Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

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Chapter 15

 

HYDRAULIC TURBINES

Turbines are hydraulic machines which convert hydraulic energy into mechanical energy.

  •  Penstock is a pipe of large diameter which carry water under pressure from storage reservoir to the turbine chamber.
  • Surge Tank is an open operation tank provided in midway of Penstock to absorb water pressure hammer during sudden stoppage of flow in the turbiness. It should be located as near to turbines as possible.

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering 

Efficiency to Turbines
Hydraulic efficiency (hh)
Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

  •   Mechanical efficiency (hmech)

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

  •  Volumetric efficiency (hvol)

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

  •  Overall efficiency (ho)

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

 Classification of Turbines on the basis of energy at inlet

  •  Impulse Turbines : These have only kinetic energy at inlet.

Ex. : Pelton Wheel, Gurard Turbine, Banki Turbine, Jonval Turbine, Turgo Impulse Wheel.

  • Reaction Turbines : These have kinetic energy and pressure energy both at inlet.

Ex. : Francis Turbine, Propeller Turbine, Kaplan Turbine, Thomson Turbine, Furneyron Turbine.
Classification of Turbines on the basis of type of flow within turbine

  • Tangential Flow Turbine :

Ex. : Pelton Wheel, Turgo Impulse Wheel.

  • Radial Flow Turbines :

Ex. : Inward-radial flow turbines are Francis turbine, Thomson Turbine, Guard Turbine. Outwardradial
flow turbine is Fourneyron turbine

  • Axial Flow Turbines :

Ex. : Jonval Turbine, Propeller Turbine, Kaplan Turbine

  • Mixed Flow Turbine :

Ex. : Modern Francis Turbine

  • Specific speed of turbines 
TurbineSpecific Speed (MKS Unit)
Pelton Turbine10 to 35
Francis Turbine60 to 300
Kaplan & Propeller Turbine300 to 1000
  •  Head of turbines
TurbineHead
Pelton Turbineabove 250 m
Francis Turbine60 m to 250 m
Kaplan & Propeller TurbineBelow 60 m

PELTON TURBINE

  • It is tangential flow impulse turbine.
  • It is high head low discharge turbine.
  • The bucket of a pelton wheel is double semi-ellipsoidal in shape. The jet of water impinges at the centre of the bucket & deflects through 160-170°, (The deflection angle is 160° to 170°).
  • The advantage of having double cup-shaped buckets is that the axial thrust neutralizes each other. A notch is cut at lower tip of bucket, which prevents the jet striking the preceding bucket and avoid the deflection of water towards the centre of bucket.
  • Theoretically six jets can be used with one pelton wheel but practically not more than two jets for a vertical runner and not more than four jets for horizontal runner should be used.
  • Work done per second

 Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

V1 = Velocity of jet coming out of nozzle
u1 = u2 = u = tangential velocity of vane
k = Bucket friction coefficient

  •   Efficiency of Pelton wheel

(i) Nozzle efficiency

 Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

(ii) Hydraulic efficiency

 Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

(iii) Mechanical efficiency

 Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

(iv) Overall efficiency
ho = hN × hh × hmech

  •  Velocity of jet, V=Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

Cv = coeff of velocity = 0.97 – 0.99

  •  Speed Ratio

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
Ku = 0.43 – 0.47

  •  Jet ratio (m) =(dia of wheel (D)/ (jet dia (d))


A jet ratio of 12 is normally adopted

  •  No. of Buckets (Z) =

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
=18 to 25
This formula is called Tygun formula.

  •  If P is power developed by the pelton wheel when working under head (H) & having one jet only, the power developed by the same wheel will be (n. P) in n jets are used under the same head.

FRANCIS TURBINE

  •  It is inward radial flow reaction turbine.
  •  Scroll casing is used to evenly distribute the water along the periphery & maintaining the constant velocity for the water 
  •  Draft Tube - The water after passing through the runner flows to the tail race through a draft tube  which is a passage of gradually increasing cross-section area which connects the runner exit to tail  race. The basic function of draft tube is to convert kinetic head into the pressure head.

Purpose of draft tube
(i) Permits the negative suction head to establish at the runner exit
(ii) It acts as a recuperator of pressure energy.
The angle of straight divergent type draft tube should not be more than 8° otherwise eddies will be formed
& efficiency will be reduced.

  •   Inward Flow reaction turbine
  • Work done per sec (Q/g)[ Vw1.u1 - Vw2.u2]
  • For best efficiency flow should be radial at outlet, Vw2 = 0

i.e., work done per sec (Q/g)Vw1u1

  • Degree of reaction

 Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

V w1 & Vw2 are whirl velocities at inlet and outlet
u1 & u2 are peripheral velocities of blades at inlet and outlet.

  • Flow ratio

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering = 0.15 0.30

  • Speed ratio

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering0.60 0.90

  • Discharge through the turbine

Q = pD1 B1 Vf1
 = pD2 B2 Vf2
B1, B2 are width of inlet & outlet
D1, D2 are diameter at inlet & outlet
Vf1 ,Vf2 are velocities of flow at inlet & outlet

KAPLAN TURBINE

  • It is axial flow reaction turbine.
  • Runner of kaplan turbine has four to six blades.
  • Runner blades of propeller turbines are fixed but of kaplan turbine can be turned about axis.
  • At part load, high efficiency can be obtained in kaplan Turbine.
  • No. of blades are 3 to 6
  • If frictional resistance is ignored, then Vr1 = Vr2
  • Velocity of flow remains constant.
  • Its velocity triangle & calculation of efficiency is similar to Francis turbine.
  • Discharge through the turbine.
  •   Flow ratio = y = 0.70
  •  Usually

Db/Do
= 0.35 to 0.61
u1=  uHydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
Do = outer diameter of runner
Db = inner diameter or diameter of boss or hub
DIAGONAL TURBINE

  •  This is intermediate between the mixed flow and axial flow turbine because the flow of water as it passes  through the runner is at an angle of 45° to the axis and hence is known as diagonal turbine.
  •  Head range is 30 m to 150 m
  •  Blades are adjustable.
  •  It can be used as turbine as well as pump.

TUBULAR TURBINE

  • Adjustable or non-adjustable runner blades.
  • Head range 3 m to 15 m.
  • Scroll casing is not provided.
  • Runaway speed

For a turbine working under maximum head & full gate opening, if the external load suddenly drops to almost
zero value and at the same time, governing mechanism fail, turbine runner will tend to race up and attains
maximum possible speed. This limiting speed of turbine is known as runaway speed.
For Pelton Turbine, Runaway speed is 1.8-1.9 times of normal speed.
For Francis Turbine, Runaway speed is 2-2.2 times of normal speed
For Kaplan Turbine, Runaway speed is 2.5-3 times of normal speed

  •  Performance of Turbines/Unit Quantities

The concept of unit quantities is required to
(i) predict the behaviour of turbines working under different conditions.
(ii) make comparison between the same type but different size of turbines.
(iii) co-relation and use of experimental data.

  •  Unit speed,

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

  •  Unit discharge,

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering 

  •  Unit power,

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

  •  Specific speed (Ns) of any turbines is the speed in rpm of a turbine, geometrically similar to the actual turbine but of such a size that under corresponding conditions it will develop unit power when working under unit head.

 Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

Note that specific speed is not a dimensions parameter, its unit is [M1/2L–1/4T–5/2]

  •  Dimensionless form of specific speed is called shape number (S).

 Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
S = 9.6 × 10–4Ns

  • Model Laws of Turbines

 

 Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
Q μ N........1st Fan law
The parameter
Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
= is called flow coefficient.or capacites co-efficient
Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
H μ N2........2nd Fanlaw
The parameter
Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
= is called head coefficient.


  • Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

P μ N3........3rd Fan law
The parameter
Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
= is called power coefficient.


  • Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

Note : Similarity of model and prototype turbines are based on the assumption that efficiency of model is equal
to that of the prototype. But the efficiency of prototype is higher than the models efficiency. This is known as
scale effect.

  • Thoma’s cavitation factor (s)

 Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

Ha = Atmospheric head
Hv = Vapour pressure head
hs = Suction head (at the outlet of reaction turbine)
H = Working head
NPSH = Net Positive Suction Head

  •  Critical value of Thoma’s number (sc) depends upon Ns and is given by :

 (i) For Francis Turbine, 

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
(ii) For Propeller Turbine,

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering
(iii) For Kaplan Turbine,sc is 10% higher than sc for properller turbine.

  •  Condition for no cavitation

Hydraulic Turbines - Notes | Study Fluid Mechanics for Mechanical Engineering - Mechanical Engineering

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