Turbomachinery (ME-209)
Dr. Sumit Kumar Singh
Guest faculty,
Mechanical Engineering Department
Tezpur University
Syllabus
➢ Turbomachines are often referred to as rotodynamic devices
because they are specifically designed to tranfer energy to or
from a so-called working fluid through the action of forces
generated fluid-dynamically by a rotor
➢ There are two broad categories of turbomachinery,
pumps and turbines.
➢ The word pump is a general term for any fluid machine
that adds energy to a fluid.
➢ Turbines are energy producing devices
Mechanism of Operation
1. The fluid flows directly into the device in an axial
direction (in the line with the machine)
2. The stator blades turn the flow so that it is lined up
with the turbine blades
3. The turbines blades turn the flow back towards the
axial direction and turn the output shaft.
View of Turbomachinery
Cascade view
Meridional view
Relative motion 1D
U
No wind
W=-U
➢ Viewing flow from the point of view of a rotating
component is known as being in the relative frame of
reference
U
Tail wind
V
W=0
➢ Viewing flow from the point of view of a stationary
observer is known as being in the absolute frame of
reference
U
V
W = V + ( – U) (vectorial addition)
U is the “frame velocity”
V is the “absolute velocity” or the velocity that an observer experiences.
W is the “relative velocity” or the velocity experienced by the walker.
Head
wind
Relative motion 2D
W=U
Velocity Triangles for an Aircraft Landing
Note : Absolute velocity is the vector sum of the frame velocity and the relative velocity. V = U + W
Graphical addition and subtraction of vectors
➢ To add two vectors A + B graphically : Place them nose – to – tail and the result is given by movement from
the tail of the first to the nose of the second.
➢ To subtract two vectors A - B graphically : Reverse the direction of B and proceed with addition of vectors as
before.
Flow through turbomachines
Cascade and Meridional Views of a Turbine Stage
Velocity Triangles for a Turbine Stage
Velocity Components
Different Turbomachines
3-D view of radial impeller
➢ Radial and Centrifugal flow machines
Radial pump
Centrifugal impeller
Hydraulic Turbines
Schematic of Hydro-electric scheme
Types of Hydraulic Turbines
Impulse turbine
Reaction Turbine
Francis turbine
Runner
Francis turbine
(inward flow turbine)
Guide vane control
mechanism
Guide vanes
Kaplan turbine
(axial flow turbine)
Difference between Francis and Kaplan turbine
Pelton turbine
Francis turbine
Kaplan turbine
NEXT LECTURE
➢ Application of the equations of fluid motion
1. Conservation of mass
2. Conservation of momentum
➢ Euler Turbine and Pump equations
THANK YOU
Equation of continuity
•
•
•
•
Consider the flow of a fluid with density ,
through the element of area dA, during the
time interval dt.
If c is the stream velocity the elementary
mass is dm = .c.dt.dAcos, where is the
angle subtended by the normal of the area
element to the stream direction.
The velocity component perpendicular to the
area dA is cn = ccos and so dm = cndAdt.
The elementary rate of mass flow is therefore,
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Euler’s equation of motion
•
For the steady flow of fluid through an elementary control volume that, in the
absence of all shear forces, following relation is obtained,
•
This is Euler’s equation of motion for one-dimensional flow and is derived
from Newton’s second law.
•
By shear forces being absent we mean there is neither friction nor shaft
work.
•
However, it is not necessary that heat transfer should also be absent.
22
Bernoulli’s equation
•
For an incompressible fluid, is constant,
•
where stagnation pressure is p0 = p+1/2c2
•
If the fluid is a gas or vapour, the change in Control volume in a streaming fluid.
gravitational
potential
is
generally
negligible and therefore,
•
i.e. the stagnation pressure is constant (this is also true for a compressible
isentropic process).
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Moment of momentum
•
For a system of mass m, the vector sum of
the moments of all external forces acting
on the system about some arbitrary axis A–
A fixed in space is equal to the time rate of
change of angular momentum of the
system about that axis, i.e.
•
where r is distance of the mass centre from
the axis of rotation measured along the
normal to the axis and c is the velocity
component mutually perpendicular to both
the axis and radius vector r.
Control volume for a generalized
turbomachine.
24
Law of moment of momentum
•
Swirling fluid enters the control volume at
radius r1 with tangential velocity c1 and
leaves at radius r2 with tangential velocity
c2. For one-dimensional steady flow,
•
which states that, the sum of the moments
of the external forces acting on fluid
temporarily occupying the control volume
is equal to the net time rate of efflux of
angular momentum from the control
volume.
25
Euler’s pump and turbine equations
•
For a pump or compressor rotor running at angular velocity , the rate at
which the rotor does work on the fluid is,
•
where the blade speed U =r.
•
Thus the work done on the fluid per unit mass or specific work is
•
This equation is referred to as Euler’s pump equation.
•
For a turbine the fluid does work on the rotor and the sign for work is then
reversed. Thus, the specific work is
•
This equation is referred to as Euler’s turbine equation.
26
Euler’s pump and turbine equations
•
In a compressor or pump the specific work done on the fluid equals the rise in
stagnation enthalpy. Thus, combining eqns,
and
We, have
•
This relationship is true for steady, adiabatic and irreversible flow in
compressors or in pump impellers.
•
Euler’s pump or compressor equation.
27
Euler’s pump and turbine equations
•
Euler’s pump compressor equation.
•
A change in total enthalpy is equivalent to a change in tangential flow speed
and/or tangential engine speed
•
For engines with little change in mean radius U2 = U1 (e.g. axial turbines, axial
compressors, fans) the change in total enthalpy is entirely due to change in
tangential flow speed h0 = Uc → blades are bowed.
•
For engines with large change in mean radius (e.g. radial engines) the change in
enthalpy is to a large degree due to the change in radius h0 = UĈ centrifugal
effect, possibility for larger change in enthalpy.
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