Principles of Energy Conversion
NAVEEN H E
Department of Mechanical Engineering
UNIT-5 Principles of Turbomachinery
Class-2: Thermodynamic Analysis
NAVEEN H E
Department of Mechanical Engineering
Principles of Energy Conversion
Class 2 : Contents
• Static and Stagnation states
• Applications of 1st law of TD to turbomachines
• Applications of 2nd law of TD to turbomachines
Principles of Energy Conversion
Static and Stagnation States
Static state:
Fluid at rest is said to be in a static state properties measured
of fluid at rest are called static properties
Note: In a turbo machine we only deal with moving fluid.
Principles of Energy Conversion
Static and Stagnation States
The Stagnation or Total State: The stagnation state is defined as the
terminal state of a fictitious, isentropic, work-free and steady-flow
process during which the macroscopic kinetic and potential energies
of the fluid particle are reduced to zero, the initial state for the process
being the static state.
Note: Even though stagnation state can never be achieved by any real
process, it is very important concept in the analysis of turbo machine
Pitot static tube
Wall pressure tap
Principles of Energy Conversion
Application of 1st law of TD
1st law of Thermodynamics for a steady flow machine and
determination of stagnation properties
(V2  V1 )
q  w  (h2  h1 ) 
 g ( z2  z1 )
2
2
2
Applying this for the analysis of turbo machine, we arrive at
stagnation state. We may write,
(V02  V 2 )
q  w  (h0  h) 
 g ( z0  z)
2
Where the subscript ‘0’ refers to the stagnation state.
Hence, we have h0, V0, z0 are the stagnation properties,
h, V, and z are the static properties.
Principles of Energy Conversion
Application of 1st law of TD
But we know that in this process
q  0, w  0, V0  0, gz 0  0
V2
0  h0  h 
 gz
2
V2
Thus stagnation enthalpy h0  h 
 gz
2
Stagnation entropy
s0  s
Since the process is isentropic
Principles of Energy Conversion
Application of 1st law of TD
For a closed system
Tds  dh  vdp
ds  0
There fore,
dh  vdp
p0
h0  h   vdp
p
r.h.s.may be integrated only if the relationship between ‘v’&’p’ is known.
Principles of Energy Conversion
Application of 1st law of TD
h0  h  v( p 0  p )
For an incompressible fluid,
The term
v 2
2
p 0  p   (h0  h)
p 0  p   (h0  h)
V2
p 0  p   [( h 
 gz )  h]
2
is the pressure equivalent of velocity.
‘ρgz’ which is the pressure equivalent of height can be neglected
since it is very small compared to other terms.
2
Hence we can write, Stagnation pressure p  p  v
0
2
According to first law of T.D , the stagnation enthalpy and
stagnation pressure should be constant along any streamline
which experiences no energy transfer as heat or as work.
Principles of Energy Conversion
Application of 1st law of TD
For a change from static to stagnation state of an incompressible
fluid since there is no entropy change and
pdv = 0
T.ds = du + p.dv
Which yields du = 0.
Hence, u = u0, the internal energies of an incompressible fluid in
the static and stagnation states are equal.
u = u0
cT = cT0
so, T = T0
Principles of Energy Conversion
Application of 1st law of TD
Perfect gas:
We have
h0  C PT0
h  C PT
Substituting in expression for stagnation enthalpy and rearranging
V2
gz
T0  T 

2CP Cp
The term
gz
CP
which may be called temperature equivalent of height is negligible
compared to other terms and may be neglected.
V2
Stagnation temperatu re T0  T 
2Cp
Principles of Energy Conversion
Application of 2nd law of TD
Apply the steady flow energy equation for the analysis of turbo machine.
V22  V12
q  w  (h2  h1 ) 
 g ( z 2  z1 )
2
It is also true that, thermal loses are minimal compared to the amount of
work transferred & hence may be neglected. Hence we may write,
V22
V12
w  (h2 
 gz 2 )  (h1 
 gz1 )
2
2
 w  (h02  h01 )
Where, h02 & h01 are stagnation exit & entry respectively.
- w = ∆h0.
In a power generating turbo machine, ∆h0 is negative
(since h02 <h01 ) & hence w is positive.
for a power absorbing turbo machine, ∆h0 is positive
(since h02>h01) &hence w is negative.
Principles of Energy Conversion
Application of 2nd law of TD
From the 2nd law of Thermodynamics:
Tds  dh  vdp
 dw  vdp  Tds
2
w    vdp   Tds
1
In the above relation, we note that vdp would be a negative quantity
for a power generating turbo machine
& positive for power absorbing turbo machine.
Hence Tds which is always a positive quantity would reduce the
amount of work generated in the former case & increase the work
absorbed in the later case.
THANK YOU
NAVEEN H E
Department of Mechanical Engineering
naveenhe@pes.edu