Hydraulic Turbines | Fluid Mechanics for Mechanical Engineering PDF Download

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.

Efficiency to Turbines
Hydraulic efficiency (h_h)

•   Mechanical efficiency (h_mech)

•  Volumetric efficiency (h_vol)

•  Overall efficiency (h_o)

 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 

•  Head of turbines

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

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

(ii) Hydraulic efficiency

(iii) Mechanical efficiency

(iv) Overall efficiency
h_o = h_N × h_h × h_mech

•  Velocity of jet, V₁ =

C_v = coeff of velocity = 0.97 – 0.99

•  Speed Ratio

K_u = 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) =

=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)[ V_w1.u1 - V_w2.u₂]
• For best efficiency flow should be radial at outlet, V_w2 = 0

i.e., work done per sec (Q/g)V_w1u₁

• Degree of reaction

V _w1 & V_w2 are whirl velocities at inlet and outlet
u₁ & u₂ are peripheral velocities of blades at inlet and outlet.

• Flow ratio

 = 0.15 0.30

• Speed ratio

0.60 0.90

• Discharge through the turbine

Q = pD₁ B₁ V_f1
 = pD₂ B₂ V_f2
B₁, B₂ are width of inlet & outlet
D₁, D₂ are diameter at inlet & outlet
V_f1 ,V_f2 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 V_r1 = V_r2
• 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

D_b/D_o
= 0.35 to 0.61
u₁=  u₂ = 
D_o = outer diameter of runner
D_b = 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,

•  Unit discharge,

•  Unit power,

•  Specific speed (N_s) 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.

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

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

 
S = 9.6 × 10^–4N_s

• Model Laws of Turbines

 
Q μ N........1^st Fan law
The parameter

= is called flow coefficient.or capacites co-efficient


H μ N²........2^nd Fanlaw
The parameter

= is called head coefficient.

P μ N³........3^rd Fan law
The parameter

= is called power coefficient.

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)

H_a = Atmospheric head
H_v = Vapour pressure head
h_s = Suction head (at the outlet of reaction turbine)
H = Working head
NPSH = Net Positive Suction Head

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

 (i) For Francis Turbine, 

(ii) For Propeller Turbine,

(iii) For Kaplan Turbine,s_c is 10% higher than s_c for properller turbine.

•  Condition for no cavitation