Effect of control modes and turbine cooling on the part load performance in the gas turbine cogeneration system

Pergamo.

Heat Recovery Systems & CHP Vol. 15, No. 3, pp. 281-291, 1995 Elsevier ScienceLtd flRq0-d~lf~klW,fl~27-H Printed in Great Britain 0890-4332/95 $9.50 + .00

E F F E C T OF C O N T R O L M O D E S A N D T U R B I N E C O O L I N G ON THE P A R T L O A D P E R F O R M A N C E IN THE GAS T U R B I N E C O G E N E R A T I O N SYSTEM TONG SEOP KIM a n d SUNG TACK R o * Department of Mechanical Engineering, Seoul National Undiversity, Seoul 151-742, Korea (Received 15 February 1994) A~traet--This work aims to analyse the part load performance in a cogeneration system which consists of a single shaft gas turbine and a heat recovery steam generator. Two distinct part load control modes are considered: the constant air flow and the variable air flow. Meanwhile, the effect of variation in the coolant fraction is evaluated, whose purpose is to maintain the blade temperature as high as possible and thus minimise the coolant consumption. The design point parameters of the heat recovery steam generator are determined by the limiting factors on the part load operation, which are represented by the pinch point temperature difference and the approach temperature difference. It turns out that for both air flow control modes, the variable control of coolant fraction leads to improvement of the gas turbine efficiency, while it reduces the heat recovery potential. On the whole, the variable control of coolant fraction has a favourable effect on the overall fuel economy in the cogeneration system.

NOMENCLATURE A ¢

Cp CC CV f h

HRSG rh P P~ PRo

0 r

TET TIT T ATLM

ATop AT~pp U VC VV

w Y

~t

7 ~c Ehr

r/c qcvc qgt qhr

r/t //tot

heat transfer area (m2) coolant fraction constant pressure specific heat (kJ kg- ~K - ~) constant air flow control with constant coolant fraction constant air flow control with variable coolant fraction fuel consumption rate for unit air flow total enthalpy (kJ kg- ~) heat recovery steam generator mass flow rate (kg s-t) total pressure (kPa) steam pressure (kPa) compressor pressure ratio recovered heat (MW) ratio turbine exhaust temperature (°C) turbine inlet temperature (°C) total temperature (°C) log mean temperature difference (°C) pinch point temperature difference (°C) approach temperature difference (°C) overall heat transfer coefficient (kW m -2 K ~) variable air flow control with constant coolant fraction variable air flow control with variable coolant fraction gas turbine power (MW) pressure loss coefficient heat transfer coefficient (kW m--' K ~) specific heat ratio cooling effectiveness heat recovery steam generator effectiveness compressor efficiency chargeable power generation efficiency gas turbine thermal efficiency heat recovery efficiency turbine efficiency total cogeneration efficiency

*Author to whom correspondence should be addressed at: Department of Mechanical Engineering, Seoul National University, Seoul 151-742, Korea. 281

282

TON~SEO~'KIMand SUNCTACKRO

Subscripts 1,2,3.... each state IN first stage nozzle a air b blade c compressor,coolant d design point ec economiser ef effectivevalue ev evaporator f fuel g gas s steam, isentropic process t turbine

1. I N T R O D U C T I O N A gas turbine engine has numerous inherent advantages compared to other combustion engines. It exhibits a large power output for its relatively small size and emits relatively low levels of environmentally harmful pollutants, especially when a gaseous fuel is used. Moreover, the thermal efficiency has been improved continuously up to as high as 35% in modern engines. In this respect, it has already been a common practice to utilise gas turbines as prime movers in industrial fields, including electric power generation. The performance of a gas turbine depends absolutely on the component performance and the efficiency drops rapidly as the load fraction decreases. Therefore, it is a decisive subject to enhance the part load performance of the gas turbine engines. The gas turbine is highly suitable to the cogeneration and the combined cycle system since it has fairly high exhaust gas temperature. The fundamentals of the gas turbine cogeneration have been well established [1, 2], while many analytical researches have been undertaken with focuses on various aspects. However, most of the studies have only focused on design point calculation and it is not common to perform the part load analysis of both the gas turbine and the heat recovery system. The performance estimation in part load operation is highly important in many applications, where the system requires frequent changes in load. Moreover, the part load simulation of the heat recovery steam generator is also of much use, in that it provides basic insights into the part load operation of the combined cycle. In general, a couple of methods are conventionally utilised to control the part load of the gas turbine. One is classical control of the fuel only and the other is control by using an inlet guide vane and/or variable vanes. In the latter case, turbine inlet temperature or exhaust temperature is maintained at design value in the part load operation, as far as air flow reduction is possible, and thus the heat recovery increases [2, 3]. In reality, the decisive factor which affects the turbine inlet temperature is the allowable turbine blade temperature. The amount of air used for cooling is determined from gas and blade temperatures and this extraction has a negative effect on gas turbine performance. There is, thus, always an optimum turbine inlet temperature and pressure ratio for a fixed blade temperature [4]. In this study, we have kept an eye on the important effect of blade temperature on the part load performance of the gas turbine and the heat recovery steam generator, for both of the air flow control methods mentioned above. This study also presents some criteria for determining the design point of the heat recovery steam generator, by considering the limitation on the part load operation. To accomplish these objectives, a general simulation program is constructed to reflect most of the essential features of the real engine characteristics. Design and part load calculations have been performed for several cases and results are compared.

2. A N A L Y S I S 2.1. Basic relations for gas turbine components The single shaft gas turbine with air cooling is treated here. This section describes the component calculation procedure briefly. The subscripts 1, 2, 3 and 4 denote compressor inlet and discharge,

Performance in the gas turbine cogeneration system

283

turbine inlet and exhaust, respectively. Each component of air and gas is treated as an ideal gas and the temperature dependent thermodynamic properties are adopted [5]. The enthalpy change through the compressor is calculated as follows: .

.

.

.

l

L\rl/

x -.

(1)

J

After the combustion calculation, the mass flow rate at the turbine inlet is expressed as rh t = (1 - c)(1 +f)ff/a"

(2)

The real situation of the turbine with cooling is much more complicated and seldom allows easy access by simple estimation. The turbine cooling effectiveness is a strong function of the specific geometry and flow patterns. Therefore, it is not easy to construct a turbine calculation routine without losing generality. In this work, several parameters are introduced to reflect the effect of turbine cooling through a relatively simple, but reasonable, calculation. Cooling calculation is applied only to the first stage nozzle, in which the most serious condition appears and the largest portion of total coolant flow is consumed, and it is assumed that the subsequent blades remain at a sufficiently safe temperature. The distribution of cooling air is estimated by a typical example of known reference [6]. The cooling process is idealised, i.e. the blade is assumed to be an isothermal wall and cooling air performs internal cooling at first, then mixes with the main stream at the end of the blade's trailing edge. These assumptions are often used and are known to give reasonable results [4, 7, 8]. The coolant flow rate of the first stage nozzle is (3)

ICVlc,lN = FIN ]]v/c= C rlN/J'/a,

where rlN is the ratio of the first nozzle coolant flow to the total coolant flow. The average gas flow rate through the turbine is estimated, as in equation (4), and this is treated as the effective flow rate rht,ef = mt + ?he,el =/~tt + ¢ (rlN + ref)/C/a •

(4)

The values, r m and rot are estimated to be 0,38 and 0.26, based on the turbine data [6]. The cooling effectiveness is defined and given in equation (5) from an existing correlation: Ec

T3-Tb 41.2~b¢ ( rhm) - T3~ - 1.0 + 53.8~bc ~c = - ~ , ,

(5)

where 7"3 is the turbine inlet temperature (TIT). This relation is based on experimental data [6]. The temperature after full mixing (T3n) is calculated by the following energy balance equation: rht Cpg(T3 -

T3n) =

the Cpa(Z3n - To).

(6)

The mixing pressure loss is estimated by applying the single stage loss calculation [7] as

AP yrhcMg( l + M, ) P3-

mtM,

~

,

(7)

where a constant of 0.25 is assigned as the loss coefficient Y [7], and M s denote molecular mass of coolant (air) and gas. As a result, the effective expansion pressure ratio is evaluated by P3

(, "

]

P_2 P4"

(8)

Consequently, the enthalpy drop that can be utilised for the turbine power is calculated as follows:

E/'ef

(9)

284

TONG SEOP KIM a n d SUNG TACK RO

The turbine exhaust temperature (TET, Tex) is estimated by considering mixing with the coolant: Cpg(T~n- Tcx) = Aht-~

rh~ -- rhc+tN

.

Cpg(T3 - T~,)z,

(10)

m c . lN

where z is determined to be 0.8, by comparing with several machine data. The final turbine exhaust gas flow rate is determined by rhg = rht-4- rne = [(1 - c)(l +.f) -4- c]rh~.

(I l)

The net gas turbine power and thermal efficiency can be calculated by I~ = mt,efAht -- rha Ahc/r/m ,

qgt

(12)

mrLHVr,

(13)

where Ylmdenotes the mechanical efficiency of power transfer from the turbine to the compressor and a constant value of 0.99 is given throughout this study. 2.2. Part load of a gas turbine We choose the air mass flow at the compressor inlet as the main independent variable and the procedure advances iteratively until designated power and temperature conditions (TIT or TET, etc. for the variable air flow control) are satisfied. For the fuel only control of high pressure ratio compressor, air mass flow is maintained at a nearly constant value. Therefore, we fix the air flow at the design value in that case and this mode is called the constant air flow control. For the variable vane control, mass flow is adjusted to meet proper temperature conditions (turbine inlet or outlet) and this mode is named the variable air flow control. The remaining issue of the calculation is to make compressor efficiency corrections for conditions other than the design point. An axial flow compressor is taken and the off-design efficiency is estimated by adopting single stage characteristics and using the relation between the flow function, pressure coefficient and temperature coefficient [9]. In this procedure, all stages are assumed to have the same stage characteristics. Further explanations are omitted here for simplicity. In the turbine, we allow the constant flow function (rhtx~3/P3) for every design and off-design condition, which is a very reasonable assumption even for considerably low pressure ratios in general engines. The off-design efficiency variation is estimated by the following equation: r/t=r/t d 1 - - ~

NddN/ hs,om-h~n

1

,

(14)

where N represents shaft speed, but the effect can be excluded in a single shaft engine. Equation (14) is obtained by modifying the coefficient of a published semi-empirical correlation equation [10, 11], where 0.5 is chosen to fit the experimental data more favourably. The part load performance of a specific gas turbine is investigated and the results are compared with the test running data. The sample calculation is performed for the model of Siemens-V64.3 [12] and the design performance data are shown in Table 1. The gaseous fuel (CH+) is considered (LHV: 50,050 kJ kg ~). Some unknown parameters, such as TIT, component efficiency and coolant fraction, are determined through a proper process of reducing the overall discrepancy between the calculation results and the test data. As clearly noticable in Table 1, agreements are fairly good. Table I. Design parameters of the gas turbine

Power output (MW) Efficiency (%) Compressor pressure ratio Turbine inlet temperature ( C ) Turbine exhaust temperature ( Ct Turbine exhaust mass flow (kg s ~) Fuel flow rate (kg s ~) Coolant fraction Compressor efficiency (%) Turbine et~ciency (%)

Estimation

Test data [12]

62.3 36. I 15.6 1232 535 187 3.45 0.12 85.7 90.7

61.5 35.8 15.6 -534 187 3.44 ----

Performance in the gas turbine cogeneration system (a)

1.1

i i

~ ! i i i i i ~urtdne eshau~t temPera!ure i

1.0 ................................ ~-J

285

(b)

i i

1.0

"" " ~ " ~ ' ~ - ' ~ ' ~ b ,! ~ ! .~-o~

il J . ~ . , ' V ' ~ , ¢ " 0.9

0.8

..........

¢1

o.a 0.7

i

i

~

,

i

. . . . . . . . . . . . . . . . . . . . . . .

i :

~

i

.

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i

i

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i

. . . . . . . . . . . . . . . . . . . . . . . .

~,i,ol .

,

i

~

,

.

.

~

~

i 0.2

i

I i i i 0.4 0.6 Relative power

~

..........

~ . i

0.2

...........

I 0.8

0.4

rr

!

o . 6 / ~ ' ~ - i 0.51 i 0.0

2 0.6

..........

i

i 1.0

0.0 0.0

I

I

I

0.2

I

I

I

0.4 0.6 Relative power

I

I

0.8

I

1.0

Fig. I. Part load performanceof the gas turbine (lines: estimation, marks: test data [12]);(a) normalised system parameters: temperatures and pressure ratio; (b) normalised efficiency. The turbine blade temperature is estimated to be 770°C, which is acceptable. This machine adopts the variable vane control and the turbine exhaust temperature remains constant, until the air mass flow decreases as low as 70%, after which air flow remains constant. The overall results of the part load performance are presented in Fig. 1 for both test data and estimation results. Figure 1 describes normalised data of inlet and exhaust temperatures of the turbine, exhaust mass flow, pressure ratio and relative efficiency as a function of load factor. Fine accuracy is manifest, which reveals that the present simulation procedures are well constructed and the component off-design calculation is reasonable. 2.3. Heat recovery steam generator Shown in Fig. 2 is the schematic feature of the heat recovery steam generator (HRSG), which is a generally used steam drum type. The pressure range of this study is 500 ~ 2500 kPa and 5% of the quality (dryness) of steam at the evaporator exit is assigned. The steam pressure remains constant for both the design and part load conditions and pressure loss is ignored. The pinch point temperature difference (ATpp= Tg2 - T,2) and the approach temperature difference (ATapp = Ts2 - Tw2) are determined as a result of optimised calculations, rather than given as fixed input conditions, which will be explained in detail later on. Steam is generated as much as the water feed rate without bypass. Overall heat balance of the H R S G is 0 = n'tgCpg(Tg, - Ts3) = rhs(hs0 - hw3),

(15)

where hs0 is equal to the enthalpy of saturated vapour. The energy balances for the evaporator and the economiser are represented by 0 e v : / 1 ; Z g C p g ( T s l - - Ts2) =

they(h,, - h,2) = rh,(h~o - hw2) and

Q= = mg Cpg(Ts2 - Tg3) = rh~(h.2 - hw3).

(16) (17)

Heat transfer capacity (UA) is calculated by

UA = QIATLM,

(18)

for the evaporator and the economiser, respectively. The heat transfer coefficient of the gas side is set at 0.1 k W m -2 K -*, which is proved to be reasonable in view of the real H R S G data [13]. The overall heat transfer coefficient (U) is evaluated with the aid of the relation between gas side and water side heat transfer coefficients as

(UA)s =

[

~

'

+ ~

'

]-'

,

(cA) .... = 5(eA)~ .... (eel)~.e~ = 10(~A )~.~.

(19a) (19b)

286

TONG S~ol, KIM and SUNG TACK Ro steam

(a)

%

\-°=/

•

feed water

~g~

(b)

economlser [

_

~

J

gl

T

evaporator I st

w2 4g

stack gas

0

gas from turbine exit

Fig. 2. Schematic of the heat recovery steam generator; (a) flow diagram; (b) conceptual temperature profile.

At the off-design condition (i.e. the part load condition of the gas turbine), an iterative calculation is performed within the constraints of the heat balance and the constant area for both the evaporator and the economiser. The evaporator exit quality is assumed to remain constant as the design value, which is reasonable to simulate the constant water level in the steam drum. In addition, the variation in heat transfer coefficient is taken into consideration. A relation for heat transfer coefficient is taken from the general correlations of internal and external flow [14]:

k/mm) <, ~=~d~~

(20)

where the effect of temperature variation is included and k and # are thermal conductivity and viscosity, respectively. The properties of air [14] are substituted for the gas properties, since the air excess ratio is still large enough. As long as the evaporating pressure remains constant in the water side, the effect of properties can be ignored. The exponent, e in equation (20), has values of 0.8 and 0.6 for the water side (internal circular pipe flow) and the gas side (flow over tube banks), respectively [14]. A similar procedure to the one mentioned here was applied to the once-through type HRSG [15]. 3.

RESULTS

3.1. Gas turbine

We chose the gas turbine whose design point parameters are given in Table 1. In the part load, both the constant and the variable air flow controls are adopted and the coolant fraction (ratio (b) 1400

Constant coolant fraction Variable coolant f r a c ~

o

TITS/.

t°°° I

1200

-

e

600

800 600

I.-- 400

~-

200 0.0

_

TIT

o~. 1000

800

0

Constant coolant fraction - - - - Variable coolant fraction

400 2O0

I

I

0.2

I

I

I

I

0.4 0.6 Relative power

I

I

0.8

I

1.0

0 0.0

I

I

0.2

I

i

I

I

0.4 0.6 Relative power

I

I

0.8

I

t .0

Fig. 3. Temperature variation in the turbine as a function of load fraction; (a) constant air flow control; (b) variable air flow control.

P e r f o r m a n c e in the gas turbine c o g e n e r a t i o n system 190

16

180

/

,¢

--

160

-- CV

......

VC

--

VV

- -

/,:,/,~

1

14~

,,J

CC

170

~

287

e, /Y.

13 tr °

a. 12

, ,/¢,'

,i

• E¢' 150

,7

11

see

140

,'/

I-" J''

10

130 120 0.0

./" " -" ."°

~

/-

-

"''"" i

i

0.2

s

I

0.4 Relative

I

I

0.6

I

I

0.8

8

1.0

power

Fig. 4. Exhaust mass f l o w as a function o f load fraction.

0.0

1

- -

1

0.2

C

C

--

CV

. . . . . . VC VV

"""

I

-

- -

i

i

0.4 Relative

t

-

--

i

0.6

i

0.8

.0

power

Fig. 5. C o m p r e s s o r pressure ratio as a function of load fraction.

of coolant flow to compressor inlet air flow) is made not only constant but also variable. Therefore the combination of control yields four different ways. As power decreases, the variable control of the coolant fraction requires the blade temperature to be maintained as high as possible; this results in minimised coolant flow for each condition, which is expected to have an advantageous effect on performance. Figure 3 shows the temperatures in various control modes. The variable air flow control with constant coolant fraction in Fig. 3(b) gives exactly the same result as that of Fig. 1(a). The exhaust gas flow and the compression pressure ratio are presented in Fig. 4 and Fig. 5, respectively. The first character of the legend denotes the type of air flow control and the second one, control type of the coolant fraction--for example, CV means the constant air flow and the variable coolant fraction. It is easily seen that the blade temperature remains constant over a wide range of power, in the case of variable control of coolant fraction. No cooling is needed in the range where turbine inlet temperature is below the design blade temperature. Comparison of Fig. 3(a) and (b) shows typical distinctions between the constant air flow and the variable air flow controls (notably large discrepancy in TET [2]). For the variable control of coolant fraction (CV and VV), all temperatures (TIT and TET) are lower than those in the constant control of coolant fraction (CC and VC) at a given power. If TIT is fixed, the reduced coolant flow for the variable control of coolant fraction causes more effective gas flow [equation (4)] and larger effective expansion ratio of the turbine [equation (8)]; this results in larger power and higher efficiency. It can thus produce the same amount of power with reduced TIT and a still higher pressure ratio. The lower TIT indicates less fuel consumption, which increases efficiency. The thermal efficiency at part load is displayed in Fig. 6. It can be seen that two modes at constant coolant fraction (CC and VC) have nearly equal efficiency. If we consider the fact that VC entails a larger decrease in the component efficiency (especially in the compressor) at part load, it is believed that the variable air flow control has inherent merit over the constant air flow control in the pure thermodynamic aspect. In other words, if the degradation of component efficiency is ignored, the variable air flow control reveals better performance. At all load fractions, the variable control of coolant fraction improves thermal efficiency (CV over CC, VV over VC), as mentioned above. Moreover, this effect is more promising in the constant air flow control (CV over CC). On one hand, at half load, 1 ~ 2% point (3 ~ 6% relatively) improvement is noticed. On the other hand, if we look at Fig. 3, along with Fig. 4, we can find that the variable control of the coolant fraction causes either lower TET (also TIT) or smaller exhaust gas flow (also air flow)--i.e, lower TET at the same air flow (CV and VV) and smaller flow at the same TET(VV). This phenomenon has a negative effect on the heat recovery, which will be explained in the next section. 3.2. Heat recovery The pinch point temperature difference and the approach temperature difference should be given at the design point. In general, the heat recovery becomes larger for smaller ATpp. However,

288

TONG SEOP KIM and SUNG TACK Ro 0.40 0.35 0,30 0.25 T, 0.20 0.15

---CC

f

0.10

:_-_.:v

0.05

- - - -- VV

0.00 0.0

I

I

0.2

I

I

I

I

0.4 0.6 Relative power

I

I

I

0.8

1.0

Fig. 6. Thermal efficiency of the gas turbine for various control modes.

extremely small design ATpp leads to a situation where the part load operation is not possible at a fixed steam pressure, which may deteriorate the system performance. Power reduction accompanies the drop in the inlet gas temperature of HRSG, which causes smaller ATop. Therefore it should be emphasised that the part load operation has to be taken into account in determining the design parameters, such as ATpp and ATdpp, etc. There are several researches which deal with the pinch point temperature difference as the prime parameter. However, most are only concerned about design point calculation and impose an arbitrary ATpp a t every steam pressure. In this work, we take special interest in the determination of the design point values of ATpp and ATap p. For a specified pressure, the design ATpp is determined as a result of an iterative routine, so that the ATpp of a zero gas turbine load condition may become 5°C, which is considered to be the minimum value to ensure the safe operation for all part load conditions. To prevent boiling in the economiser at part load operation, we determine the design approach temperature difference (A Tdpp), through a procedure in which feed water just becomes saturated at a zero gas turbine load. Water inlet temperature (Tw3) of 100°C is given. Temperature differences ATpp and ATap p and recovered heat at the design point are shown in Fig. 7. As expected, the recovered heat decreases as steam pressure rises. As the steam pressure gets higher, larger design ATpp and AT, pp should be assigned to guarantee safe operation up to a sufficiently reduced power output. It is natural that recovered heat decreases with increasing ATpp. In addition, however, large ATap p also reduces heat recovery, since it brings about a low economiser heat transfer rate and thus a small amount of steam generation [equations (15)--(17)]. The variable air flow control leads to larger heat recovery than the constant air flow control at the same steam pressure. Moreover, it allows less decrease in the recovered heat with pressure rise, which comes

(a)

I00

50

(b) 85

CC 45

--

--CV

40

---vv

......

VC

/

/ /

50 .~o

L.) 35 o._.

h ~ 30 <1 25 20

75 ~

25

/

80

g 75 ~ .0

70

0

CC 55

15 10

60 500 1000 1500 2000 2500 Ps (kPa)

--

-- CV

......

VC

---

VV

--

I

500

\

\ I

I

I

I

1000 1500 2000 2500

Ps (kPa)

Fig. 7. Effect of control modes on the design parameters of HRSG ('T~,3 = 100 C); (a) pinch point and approach temperature differences; (b) recovered heat.

Performance in the gas turbine cogeneration system 50

289

35

,.f .....

o•40 . .-.-.v. .v. vc

/f')

,)" ,,,-

//,y

,"/

3O

30

• c-v

25

~, ATm

o-"'//

.'7

.¢ .E=15

20

10

E

,;-7 / ..';,

_ . . . . . . VC -----W

0

)"4//

0.0

I

0.2

=

I

I

I

0.4 0.6 Relative power

I

I

0.8

I

0

1.0

0.0

I

I 0.2

I

I I I I t 0.4 0.6 0.8

I 1.0

R e l a t i v e power

Fig. 8. Pinch point and approach temperature differences in part load (P, = 1500 kPa, T,3 = 100°C).

Fig. 9. Rate of steam generation in part load (P, = 1500 kPa, T,3 = 100°C).

from the weak pressure dependence of ATpp and ATapp. The variable control of coolant fraction (CV and VV) produces less recovered heat at the design point, due to the lower TET at a smaller load (Fig. 3). Now, part load performance of the HRSG is investigated, with the same design parameters for all the four control modes. A steam pressure of 1500 kPa is chosen. The design point is as for the case of constant air flow control with constant coolant fraction (CC). As shown in Fig. 8, controls other than CC lead to a smaller ATpp at part load. This effect can be deduced easily when we consider the fact that they have larger design ATop than CC at the condition of constant ATpp at zero gas turbine load conditions (Fig. 7). The variable air flow control (VC and VV) exhibits nearly constant ATopo for the constant Tg~ region (up to about 50% power); this reveals that ATapp is a function of inlet gas temperature and seldom depends on gas flow rate. The steam generation rate, that is directly proportional to the recovered heat, is presented in Fig. 9. The variable air flow control brings much improved part load heat recovery; this is why it is taken as the control method in many conventional gas turbines [2, 3]. The variable control of coolant fraction lessens heat recovery. With reference to Fig. 3 and Fig. 4, we can see that it is the effect of a decrease in Tgl [CV and VV for constant (70%) air flow] and reduced gas flow (VV when Tg~ is kept constant). The reduction due to variable coolant fraction is dominant in constant air flow control. Therefore, it turns out that the gain in gas turbine efficiency (Fig. 6) by reducing the coolant fraction inevitably accompanies a loss in heat recovery. Overall performance of the HRSG can be represented by some distinct efficiency parameters. The heat recovery efficiency is a simple ratio of recovered heat to gas turbine input energy, while the HRSG effectiveness is the ratio of the heat recovery to the maximum possible enthalpy which could be obtained if the gas were cooled to the ambient temperature. They are defined respectively as ~hr =

0 rhf. LHVr

and

0 ~"' = m , G , ( r , ,

-

T.m~,o.,)"

(21)

There are also several ways in which we can evaluate the total cogeneration system effectiveness. One is the total cogeneration efficiency, which is deduced simply from an energy balance. Another parameter that is appropriate to represent the overall fuel economy of a cogeneration system, is the chargeable power generation efficiency. It is the ratio of net power output to the excess fuel

290

TONG SEOP KIM and SUNG TACK RO

,.,,0j co

l, i,0J

o. 1- __-_____cv 0.6

I

o.sr

S.-~-"

-ii O0

I

0.0

I

0.2

I

I

0.4 Relative

I

I

I

0.6

I 0.8

I

00 ~ 1.0

0.0

0.2

power

0.4 Relative

0.6

0.8

1.0

power

Fig. 10. Various efficiencies of the cogeneration system in part load (Ps = 1500 kPa, T,3 = 100°C); (a) heat recovery efficiency and HRSG effectiveness; (b) total efficiency and chargeable power generation efficiency.

that the system consumes, over what is normally required in a separate steam boiler without heat recovery. They are expressed as r/lot - rhr L H V r and r/CPG= r h f L H V f - Q/0.9'

(22)

where the constant, 0.9, is imposed as the boiler efficiency. The heat recovery efficiency and H R S G effectiveness are depicted in Fig. 10(a). We can easily see the superiority of the variable air flow control. In the variable air flow control, the continuous increase of both parameters, rlhr and Eh,, up to about 50% power is caused by a high Tgj and decreasing Tg3. As clearly presented, the variable control of coolant fraction generally leads to lower heat recovery effectiveness, due to lower T0 . In the variable air flow control, however, there is no difference in the two parameters between the two coolant fraction control methods, up to about 50% power. Figure 10(b) presents the total cogeneration efficiency and chargeable power generation efficiency. The difference in overall system efficiencies between the variable and the constant air flow control is remarkable, as expected. The total efficiency is hardly affected by coolant fraction control, except at very low load fractions. It does, however, improve the chargeable power generation efficiency at all power outputs, which means that the reduction in fuel input is more than the decrease in heat recovery. This result means that the real system effectiveness can be evaluated if we adopt a suitable efficiency parameter. As a result, it can be concluded that the variable control of coolant fraction gives rise to a real improvement in system fuel economy.

4. C O N C L U S I O N A gas turbine performance analysis routine is established and its appropriateness is ascertained by comparison with real test data. Part load performance has been investigated for a gas turbine and heat recovery system with a couple of power control methods and special focus is placed on the effect of minimising coolant consumption. The results of this study are summarised as follows. (1) When the coolant fraction remains constant as the design value, both the variable and constant airflow controls represent similar gas turbine part load efficiency, while the former exhibits much larger heat recovery and higher total efficiency. (2) Part load efficiency of the gas turbine is always improved for both air flow control methods by varying the coolant fraction and thus maintaining blade temperature as high as possible. The

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improvement is possible due to an increased effective turbine gas flow and a larger effective expansion pressure ratio caused by a reduced coolant flow requirement. (3) It turns out that the system design parameters of a heat recovery steam generator, such as pinch point temperature difference and approach temperature difference, are much more dependent upon the steam pressure if the favourable part load operation is considered. (4) When the same parameters of the heat recovery steam generator are imposed at a zero gas turbine load condition, the variable control of coolant fraction produces less recovered heat at the design point, compared to the constant control of coolant fraction. In the same manner, it exhibits less heat recovery at part load if the design parameters are equal. (5) The simple total efficiency is insensitive to the control method of the coolant fraction, up to considerably low power. The variable control of coolant fraction, however, gives rise to higher chargeable power generation efficiency, which signifies the improvement in overall fuel economy. In this respect, the importance of the correct choice for the efficiency parameter is manifested for the evaluation of the real system effectiveness (economy). Acknowledgement--This research has been supported by the Turbo and Power Machinery Research Centre of Seoul National University.

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