turbogas matching

8/12/2019 Turbogas Matching

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Off-design performance of gas turbines

1) Equilibrium

2) Equilibrium running line (ERL)

3) Off-design efficiency

4) Surge

5) Specific fuel consumption at part load6) Effect of ambient conditions

Matching compressor-turbine: compatibiliy of

mass flow, rotational speed, power.

All figures are taken from the reference book Gas TurbineTheory, Cohen et al., Pearson ed.


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Simple units


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Compressor and turbine characteristics


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Off-design operation of the single-shaft gas turbine


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Choose a compressoroperating point:

0101 pTm 0102 pp 01TN

Assume losses in the combustion chamber: 0203 pp

Compute the turbine pressure ratio:

010202030403 pppppp

Compute from equation 8.2 03T

Compute from equation 8.103TN

Obtain the turbine efficiency from the characteristic (fig. 8.3): t

aTT 01assuming

Off-design operation of the single-shaft gas turbine


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Compute the turbine temperature drop

/1

0403

03034

1

1 ppTTt

Compute the compressor temperature rise:

Compute the net power output:

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01

0203012

p

pTT

c

012034

1TcmTcmP pa

m

pg

Assume: aa ppTT 0101 , Compute the mass flow m

(8.3)

(8.4)

(8.5)


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Equilibrium running lines for a single-shaftgas turbine

Using the previous procedure, we have found one possible point of the equilibrium

running line with output power P. To determine a particular ERL, we need to specify

the characteristics of the load.


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Different kinds of loads

1) Hydraulic or electrical dynamometer (any admissible load)

2) Propeller (To find the ERL, take a point on the

load characteristic and match N and P on the

compressor characteristic by trial and error)

3) Electric generator (N = constant)

Propeller: the ERL is generally in the high efficiency region.

The ERL may intersect the surge line (a blow-off valve

may be needed at the rear of the compressor for

initial acceleration).

Generator: low efficiency region (the no-load line is away fromthe surge line; the generator may be accelerated to full

speed before applying the load)

3NP


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SFC for a single-shaftgas turbine

From T012 and T01 read the fuel/airratio f.

Compute the fuel mass flow as mf

and the specific fuel consumption

SFC=mf/P.

The performance depend on ambient

conditions pa and Ta.


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Off-design operation of the gas generator

Equilibrium of power: tc PP

mpg

pa

c

c

T

T

T

T

T

T

03

01

01

012

03

034

(8.6)

where is the product of the mechanical efficiencies of thecompressor and the turbine.

Equations (8.1), (8.2), and (8.6) are linked by a unique value of

the ratio which must be determined by trial and error.0103 TT

The gas generator provides a continuous flow of gas at high

pressure and temperature which can be expanded to a lowerpressure either to produce shaft work or a high velocity

propulsive jet.

m


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Iterative procedure for off-

design operation of the gas

generator


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Off-design operation of the free turbine engine

The mass flow leaving the gas generator must equal the

mass flow through the power turbine:

03034 /TT

03

04

04

03

03

03

04

04

T

T

p

p

p

Tm

p

Tm

03

034

03

04 1T

T

T

T

(8.7)

where and is given by (8.3)

Moreover,03

04

02

03

01

0204

p

p

p

p

p

p

p

p

a (8.8)

/1

0403

03034 11pp

TT t


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Iterative procedure for off-

design operation of the free

turbine engine

The running line of a free turbine

engine is independent of the load

and is determined by the

swallowing capacity of the

power turbine. This is opposite tothe behavior of a single shaft

engine whose running line is

determine by the load.


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Equilibrium running line for a free turbine

Better efficiency at off-design with respect to single-shaft.

At part load, mass flow is reduced whereas, for a single-shaft unit, it barely increases.

The compressor power decreases.

The lines of constant temperature represents the equilibrium points of the gas generator.


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Matching of two turbines in series (simplified procedure)

In practice the variation with N of the turbine efficiency can be neglected and

for simplicity it can be assumed that the efficiency is only function of the

pressure ratio, so that the turbine characteristic reduces to a single curve (see

figure 8.8). Therefore, from equations 8.7 and 8.3, the output mass flow curve

for the gas generator (dashed line in figure 8.8) can be obtained knowing the

curve of the turbine efficiency .)/( 0403 pptt


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Using the characteristic of the power turbine (see figure 8.8), the mass flow

coefficient at the exit of the gas generator (state 4) can be obtained (by the

mass flow conservation). In particular, the maximum pressure ratio across

the gas generator turbine (p03/p04) is determined by the chocking

conditions of the power turbine (point (a) in figure 8.8).

Furthermore, it is possible to plot the gas generator pressure ratio p03/p04

versus the compressor pressure ratio p02/p01:


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In fact:

Matching of the free turbine (simplified procedure):

Choose a compressor operating point: ( , )

p02/p01 (fig 8.9) p03/p04 (fig 8.8) m T03/p03(eq 8.3) T034/T03

Eq 8.2T03/T01

Eq 8.6verify that the gas-generator power equilibrium gives the same

value of T03/T01 (if not repeat for a different p02/p01).

0101 pTm0102 pp01TN


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Power output vs output speed (fixed ambient conditions)


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SFC vs output speed for a free power turbine

The fuel consumption is computed as in the case of the single shaft system. The

SFC depends also on the power turbine and on its speed (Np). For each

equilibrium running point and Np, the SFC is computed and plotted as in figure8.11.

The SFC increases as the power output is reduced since the reduction of the fuel

flow leads to a reduction of the compressor speed and, therefore, to a reduction of

the turbine inlet temperature. This poor part load efficiency is one of the major

disadvantages of the simple gas turbine.


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Key variables vs gas generator speed


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Single-shaft vs free turbine

Driving a generator (constant speed).

Reducing the power (fuel flow reduction):

Single shaft: mass flow slightly increases (fig. 8.5); efficiency reduces (fig.

8.5); pressure ratio reduces (fig. 8.5); temperature rise remains unchangedcompressor power is unchanged.

Free turbine: compressor speed reduces (fig. 8.7); mass-flow and pressure

ratio reduce (fig. 8.7); efficiency is almost unchanged (fig. 8.7);temperature

rise reducescompressor power reduces.

Cogeneration plant (mechanical power plus thermal power).Reducing the power (fuel flow reduction):

Single shaft: since mass flow and compressor power are almost constant (fig. 8.5

and comments above)large decrease in exhaust temperature.

Free turbine: smaller decrease in exhaust temperature due to the decrese of

compressor power.

The choice depends on the characteristics of the load. With constant speed load,

as an electric generator, a single shaft unit is usually chosen. An alternative is an

aeroderivative unit with a free power turbine in the place of the propelling nozzle.


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Torque characteristics: single-shaft vs free turbine

Reducing the load rotational speed:Single shaft: the compressor speed reduces since it is coupled (by a fixed ratio)

to the load speed;mass flow reduces (from the compressor characteristic)

the output torque reduces (see curve (a) in fig. 8.13.

Free turbine: output power (P) remains almost constant over a wide load

speed range at constant compressor speed (fig. 8.10) (this because the mass flow

of the compressor is almost constant at constant speed);

if the load speedreduces the output torque must increase (P=C), see curve (b) in fig. 8.13.

The torque characteristics are very different. It is important for some kinds of

applications, for example, for traction purposes a high starting torque is needed.

The dashed line is the torque curve

of a reciprocating internal

combustion engine.


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Influence of ambient conditions

This example shows the influence of the ambient conditions on the performance.

In particular, at constant speed, a decrease of the ambient temperature T01

induces a reduction of the maximum cycle temperature (from 1200 K to 1163

K) even if T03/T01 increases due to the increase of N/T01.

The power output increases due to the increase of the mass flow and of the

pressure ratio p03/p01. Conversely, an increase of the ambient temperature

reduces the power output.

For peak power requirements during summer, it could be useful to cool the air

entering the gas turbine by evaporative coolers or by refrigerator chillers which

produce overnights large quantities of ice.


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Displacing the equilibrium running line

With most modern compressors, surge is likely to be encountered at low values of

N/T01. Many axial compressors exhibit a kink in the surge line as shown infigure 8.19 (see also fig. 5.42). To overcome this problem it is possible to:

1) Raise the surge line by using variable stators in the compressor(see figure5.44) and decreasing 1.

2) Lower the equilibrium running line by using either variable area power-

turbine statorsor a blow-off valve.


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Variable area power-turbine stator (PTS)

Assume, for simplicity that we are in the high-speed region where constant speed

lines on the compressor map are almost vertical (mT01/p01=const.) and whereboth the gas generator turbine (GGT) and the power turbine nozzles are chocked.

Figure 8.20 shows that increasing the area of the PTS an increase in the GGTpressure ratio is obtainedan increase of the non-dimensional temperature drop

T034/T03.


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Variable area power-turbine stator (PTS)

The area of the power turbine stators can be controlled so that the turbine inlet

temperature T03/T01 is maintained at its maximum value as shown in figure 9.5:

the area is decreased with the speed N/T01. If the running line at maximum

temperature moves to intersect the surge line at low speeds, it then becomesnecessary to reopen the stator for this part of the running range (see fig. 9.5).

Increasing the stator area is also advantageous with respect to starting and

accelerating the gas generator.

Bl ff


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Blow-off

Using a blow-off valve, m1>m3, therefore

1

3

01

03

11

3

033

03

01

03

03

02

01

011

01

02

m

m

T

T

Km

m

Tm

p

T

T

p

p

p

Tm

p

p

With the power turbine remaining chocked, the GGT operating point

remains unchanged. From the compatibility of work, eq. 8.6, one has:

3

14

034

03

01

012

3

1

01

03

m

mK

c

c

T

T

T

T

m

m

T

T

mpg

pa

Using the blow-off valve, m3 is smaller than m1 and the reduction of the

compressor pressure ratio will lower the running line. Since m3 decreases, the

second equation above shows that the turbine inlet temperature increases in

order to match the compressor power.

415

1

35

01

02 KKKwithm

mK

p

p

where K4 is a constant if we assume that T012/T01 is constant for a givenvalue of N/T01. Combining the equations above, one obtains:


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turbogas matching

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