixed blades are used to guide the outlet steam/gas from the previous stage in such a manner so as to smooth entry at the next stage is ensured.

44. The Velocity - Compounding of the Impulse Turbine
(axial thrust; undesirable)
The optimum velocity ratio will depend on n the number of stages (rows of moving blades) and is given by,
Note that the optimum blade velocity is (1/n)th that of a single-stage impulse.
Work is not uniformly distributed (1st >2nd ) due to fluid friction in blades.
The fist stage in a large (power plant) turbine is velocity or pressure compounded impulse stage.
The work ratio of the highest-to-lowest pressure stages, in an ideal turbine, can be found to have the ratio 3:1 for a two-stage turbine (Curtis), 5:3:1 for three-stage turbine, 7:5:3:1 for a four-stage turbine. This points two major drawbacks of velocity compounding
That the lower-pressure stages produce such a little work that staging beyond two stages (Curtis) is uneconomical.
That still-high velocities that result in large friction, especially in the high-pressure stages

45. Pressure Compounding or Rateau Staging Impulse turbine
The Pressure - Compounded Impulse Turbine
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 ( see Figure).
Such a turbine is called a Rateau turbine , after its inventor. Thus the inlet steam velocities to each stage are essentially equal and due to a reduced Δh.
Pressure drops in nozzle, remains constant in moving blades
Velocity increases in nozzle, drops in moving blades.

46. Pressure Compounding or Rateau Staging Impulse turbine
Instead of expanding the steam completely in a single set of nozzles, the expansion of steam is splitted into a number of phases by arranging a number of moving and fixed blades in series, thus the rotor speed is obtained in practical range.
The fixed blades act as nozzles. The steam expands equally in all rows of fixed blades.
Thus, this arrangement can be viewed as a number of simple impulse machines in series on the same shaft, allowing the exhaust steam from one turbine to enter the nozzle of the succeeding turbine. Each of the simple impulse machines would be termed as a “stage” of the turbines, since each stage comprises its set of nozzles and moving blades.
This arrangement is equivalent to splitting up the whole pressure drop into a series of small pressure drops, hence arrangement is known as pressure compounding.

47. Pressure Compounding or Rateau Staging Impulse turbine
The lower part of Fig. shows the velocity and pressure distribution.
Steam enters the first row of the nozzle, a small pressure drop takes place with increase in steam velocity.
The steam passes over the first row of moving blades,
The steam pressure remains constant, but steam velocity decreases.
It constitutes one stage.
The variation of pressure velocity gets repeated for a number of stages until condenser pressure is reached.
In a pressure-compounding steam turbine, a partial enthalpy of steam is transformed into kinetic energy in each stage. Hence, steam velocity is much lower than the simple impulse and velocity- compounded steam turbines, and thus the operation is salient and more efficient.
The example of pressure-compounded steam turbine is Rateau and Zeolly turbine.

48. Pressure Compounding or Rateau Staging Impulse turbine
Pressure drop - takes place in more than one row of nozzles and the increase in kinetic energy after each nozzle is held within limits. Usually convergent nozzles are used.
We can write,
Where  is carry over coefficient

49. Pressure – velocity compounded impulse turbine
This is a combination of pressure and velocity compounding.
The total pressure drop of steam is divided into a number of stages as done in pressure compounding.
Each stage has a number of rows of fixed and moving blades working as an independent velocity compounded stage.
Each stage is separated from the adjacent stage by a row of stationary ring of nozzles for expansion of steam for the next stage.
The set of moving and fixed blades is used for velocity compounding and a set of nozzle rings in between stages is utilized for pressure compounding.
Such type of compounding offers a larger pressure drop in each stage with less number of stages. Therefore, the turbine is simple in construction and compact in size.
The diagrammatic arrangement shown in Fig. explains the principle of working, construction and pressure-velocity diagrams.

50. Pressure Compounding or Rateau Staging Reaction turbine
A reaction turbine, therefore, is one that is constructed of rows of fixed and rows of moving blades. The fixed blades act as nozzles.
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.
In other words, they also act as nozzles. The enthalpy drop per stage of one row fixed and one row moving blades is divided among them, often equally.
Thus a blade with a 50 percent degree of reaction, or a 50 percent reaction stage, is one in which half the enthalpy drop of the stage occurs in the fixed blades and half in the moving blades.
The pressure drops will not be equal, however. They are greater for the fixed blades and greater for the high-pressure than the low-pressure stages.

51. Pressure Compounding or Rateau Staging Reaction turbine
The moving blades of a reaction turbine are easily distinguishable from those of an impulse turbine in that they are not symmetrical and, because they act partly as nozzles, have a shape similar to that of the fixed blades, although curved in the opposite direction.
The schematic pressure line (Fig.) shows that pressure continuously drops through all rows of blades, fixed and moving. The absolute steam velocity changes within each stage as shown and repeats from stage to stage. Figure below shows a typical velocity diagram for the reaction stage.
Three stages of reaction turbine indicating pressure and velocity distribution
The velocity diagram of reaction blading

52. Reaction Turbine
In a reaction turbine, the moving blades have converging steam passage. Therefore, when steam passes over the moving blades, it expands with a drop in steam pressure and increase in kinetic energy.
Thus in a reaction turbine, the steam jet leaves the moving blades with higher velocity than it enters the blades.
The higher velocity steam jet coming out of the moving blades, reacts on the blades and causes them to rotate in opposite direction.
The Parson turbine which is named after its inventor, Sir Charles A Parson, in 1884 is a good example of a reaction turbine. It developed 7.5 kW running at rpm.
In modern steam turbines, both impulse and reaction principles are used simultaneously. In this turbine, the steam does not expand completely in the stationary nozzle, but it expands in the fixed as well as moving blades, both acting as nozzles.
The motive force is partly impulsive and partly reaction force due to continuous expansion of steam in fixed and moving blades. The work output from the turbine is due to both impulsive and reactive forces. Therefore, these turbines are also called the impulse-reaction turbines.
However, the work produced by reactive force is higher than the impulsive force, and hence these turbines are also simply referred as reaction turbines.

53. Reaction Turbine…
The pressure falls continuously as the steam flows over the fixed and moving blades of each stage. The steam velocity increases in each set of the fixed blades while it decreases in the moving blades.
There are a number of rows of moving blades attached to the rotor and an equal number of fixed blades attached to the casing. Thus these are referred as rotor blades and stator blades , respectively.
The fixed blades are set in the reversed direction of moving blades as shown in Fig a.
Due to the fixed blades at the entrance, the steam is admitted for the whole circumference and hence there is a full admission.
Fig. (b) shows the effect of friction, when steam glides over the fixed and moving blades. The actual enthalpy drop is less than the isentropic enthalpy drop. The reaction turbines are also compounded to reduce the rotor speed.

54. Reaction Turbine…
The variation of pressure and velocity through a three-stage reaction turbine is shown in Fig.
In an impulse turbine, the steam pressure remains constant while steam flows through the moving blades and no thrust is exerted by the steam in the direction of the rotor axis, while in the reaction turbine, the axial thrust is considerable due to pressure difference of either sides of moving blades.
Dummy pistons and thrust bearings are used to balance this axial thrust.

55. Comparison betwn blade designs of impulse and reaction turbine
Blades asymmetrically aligned
Increasing steam passage area
Pressure changes in M and F
Blades symmetrically aligned
Constant passage area
Pressure remains contact in M and F blades

56. Comparison betwn velocity diagrams of impulse and reaction turbine

57. Reaction Turbine… Degree of reaction (R)
The degree of reaction of a reaction turbine is defined as the ratio of the enthalpy drop in moving blades to the total enthalpy drop in the stage.
R =
h0 = Enthalpy of the steam at inlet of fixed blades,
h1 = Enthalpy of the steam at entry of moving blades, and
h2 = Enthalpy of the steam at exit from the moving blades.
The total enthalpy drop in a stage = Enthalpy drop in fixed blades + Enthalpy drop in moving blade
The total enthalpy drop for a stage (hm + hf) is equal to work done by the steam in the stage and it equals to,

58. Reaction Turbine
Pressure and enthalpy drop both in the fixed blade or stator and in the moving blade or Rotor
A very widely used design has half degree of reaction or 50% reaction and this is known as Parson's Turbine. This consists of symmetrical stator and rotor blades.
The velocity triangles are symmetrical and we have

59. Parson's Turbine (50% reaction) velocity diagram
Vr2
Vr1 V2
Vf2 V1
Vf1
Vw1
Vw2 U 1 2 2 1

60. Parson's Turbine (50% reaction) velocity diagram
Vr22
Vr12
V22
Vf22
V12
Vf12
Vw12
Vw22 U
12
22
22
12

61. 2nd stage 1st stage Inlet of moving blade/exit of fixed blade
exit of moving blade/inlet of
fixed blade
1st stage

62. Enthalpy drop in fixed and moving blades in terms of velocities
In terms of velocities, the enthalpy drop in moving blades
(contributes to static pressure change)
Enthalpy drop in fixed blades, with assumption that the velocity of steam entering the fixed blades is equal to the absolute velocity of steam leaving the previous moving blades.
V0 is small, can be neglected.
In reaction turbines, the steam expands continuously while passing over the rings of fixed and moving blades.
It is accomplished by using a tapered rotor with progressively increasing blade height. The effect of expansion of steam on the moving blade is to increase the relative velocity at the exit. Therefore, the relative velocity Vr2 is always greater than the relative velocity at the inlet Vr1 .

63. Energy input to the blades in a stage,
Reaction Turbine
Blade efficiency
Energy input to the blades in a stage,
E = h = Kinetic energy supplied to the fixed blades (F) + Kinetic energy supplied to the
moving blades (M)
or E = enthalpy drop in F + enthalpy drop in M
For symmetrical triangles
From the inlet velocity triangle we have,
Work done (for unit mass flow per second) ,
Therefore, the Blade efficiency

64. Condition of maximum blade efficiency
Reaction Turbine
Condition of maximum blade efficiency
Put
,then
For the maximum efficiency
and we get
Velocity diagram for maximum efficiency
from which finally it yields
Absolute velocity of the outlet at this stage is axial (see figure above). In this case, the energy transfer
(b)maximum can be found out by putting the value of  = cos(1) in the expression
for blade efficiency
 is greater in reaction turbine. Energy input per stage is less, so there are more number of stages.

65. Comparison of efficiency variation in impulse and reaction turbine
Wikipedia article
Steam turbine efficiencies
E-book reference:
Thermal engineering (TMH)
Author: RATHORE, MAHESH M
Chapter: Steam turbines
The variation of diagram efficiency with blade speed ratio, U/V1 for the simple impulse turbine and a reaction stage shown in Fig.
The efficiency curve for reaction turbine is flat for maximum value of blade speed ratio.

66. Comparison between impulse and reaction turbines

67. Losses in steam turbines
1. Admission losses
2. Leakage losses
3. Friction losses
4. Exhaust losses
5. Radiation and convection losses
6. Losses due to moisture
7. Carry over losses

68. Governing of steam turbines
The purpose of governing of steam turbine is to maintain its speed as constant, irrespective of its load. The turbine speed is controlled by varying the steam flow rate by means of valves interposed between the boiler and turbine. The steam turbine may be governed by the following possible methods:
1. Throttle governing
2. Nozzle control governing
3. By-pass governing
4. Combination of any of the above two methods
5. Emergency governing

69. Tutorial Question 1
In a single stage steam turbine, the velocity of steam leaving a nozzle is 925 m/s and the nozzle angle is 200. The blade speed is 250 m/s. The mass flow through the turbine nozzles and blading is kg/s and the blade velocity coefficient is 0.7. Calculate the following:
1. Velocity of whirl at inlet and outlet
2. Tangential force on blades.
3. Axial force on blades.
4. Work done on blades.
5. Efficiency of blading.
6. Inlet angle of blades for shockless inflow o f steam .
Assume that the inlet and outlet blade angles are equal i.e. blades are symmetrical.
Answer
1. Vw1 = m/s, Vw2 = m/s N N KN %
6. 1 = 2 =

70. Solution

73. Question
The steam expands isentropically in a simple impulse turbine from 12 bar, 2500 C with an enthalpy of 2935 kJ/kg to an enthalpy of 2584 kJ/kg at 0.1 bar. The nozzle makes 200; with blade motion and the blades are symmetrical. Calculate the blade velocity that produces maximum efficiency for a turbine speed of 3600 rpm. Assume that the steam enters the nozzle with negligible velocity.
Answer
m/s

74. Question
The nozzles of a two-row velocity compounded impulse turbine, have outlet angle of 22° and utilize an isentropic enthalpy drop of 220 kJ/kg of steam. All moving and guide blades are symmetrical and mean blade velocity is 150 m/s. Assume an isentropic efficiency of for the nozzle as 90%. Calculate the specific power output produced by each kg of steam. The velocity at the inlet to nozzle and frictional effects in all blades can be neglected.
Answer kW

75. 2nd stage 1st stage Inlet of moving blade/exit of fixed blade/nozzle
exit of moving blade/inlet of
fixed blade
1st stage

76. Question
The following particulars relate to a two-row velocity compounded impulse wheel:
Steam velocity at nozzle outlet = 650 m/s
Mean blade velocity = 125 m/s
The nozzle outlet angle = 160;
Outlet angle of first row of moving blades = 180;
Outlet angle of fixed guide blades = 220;
Outlet angle of second moving blades = 360;
Steam flow rate = 2.5 kg/s
The ratio of relative velocity at the outlet to that at the inlet is 0.84 for all blades.
Determine the following:
Axial thrust on blades,
The power developed, and
The efficiency of the wheel.
Answer
142.5 kN
390 kW
73.84 %

77. Solution

78. Tutorial Question 2
From the following data for a two-row velocity compounded impulse turbine, determine (a) the power developed (b) the blade efficiency, (c) total axial thrust developed.
Blade speed : m/s
Velocity of steam exiting the nozzle: 590 m/s
Nozzle efflux angle:
Outlet angle from first moving blades: 200
Blade velocity coefficient all blades : 0.9
Answer
kW per kg/s
70.05%
47.63 kN per kg/s

79. Solution