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Jet Engine Operation As An Integrated System INME5702 Class 2

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Title: Jet Engine Operation As An Integrated System INME5702 Class 2


1
Jet Engine OperationAs An Integrated
SystemINME5702Class 2
2
Agenda for Class 2
  • Dimensional Analysis
  • Compressor and Turbine Representations ( Maps )
  • Compressor and Turbine Processes
  • Adiabatic Compression
  • Adiabatic Expansion
  • Energy Balance
  • Burner Pressure Loss
  • Homework 1

3
Dimensional Analysis
  • Process of reducing the number of variables in a
    problem by appropriate combinations of basic
    variables.
  • The object may or may not be to create
    dimensionless variables, but it is always to
    create appropriately scaled variables and to
    reduce the problem to the minimum number of
    variables required to adequately describe the
    problem.
  • Compressor and Turbine Maps are two examples of
    the output of the Dimensional Analysis.

4
Compressor
The compressor consists of alternating rows
of rotors ( rotating air foils ) followed by
stators ( stationary air foils ). Each row or
stage increases the pressure of the incoming
fluid by Imparting tangential velocity to
the flow ( turning ). Converting the
new kinetic energy to pressure ( diffusing )
while straightening the flow, i.e., turning it
back toward the axial direction.
5
Compressor Parameters
W , Rotational Speed, rad/s
W, Mass Flow, lbm/s
Pi, Inlet Pressure, psia Ti, Inlet Temperature, R
Po, Outlet Pressure, psia
D, Characteristic Diameter, in hC, Adiabatic
Efficiency Design, i.e., entire geometry
expressed in terms of D.
Fluid Properties g, Ratio of
Specific Heats R, Gas Constant, lbm-ft/lbf-R
n, Kinematic Viscosity
6
Compressor Governing Relation
Nine variables govern the behavior of the
compressor. Can we simplify the task of testing
and modeling the behavior of the compressor by
combining variables ?
7
Can we simplify the task of testing and modeling
the behavior of the compressor by combining
variables ?
  • The answer is yes.
  • How ?
  • Guess ( intelligently, i.e., using reason ).
  • Write governing equations ( if possible ) and
    nondimensionalize.
  • Buckinghams Pi Theorem.
  • We will use the first method.

8
Ideas ?
9

Think in terms of F ma What does this idea
suggest ?
10
F ma PipD2 WV , ratio of
Force/Momentum

What about the remaining variables ?
11
W, rotational speed, multiplied by D gives a
velocity. WD , ratio of velocities.

12

n, Kinematic Viscosity, suggests Reynolds Number
13
n, Kinematic Viscosity, suggests Reynolds Number
14
Now the compressor governing relation is reduced
to five variables. For a given design and working
fluid, we can assume that g, R, and the
compressor geometry and Design are captured in
our compressor testing so the governing relation
now has three variables
15
If we further assume that Reynolds effects are
either negligible or of second order importance,
we then reduce the governing equation to a
function of 2 variables with efficiency as a
parameter
Introducing constants does not alter the
character of the functional relationship between
the variables, and it is customary to use
normalized temperatures and pressures on the
right hand side
16
So we arrive at the appropriate general
representation of compressor performance
The compressor map relates Compressor Pressure
Ratio and Efficiency to Compressor Inlet
Corrected Flow and Inlet Corrected Speed. The
representation is general in the sense that it is
true for any combination of inputs W, Ti, Pi, N.
17
Compressor Map
18
Example
If W, Ti, Pi, and N, are at these percentages of
their design values W 90 Ti 90 Pi 94.8
N 91.1 what are the Pressure Ratio and
Efficiency of the compressor represented in the
previous slide ?
19
Wc ( Design ) 0.9 (0.9)0.5 / .984 0.90
Example Solution
Nc ( Design ) 0.911 / (0.9)0.5 0.96
From the map at these coordinates Pressure
Ratio 4.3 Efficiency 90
20
Turbine
The turbine consists of alternating stators
( stationary air foils ) followed by rotors (
rotating air foils ). Each row decreases the
pressure of the incoming fluid by
Converting the incoming pressure energy to
kinetic energy ( expanding ) by turning the
flow. Extracting tangential velocity from
the flow to power the compressor. The
dimensional analysis of the turbine follows the
same reasoning as the compressor, so the
component maps are fundamentally similar.
21
Turbine Map
Note both the similarities and differences
between compressor and turbine maps.
22
Compressor and Turbine Processes
4
Recall that the energy extracted from the working
fluid by the turbine is expended in driving the
compressor.
3
5
2
h
PAMBIENT
0
S
23
Compressor and Turbine Processes
COMPRESSION
P CONSTANT
ACTUAL
T
IDEAL
EXPANSION
S
ACTUAL
T
IDEAL
S
24
Pressure Ratio Temperature Ratio Relationship
for Any Isentropic ( Ideal ) Process. For
Compression
P3
T3
REAL
T3
T
IDEAL
P2
T2
S
25
Compressor Adiabatic Efficiency
26
Turbine Adiabatic Efficiency
27
Efficiency ( Compressor or Turbine ) Relates
Ideal to Real Temperature Rise
Ideal Temperature Rise ( from previous slide )
Compressor efficiency defines relationship
between compressor pressure ratio and compressor
temperature ratio.
Turbine efficiency defines relationship between
turbine expansion ratio and turbine temperature
ratio.
28
Compressor-Turbine Energy Balance
Real Work Into Compressor Real Work Out of
Turbine ( The turbine drives the compressor )
mC cp DTC mT cp DTT ( m Mass Flow )
EXPANSION
P CONSTANT
T4
REAL
T
IDEAL
T5
T5
S
29
Burner Pressure Loss
The Burner serves to convert fuel chemical energy
into thermal energy by the process of combustion.
It is desirable to perform this conversion with
minimum loss of the pressure that has been
generated by the compression system, so pressure
loss is a major figure of merit for the burner.
We write this pressure loss as
30
Homework 1Due Tuesday, 1/23/07To be supplied
during 1/16/07 class.
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