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**STEAM **

- A steam turbine is a prime mover which continuously converts the energy of high pressure, high temperature steam supplied by steam generator into shaft work with the low temperature steam exhausted to a condenser. The energy conversion essentially occurs in two steps.
- The high pressure, high temperature steam first expands in nozzle and then comes out with a high velocity.
- The high velocity jet of steam coming out of nozzle impinges on the blade mounted on wheel, get deflected by an angle and suffer a loss of momentum which is absorbed by rotating wheel in producing torque.
- A steam turbine in basically assemblage of nozzle and blades. Steam turbines are used
- To operate electric generator in thermal and nuclear power plants
- To propel large ships, submarine
- To drive power absorbing machines like large compressors, blowers

**IMPULSE TURBINES**

- All the pressure drops of steam occurs in the nozzles and there is no pressure drop as steam flow through the moving blades. Steam enters the nozzle at pressure P
_{0}and velocity_{0}, undergoes expansion to pressure P_{1 }with velocity increased to_{1}. The pressure of steam P_{1 }remains essentially constant as steam flows through the moving blades.

Using principle of conservation of momentum momentum absorbed by wheel = momentum of steam jets at inlet to blades – momentum of jet at exit from blades The mean peripheral speed of blade

where,

D_{m} is mean diameter of wheel

N is rpm

The area of flow or blade annulus

where,

D_{1} is root diameter

D_{2} is tip diameter

h_{b} is height of blades

Analysis of Impulse turbine

• Velocity diagram_{1} is absolute velocity_{r1 }is relative velocity_{b} is peripheral velocity_{r2} is exit relative velocity_{2} is exit absolute velocity

a is nozzle angle

b_{1} is inlet blade angle

b_{2} is inlet blade angle

The inlet and exit velocity triangle are shown in figure.

**Diagram Work W _{D}**

Where,

P_{t} is tangential thrust

w_{s} is steam flow rate_{b} is peripheral velocity of blade

Axial thrust = P_{a} =DV_{a} ×w_{s}**Diagram Efficiency**

- It is also called blading efficiency. The energy input to blade is

Diagram efficiency is defined as

**Optimum velocity ratio**

• The velocity ratio is defined as

where, b is peripheral velocity 1 is jet velocity

Since, diagram efficiency

where

= 2(r cos a – r^{2}) (1 + K_{b})

Differenting it w.r.t. r

Optimum velocity ratio

- Maximum blading efficiency is

If energy loss is small i.e.

Note: The lower is the nozzle angle, higher is the blading efficiency. But, too low angle may cause energy loss at blade inlet.**Compounding of SteamTurbines **

- One row of nozzle followed by one row of blades is called a stage of turbine. If steam is allowed to expand from boiler to condenser in a single row of nozzle, the velocity at exit from nozzle is very large. For example, single stage impulse turbine called de laval turbine have high rotational speeds (N).

Such large rotational speeds are not properly utilized. It entails large frictional lossed and high centrifugal stresses.

- So the turbines are compounded or stage. Basically there are two way of compounding steam turbines.
- Pressure compounding
- Velocity compounding

**PRESSURE COMPOUNDING OR RATEAU STAGING**

- In this, the total enthalpy drop is equally divided into no. of stages and available kinetic energy due to enthalpy drop is utilized in subsequent moving bladed.
- Enthalpy and pressure drop occurs only in nozzle or fixed blades, not in moving blades.
- For a 4-stage Rateau Staging The velocity of steam at exit from first row of nozzles

The jet velocity for single stage turbine V_{1} = 44.72 (h_{0} – h_{4})^{1/2}

For 4-stage turbine, the velocity of steam leaving the nozzle is each stage is half that of single stage turbine. For a nine stage it will be one-third.

For each impulse stage operating at maximum blading efficiency, the blade velocity

If there are n stage in series in a turbine, the isentropic enthalpy drop per stage will be

The number of impulse stages required for certain enthalpy drop (Dh)_{total }under ideal condition are

**Velocity Compounding **

- It is also called curtis staging. In velocity compounding, all the pressure drop, and enthalpy drop of steam takes place in a single row of nozzles and resultant kinetic energy of steam is absorbed by wheel in number of rows of moving blades with guide blades in between two rows.
- The kinetic energy of steam jet at nozzle exit is partially converted to shaft work in first row of moving blades with velocity decreasing from V
_{1}to V_{2}. The existing steam jets are deflected by stationary guide blades to the next moving blade where part of kinetic energy in converted to shaft work. - It is two row velocity stage having two row of moving blades with one row of guide blade in between.

Where, K_{b} is blade friction factor

a_{1} is exit angle of guide blades

b_{1} is inlet angle of first row of moving blade

b_{2} is exist angle of first row of moving blade

b_{3} is inlet angle of second row of moving blade

b_{4} is exit angle of second row of moving blade

DV_{a1} is change in axial component of velocity in first row of MB.

DV_{a2} is change in axial component of velocity in second row of moving blade

DV_{w1} is change in velocity of whirl in first row of moving blades

DV_{w2} is change in velocity of whirl in second row of moving blades

**Tangential thrust**

**Axial thrust**

**Blading or diagram work W _{D} = P_{t.}V_{b} Diagram efficiency**

**Effectiveness of moving row in curtis stage**

**Assuming : Blade friction factor k _{b} = 1**

It means that the three-fourth of total work is done by steam jets on the first row of moving blade and 1/4 of work by second row of moving blade. In 3-row curtis stage W_{D1} : W_{D2} : W_{D2} = 5 : 3 : 1**Optimum Velocity ratio for curtis stage **

- Consider two-stage curtis stage having symmetrical blading and discharge is not axial. The velocity diagram is shown in figure.

h_{D }= 8 (r cos a – 2r^{2})

For curtis stage having z-rows of moving blades

Maximum diagram efficiency

This is applicable when there is no friction and blades are symmetrical. If friction is considered, the blading efficiency of curtis stage would be lower.**REACTION TURBINES**

- In these turbines, pressure drop occurs both in the nozzle or fixed row of blades and in moving row of blade, since moving blade channels are also of nozzle shape.

Due to expansion of steam flowing through blades, there is increases in kinetic energy which give rise to reaction in opposite direction. - The blades in reaction turbine rotates due to both impulsive effect of jet and reaction force of existing jets impressed on blade in opposite directions. These turbine are also
**impulse-reaction turbine.**

The degree of reaction (R) is defined as

Where, D_{hmb} is enthalpy drop in moving blade

D_{hfb} is enthalpy drop in fixed blade

- Hero's turbine is pure reaction turbine where R = 1.

R = 1/2 is called 50% reaction turbine and are called parson's turbine.

- The velocity diagram for moving blade of 50% reaction turbines is shown in fig. Both fixed and moving blades are similar in shape.

The diagram work

**Energy input to blade per kg of steam**

**Diagram efficiency of blade**

**Differenting h _{D} w.r.t. r and equating it to zero gives**

**Specific blading work **corresponding to maximum blading efficiency

W_{D} = (2V_{b} – V_{b}) V_{b} = V_{b}^{2}

In reaction turbines both fixed and moving blade acts as nozzle. Fixed blades are referred as stator or fixed blade and moving blades as a rotor, Since the isentropic enthalpy drop of stage is equally divided between fixed blades and moving blades.

**Carry-over efficiency **

- The kinetic energy associated with leaving steam of preceding stage is available to do work in following stage, some loss in involved in journey from one stage to next. It is considered and known as carry-over efficiency (h
_{co}).

- This is the energy available for conversion in one stage.

Combined nozzle and carry over efficiency

Note: The optimum efficiencies for simple impulses, curtis and reaction blading are all equal. When friction is taken into account, the reaction turbine is more efficient.**Enthalpy drop in various stages **For 50% reaction turbine,

**Impulse stage :**

**2-stage curtis stage :**

Therefore, 2-row curtis stage is equivalent to four simple impulse stages and eight 50% reaction turbines. For same mean blade speed V_{b},

for 50% reaction turbine

for simple impulse stage

for 2-row curtis stage

Nozzle and blade heights

Nozzle or blade height depend on total annular area required to pass the desired flow of fluid. Area available for flow at exit

A = Oh_{n}

Where, O is width of flow passage at exit hn is nozzle height From figure,

P sin a = O + t

Where, P is pitch of nozzle t is nozzle wall thickness

Assuming full peripheral admission,

Total nozzle area

where k_{th} is nozzle thickness factor area available for flow at entrance of blade is

where k_{tb} is edge thickness factor for blades for all practical purposes k_{th} = k_{tb}

- So, the blade height at entrance is equal to nozzle height at exit. It is customary to increase the blade entrance height slightly. This is done in order to avoid spilling of fluid issuing from nozzle. This increase in blade height is called 'overlap'.

**Turbine governing and control **

- Governing of steam turbine means to regulate the supply of steam to the turbine in order to maintain constant speed of rotation under varying load condition.
- Method of turbine governing are

(a) Throttle governing

(b) Nozzle governing

(c) By-pass governing

**Reheat factor and Condition Line **

- There are various losses in the stage and the portion of the available energy not converted to work and remaining in the fluid is termed as “reheat”.

1. Reheat takes place with increase in entropy.

2. The reheat in a given stage is available to do work in the succeeding stage except the last stage where the reheat is a loss.

3. The constant pressure lines diverge from one another, thereby increasing the enthalpy drop for the same pressure drop.

4. Because of 2 and 3 the sum of the available energies (isentropic enthalpy drops) for each stage is greater than the available energy (isentropic enthalpy drop) for the whole turbine.

5. The condition representing the actual expansion in the turbine is approximately the locus of points indicating the actual condition of steam at the exit of each stage. - The effect of item 4 may be expressed, assuming equal available energy per stage, by a term called “reheat factor” RF.
- The actual conditions of steam at exit from each stage and the locus through these states is called the “condition line”. The reheat factor is defined as

**Losses in Steam Turbines **

- Losses in regulating valves. Steam, before entering the turbine passes through the main valve and the regulating valves, the flow through these being accompanied by pressure losses. Thus some available energy of steam is lost due to the irreversible process of throttling. The pressure drop varies from 3 to 5% of the inlet steam pressure po.
**Nozzle Friction Losses.**Losses due to the growth of boundary layer and formation of eddies in the wake, apart from frictional resistance of walls, which varies with the height and length of passage. Losses are higher in a turbulent boundary layer than in a laminar one. In reaction turbine where pressure or enthalpy drop per stage is less due to lower velocity, the laminar condition persists over a greater length of passage.

So the friction loss is less than the impulse stage. However, due to the large number of stages, the total surface area exposed to flow is more, which increases friction loss. **Blade friction losses :**Losses in moving blades are caused by various factors : - Impingement losses
- Frictional losses
- Turning losses
- Wake losses

- Disc Friction losses : When the turbine disc rotates in the viscous steam, there is a surface friction loss due to relative motion between the disc and steam particles.

Some part of the kinetic energy of steam is lost due to this friction. ** Partial Friction losses :**An impulse stage operating with partial admission, or an early stage i such a turbine with nozzles provided only over a part of the blade periphery will have blades idle during part of the revolution. Some portion of kinetic energy of the incoming steam is spent in clearing away the steam existing within the blade passage. These are called “Scavenging losses” which together with disc friction losses are often referred to as “windage losses” in which some kinetic energy is imparted to the fluid at the expense of the kinetic energy of the blades. **Gland leakage losses :**Leakage of steam can occur between stages and along the shaft at inlet and exit ends of the casting. Diaphragm leakage takes place in both impulse and reaction stages through the radial clearance between the stationary nozzle diaphragm and the shaft or drum. Shaft leakage occurs through the radial clearance between the shaft and casing at both high and low pressure ends of turbines. **Residual Velocity loss :**Steam leaving the last stage of the turbine has a certain velocity which represents an amount of kinetic energy that cannot be imparted to the turbine shaft and is thus wasted. **Carry-over losses :**Some energy losses take place as steam flows from one stage to the next. The kinetic energy leaving one stage and available to the next is given by h_{co}(V^{2}_{2}/2), where h_{co}is the carry-over efficiency. - In addition there are some losses of energy due to wetness of steam. If the quality of steam is less than 0.88, erosion and also corrosion can take place. Since the velocity of steam leaving the last stage of turbine is quite large, there will be energy losses due to friction in the exhaust hood of the turbine.
**External losses :**There are some energy losses in the bearings and governing mechanism which can be reduced by improving the lubrication system. Some energy is consumed by oil pumps. Since the turbines are adequately insulated the surface heat loss by radiation and convection is small.

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