APPENDIX A
THERMAL EFFICIENCY OF A SIMPLE-CYCLE GAS TURBINE

 

Thermal efficiency, , of the simple-cycle system, shown in Fig. A.1, is expressed as the net work divided by the heat added to the system (see Eq. A.1).

Fig. A.1 Thermodynamic Cycle of a Simple Cycle Gas Turbine

 



(Eq. A.1)

where:

 

=

net work [sum of the work produced in expansion process(positive quantity) and the work absorbed in compression process (negative quantity)]

=

heat added to the system (thermal equivalent of fuel flowrate).

      The compressor efficiency is defined as:





(Eq. A.2)

where:

      Pr = P2/P1;
      T1 is the inlet (ambient) absolute temperature;
      and is given by:


(Eq. A.3)

      The actual work of compression is given by:

(Eq. A.4)

      Substituting for from Eq. A.2,


(Eq. A.5)

Turbine efficiency may be defined in a manner similar to that of compressor efficiency as follows:





(Eq. A.6)

where is given by:


(Eq. A.7)

      The actual work of the turbine is computed by:

(Eq. A.8)

which after substitution for , has the form:



(Eq. A.9)

(Eq. A.10)

After substituting Eqs. A.5,A.9 and A.10 and rearranging terms, the thermal efficiency of the cycle can be expressed as:






(Eq. A.11)

where:


(Eq. A.11a)


(Eq. A.11b)

and



(Eq. A.11c)

 

A.1 THERMAL EFFICIENCY OF A REGENERATIVE CYCLE GAS TURBINE

The procedure for calculating thermal efficiency of a regenerative-cycle gas turbine is similar to that for a simple cycle. The only difference is the introduction of a regenerator into the system. The thermodynamic process is illustrated by Fig. A.2.

 

Fig. A.2 Thermodynamic Cycle of a Regenerative-Cycle Gas Turbine

 

The regenerator effectiveness was defined by Eq. 3.1 in the text and is given by:


(Eq. A.12)

The compressor efficiency is the same as Eq. A.2; the actual work of compression is calculated in the same manner, and is given by:



(Eq. A.13)

where:







(Eq. A.13a)

      Turbine efficiency is expressed by the following relation:






(Eq. A.14)

The parameter, Pe, incorporates pressure losses in the regenerator and can be expressed as:


(Eq. A.15)

where:

is pressure in the air side of regenerator, and

denotes the increases in the turbine back pressure due to pressure drop in the gas side of regenerator

      The work of the turbine is given by:

(Eq. A.16)

      The work added to the system is given by:



(Eq. A.17)

Substituting Eqs. A.14, A.16, and A.17 and rearranging terms, the following relationship for thermal efficiency is obtained.






(Eq. A.18)