1

GAS TURBINESA gas turbine is a device used to develop power from asource of high pressure gas, using aerodynamic meansas opposed to positive displacement.

Two methods may be used:-(i) Accelerate the gas in a nozzle and deflect it against aset of rotating vanes (impulse):

Obviously, in order to run continuously, a continuoussource of high pressure gas is required. This requires acompressor and the power to drive it.The turbine can be used to drive the compressor butunless extra energy is provided there would not beenough power available from the turbine to drive thecompressor let alone have any left over.Energy is therefore supplied in the form of heat to'expand' the compressed gas and obtain a net positiveenergy output.

(ii) Accelerate the gas within a passage and use thereaction force to rotate the passages:(reaction)

In practice a mixture of both types is used in what isknown as impulse-reaction blading.

2

THE IDEAL JOULE CYCLE

Gas is compressed isentropically, heated at constantpressure then expanded isentropically

Wnet = |Wturb| - |Wcomp|

= mcp(T3-T4) - mcp(T2-T1))

Specific work output: wnet= cp(T3-T4) - cp(T2-T1)T2T1

(1- rp ) - (rp -1)

g-1 gp2

p1But ( ) = ( ) and ( ) = ( ) = rpT3T4

p2p1

g-1 g

.

.. .

. .

1-g g

g-1 g

g-1 g

substituting for T2/T1 and T4:

wcpT1

T3T1

12 3 4

T

s1

2

3

4

COMPRES TURBINE

HEATING(COMBUSTION)

Power output: Wnet

p1

p2

= ( - ) - ( - 1 )T4T1

T2T1

T3T1

wcpT1 =

3

It can be seen that for every value of T3/T1 there is anoptimum pressure ratio for maximum specific workoutput.

It can be shown that maximum specific work output isobtained when:

rp =( )T3T1 g2(g-1)

Specific work is related to the physical size of the GT.If the GT is designed with a low specific work for agiven actual power output it has to be made larger inorder to 'swallow' more air.

00.20.40.60.8

11.21.41.61.8

0 10 20 30

ND

Spe

cific

Wor

k

Pressure ratio

T3T1

2

3

4

5

4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40

Thermal Efficiency(hth)

m cp (T3 - T2)

Again = rp and = rpg-1 g

T2T1

..

hth = 1 - 1rp

g-1 g

\

hth = = m cp (T3-T4) - m cp (T2-T1)WQ

...

T3T1

T4T1( - ) - ( - 1)

T3T1

T2T1

=-

T2T1

T3T4

g-1 g

T4T1

T3T1

T2T1( - ) - ( - 1)

T3T1

T2T1

=-

= 1 -T3T1

T2T1-

T4T1 - 1

substituting for T2/T1 and T4:

Pressure ratio

Ther

mal

effi

cien

cy

5

IRREVERSIBILITY EFFECTS

In practice isentropic compression and expansion is notpossible. We therefore introduce the isentropicefficiencies of compression and expansion.

For a compressor the isentropic efficiency is defined as :

hc = isentropic power inputactual power input

m cp (T2' - T1)m cp (T2 - T1)

(T2' - T1)(T2 - T1)

.

.=

T2' is the (theoretical) ideal temperature reached byisentropic compression.For an isentropic process we know that :

and for a perfect gas we know that :

pvT

pv = constant

= constant

gor p1v1 = p2v2'

p1v1

T1

p2v2'

T2'

g g

=or

Eliminating v1 & v2 gives:

T2'T1

p2p1

g-1 g

=( ) = rpg-1 g

hc = (i)

(ii)

From (i) & (ii) above:-

T2T1 = 1 + (rp -1)

g-1 g1

hc

\

6

For a turbine the isentropic efficiency is defined as:

actual power outputisentropic power poutput

ht =

m cp (T3 - T4)m cp (T3 - T4')

(T3 - T4)(T3 - T4')

.

.=

ht =i.e.

The expressions forspecific work and thermalefficiency remain unchanged, so we can substitute in:

T2T1

wcpT1

T3T1= ( - ) - ( - 1 )

T4T1

giving:

T3T4'

p2p1

g-1 g

=( ) = rpg-1 g

(iii)

again: (iv)

From (ii) & (iv):-

= 1 -ht (1 - rp )1-g gT4

T3 NB:T4T1

T4T3

T3T1=

wcpT1

T3T1= ht (1 - rp )

1-g g - (rp -1)

g-1 g1

hc

7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 5 10 15 20 25 30

and in: 1 -T3T1

T2T1-

T4T1 - 1hth =

giving:

We can plot the variation of specific work and thermalefficiency as a function of pressure ratio andtemperature ratio.

In particular we can fix the temperature ratio and plotperformance against pressure ratio for various values ofhc andht.[A good way of doing this is to use a spread sheet]

If T3 = 1000C and T1 = 15C, T3/T1 = 4.42

and withhc = 0.85 andht = 0.90 we obtain:

- { 1 + (rp -1)}g-1 g1

hc

hth = 1 -

T3T1T3T1

{ 1 - ht (1 - rp )} -11-g g

wcpT1

hth

rp

8

It can be shown that formaximum specific work:

An expression giving the pressure ratio for maximumthermal efficiency can also be derived, but it is morecomplex than the above.

The T-s diagram changes to reflect the compressorand turbine isentropic efficiencies:

12 3 4

T

s1

2'

3

4'

COMPRESSOR TURBINE

HEATING(COMBUSTION)

p1

p2

24

The primed station numbers show thetheoretically ideal (isentropic) process end-points.

rp = (hc ht )T3T1

g2(g-1)

9

GAS TURBINE CONFIGURATIONS

Open cycle:

Closed cycle:

Free turbine:

Regenerative:

Turbo-prop:

Turbo-jet:

By-pass:

Qin

Qout.

.

Gas generator

HX