Question

Assume you are working on an ideal gas-turbine cycle that has three stages of compression with intercooling and three stages of expansion with reheating at 100 kPa and 290 K. This system uses a regenerator as well. The pressure ratio across each stage of the compressor and turbine is 3; the air temperature when entering the turbine is 1300 K; and the regenerator operates perfectly. Draw the T − s diagram of this system. Determine the mass flow rate of the air passing through the system, the rates of heat addition and rejection when this cycle produces 1000 hp and thermal efficiency of the system. Assume isentropic operations for all the compressor and turbine stages and use constant specific heats at room temperature. Also assume negligible changes in kinetic and potential energy

Answer 1

Draw the schematic of the cycle with components

List the given numerical values

(pressure ratio of compressors and turbines)

(turbine inlet temperature)

, and , which implies (perfect operation of regenerator)

Specific work done by the compressors are

Assume that all intercoolers cool the gas to

In the compressors, for adiabatic process,

Assume that the gas is air & ideal gas then . Substituting this and

Similarly,

Substituting these in (1),

Specific work done by the turbines are

Assume that all reheaters heat the gas to

In the turbines, for adiabatic process,

Assume that the gas is air & ideal gas then . Substituting this and

Similarly,

Substituting these in (1),

The temperature at 6 is

The temperature at 13 is

The regenerator works perfectly

The heat added in the burner is

The net specific work output from the cycle is

Substituting ,

For a net power output of , the mass flow rate is

Heat addition rate is

Applying Law of energy conservation, as T1=T14,

The thermal efficiency of the system is