Comparative analysis of the off design performance for gas turbine cogeneration systems

Heat Recovery Systems & ClIP Vol. 14, No. 2, pp. 153-163, 1994 ElsevierScienceLtd Printed in Great Britain. All rights re~tved 08904332/94 $6.00 + .00

Pergamon

C O M P A R A T I V E A N A L Y S I S OF THE O F F D E S I G N PERFORMANCE FOR GAS TURBINE C O G E N E R A T I O N SYSTEMS ToNo SEOPKIM, CHANGHOON OH and SuNo TACKRO* Department of Mechanical Engineering, Seoul National University, Seoul 151-742, Korea (Received 19 April 1993) Abstract--Comparison of the off design performance for the cogeneration systems utilizing single and two shaft gas turbine engines is presented in this study. Gas turbine performance is estimated using realistic compressor and turbine performance maps. There is no significant difference in part load thermal efficiency of single and two shaft gas turbines. Performance of the heat recovery steam generator is examined by reasonable modelling of the heat transfer process. Differences in the heat recovery performance of the two systems are analyzed with the aid of system parameters. The heat recovery efficiency of the two shaft system increases as power is reduced, while that of the single shaft system decreases. In the two shaft system, a larger temperature difference between gas and water overcomes the lower gas flow rate and leads to better heat recovery capacity than single shaft system. Total cogeneration efficiency of the two shaft engine does not decrease significantly as power is reduced and is higher than that of the single shaft engine at every part load.

NOMENCLATURE A

dp h HRSG N P T

ATLM U

i¢ 6 0

heat transfer area (m 2) design point enthalpy (kJ/kg) heat recovery steam generator mass flow rate (kg/s) rotational speed (rpm) pressure (kPa) heat transfer rate (MW) fuel energy input (MW) temperature CK) log mean temperature difference (K) pinch point temperature difference (K) overall heat transfer coefficient (kW/m2K) power (MW) heat transfer coeffcient (kW/m2K) nondimensionalized pressure efficiency nondimensionalized temperature

Subscripts 0 stagnation 1, 2, 3, 4, 4' each state a air c compressor d design point ec economizer ev evaporator g exhaust gas gt gas turbine rec heat recovery s water, steam t turbine

*Correspondence should be addressed to: Prof. Sung Tack Ro, Department of Mechanical Engineering, Seoul National University, Seoul 151-742, Korea, Fax: 82-2-883-0179; Tel: 82-2-880-7111. 153

154

TONG SEOP KIM et al.

1. I N T R O D U C T I O N Recently much attention has been paid to the cogeneration (or CHP) system, due to its inherent highly effective energy utilization, and various power generating machines are used as prime movers [1]. Among others, the gas turbine especially is in the stage of increasing installation. The gas turbine has relatively lower efficiency, while it releases large amounts of thermal energy by the exhaust gas. For this reason, the gas turbine is suitable for the topping cycle application in the cogeneration and combined cycle systems. There have been many efforts to fully use the advantages of the gas turbine and make the cogeneration system compact and efficient [2]. There are also many high-performance gas turbine engines which have been constructed with the prime purpose of application to cogeneration and combined cycle power generation systems [3, 4]. This is attributed to recent strong demands for effective cogeneration and combined cycle systems, and is supported by the advances in gas turbine design and manufacturing technologies. Gas turbines exhibit higher power density than any other combustion engine, i.e. high power for their size. Accordingly, they were frequently applied to the aircraft engine [5]. Nowadays, however, it has been a common practice to use gas turbines in the industrial field, especially for electricity production, with the aid of enhanced thermal efficiency due to the advanced blade cooling technology and advent of high durability material, etc. As a result the maximum (turbine inlet) temperature of heavy duty engines reaches 1300°C and a thermal efficiency of over 30% is possible [6]. The performance of a gas turbine engine is greatly affected by the component performance and the efficiency goes down sharply at off-design conditions, especially at part load [4, 5]. Therefore, it has been the primary subject for gas turbine engineers to enhance the part load performance. Gas turbines can be classified into two categories by power generating techniques--single shaft and multi-shaft engines. The thermodynamic states through the operating process are shown in Fig. 1. Since the two shaft engine is most generally used among multi-shaft engines, it is regarded as the representative case of multi-shaft engines here. In the single shaft engine, compressor and turbine are linked by the same power transmitting shaft which results in the same rotational speed of the two components. It can respond to load variation fast at constant speed operation and has many advantages for application to the electricity production unit. The gas expansion of a two shaft engine takes place in two parts, i.e. gas generating turbine and power generating turbine, and the rotational speed of the compressor is independent of that of the power turbine. In the application to electricity generation, the compressor changes speed with load variation, while the power turbine should operate at constant speed. Moreover, a unique operating condition exists at a fixed rotational speed of compressor. There have been several researches related to cogeneration and combined cycle systems [7, 8]. However, there are few studies concentrated on the off-design performance, as well as design performance, of the gas turbine cogeneration system. In this study the performance of the gas turbine itself and heat recovery system at off-design operation is analyzed and compared for the single and two shaft gas turbine engines. For the purpose of comparison between the two engines, the design capacities and performance of the two engines are made almost equal by adopting an identical compressor. In the analysis of the heat recovery process reasonable assumptions for thermodynamic and geometric conditions are employed to simulate the real heat recovery system.

2. SYSTEM DESIGN 2.1. Gas turbine The main design parameters of both the single and two shaft gas turbines are shown in Table 1. For the single shaft engine a compressor pressure ratio of 12 is selected at which maximum design specific power can be obtained. The compressor pressure ratio and air flow rate of a two shaft engine are the same as those of a single shaft engine. The overall turbine eflieiency of a two shaft engine is higher than that of a single shaft engine because multiple expansion exhibits better

Comparative analysis of the off design performance

155

Ah c : m m p m u o r w o r k

Ale. : r n e a m n ~ l toss Ahr~ : tuaym v~rk {I stun}

AhT2: turbkle work (2 shalt) ,~,~ : net work (1 ~ )

/ ap a , 3/

VA

.,h,:

zipe com~stOrlXeSsureloss

//~

~l

t

t t/

~ ahc+,ak,,, /

T

1 $

Fig. 1. Enthalpy--entropy diagram showing gas turbine operating processes.

efficiency than single expansion at the same stage efficiency. Therefore the two shaft engine shows higher thermal efficiency than the single shaft engine. After the design point has been determined, the characteristic performance maps of compressor and turbine are needed in order to accomplish the gas turbine off-design performance. The maps conforming to present design parameters are proposed based on the already existing realistic maps

[9]. In~neral, performance maps are_constructed for several parameters such as flow function speed (N/~To) and pressure ratio [5, 10]. The compressor map of our study (Fig. 2) adopts corrected mass flow (tha~c00/6c) and pressure ratio (Po2/Po])as the variables, and corrected speed (N/,,//-Oc) as a parameter. The inlet temperature and pressure are nondimensionalized by ambient conditions (T0].r~r= 288 K, P0,.ref= 101.3 kPa) as follows:

(rhax/To/Po), rotational

To, 0c ---- T01,ref ,

e0, 6c = P0,,ref

(1)

Presented in Fig. 3 is the turbine map of a single shaft engine based on the design parameters of Table 1. The values, 0t, 6i are the turbine inlet temperature and pressure nondimensionalized by the design values (To3o and P03d) in the same way as equation 1. Figure 3 is reproduced by the design parameters of Table 1 to construct the maps of both the gas generating turbine and power turbine of a two shaft engine. Dry air and combustion gas are treated as ideal gases and the temperature-dependent specific heat [11] of each component is employed to calculate enthalpy and entropy. Methane (CH4) is selected as the fuel with a lower heating value (LHV) of 50000 kJ/kg. Reasonable values of 1-5% are assigned to total pressure loss and other losses of auxiliary parts (combustor, generator, power transmission, etc). The calculation procedures for compressor, combustor and turbine stages are fully acknowledged [5, 10, 11] and hence omitted here. Table 1. Design parameters of gas turbines Parameters Single shaft Two shaft Thermal efficiency (%) 30.02 30.95 Output at generator (MVO 10.00 10.31 Compressor pressure ratio 12 12 air flow (kg/s) 33.2 33.2 bleed air fraction (%) 10.0 10.0 Turbine* pressure ratio 11.41 3.79 inlet temperature (K) 1500 1500 gas flow (kg/s) 30.54 30.54 exhaust temperature (K) 914.0 1197.6 Power turbine pressure ratio 3.01 gas flow (ks/s) 30.54 exhaust temperature (K) 905.1 *Gas generating turbine for two shaft engine

156

TONGSEOPKIM et al. l .0

t

dp

0.8 relative to dp)

0.6

15

--

0.4

~10

\

~s 0

l

,

,,

I

10

t

',i

15

""1;

m. ~-~ / ~

0.84 - - 0.94

!

25

- 0.74

.....

i iI ',

'

20

- 0.63 -

.....

0.97 1.0

:

i

.....

li i

,

.......... 1.16

i 30 35 (kg/s)

I 40

1.05

45

Fig. 2. Compressor performance map. 2.2. H e a t recovery steam generator ( H R S G ) A unfired H R S G is adopted in which saturated steam is produced using gas turbine exhaust gas (Fig. 4). A once-through type heat exchanger is considered and a stack temperature (Ts3) of 180°C is selected. The evaporating pressure of steam (water) is 9 x 1.013 bar and inlet water temperature is 100°C. Pressure drop and heat loss are neglected. Determination of overall heat transfer coefficient (based on gas side) is represented by equation 2, where tube wall resistance is neglected. The heat transfer coefficient on the gas side (as) is set at 0.1 kW/m2K, which is a reasonable value in the case of cross flow over tube banks [12]. The design heat transfer coefficient on the water side (a,) is determined by employing relations like equation 3 for economizer and evaporator sections respectively.

Vs=( ,_L_+

1

(2)

\(aA), (=A)J As (aA),.o: = 5(aA)s.o:,

(aA),.ev = 10(aA)s.ev.

(3)

After U~ and U~, have been obtained by these relations, heat recovery rate ({~¢) and steam generation rate (m.) are calculated from the following equation: ~

= m e Ahr,,~r~

= ms A h r , , ~ r , 3 .

(4)

1.0

,,

....

-0.8

3 relative to dp)

m

V.

S

• • ,.~.....

- 0.6 -- 0.2

35

f

',

e*

- 0.4

--

--

-- 0.4

..... .

..

30

2s

-=.'=..:_--_-'--

-

:

-

. . . . . . .

--

:

J

-/,.V"

"E 20

I

I

3

5

I

I

I

7

9

11

P03/PO4

13

Fig. 3. Turbine performance map of single shaft gas turbine.

0.6 - -- 0.8 1.0

.....

1.2

.....

1.4

..........

1.6

Comparative analysis of the off design performance

157 gl

T

/Gas f

pinchpo--mt

~

S2

Sl Economizer

S3

Eva~rator

Fig. 4. Conceptual configuration o f the heat transfer process at the heat recovery steam generator.

Heat recovery efficiency and total cogeneration efficiency along with gas turbine thermal efficiency are defined as follows:

(5) Heat balance relations for the economizer and evaporator sections are: m s A h r ~ . r ~ = rh~ Ahr~,-~ra = U ~ A ~ ATLM~

(6)

th s Ahrs,_.r~ = th, Ahr~-.re = U~,A~ ATLM,.

(7)

and

where the heat transfer areas for both economizer and evaporator sections are obtained. The total heat exchanger area is the sum of the two values. The design parameters of the HRSG are shown in Table 2. 3. OFF DESIGN ANALYSIS 3.1. Gas turbine The basic operational characteristics of both single and two shaft gas turbines when applied to electricity generation are already explained briefly in the introduction of this article. Only fuel control (without inlet guide vane) is considered as the part load control method of a single shaft engine, and also fuel control and the standard technique of variational compressor speed is adopted for the two shaft engine. As a result, power is changed along the constant compressor speed line by varying pressure ratio and air mass flow in the single shaft engine, while a unique condition exists for a compressor speed in the two shaft engine because mass flow should be maintained between a gas generating turbine and a power turbine. A brief and simplified method of off-design Table 2. Design parameters of heat recovery steam generators Parameters Single shaft Two shaft Evaporator gas flow (kg/s) 30.M 30.54 gas inlet temperature (K) 914.0 905.1 steam flow (ks/s) 6.800 6.662 steam pressure (kPa) 911.7 911.7 steam temperture (K) 449.1 449.1 heat transfer surface (m2) 723.4 722.5 heat recovery (MW) 13.79 13.51 Economizer gas inlet temperature (K) 520.1 518.8 stack fits temperature (K) 453.2 453.2 water inlet temperature (K) 373.2 373.2 water outlet temperature (K) 449.1 449.1 heat transfer surface (in2) 352.7 348.8 heat recovery (MW) 2.22 2.17

158

TONG SEOP KIM et al.

calculation can be found in the literature [5]. In this study, no simplifying assumptions are used for the compressor and turbine operation, and analyses are performed with the aid of realistic performance maps. 3.2. HRSG The values which should be found at the off-design state are stack temperature (Tg3), steam flow rate (rhs), etc. They are obtained under heat balance requirement and constraint of fixed heat exchanger area condition. For the once-through type heat exchanger, when system parameters depart from design values the area of economizer and evaporator sections may vary without a change in total area. Mass flow rate also departs from the design value at off-design operation and this affects the heat transfer coefficient. Therefore the effect of the variational heat transfer coefficient must be taken into account. With the assumption of negligible change in the thermophysical properties, heat transfer coefficient can be represented as a function of mass flow rate as follows, based on an experimentally obtained correlation [12].

f

~ = ~gd/'~-~'z \toga }/

(

as = ~sd - -

•

(8)

The exponents are determined based on cross flow for gas side and flow inside a circular tube for water side [12]. Resulting overall heat transfer coefficients are given by equation 2. If the outlet state of produced steam at off-design is saturated vapor as it is at the design point, there exist 12 variables ( T g l , Tg2, Tg3, T s l , Ts2, Ts3, U~¢, Uev,A~, Aev,rhg, rhs), where Tg~, T~, Ts2, Ts3, rhg are given parameters. The unknowns to be determined and the constraint equations needed are as follows: unknowns: equations:

Tg2, Tg3, A~c, Aov, Uec, U¢v,rhs; four heat balance equations (see equations 6, 7), two overall heat transfer coefficient relations (see equation 2), condition of fixed total heat transfer area.

Steam may be superheated depending on the water feed rate, when the analysis of superheated heat exchanger section should be included. In that case, three unknowns and as many constraint equations are added. Equation 2 is also applied to the superheater section and steam side heat transfer coefficient is set at 1.5 times that of the gas side in equation 3. The flow rate-dependent correction (equation 8) is also made. 4. RESULTS

4.1. Part load performance of gas turbine The gas turbine parameters are normalized by design values and presented in Fig. 5 with respect to the gas turbine power production. The thermal efficiency goes down as power is reduced, which follows the general tendency. In the case of a single shaft engine, air flow rate increases slightly and pressure ratio decreases moderately with a large decrease in turbine inlet temperature (T03) as power is reduced. In the case of the two shaft engine, all of them decrease; but T03 of the two shaft engine is still far higher than that of the single shaft engine at the same part load. Variation in T03 can be deduced by considering equation 9 which shows the relation between the flow functions of compressor and turbine.

rhs ~

Po3

=

I'h a

px~0Ti0 I x-Tx--x--x rh~ Po2 Po, ~ . ma P03 P02 X/T01

(9)

With the single shaft engine, since power reduction hardly accompanies variation in air flow rate, turbine inlet temperature decreases nearly in proportion to pressure ratio squared. With the two shaft engine, power reduction is achieved by reducing compressor speed (power is reduced to less than 20% design power at 50% design speed), mass flow and pressure ratio. In the two shaft engine, however, turbine inlet temperature at every part load is higher than that in the single shaft engine

Comparative analysis of the off design performance

(a)

(b) 1.2

1.2

1.0

0.8

159

. . . . . -:.==-. ..... ,4

..=

TO2 .,- ......... ,," ...... " .,p" - - t ' C

~

..

7-~

~

_L__

1.o T°~

=.:.~,

t

!

1

~-"-~

I t/.j

0.8 ........ -"

¢1 0.6

~

0

.

6

.

.

.

.

.

";,,: °,

0.4 , - - -

!-:-i

o Z

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

|

f

I

I ......... i- ..... I

0.2

0.2

0.0 0.0

.

0.0 I

0.2

0.4

0.6

0.8

1.0

1.2

0.2

0.0

0.4 0.6 0.8 Relative power

Relative power

1.0

1.2

Fig. 5. Gas turbine performance vs power. (a) Single shaft gas turbine; (b) two shaft gas turbine.

because the ratio of pressure ratio to mass flow is much higher (see Fig. 5 and equation 9). At considerably lower powers (less than 30% design power), the reduction rate of mass flow becomes larger than that of pressure ratio, which leads to a rise in turbine inlet temperature. It is usually accepted that a multi-shaft engine shows better efficiency than a single shaft engine at part load [5] and this is explained by the higher compressor and turbine efficiency at off-design operation. In this study, however, cannot be found a large difference in thermal efficiency of the two engines at part load 1, that is, two shaft engine efficiency is only slightly higher by a similar amount of the difference between the two efficiency values at the design point. For the condition where load does not deviate much from the design value, component efficiency of a two shaft engine maintains a higher level, but it becomes lower than that of the single shaft engine as power decreases further. Consequently it should be acknowledged that if a comparison is made between single and two shaft engines using the same compressor and turbines in a wide part load range, the two shaft engine has no notable merits in part load performance compared to the single shaft engine. In addition it should be also kept in mind that compressor design criteria must conform to the field of its application, i.e. single or multi-shaft system, for the best part load performance. These results for the gas turbine performance agree well with characteristics of current commercial engines qualitatively. Component performance maps turned out accordingly to be reasonable and realistic, and the off-design calculations are thought to be fully accomplished in a wide operation range. Therefore these results are enough to be used for a reasonable estimation of the waste heat recovery system performance. 10.0

1400

9.0

1200

•,

8.0

single shaft (51.5 % power) m

_

-

two shaft

(45.5

%

1000

power)

• O ~ 7.0

800

6.0

600

5.0 2.6

I

I

I

2.8

3.0

3.2

I

I

3.4 3.6 ms (k~s)

I

I

3.8

4.0

400 4.2

Fig. 6. Effect of steam flow rate on the heat transfer rate.

TONG SF,OP KIM et al.

160

1.2

I

[

1.2

,"

To~li

,,o .=

::! ..... i ..... ...... i| [/ ,"i

0.8 --:~-I---I:.-'~---

...... !

0.8

...... ~_

71 g L e~ E 0.4 .... ~ " - ' - ' ~ - . l : : ' : - i - ~

~. . . . . . . .

...............'J,----

I~-.. 7.,

N

4--:--~

•i ~ " ~

m

~

I"

',

l

~. . . . . . . . . . . . . . ~-................. 4 - . . . .

~

~

I

. . . . . 4. . . . . ~ . . . . . J. . . . . .

E 0.4

.......

O

I-"1

........ f. . . . . . ~ _ . - . _ _ ~ ........ ~ _ _ ~

~l'qt°t i J ! 0.6

[ .....

!

........-ti-:=~-.~_.-.~~

¢0

a.

,.

1.0

I

O

z

z

0a

0.2

.............. !........ ~ ........ ~.......... ~........ ,-I ......... i ~

o.0

0.0

0.2

i i

! i

0.4 0.6 0.8 Relative power

1.0

0.0 0.0

1.2

l

0.2

0.4 0.6 0.8 Relative power

1.0

1.2

Fig. 7. Heat recovery performance vs gas turbine power. (a) Single shaft gas turbine system; (b) two shaft gas turbine.

4.2. Part load performance of HRSG In order to determine the optimum steam outlet condition for off-design operation, heat recovery performance is analyzed with varying degrees of superheating at the HRSG outlet. Results show that heat recovery rate is reduced by increasing superheating, i.e. it is a maximum when steam is produced at saturated vapor condition. A typical result is presented in Fig. 6 for about 50% design gas turbine power. With a fixed gas inlet temperature, an increase in steam outlet temperature accompanies a reduction in heat recovery rate and steam production rate, which is reflected in a rise in stack temperature and pinch point temperature difference. In real system operation, this means that feed water reduction gives rise to an increase in outlet steam temperature and a decrease in recovered heat. The two shaft system shows better heat recovery effidency and a wider operational range of steam flow rate than a single shaft system. Consequently, steam outlet condition is fixed at the saturated state at which the heat recovery system exhibits best performance for a given gas turbine power. Parameters of HRSG and total cogeneration system efficiency are presented in Fig. 7. In the single shaft system, gas inlet temperature (Tsl) drops sharply as power is reduced, which causes a decrease in heat recovery rate (Q~). Moreover, heat recovery efficiency 01~) decreases as well as Q~ itself. Accordingly, power reduction goes with a monotonous decrease in total cogeneration

0.10

evapor=tor

0.09 ~ - 0.08

I

s~

0.07 0.06

~ ~

~r

/'. /

singleshaft m . -- two shaft

0.05 dp

0.04

0

i

i

i

,

2

4

6

8

~J,I

Itwo

10

12

Power (MW)

Fig. 8. Variation in overall heat transfer coefficient at HRSG with power output.

Comparative analysis of the off design performance

161

100 - -- two shift

80

~qxxmr

60 40

( r

20 0

I

economizer I I

2

4

'

6 8 Power (MW)

sinOlelltW°" 10

12

Fig. 9. Variation in UA at HRSG with power output.

efficiency. This effect is dominant at relatively low powers, and total efficiency becomes as low as 40% at zero load. The heat recovery of the two shaft engine also decreases at part load. However, Tgl is considerably higher and To is moderately lower than those of a single shaft system, which means larger temperature change on the gas side. As a result ~ of the two shaft system is much larger. Moreover, r/r~ increases as power is reduced since the rate of reduction in ~ is less than that of fuel energy input. This is the most predominant discrepancy between single and two shaft systems. At round 50% design power, the two shaft system shows a higher r/~ than a single shaft system by 20%, which is a considerable amount. The reversal increase in Tgl at lower power (below 30% design power) results from the increase in T03 (see Fig. 5). By this effect, heat recovery efficiency and total efficiency rise in that region. Shown in Figs 8 and 9 are U (overall heat transfer coefficient) and UA of the economizer and evaporator sections. With the two shaft system, a decrease in U and UA is noticeable with power reduction since both of the gas and water flow rates decrease (see equation 8), while a smaller decrease in U and UA for the single shaft system is observed because only the water flow rate falls. However, mean temperature difference between gas and water is much larger in the two shaft system (refer to Fig. 9) and this effect is greater than the effect of a smaller UA. As a result the heat transfer rate of the two shaft system is larger and this phenomenon is dominant in the evaporator section. In the single shaft system, the area of evaporator section increases continuously as power is reduced (compare U and UA), that is, evaporation occurs at the rear part of the original economizer section. In the two shaft system, however, no discernible change in each area 100

singleshaft - -- two shaft 80

~-

io..o..

~" ~ J "

60

!

20

dp I

o 0

i 2

i 4

i i 6 8 Power (MW)

l

singl'l I ~ 10

12

Fig. 10. Variation in pinch point temperature difference with power output.

162

TONGSEOPKIMet al.

size takes place with power reduction although at smaller power the economizer area slightly increases, which is contrary to the single shaft case. Figure 10 presents the pinch point temperature difference that is one of the important parameters to be considered in a thermal system including phase change processes. Both systems have ATpp of above 20 K up to considerably lower power levels. This fact confirms that the design steam pressure and stack temperature (9 x 1.013 bar and 180°C) in this study are reasonably assigned values which make the system operation favorable at all conditions. In addition the two shaft system has larger ATpp and guarantees more stable and effective operation. In the single shaft system, raising the steam pressure at a lower power level requires outlet superheating to maintain enough ATpp and this causes a reduction in recovered heat (see Fig. 6). Therefore the two shaft system is more advantageous in arranging the evaporating pressure of water, with efficient heat recovery at all part loads. Moreover, a design with both lower stack temperature and higher steam pressure is possible. The heat recovery capacity of the two shaft system turned out to be much larger than that of the single shaft system, although there is almost no difference in gas turbine performance itself. This effect becomes dominant as power is reduced. In many cogeneration systems, thermal energy requirement is still considerable although electric load is reduced. Consequently, the two shaft system is advantageous due to the good heat recovery performance, especially in a field where thermal to electric demand ratio is high. 5. C O N C L U S I O N The off design performance has been analyzed for the cogeneration systems utilizing both single shaft and two shaft gas turbine engines with similar design parameters. Realistic performance maps of compressor and turbine were adopted and reasonable part load performance of the gas turbine has been obtained. The off design analysis of an unfired once-through type H R S G was also performed with the aid of the simple modelling of flow-dependent heat transfer coefficient. The overall performance was compared and the following results have been obtained. (1) No significant difference in part load thermal efficiency is observed between single and two shaft engines. (2) The two shaft system offers larger heat recovery than a single shaft system at part load owing to the larger temperature difference between gas and water. In the single shaft system, power reduction accompanies a continuous decrease in total cogeneration efficiency. In the two shaft system, however, the total efficiency is nearly maintained at design value since the heat recovery efficiency is enhanced as power is reduced. (4) The two shaft system is more flexible in determining the design evaporating pressure of water, taking into consideration the efficient heat recovery at all part loads. (5) The superiority of the two shaft engine can be found in the application of cogeneration systems rather than in the gas turbine system itself. Acknowledgement--The

University.

work has been supported by the Turbo and Power MachineryResearchCentre of Seoul National

REFERENCES 1. S. D. Hu, Cogeneration. Reston Publishing Company(1985). 2. H. Leibowitzand E. Tabb, The integrated approach to a gas turbine toppingcyclecogenerationsystem Trans. A S M E J. Engng Gas Turbine Power, 106, 731-736 (1984). 3. K. Kumada and T. Sasada, Development of high-efficiencyheavy-duty25 MW new H-25 gas turbine Hitachi Review 38, 151-156 (1989). 4. T. Nakanishi, T. Yamane and A. Hoshino, Development of small-capacity gas turbines for cogenerationsystems.Proc. 1990 A S M E COGEN-TURBO conf. 27-34 (1990). 5. H. Cohen, G. F. C. Rogers and H. I. H. Saravanamuttoo,Gas Turbine Theory, 3rd edn. John Wiley& Sons (1987). 6. A Pequot Publication, Gas Turbine World--The 1990 Handbook (1990). 7. G. Cerri, Parametric analysis of combinc~dgas-steam cycles, Trans. A S M E J. Engng Gas Turbine Power 109, 46-54 (1987). 8. G. Gyarmathy and P. Ortman, The off design of singleand dual pressure steam cycles in CC plants Proc. 1991 A S M E COGEN-TURBO conf. 271-280 (1980).

Comparative analysis of the off design performance

163

9. J. F. Seller and C. J. Daniele, D YHGEN--A Program for Calculating Steady-State and Transient Performance of Turbojet and Turbofan Engines. NASA, U.S.A. (1975). 10. S. L. Dixson, Thermodynamics of Turbomachinery, 3rd Edn. Pergamon Press (1978). 11. R. E. Sonntag and G. J. Wylen, Introduction to Thermodynamics Classical and Statistical, 2nd edn. John Wiley & Sons (1982). 12. F. P. Incropera and D. P. DeWitt, Introduction to Heat Transfer, 2rid Edn. John Wiley & Sons (1990).

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