2. chapter 2

BITS PilaniK K Birla Goa Campus

ME F341Prime Movers and Fluid Machines

Dr. Sandesh S. ChouguleDepartment of Mechanical Engineering

BITS Pilani, K K Birla Goa Campus

Hydraulics Turbines


Hydroelectric Power Plant


Hydraulic efficiency

Efficiencies of a Turbine


Mechanical efficiency

Volumetric efficiency


Overall efficiency


According to action of flow

Impulse turbines Reaction Turbines

According to direction of flow

Tangential flow Radial flow Axial flow Mixed flow

Classifications of Hydraulic Turbines


According to Head and Quantity of water

High head (150 m to 2000 m) Medium head (30 m to 150 m) Low head (< 30 m)

According to Specific speed

Low specific speed (10 to 50) Medium specific speed (50 to 250) High specific speed (> 250)


• In an impulse turbine, all the available energy of water isconverted into kinetic energy or velocity head by passing itthrough a contracting nozzle provided at the end ofpenstock.

• The runner revolves freely in air.• The water is in contact with only a part of the runner at a

time and throughout its action on the runner and itssubsequent flow to the tailrace, the water is at atmosphericpressure.

• Eg. Pelton wheel, Girard turbine, Banki turbine, Jonval,Turgo-impulse wheel etc…

Impulse and Reaction Turbines


• In reaction turbine, at entrance of the runner, only part ofthe available energy of water is converted into kineticenergy and substantial part remains in the form of pressureenergy.

• As water flows through the runner the change frompressure to kinetic energy takes place gradually.

• As such the pressure at the inlet of turbine is much higherthan the pressure at outlet and it varies throughout thepassage of water through turbine.

• The difference of pressure between the inlet and the outletof runner is called reaction pressure and these turbine isknown as reaction turbines.

• Eg. Thomson, Francis, Propeller, Kaplan, Fourneyron etc.


Pelton Turbine


Introduction

• Named after the designer Mr. A. Pelton in California at

1810

• Impulse turbine- as there is no pressure drop across the

buckets

• Suitable for high heads of about 100-500m

• Requires comparatively less quantity of water


Schematic Diagram


Working

• Water supplied is from a high head through a longconduit called penstock.

• The water is accelerated in nozzle and the head isconverted into velocity and discharges at high speed inthe form of a jet at atmospheric pressure

• The jet strikes buckets attached to the rim of a rotatingwheel (runner)

• Impact of water on buckets produce a force whichcauses the wheel to rotate by supplying a torque on theshaft

• water discharged at relatively low speed falls into lowerreservoir or tail race


Nozzle Assembly


• Power produced by turbine proportional to QxHwhere Q : Volume flow rate

H : effective head• Since H cannot be varied easily, Q (cross sectional area x

velocity of flow is varied)• For wheel speed to be maintained constant, jet velocity is

not varied.• Cross sectional area is varied using a spear valve• Spear valve is actuated to and fro as per the power

demand


Deflector

• Sometimes, need arises for immediate closure of nozzle.

• If flow is reduced suddenly, high back pressure waves

will be generated on penstock pipes

• Deflector alters the jet trajectory

Runner with Buckets

Undercuts are provided so that the jet bye-passes the inclined blades which are obstructing the jet to strike the blade which is vertical in position


• Usually more than 15 buckets• Each bucket is split vertically into two parts by a splitter

that has a sharp edge at the center• Striking jet of water is divided into two parts by the splitter• each part of jet flows sideways round the smooth inner

surface of the bucket and leaves it with a relative velocityalmost opposite in direction of the original jet

• Notch at the edge of outer rim of each bucket ensures aloss free entry of the jet into the buckets.

Bucket of pelton turbine


• Maximum change in momentum is obtained when the jet is180°

• But angle is restricted to 165° so that the fluid leaving onebucket does not strike back the succeeding bucket

• Buckets are made of special bronze- steel alloys withNickel, Chromium or stainless steel.

• Buckets are properly polished for smooth change indirection and the formation of low pressure pockets causeddue to erosion are avoided

• Buckets can be bolted construction( for large turbines) orof single cast


• Prevents splashing of water

• Guides water to flow through the tail race

• Provides housing and support to the thrust bearings and

shaft

• Since the buckets are symmetrical, side or axial thrusts

produced by water in each half is balanced

• Provides safety against accidents

Casing


Indian Scenario


Analysis of Pelton Wheel Turbine


Work done by Pelton Wheel


……Eq. (1)


………….Eq. 2

…….Eq. 3


……………Eq. 5

……………Eq. 4


Problem 1:

Two jet strike the buckets of a pelton wheel, which is

having shaft power as 15450 kW. The diameter of each jet

is given as 200 mm. If the net head on the turbine is 400

m. Find overall efficiency of the turbine. Take Kv = 1.0


Problem 2:

A Pelton wheel has a mean bucket speed of 10 m/s with a jet of water flowing at the

rate of 700 liters/s under a head of 30 m. The bucket deflect the jet through an

angle of 1600. Calculate the power given by water to the runner and hydraulic

efficiency of the turbine. Assume co-efficient of velocity as 0.98


Design of Pelton Wheel Turbine


Design of Pelton wheel means the following data is to be

determined :

Diameter of the jet (d)

Diameter of wheel (D)

Width of the buckets which is = 5 × d

Depth of the buckets which is = 1.2 × d

Number of buckets on the wheel


Problem 1

A Pelton wheel is to be designed for a head of 60m when

running at 200 rpm. The Pelton wheel develops 95.64 kW

shaft power. The velocity of the buckets = 0.45 times the

velocity of the jet, overall efficiency = 0.85 and co-efficient

of the velocity is equal to 0.98


Problem 2The three jet Pelton turbine is required to generate 10,000kW under net head of 400 m. The blade angle at outlet is 150

and reduction in the relative while passing over the blade is5%. If the overall efficiency of the wheel is 80%, Kv = 0.98and speed ratio = 0.46, then find: (i) the diameter of the jet,(ii) Total flow in m3/s and (iii) force exerted by a jet on thebuckets. If the ratio of jet not to be less than 10, find thespeed of the wheel for frequency of 50 Hz/sec and thecorresponding wheel diameter.[Ans. (i) 125mm, (ii) 3.18 m3/s, (iii) 94.05 kN, (iv) 600 rpm]


Problem 3:

A Pelton wheel turbine is to be designed for following specifications:

Shaft power = 11,772 kW;

Head = 380 m;

Speed = 750 rpm;

Overall efficiency = 86%.

Jet diameter is not to exceed one-sixth of the wheel diameter.

Determine:

(i) The wheel diameter [Ans. 0.989 m]

(ii) The number of jets required [Ans. 2]

(iii) Diameter of jet [Ans. 0.165m]

Take Kv1= 0.984 and Ku1=0.45


Problem 4The following data is related to a Pelton wheel turbine:Head at base of the nozzle = 80 mDiameter of jet = 100 mDischarge of the nozzle = 0.30 m3/sPower at the shaft = 206 kWPower absorbed in Mechanical resistance = 4.5 kWDetermine (i) Power lost in nozzle [Ans. 16.59 kW ],

(ii) Power lost due to hydraulic resistance inthe runner. [Ans. 8.35 kW ]


Problem 5:

A Pelton wheel nozzle, for which Cv= 0.97, is 400 m below

the water surface of a lake. The jet diameter is 0.6 m, its

length is 4 km and f = 0.0032. The buckets , deflect the jet

throgh 1650 and they run at 0.48 times jet speed, bucket

friction reducing the relative velocity at outlet by 15% of

relative velocity at inlet . Mechanical efficiency = 90%. Find

the flow rate and shaft power developed by the turbine.

[Ans. Q = 0.419 m3/s, SP = 1194 kW ]


Problem 6

Determine the power given by the jet of water to the runner

of a pelton wheel which is having tangential velocity a 20

m/s. The net head on the turbine is 50 m and discharge

through the jet water is 0.03 m3/s. The side clearance

angle 150 and take Kv= 0.975.

[Ans. 12.43 kW ]

2. chapter 2

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