GAS TURBINE ANALYSIS AND DESIGN

NOMENCLATURE

=mass rate of air mass rate of gas CC=Combustion Chamber

C = compressor GT = gas turbine (drives compressor) PT = power turbine

r = compression ratio i = isentropic process a = actual process

compressor work gas turbine work = power turbine work

= mechanical efficiency Note: small stands for work per unit mass.

The diagram below shows the principal components of a gas turbine for power production. The gases exiting state 5 may be diverted to a stack or to heat recovery components. Also shown is a T-s diagram of the thermodynamic cycle.

State 1 is known ( and ).

State 2. For a given pressure ratio, state 2i is known ( ; ). The actual state leaving the compressor (2a) is found from the definition of compressor efficiency which can be estimated with reasonable accuracy.

Neglecting potential and kinetic energies, the actual compressor work per unit mass is:

State 3 is found by estimating the percent pressure drop in the combustion chamber ( ) and selecting the highest temperature (for best efficiency) compatible with the turbine nozzle/blade material.

State 4. The ideal work of the gas turbine is found from the definition of turbine efficiency. The actual work is equal to that of the compressor but opposite in sign.

Furthermore:

From this relation, and the knowledge that , state 4i is found. The enthalpy of state 4a is found from the

definition of turbine efficiency and knowledge of :

C

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State 5i is found from the power turbine exit pressure , which will depend on any components installed for

noise abatement or heat recovery, and the enthalpy . State 5a is then found from the estimated power turbine efficiency:

The work of the power turbine is:

The heat energy added in the combustion chamber is:

The thermal efficiency is:

Two useful quantities for comparing engines are the specific fuel consumption (SFC) and the heat rate (HR). The SFC is mass rate of fuel divided by the power:

The heat rate is the rate of heat energy added divided by the power output:

TURBINE DIMENSIONS

Turbine dimensions are determined largely by the required mass rate. Starting with the client’s requirement for power at the generator bus, estimate the generator efficiency and calculate the required brake power:

The required area of the turbine nozzle and blade rings can be calculated, for each stage, from:

REFERENCE

Bathie, W. W., Fundamentals of Gas Turbines, 2ed, John Wiley & Sons,1996.

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