Lecture 11

1
Lecture 11 Performance of simple cycles

• The off-design problem
• Off-design operation for
• the single shaft engine
• free turbine engine
• the jet engine
• Design Task 3 description

2
The off design problem

• Chapter 1-3 describes the (on) design problem
• Downstream engine components are adapted to
  upstream. For instance
• Turbine pressure ratio is selected to deliver
  power required by compressor
• Exhaust nozzle is sized to swallow flow exiting
  from turbine

Design rubberengines
Every point correspondsto new engine design -
new turbine/compressor blading nozzle areas etc
3
The off design problem

• What happens when control signals are changed
  such as
• Fuel flow
• Nozzle exit area
• Compressor variable geometry
• Conservation of mass flow, energy and
  turbine/compressor rotational speed compatibility

Shows proximity to surge line
Operating space reduced to an equilibrium
runningline
4
The off design simulation - component models

• Component performance
• Semi-empirical models
• Models with some constants set by measurements
  or design experience. Ex
• Scaled maps
• Existing performance maps are scaled to new
  design point.
• Data from component rig tests
• Higher order models (2D or 3D simulation)

Obtained from experiments
5
The off design simulation - component models

• Engine system model is built by its component
  models
• Iteration is frequently required to determine
  the running line
• Some engine specific algorithms are found in
  chapter 8 and 9.

6
Part load importance

• Aircraft
• High. Taxiing and landing.
• Power generation
• Low (except for ambient conditions). However,
  surge free starting and shut down as well as
  time to max. power is important.
• Naval
• High. Poor gas turbine part load performance has
  given rise to a number of combined cycles
• CODOG, COSAG, COGAG
• Vehicular gas turbine
• High.

WR21 better fuel efficiency than simple cycle
1 fuel efficiency idle
7
Layout types to be studied off design

• Single shaft engine
• Free turbine engine
• Jet engine

Poses the same restriction on upstream
components
8
Off-design of single-shaft engine

• Select a constant speed line on compressor
  characteristic. Reading of point gives

• By approximating the fuel flow as equal to
  bleeds, compatibility of flow gives

• Turbine pressure ratio is obtained from (neglect
  inlet and exhaust losses)

9
Off-design of single-shaft engine

• The turbine rotational speed is now obtained

• Rotational speed and corrected mass flow gives
  turbine efficiency from turbine map.
• The power output is then

10
Off-design of single-shaft engine

• We have now determined the power output
  corresponding to the selected point in the
  compressor map.
• Does it match the load?

Performance problemexam 2003
11
Gas generator performance
Free turbine engine
Derive common procedure for bothengines -
GAS GENERATORmatching!
Poses the same restriction on upstream
components
Jet engine
12
Off-design of gas generator

• Select a constant speed line on compressor
  characteristic. Reading of point gives

• By approximating the fuel flow as equal to
  bleeds, compatibility of flow gives

• Turbine pressure ratio is relatedto (neglect
  inlet and exhaust losses)

13
Off-design of gas generator

• Guess turbine pressure ratio and proceed as
  usual

Verify assumption with power balance
14
Off-design of gas generator and load

• Every point on compressor rotational speed has a
  matching point, but only one of these will match
  the exhaust nozzle/free turbine!!!
• A simple nested iteration will do

match_load DO match_gas_generator DO ! gas
generator simulation code END DO
match_gas_generator !
load check simulation code END DO match_load
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Off-design of free turbine engine - load match

• For the free turbine we obtain acorrected mass
  flow as input

where
Do they match ??

• The free turbine pressure ratio is obtained from
  (power turbine exit pressure is approximately
  pa)

16
Off-design of jet engine

• The characteristics of the turbine nozzles are
  the same as the exhaust nozzle gt we have already
  solved the problem
• Use same procedure but check with exhaust nozzle
  characteristic instead of turbine characteristic!

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Design Task 3
Klassens, Wood, Schuman Experimental
Performance of a . Centrifugal Compressor
Designed for a 61 Pressure RatioNASA TMX-3552
1977
You receive a Start Kit which contains
characteristics Start by solving warm up task
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Design Task 3 two nested iterations
Gasgen.
Odp.m (off-design performance)
Turbojet.m
Gasgen.m

• Start with inner loop gas generator
• Check that you get (T3/T1)work(T3/T1)flowwhen
  you run with Design Task 1 data
• Then solve inner loop with fminbnd and continue
  with outer

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Design Task 3

• Predict off-design T5,Thrust and SFC
• Determine engine conditions at 500 mph and 30000
  feet

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Use of fminbnd

• Minimize a function of one variable on a fixed
  interval. Syntax
• x fminbnd(fun,x1,x2)
• x fminbnd(fun,x1,x2,options)
• x fminbnd(fun,x1,x2,options,P1,P2,...)
• Start by solving test example Fig217_test, that
  is make sure that you obtain fa 0.01452 for
  t02482.0 and t031046.0. (faair 0.0, fastoch
  0.06760, Qnet43200000 ) Make sure you
  understand the manual for fminbnd.

Solve non-linear 1D equation by minimization fa
fminbnd('fa_err',faair,fastoch,,t02,t03,Qnet)

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Use of non-dimensional numbers
function mfp4_err Turbojet(rc,i,pa,P01,T01,eta_t
,eta_m,eta_j,deltaP_b,A3,A5,
gamma_a,gamma_g,cp_a,cp_g,R) mcorr1,eta_c,ncorr1
CompChar(i,rc) p02 rcP01 p03
p02(1.0-deltaP_b) r_b p03/p02 theta
T01/288.15 delta P01/101325.0 m
(mcorr1delta)/sqrt(theta) mfp1
msqrt(T01)/P01 ..
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Approximation for two turbines in series

• For the gas generator exit we have

Typically, variation in turbine efficiency
will be limited
we can plot outflow and inflow in same turbine
map!
Same effect with nozzle downstream of
gas-generator turbine!!!
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Theory 11.1 Simplified turbojet running line
The compressible continuity function (x-function)
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Theory 11.1 Simplified turbojet running line
Assume that both exhaust nozzle and turbine
operate choked
Exhaustnozzle
Nozzle choked andefficiency approx. const. gt
temperature and pressure ratio is constant over
turbine
If the exhaust nozzle operates choked, the
turbine will remain in the same non-dimensional
point! Assuming a fixed efficiency gt
temperature ratio will then remain constant.
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Theory 11.1 Simplified turbojet running line
Finally, a work balance will be introduced
The compressor pressure ratio is obtained from
Combining yields
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Theory 11.1 Simplified turbojet running line
Combining the two equations yield
We have derived an explicit expression for the
running line!!!
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Learning goals

• Master algorithms for calculating performance
  for
• Single shaft engine
• Jet engine
• Free turbine engine
• Know how to derive an expression for the running
  line as well as to state the requirements for
  this expression to hold