Turbine Fundamentals

12/2006 School of Marine Science and TechnologySchool of Marine Science and TechnologyUniversity of NewcastleUniversity of Newcastle

GAS TURBINE DESIGN FUNDAMENTALS


GAS TURBINE DESIGN FUNDAMENTALSLearning 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;



CentrifugalTurbine andcentrifugalcompressor



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


(Illustration © Rolls-Royce Ltd., 1969)


GAS TURBINE DESIGN FUNDAMENTALScompressors

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


GAS TURBINE DESIGN FUNDAMENTALScompressors


GAS TURBINE DESIGN FUNDAMENTALSBurners

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.



• 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.


GAS TURBINE DESIGN FUNDAMENTALSTurbines

• There are two basic types of turbines, comparable to the two types of compressors. Due to the sizable stresses involved, the radialturbine 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 may be of the impulse or reaction type depending on rotor blade design.



(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.


GAS TURBINE DESIGN FUNDAMENTALSGT PTO


GAS TURBINE DESIGN FUNDAMENTALScomplex power system



Calculations exercisesExample 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

γγ



2

2

0vhh +=

02,23,2301 hWQh ININ =++

( )12010212 TTChhW p −=−=

( )2323 TTCQ p −=

( ) ( )( )23

1243

23

3412 )(inputheat

net workTTC

TTCTTCQ

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

TT

TT

PPk ==⎟⎟⎠

⎞⎜⎜⎝

⎛=

−γγ

( ) ( ) ( )( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

−=−=−

−−=

−−−−

= γγ

η1

23

23

23

23 11111 rkTT

kTTTT

kTkT

1

2

PPr =

1

3

TTt =

( ) ( )1243 TTCTTCW pp −−−=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛−=

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

1111

1

γγ

γγ

rrtTC

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)


GAS TURBINE DESIGN FUNDAMENTALSPlotting 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 exercisesExample 2


Example 2A 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


GAS TURBINE DESIGN FUNDAMENTALSrecuperated 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

TT

t =

The ideal cycle efficiency is then a function of both pressure ratio and the temperature ratio


GAS TURBINE DESIGN FUNDAMENTALSAs 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).


GAS TURBINE DESIGN FUNDAMENTALS 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 streamline2 - By consideration of the overall power input (Euler equation) resulting from the change in angular momentum across the rotor.



( )2 2

1 101, 01 01 1 12 tan

2 2 2rel ap p p

C V UT T T U CC C C

α= − + = + −

1

01

,01

01

,01−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

γγ

TT

PP 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).



relrel TT ,01,02 =

( )2 2

2 202 02, 02, 2 22 tan

2 2 2rel rel ap p p

V C UT T T U CC C C

β= − + = + −

( )02 01 1 1 2 2tan tana ap

UT T U C CC

α β= + − −

relrel PP ,01,02 =

102 02

01 01

P TP T

γγ −⎛ ⎞

= ⎜ ⎟⎝ ⎠

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:



V1 Air relative velocity

Ca1Axial velocity component

C1Axial velocity component

U Blade velocity

α, β fluid angles


GAS TURBINE DESIGN FUNDAMENTALS 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.



)2

()2

( 5

25

55...

4

24

44.

zvhmWQzvhm ++=++++

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⇒

⇒

⇒



04

05

0404

04

05

)1(

1

p

p

p

fb

CC

f

TChf

TT

+

+

=

η

Burner temperature ratio Nomenclature:T04 = Stagnation temperature at inlet to combustorT05 = Stagnation temperature at outlet from the combustorηb= Adiabatic efficiencyhf= Calorific value of fuelCp04= Specific stagnation heat capacity at inletCp05= Specific stagnation heat capacity at outletf = Fuel air ratio



Graph for estimatingthe gases temperature at thecombustor outlet for a variety of fuels


GAS TURBINE DESIGN FUNDAMENTALS Turbines


GAS TURBINE DESIGN FUNDAMENTALS Turbine

• As with the compressor, we can trace the variation of temperature through the turbine using velocity triangles.

( )202

22

22

02,02 tan2222

αaxppp

rel CUCUT

CV

CC

TT −+=+−=

1

02

,02

02

,02−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

γγ

TT

PP relrel

relrel TT ,02,03 =if uncooled


GAS TURBINE DESIGN FUNDAMENTALS Turbine

( )3,03

23

23

,0303 tan2222

βaxp

relpp

rel CUCUT

CC

CV

TT −+=+−=

( )320103 tantan βα axaxp

CCUCUTT −−+=∴

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−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

γγ

TT

PP

02 01,

02 01is T

isen s

T TWW 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.


GAS TURBINE DESIGN FUNDAMENTALSLeading 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.


GAS TURBINE DESIGN FUNDAMENTALS Turbine blade cooling

Cooling is provided by:1 - convection inside the blade2 - impingement of air jets inside the NGV3 - convection within film cooling holes4 - an insulating “film” of air around the outside the aerofoils.


GAS TURBINE DESIGN FUNDAMENTALSTurbine 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


GAS TURBINE DESIGN FUNDAMENTALSCOMPRESSOR 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.


GAS TURBINE DESIGN FUNDAMENTALSaxial flow compressor map


GAS TURBINE DESIGN FUNDAMENTALScentrifuge 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.


GAS TURBINE DESIGN FUNDAMENTALS• 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.

Turbine Fundamentals

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