Turbine Fundamentals

12/2006 School of Marine Science and TechnologySchool of Marine Science and Technology
University of NewcastleUniversity of Newcastle
GAS TURBINE DESIGN
FUNDAMENTALS

GAS TURBINE DESIGN FUNDAMENTALS
Learning goals
• This unit is dedicated to gas turbines and
students are expected to gain knowledge and
understanding of:
Gas turbine theory,
Design fundamentals;
Practical considerations of gas turbines;
Gas turbine comparison.

• Gas turbines have been gradually evolved on
the dominant main propulsion and ship-service
prime movers for destroyers, frigates, cruisers
as well as the foil-borne engines for hydrofoil
crafts.

• A gas turbine is a rotodynamic machine which
uses a gas compression – combustion –
expansion cycle. It differs from a reciprocating
internal combustion engine in that:
1 - The compression and expansion is
performed using rotodynamic components
2 - The combustion takes place at constant
pressure

• GT are characterised by:
– High power to weigth ratios;
– Lower thermal efficiency;
– High output shaft speed;
– Better quality fuels;
– High air to fuel ratios;
– High power to volume ratios;
– High availability;
– Lower exhaust gas emissions;

Centrifugal
Turbine and
centrifugal
compressor

• The Centrifugal Compressor
The centrifugal compressor consists of an
impeller enclosed in a casing which contains the
diffuser.

(Illustration © Rolls-Royce Ltd., 1969)

compressors
(Reprinted with permission of copyright owner, United Technologies Corporation)

compressors

Burners
About 15-20% of the air from the compressor passes over swirl vanes as it enters the primary zone of the burner. Here
also the fuel is introduced through nozzles as a fine spray of droplets. The swirling air causes the good mixing
necessary to support rapid, high temperature combustion.

Burners

Burners
• The annular burner is well-suited for an axial
flow compressor. It is shown in the air
distribution pattern in this type may involve
introduction of the compressor air in only the first
two zones. The tertiary zone may involve final
mixing only. The advantage of this type of
burner is that it minimizes size and weight
with a sound aerodynamic design.

Turbines
• There are two basic types of turbines,
comparable to the two types of compressors.
Due to the sizable stresses involved, the radial
turbine is generally not suitable for the high
temperatures necessary in a gas turbine engine.
Therefore, the axial flow turbine is the only type
that will be discussed here. (See slide nº7)

Turbines

Turbines
• Turbines may be of the impulse or reaction type
depending on rotor blade design.

Turbines
(a) Impulse turbine rotor blades -
The flow passages are of constant
cross--sectional area resulting in
essentially no flow speed,
pressure, or temperature change.
Those changes occur in the
stationary blades (nozzles). The
turning of the flow causes the
rotor to move.
(b) Reaction turbine rotor blades -
The blades act as nozzles to
accelerate the flow as pressure
and temperature decrease. These
processes take place in both the
stationary and moving blades.

GT PTO

complex power system

Calculations exercises
Example 1

Example 1
A gas turbine unit has a pressure ratio of 10:1 and a
maximum cycle temperature of 700ºC. The isentropic
efficiencies of the compressor and turbine are 0.82 and 0.85
respectively.
Calculate the power output of an electric alternator geared to
the gas turbine when the air enters the compressor at 15ºC
at a rate of 15kg/s.
Take Cp=1.005 kJ/kgK and = 1.4 for the compression
Take Cp=1.110 kJ/kgK and = 1.333 for expansion
γ
γ

2
2
0
v
hh +=
02,23,2301 hWQh ININ =++
( )12010212 TTChhW p −=−=
( )2323 TTCQ p −=
( ) ( )
( )23
1243
23
3412 )(
inputheat
net work
TTC
TTCTTC
Q
WW
p
pp
−
−−−
=
+−
==η
The steady flow energy equation applies to each component of the turbine. Defining
stagnation enthalpy
one can analyse the compressor, for instance, using:
In the idealised cycle there is no heat transfer during compression and
expansion so (for instance) the specific work (per kg of fluid)
Similarly there is no work done in the combustion chamber so
The efficiency can then be calculated using

3
4
2
1
1
2
1
T
T
T
T
P
P
k ==⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
−
γ
γ
( ) ( ) ( )( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
−
−=−=
−
−−
=
−
−−−
= γ
γ
η
1
23
23
23
23
11
111
rk
TT
kTT
TT
kTkT
1
2
P
P
r =
1
3
T
T
t =
( ) ( )1243 TTCTTCW pp −−−=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
−
11
11
1
γ
γ
γ
γ
rrt
TC
W
p
Let us assume the compressor and turbine are 100% efficient (no entropy rise) and define the temperature ratio using isentropic formulae as
Substituting in equation 4.3 we have
(4.4)
where r is the pressure ratio,
The specific work output can be calculated as a function of pressure ratio r and the non-dimensional peak temperature,
i.e. turbine inlet to compressor inlet temperature.
(4.5)
so
(4.6)

Plotting these efficiency and work relationships with
pressure ratio from equations 4.4 and 4.6, we see that
efficiency rises with pressure ratio (figure 4.4)
for any given peak temperature t there will be some
pressure ratio that produces the peak specific power
(figure 4.5).
At any given pressure ratio, increasing the peak
temperature (by injecting more fuel) increases the work
output.

• In practice only the simplest gas turbines, driving electrical
generators at constant speed, extract power directly from the gas
generator shaft as in Figure 4.2. When driving any other load a
separate power turbine is desirable:
– Increases in load do not slow down the compressor
and cause a drop in pressure ratio
– The speed:torque characteristic, for a given fuel flow,
is much more stable (see figure 4.6)
– The starter can rotate the gas generator spool without
turning the load

Calculations exercises
Example 2

Example 2
A gas turbine takes air at 17ºC and 1.01bar and has a compression ratio of 8:1. The
compressor is driven by the HP turbine and the LP turbine drives a CPP via a gear
box.
The isentropic efficiencies of the compressor and turbines are respectively 0.80,
0.85 and 0.83.
Determine the pressure and temperature of the gases entering the power turbine,
the net power developed by the unit per kg/s mass flow rate, the net work ratio and
the cycle efficiency of the unit.
The maximum cycle temperature is 650ºC
For the compression process take Cp= 1.005 kJ/kgK and gamma=1.4
For the expansion process take Cp=1.15 kJ/kgK and gamma=1.333
Neglect the fuel mass flow rate.

• The efficiency of an ideal simple cycle gas turbine is
purely a function of its pressure ratio. This has two
implications:
– Efficiency is poor at part-load, when the shaft speed
and pressure ratio is lower and one is closer to the
self-sustaining point where all the fuel is used purely
to overcome component losses
– When the effect of component losses is considered,
we find that for any peak temperature there is some
pressure ratio at which the efficiency peaks: adding
further compressor stages will then reduce rather
than increase the efficiency.

• The heat exchange cycle overcomes some of these
difficulties. The main result of inefficiency in a simple
cycle is that the exhaust is hot. Providing it is hotter than
the compressor exit temperature one can use a heat
exchanger to transfer heat from the exhaust to the air
before it enters the combustion chamber: a given turbine
entry temperature can thus be achieved with a lower fuel
flow than in the equivalent simple cycle

recuperated cycle

Efficiency increases with temperature ratio
so the provision of sophisticated turbine
cooling systems is beneficial. Efficiency
also rises as pressure ratio is reduced but this
is at the expense of a drop in specific work so
some compromise must be found. Typically
heat exchange cycles operate with a pressure
ratio of 4 to 5 (compared with 11 to 30 for a
large simple cycle engine).
1
3
T
T
t =
The ideal cycle efficiency is then a
function of both pressure ratio and the
temperature ratio

As a further refinement the WR-21 includes an intercooler to cool the air
between the LP and HP compressor stages. This leads to a rise in specific
power, since less turbine work is required to drive the HP compressor. By
itself the intercooler would lead to a drop in efficiency (heat is being wasted);
in a recuperated cycle, however, the lower HP compressor exit temperature
means that the exhaust gases passing through the recuperator can be cooled
further and there is a corresponding rise in efficiency.

The final WR-21 novelty is that the power turbine has
variable throat area nozzle guide vanes. At low powers
in a conventional engine the combustor exit temperature
must be reduced to limit the power; with a variable area
nozzle the power can be reduced by lowering the mass
flow whilst maintaining the temperature. Compressor
surge is avoided because the gas generator turbine,
seeing a higher back pressure, generates less power so
the shaft speed and compressor pressure ratio are
reduced (which does not have a severe adverse effect
on the efficiency since this is a recuperated cycle).

Compressor theory

Compressor theory
There are basically two ways to analyse how
turbomachinery (compressors or turbines) works.
1 - Trace the changes in temperature and pressure from
one blade row to the next using velocity triangles, in
which we consider flow within each frame of reference
(stationary or rotating) to have constant total
temperature and pressure along a streamline
2 - By consideration of the overall power input (Euler
equation) resulting from the change in angular
momentum across the rotor.

Compressor theory
( )
2 2
1 1
01, 01 01 1 12 tan
2 2 2
rel a
p p p
C V U
T T T U C
C C C
α= − + = + −
1
01
,01
01
,01
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
γ
γ
T
T
P
P relrel
The “rel” suffix indicates that this is a stagnation
quantity in the rotating frame. (The total temperature as measured
by a thermocouple mounted on the rotor would be different to that
measured by a stationary one).

Compressor theory
relrel TT ,01,02 =
( )
2 2
2 2
02 02, 02, 2 22 tan
2 2 2
rel rel a
p p p
V C U
T T T U C
C C C
β= − + = + −
( )02 01 1 1 2 2tan tana a
p
U
T T U C C
C
α β= + − −
relrel PP ,01,02 =
1
02 02
01 01
P T
P T
γ
γ −⎛ ⎞
= ⎜ ⎟
⎝ ⎠
In the absence of heat transfer
.
(4.8)
If we neglect frictional losses and changes in radius
and we can apply an isentropic relationship across the whole stage:

Compressor theory
V1 Air relative velocity
Ca1Axial velocity component
C1Axial velocity component
U Blade velocity
α, β fluid angles

Combustor
• The calculation is based on the following assumptions
(figure 4.19):
– No pressure drop takes place across the combustor
i.e. burner pressure ratio P4/P5.
– Heat addition takes place under constant pressure
with no work output
– The specific heat capacity of flue gas leaving the
combustor is equal to that of hot air at the exit
temperature.
– Fuel used has got a calorific value of 42.7 MJ/kg
– Use of the steady flow energy equation with no heat
loss to the surrounding and neglecting velocity and
potential heads.

Combustor

Combustor
)
2
()
2
( 5
2
5
55
...
4
2
4
44
.
z
v
hmWQz
v
hm ++=++++
55
..
44
.
hmQhm =+
05055
.
04044
.
TCmhmTCm pffbp =+η
05054
.
404044
.
)1( TCmfhmfTCm pfbp +=+η
05050404 )1( TCfhfTC pfbp +=+η
Based on the following assumptions the general steady flow energy equation
Can be re-written as
⇒
⇒
⇒

Combustor
04
05
0404
04
05
)1(
1
p
p
p
fb
C
C
f
TC
hf
T
T
+
+
=
η
Burner temperature ratio Nomenclature:
T04 = Stagnation temperature at
inlet to combustor
T05 = Stagnation temperature at
outlet from the combustor
ηb= Adiabatic efficiency
hf= Calorific value of fuel
Cp04= Specific stagnation heat
capacity at inlet
Cp05= Specific stagnation heat
capacity at outlet
f = Fuel air ratio

Combustor
Graph for estimating
the gases
temperature at the
combustor outlet for
a variety of fuels

Turbine
• As with the compressor, we can trace the
variation of temperature through the turbine
using velocity triangles.
( )202
2
2
2
2
02,02 tan2
222
αax
ppp
rel CU
C
U
T
C
V
C
C
TT −+=+−=
1
02
,02
02
,02
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
γ
γ
T
T
P
P relrel
relrel TT ,02,03 =if uncooled

Turbine
( )3,03
2
3
2
3
,0303 tan2
222
βax
p
rel
pp
rel CU
C
U
T
C
C
C
V
TT −+=+−=
( )320103 tantan βα axax
p
CCU
C
U
TT −−+=∴
Neglecting frictional losses and changes in radius relrel PP ,02,03 =
and we can apply an isentropic relationship across the whole stage:
1
01
03
01
03
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
γ
γ
T
T
P
P
02 01
,
02 01
is T
isen s
T TW
W T T
η
−
= =
−
The turbine isentropic efficiency:

• Raising the pressure ratio by adding more compressor stages
increases the efficiency but also raises the combustor inlet
temperature: for a given metallurgical limit for the turbine entry
temperature (TET) or (TIT) turbine inlet temperature, this implies a
reduction in fuel: air ratio and hence on the specific work.

Leading particulars
"leading particulars" characterize the engine so that
potential customers can tell at a glance whether the engine
might suit their needs. Additional factors can then be
considered if the engine seems appropriate.

Turbine blade cooling
Cooling is provided by:
1 - convection inside the
blade
2 - impingement of air
jets inside the NGV
3 - convection within film
cooling holes
4 - an insulating “film” of
air around the outside
the aerofoils.

Turbine inlet temperature can be an indicator of certain design
features of the engine. Higher inlet temperatures necessitate more
sophisticated blade and vane cooling mechanisms and more heat
resistant metal components. With present technology, 980ºC –
1100ºC is commonly the maximum for continuous use;
The engine rotor speed is of importance for applications which
require gearing to electric generators, compressors, pumps, or other
direct-drive components;
The type and number of compressor and turbine stages,
pressure ratio, and air flow are mainly of informational interest. These
are rarely a determining factor in selection of an engine.
Heat Rate (HR) and/or Specific Fuel Consumption (SFC) are
often included in the engine description as a measure of engine
efficiency.

GT alternator pack
GT tandem alternator pack
GT compressor pack
GT marine propulsion pack

Main components of a gas turbine

GT maintenance

GT main performance curves

COMPRESSOR CHARACTERISTICS
• The most important compressor performance characteristics are the
pressure ratio, air flow, and rotational speed. The like-new unit has
certain physical capabilities which usually represent a maximum for
that design.
• To characterize the compressor overall operating conditions would
involve an unrealistic number of tables and/or graphs.

axial flow compressor map

centrifuge flow compressor map

• The absolute pressure ratio across the compressor is
plotted versus the equivalent flow∗ for several equivalent
speeds. The dotted lines indicate efficiency levels.
• The equivalent speed and flow (sometimes called
corrected speed and flow) refer to the rotational speed
and air flow corrected for inlet temperature and pressure.
∗ Several terms, including "referred," "corrected" and
"equivalent" flow and speed are in general use.
Equivalent flow and speed are the terms used in this
course.

• Surge is a damaging process which should be avoided if at all
possible, and choke (maximum) flow represents a condition of
lowered efficiency as concerns the compressor.

• The following generalizations should be kept in mind when
evaluating compressor performance (at a given speed) with the aid
of a map:
An increase in pressure ratio moves the compressor closer to
surge.
A decrease in pressure ratio moves the compressor toward
maximum flow (choke). For ambient temperature below 15°C, the
equivalent speed is greater than actual, and above 15ºC, it is less
than actual.
An increase in pressure ratio is accompanied by a decrease in
mass flow.

• Considering the fact that under full load
conditions, approximately 2/3 of the turbine
power goes toward running the compressor. For
this reason, a 5% loss in compressor efficiency
can cause as much as 10% loss in overall
efficiency!
• Another possible source of inefficiency is the air
filter. Inlet air filters are generally used in
non-aircraft gas turbines.

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