Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng.

4503 (TM)

Department of Mechanical and Vehicle Engineering

School of Engineering (ASTU), Adama University, ADAMA
MEng. 4503 (Turbomachinery) UNIT 1

INTRODUCTION OF TURBOMACHINE

1.1 INTRODUCTION
A Turbo machine is a device which converts the energy stored by a fluid into mechanical energy or
vice versa. The energy stored by a fluid mass appears in the form of potential, kinetic and intermolecular
energy. The mechanical energy, on the other hand, is usually transmitted by a rotating shaft. Machines
using liquid (mainly water, for almost all practical purposes) are termed as hydraulic machines. In this
chapter we shall discuss, in general, the basic fluid mechanical principle governing the energy transfer in
a Turbo machine and application of tharmodynamic law to turbomachine.
1.2 DEFINITION OF TURBOMACHINES
 All those devices in which energy is transferred either to, or from, a continuously flowing fluid by
the dynamic action of one or more moving blade rows.
 The word turbo or turbinis is of Latin origin and implies that which spins or whirls around.
 Essentially, a rotating blade row, a rotor or an impeller changes the stagnation enthalpy of the
fluid moving through it by either doing positive or negative work, depending upon the effect
required of the machine.
 These enthalpy changes are intimately linked with the pressure changes occurring simultaneously
in the fluid.
1.3 Principle of Turbomachine
The important element of a Turbomachine is a rotor consisting of a number of vanes or blades. There
always exists a relative motion between the rotor vanes and the fluid. The fluid has a component of velocity
and hence of momentum in a direction tangential to the rotor. While flowing through the rotor, tangential
velocity and hence the momentum changes.
The rate at which this tangential momentum changes corresponds to a tangential force on the rotor. In
a turbine, the tangential momentum of the fluid is reduced and therefore work is done by the fluid to the
moving rotor. But in case of pumps and compressors there is an increase in the tangential momentum of
the fluid and therefore work is absorbed by the fluid from the moving rotor.

Turbo ........ Latin world  Which means “Spins” or “Whirls” around

Due to Newton’s Second Law of Motion

Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

It means if we provide a force through jet on blade. There will change in linear velocity and if blade is
fixed on runner then it will start to rotate at particular angle due to rate of change of angular momentum

1.4 CLASSIFICATIONS OF TURBO MACHINES

The Turbo machines may be classified under different categories as follows:
1. On the Basis of Direction of Energy Conversion:
The device in which the kinetic, potential of the fluid is converted in the form of mechanical energy of a
rotating member is known as a turbine. The machines, on the other hand, where the mechanical energy from
moving parts is transferred to a fluid to increase its stored energy by increasing either its pressure or velocity
are known as pumps, compressors, fans or blowers.

2. On the Basis of Power:

(a) Power producing machine- Fluid transfer its energy to the machine
Pressure Energy (Pr E) of fluid is converted into mechanical energy in a close container by a machine- Hydro
static machine
Pressure Energy (Pr E) of fluid is converted by the dynamic action of fluid due to relative motion between
the fluid and machine - Hydro Dynamic machine
Hydraulic turbines (the work is done by the fluid on the rotor).
(b) Power Absorbing machine- Energy supplied to the shaft of a machine (Shaft Power) is transfer to the
Fluid due to relative motion between the fluid and machine
Pump, compressor, fan or blower (the work is done by the rotor on the fluid element).

3. On the Basis of Main Direction of Fluid Path in the Rotor:

(a) Tangential flow- Fluid velocity is in the direction of tangent to the runner and it strikes in the form
of jet.
V

(b) Radial Flow- flow of fluid is in radial direction

(i) Radial inward flow- The flow is towards the center of the rotor and away from the Rim.
Eg. Inward flow Turbine
(ii) Radial outward flow- The flow is away from the center and towards to Rim
Eg. Pumps and Compressors
Examples of radial flow machines are the Francis turbines and the centrifugal pumps or compressors
(c) Axial flow- If flow is axially to the machine means fluid insert at center and exit at center also
Eg. Axial flow turbine, axial flow pump and compressor.
(d) Mixed flow- If the flow is partly radial and partly axial, the term mixed-flow machine is used.
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

RADIAL AXIAL
AIR AIR
FLOW FLOW

PROPELLER
TYPE FAN
(TWO STAGE)

CENTRIFUGAL
TYPE FAN

Fig. : Turbomachine on the basis of fluid path

Types of Flow

Axial Flow
Tangential
or Radial Flow Mixed Flow
Flow
Parallel Flow

Pelton wheel Kaplan

Turbine, Turbine. Radial + axial
Centrifugal Outward Inword
Axial Flow
Pump, Radial Radial
Pump,
Centrifugal Axial Flow
Compressor Compressor
Modern
Fourneyron Old Francis
Francis
Turbine Trubine
Trubine

4. On the Basis of Fluid Used:

The machine transferring mechanical energy of rotor to the energy of fluid is termed as a pump when it
uses liquid, and is termed as a compressor or a fan or a blower, when it uses gas. The compressor is a machine
where the main objective is to increase the static pressure of a gas. Therefore,
The mechanical energy held by the fluid is mainly in the form of pressure energy. Fans or blowers, on the
other hand, mainly cause a high flow of gas, and hence utilize the mechanical energy of the rotor to increase
mostly the kinetic energy of the fluid. In these machines, the change in static pressure is quite small.
For all practical purposes, liquid used by the turbines (for producing power) is water, and therefore, they
are termed as water turbines or hydraulic turbines. Turbines handling gases, steam in practical fields are
usually referred to as steam turbine, gas turbine, and air turbine depending upon whether they use steam, gas
(the mixture of air and products of burnt fuel in air) or air.

5. On the Basis of Fluid Action on the machine (Operation):

On the basis of operation turbomachines are two types:
(1) Impulse
(2) Reaction
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

6. Based on Operating Head:-

(a) Low Head – (< 60 m) – Kaplan Turbine
(b) Medium Head – (60 m < H < 250 m) – Francis Turbine
(c) High Head – (> 250 m) – Pelton wheel Turbine

7. Based on Specific Speed:-

(a) Low Specific Speed – (< 50 RPM) – Pelton wheel Turbine
(b) Medium Specific Speed – (50 RPM < Ns < 400 RPM) – Francis Turbine
(c) High Specific Speed – (> 400 RPM) – Kaplan Turbine

8. On the Basis of Fluid used:

(i) Incompressible Fluid ( = C)
Ex.–Liquid Pump
(ii) Compressible Fluid ( # C)
Ex.– Compressor (air), fan and Blower
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

(a)Single stage axial flow compressor or pump, (b) Mixed flow pump (Radial + Axial), (c)
Centrifugal Compressor or Pump, (d) Francis Turbine (mixed flow type), (e) Kaplan Turbine
(Axial Flow), (f) Pelton wheel (Tangential Flow)
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

1.5 Dimensionless parameters

Using the principles of dimensional analysis (Pi theorem), sets of non-dimensional groups may be obtained.
One such being
P / (D5ω3ρ) = f [Q / (ω D3), gH / (ω2D2), ρ ω D2 / (μ), ρ ω2 D2 / (k)]
Grouping 1 is a power coefficient.
Grouping 2 is often known as a flow coefficient Φ (Where Q α V D2 and ω D α μ or Φ = V/u which is a
velocity coefficient).
Grouping 3 can be written as gH / u2 (Since ω2 D2 α u2) and without g is known as Ψ. the head coefficient.
Grouping 4 is a Reynolds number based on a typical machine dimension.
Grouping 5 is a form of Mach number irrelevant in pumps, fans and water turbines. But not in other
turbomachines.

Reynold’s No. (Re) = Fi / Fv = ρ l v / (µ)

Froude No. (F) = Fi / Fg = v2/lg
Euler’s No. (E) = Fi / Fp = ρ v2/p
Weber No. (W) = Fi / Fs = ρ l2 v/ σ
Mach No. (M) = Fi / Fe = ρ l v2/ k = Vfluid / Vsound

So most of purpose we use first three dimensionless parameters in Turbomachine are

(1) Head Coefficient (Ψ)

Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

(2) Flow Coefficient (Φ)

(3) Power coefficient or Specific Power (p¯)

Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

Conversion Factors (Pressure) ---------------Multiply by

Convert Convert to
from Pa (N/m2) bar atmosphere mm Hg mm H2O m H2O kg/cm2
Pa (N/m2) 1 10-5 9.87 10-6 0.0075 0.1 10-4 1.02 10-5
bar 105 1 0.987 750 1.0197 104 10.197 1.0197
atmosphere 1.01 105 1.013 1 759.9 10332 10.332 1.03
mm Hg 133.3 1.33 10-3 1.32 10-3 1 13.3 0.013 1.36 10-3
mm H2O 10 0.000097 9.87 10-5 0.075 1 0.001 1.02 10-4
m H2O 104 0.097 9.87 10-2 75 1000 1 0.102
kg/cm2 9.8 104 0.98 0.97 735 10000 10 1
pound
47.8 4.78 10-4 4.72 10-4 0.36 4.78 4.78 10-3 4.88 10-4
square feet
pound
square 6894.76 0.069 0.068 51.7 689.7 0.690 0.07
inches (psi)
inches Hg 3377 0.0338 0.033 25.4 337.7 0.337 0.034
inches H2O 248.8 2.49 10-3 2.46 10-3 1.87 25.4 0.0254 0.0025
Multiply by
Convert to
Convert from pound square pound square inches
inches Hg inches H2O
feet (psi)
Pa (N/m2) 0.021 1.450326 10-4 2.96 10-4 4.02 10-3
bar 2090 14.50 29.61 402
atmosphere 2117.5 14.69 29.92 407
mm Hg 2.79 0.019 0.039 0.54
mm H2O 0.209 1.45 10-3 2.96 10-3 0.04
m H2O 209 1.45 2.96 40.2
kg/cm2 2049 14.21 29.03 394
pound square feet (psf) 1 0.0069 0.014 0.19
pound square inches (psi) 144 1 2.04 27.7
inches Hg 70.8 0.49 1 13.57
inches H2O 5.2 0.036 0.074 1
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

Department of Mechanical and Vehicle Engineering

School of Engineering (ASTU), Adama University, ADAMA
MEng. 4503 (Turbomachinery) UNIT 2

PRINCIPLE OF OPERATION OF TURBOMACHINES

Impulse Momentum Principle (Conservation of linear momentum principle)

Momentum (P) = M V

According to Newton’s IInd law of motion – The magnitude of applied force is equal to the Rate of change
of Linear momentum in the direction of applied force.

BUT – the direction of force will depends on the direction in which the change of momentum takes place.

F = d/ dt (mV) --------1
= m * dV/dt + V *dm/dt
For solid body M = Constant so dm/dt = 0
F = m * dV/dt
F=m*a --------2

For fluid mechanics we are concerned with constant mass flow rate of a continuous fluid.

F = (m/dt) * dV

For initial condition F = (m/t) * (Vf -Vi)

F = ṁ * (Vf -Vi) Force Exerted by the body on the fluid

Or F = (m/t) * (Vf -Vi)

F * t = m * (Vf -Vi) Impulse Momentum Principle

Case: Force exerted by the fluid on the body (By Newton’s III law of motion) – Equal & opposite

F = ṁ * (Vi -Vf) Force exerted by the fluid on the body (It is used for impact of Jet)

F = (ṁ Vi ) – (ṁ Vf )
(Force exerted by Fluid on body) = (Rate of momentum in) – (Rate of momentum out)

Note:- Fluid Mechanics ṁ = ρ A V = m/t (Mass Flow Rate)

Discharge (Quantity of Water) = Q = A V or ṁ = ρ Q

F = ρ Q * (Vi -Vf) Force exerted by the jet of fluid striking on moving or fixed plate
Surface
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

Principle of Turbomachine (Euler’s Energy Equation)

(Principle of conservation of angular momentum)
(Newton’s second law of motion applied to turbo machines)

If we provide a force through jet on a blade there will be change in velocity in linear direction
due to change of linear momentum (P) and it will move in a line (Impulse momentum
principle).

But If blade is mounted or fixed on runner (Rotor) then it will start to rotate at particular angle
due to rate of change of angular momentum (J)----
This is called Principle of Turbomachine
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

Velocity Triangle

The component velocities of flow through the impeller passages are studied graphically by means of
velocity vectors which form triangular shapes and, therefore, these figures are called velocity triangle. They
can be drawn for any point of the flow path through the impeller, but the usual procedure is to study the
velocity triangles of an impeller at its inlet point and at discharge point.

Rules to draw Velocity Triangle

Velocities to be used :
(a) V or C = Absolute velocity of liquid or exit velocity of liquid through nozzle or actual velocity.
(b) u = Tangential velocity or blade velocity. (It is tangent on impeller or it is parallel to tangent on
impeller.)
It’s direction is same as rotational direction of rotor.
(c) Vr or W = Relative velocity or imaginary velocity.
– It shows relativity of V and u.
– It is tangent to blade.
RTR
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

Assumptions:
(1) For Infinite No. of Vanes: Liquid flowing in the passage follow the path out lines by the vanes.
(2) No energy loss in the impeller due to friction and eddy formation.
(3) Even/uniform velocity distribution in the narrow passages formed between two adjacent vanes.
(4) No Loss due to shock at entry i.e. inlet edge of the impeller blades is parallel to the relative velocity
(5) For the best efficiency of pump it is assumed that 1 = 90º, liquid enters in impeller eye in an axial or
radial direction i.e. the whirl component (Vf1) of inlet absolute velocity (V1) is zero i.e. Vw1 = 0 and V1= Vf1
by diagram.

Performance of Vane (Blade) Shapes

The exit relative velocity Vr2 is fixed by 2, hence the exit velocity triangle depends upon 2 and 2
depends upon blade profile.
1. Forward curved vanes
The vane is curved in the same direction of rotation and 2 > 90º.
2. Radial Vanes
Liquid leaves the vane in radial direction as 2 = 90º so Vw2 = u2

(a) Forward facing blade (b) Radial blade (c) Backward facing blade

Different Shapes Blade

3. Backward Curved Vanes :
The vane is curved in the opposite direction of rotation and 2 < 90º
Notes :-
 The curve rises upwards.
 The efficiency increases with decreases of 2.
 For radial blades,η = 80% – 85% – for blower and fans
 For forward curved blades, η = 75% – for compressor and fans
 For backward curved blades, η = 85 – 90% – for centrifugal pump.
The energy conversion efficiency is maximum for forward-curved vanes, but the exit velocity (V2) is very
high which is not desirable. Normally backward-curved vanes with 2 between 20° and 30° are used for low
and medium head pumps. For high head pumps, forward-curved or radial vane impeller are preferred.
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

Vane Congruent Flow

When the value of flow angles at the rotor inlet and exit are not known they are assumed equal to the
blade angles of the rotor at the inlet and exit. And this assuming that the fluid follows the blade surfaces
and is known as ideal or vane congruent flow
This flow can only be realized if there is an infinite no of infinitely thin blades. However this assumption is
never valid in practice.
Turbomachine always have a finite no of blades with finite thickness. Hence the actual flow in
turbomachine’s blade passages differs or deviates from the ideal flow and this flow is said to take place
with SLIP.
Wactual < Wideal
Wideal - Wactual = SLIP POWER

Actual Flow patterns in the rotors


 Due to Inertia Forces liquid is reluctant to move round with the impeller (which trapped between the
impeller blades). This result in a difference of pressure forces across the vane (blades) and this develops.
+ Pressure  outerside of blades
– Pressure  inner side of blades
 The pressure difference is called Vane Loading and it increases with no. of Vannes increased.
 Due to pressure variation a velocity gradiant exit across the channel.
 On High pressure side  Liquid leave tangentially.
 On lower pressure side  Liquid leave circumferentially. This developed path deviation.
 Due to this path deviation exit Blade angle shift from  to  and blade angle reduced.
 So due to this, there is fluid deviation and the tangential componant get reduced from
Vw2 to Vw2 ' and Vw2  Vw2 ' is called slip
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)

Slip Coefficient:
The ratio of whirl component with fluid deviation (Vw2’) to the whirl component without fluid deviation
(Vw2)
Vw2’ / Vw2 = σs
 Due to real fluid effects (Friction and Separation) the radial velocity (Vf) may not be uniform around the
periphery of the impeller.
 The net effect of slip and non-uniform velocity is to reduce the Euler’s Head (He) also.

Energy Losses and Efficiencies of Turbomachine

Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)
Er. Mukesh Didwania, M. Tech. (Thermal Engineering), ASTU, Adama University---MEng. 4503 (TM)