Jet Engine Operation As An Integrated System INME5702 Class 3

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Jet Engine OperationAs An Integrated
SystemINME5702Class 3
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Agenda for Class 3

• Class 2 Review
• Flow Parameter and Choked Flow
• Combustor Energy Balance
• Nozzle Expansion

3
Class 2 Review

• We used dimensional analysis to reduce the
  representation of a general compressor from nine
  variables to five variables
• Inlet Corrected Air Flow
• Inlet Corrected Speed
• Reynolds Number
• Fluid Property ( g )
• Design ( Airfoil counts, shapes, sizes, etc.,
  i.e., a complete hardware description )
• We then assumed that Reynolds effects are of
  second order importance and we regarded the
  working fluid as fixed and known ( air ) and the
  Design as given.
• These considerations reduce the problem of
  compressor representation to two variables

4
Class 2 Review

• Turbine representation follows the same logic as
  the compressor, so their maps are fundamentally
  similar. We noted that the corrected speed lines
  on a turbine map span a much smaller range of
  corrected flow than compressor corrected speed
  lines.
• We established that compressors and turbines are
  corrected parameter devices, i.e., their output
  depends not only on the quantity of incoming mass
  flow but also on the energy content of that mass
  flow, as described by Ti and Pi.

5
Class 2 Review

• We described the processes used by the compressor
  and turbine to add and extract energy from the
  flow and defined efficiencies.
• We wrote the energy balance between the turbine
  and the compressor and defined combustor pressure
  loss.

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Flow Parameter
QUESTION HOW MUCH AIR ESCAPES ?
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QUESTION HOW MUCH AIR ESCAPES ?
V 0 Air P gt Pamb T gt Tamb
V gtgt 0 Pamb
Ptotal Ttotal
V gtgt 0 Pamb Pstatic
Converging Nozzle
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QUESTION HOW MUCH AIR ESCAPES ?
Compressible Flow Relationships Required for The
Answer Mach Number Total-to-Static
Temperature and Pressure Note P T without
subscripts denote total values. Subscript s
denotes static values. Flow Parameter
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Compressible Flow Relation Mach Number C
Speed of Sound All Gases C2 gcRTs Air
C2 1.4 x 32.2 x 53.3 x Ts
1,116 fps (Tstd,sea level 59
459.67 R) Mach No. (M) V/C
g
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Compressible Flow Relation Total/Static
Temperature T - Ts V2 / 2gcJCp
Cp constant Giving T/Ts
1 ( - 1)/2 M2
g
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Flow Parameter as Function of Mach Number

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MAJOR INFERENCES FROM FLOW PARAMETER FUNCTION
It can Be Shown (set d(FP)/d(Mn) 0 )
that FP max when M 1.0 (sonic)

Mach No
Max
? constant
Subsonic M lt1 Supersonic Mgt1
Sonic M1
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MAJOR INFERENCES FROM FLOW PARAMETER FUNCTION
Minimum Area (Throat)

Increasing Area
Decreasing Area
1.0 Mach No.
Transition to Mach Number gt 1.0 Requires
Converging-Diverging Nozzle
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x
The throat is the point of maximum flow rate per
unit area. The flow rate ( lbm/s ) is constant
throughout the nozzle. The area varies with x.
When M reaches 1.0, the maximum flow rate per
unit area has been reached.
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CONVERGING - DIVERGING NOZZLE - (IDEAL)
Throat Min area
Pt Tt
M lt 1 M 1 M gt1
Pamb
Ptot Pstatic Mach No
P Pamb (Fully Expanded)
1.0
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CONVERGING - DIVERGING NOZZLE - (NON - IDEAL)
Throat Min area
P T
M lt 1 M 1
Pamb
Ptot Pstatic Mach No
(A) Ps lt Pamb (Overexpanded) (B) Ps Pamb
(Fully Expanded)
( C ) Ps gt Pamb
(Underexpanded)
(B)(C)
1.0
(A)
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CONVERGENT NOZZLE P
Pamb

T
P/Pamb

• When the nozzle is choked, flow rate W depends on
  three variables
• Physical Area
• Upstream Total Temperature
• Upstream Total Pressure

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How Does the Concept of Choked Flow Relate to
Engine Operation ? Recall the turbine map and
its principal difference from the compressor map
Flow Parameter is nearly constant across a wide
range of both corrected speed and pressure ratio.
Flip back and forth between this and the
preceding chart.
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Over Much of Its Operating Range the Turbine Acts
Like a Choked Nozzle
P/Pamb
This is a characteristic of the turbine.
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Consequences of Turbine Choking We will assume
through most of the semester that turbine inlet
and exit and exhaust nozzle exits are
choked. What are the implications ?
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• Consequences of Turbine Choking
• We will assume through most of the semester that
  turbine inlet and exit and exhaust nozzle exits
  are choked.
• What are the implications ?
• The turbine(s) and nozzle can act as valves,
  setting flow rate through the engine.
• The turbines set the level of energy extraction
  from the working fluid ( as a function of turbine
  inlet temperature ).

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Combustor Energy Balance
Wa
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Combustor Energy Balance
If T4 is fixed then Wf is calculated from Wa and
T3.   If Wf is neglected in FP4, FP5 and turbine
energy balance, (because Wa gtgt Wf) then the
equilibrium problem solution is reduced by one
variable and one equation (thus Wf appears only
in combustor energy balance equation).
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Nozzle Expansion Process
4
We will normally assume isentropic nozzle
expansion. Dh can be calculated from nozzle
expansion ratio, P5/PAmb, since T5/TAmb is known
( How ? )
3
5
2
h
PAMBIENT
0
S
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Nozzle Expansion Process
The nozzle produces thrust by expanding (
accelerating ) the flow. Static pressure and
temperature decrease as the flow accelerates (
thermal energy is converted to kinetic energy
). If we assume the process is isentropic, then
total pressure and total temperature are
constant throughout the process. Remember from
Class 2 that we said the isentropic relationship
between pressure ratio and temperature ratio
applies to any isentropic process.
Pi
Po

Psi
Pso

Apply isentropic relation to P/Ps at the nozzle
exit plane ( next slide ).
W
Tso

Tsi
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Nozzle Expansion Process
Nozzle Thrust
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Nozzle Expansion Process

• Calculate Nozzle Thrust from
• Mass flow through the nozzle, W
• Total Temperature entering nozzle, T
• Expansion Ratio of the Nozzle, P/Ps