Analysis And Optimization Of Brayton And Rankine Cycles

Brayton Cycle

The Brayton cycle consist of three major components to be used in the process-

1. Compressor
2. Mixing chamber
3. Expansion valve

Mainly the gas turbines work on the Brayton engines and it has three component  such as a gas compressor, combustion chamber and the expansion valve. The basic process involves the four process used in the ideal Brayton process-

Process 0-1 (Isobaric process) – The atmospheric air is drawn from atmosphere.

Process 1-2 (Isentropic process) – The compressed air is sent to the combustion chamber

Process 2-3 (Isentropic process) – The energy is obtained from the pressurized air

Process 0-1 (Isentropic process) – The heat rejection process to atmosphere

Process 0-1 (Adiabatic process) – Compression process of atmospheric air

Process 1-2 (Isobaric process) – heat addition

Process 2-3 (Adiabatic process) – expansion

Process 0-1 (Isobaric process) – The heat rejection process to atmosphere

The Rankine cycle is basic cycle of all power plants where a working liquid is ceaselessly vanished and dense. The determination of working liquid depends essentially on the accessible temperature extend.

The enthalpy (p-h) and temperature-entropy (T-s) charts of this cycle. The Rankine cycle works in the accompanying strides:

1-2-3 Isobaric Heat Transfer

3-4 Isentropic Expansion.

4-5 Isobaric Heat Rejection.

5-1 Isentropic Compression.

Calculation part for the combined cycle-

Here as per the data given in the part 1, we have-

Required power output = 2MW

Basic cycle used in the system-

Maximum turbine inlet temperature =

Compressor inlet temperature =

The process used in the turbine and compressor are adiabatic having the isentropic efficiency =

For the gas cycle the pressure ratio =

 Now considering other gas cycle in the operation =

The pressure of the condenser = 0.5 bar

The pressure for the both high and the low pressure turbine

Also the effectiveness for the HRSG/Boiler = 90%

In the turbine the maximum possible steam temperature for both the turbine =

The maximum steam pressure in the HRSG = 10MPa

The minimum quality of the turbine exists = 0.95

To the combined cycle used in the part, the addition of the regenerator and the reheater is there in order to increase the efficiency of the combined cycle-

Here we have to check for the system, by adding the Regenerator (R2) in the model is used.   And the flow division is done by the flow control valve R1 and R2 in the turbine and the compressor.
The basic paths are mentioned in the above flow chart.
Terminology and symbols used for different mass flow rate=    

= mass flow rate exits from the compressor.

By this we have to use the flow valve in the plant and the flow of the mass is done by the mass balance. 
We have the initial condition of the regenerative process-
The available power for the amount the total amount of the air compressed in the compressor per unit time.
The mass flow rate of the air 
The mass flow rate of the water = 0.5kg/sec

we know by installing the regenerative cycle to the Rankine cycle the efficiency will increase to 74.58%. Here by the efficiency so calculate we came to know the pressure and the temperature’s higher and the lower limit by using it with  the interpolation method.

Actual Brayton Process

By this we have to use the flow valve in the plant and the flow of the mass is done by the mass balance.

We have the initial condition of the Reheat process –

The available power for the amount the total amount of the air compressed in the compressor per unit time.

The mass flow rate of the air

The mass flow rate of the water = 0.5kg/sec

Here for the above case- the turbine and compressor power are occurring the steady. By applying the conservation of energy and mass, we have 

Here we consider for the process we have,

From the above process we consider the process of the Rankine process as per the process, here we have-

Assuming the data for the above process from 1 to 4 process.

Assuming the standard values for the cycle:

For the state1:

 = 393K  

Form above we came to know we know that by installing reheat set the efficiency of the plant increases as 24.8%.

Now we install series of the regenerator to increase the efficiency of the plant, it is done given below-

For the mass balance for the Regenerator 1, we have R1,

For the Regenerator 2, the mass balance is equal to,

For the Regenerator 3, the mass balance is equal to,

Mass balance for the turbines (low pressure and the high pressure turbines)  

In additional for the flow control valve 1, we have the mass balance 

Here in the above Plant, we have Fan’s temperature of the inlet and the outlet of the temperature of the fans is equal,

As for the assumption here the efficiency for the Turbine 

Flow condition

As per the flowing condition we have, 

Here the above condition, we have the condition like in which the fluid is in the saturation state so it is having the dryness fraction is  masses used.

So for this the value of the mass flow rate 

And now the temperature used for the plant here as per the given values 

And by the condition used here we can have the value of the 

Here the value used here = 0.95 (as per the standards used here for the fluid in the saturation state) 

And for the above equation we have the value of the  Regenerator ,

For R1

Here from this we have the equation  as 

By this the equation comes as, 

For R2: 

By solving the above equation by putting the given values we have equation, 

For R3:

Here in this the value of the mass flow rate becomes, as 

So by this by solving the equation 4, 5, 6 together and by taking the values of the dryness fraction from the steam table we have 

 And   

And the temperature from the Regenerator  can be calculated by seeing the adjacent values from the steam table, by this we have 

And for the junction point, for the different masses we have,

By this we have, 

And in order to calculate the value of the 

By putting the values of the temperature and the mass flow rate from the above values we have, 

Similarly in the same fashion we can calulate the value of the (T(PC)

And in this respect we have the value of the 

Solving the above equation we have the value of the , 

Turbine power

(High Pressure Turbine)=  

 (Low Pressure Turbine)=  

The value of the  at the 289psi  (from the steam table)

The value of the  at the 120psia  (from the steam table)

Turbine power=  

In the previous cycle used, the heat input in the cycle

 Heat added by the Regenerator 2 =  

= x (

= 234.43 x  KJ/Kg

And for the Regenerator 2, we assume that the total mass flow rate is towards the reactor, so here 

So the value of the heat input by using the new  Regenerator 2 Qin =   146.57 + heat added in the previous process with  Regenerator  2 

= 404.44   kJ/kg

Similarly for R3

Here in this the value of the mass flow rate becomes, as 

Total net work done obtain from this modified cycle=   

= 370.2  

The TS for the reheating process-

In the reheating cycle there is an expansion of the steam from the initial state 1 with the condenser pressure is carried out in the combined process which is totally dependent on the number of the reheats used. Cycle efficiency for the combined process improves with the reheating process and by this process the single reheat plant is influenced by the pressure ate which the steam is again reheated. Here in this combined cycle the efficiency of the plant increases with the decreases in the pressure. For this cycle the pressure ration given = 8 to 14  

By the installment of the reheating principle for the combined process we have-

Here in order to calculate the efficiency of the cycle by using the Regenerator 2 

= ( /404.44)   

=91.5 %

By this way, we can calculate the thermal efficiency of the plant = 91.5%

And we got the increase in the efficiency by = 91% – 82% = 9%

So by this we can have the change in the efficiency obtained by using Regenerator and reheater. 

References

Afanasyeva, S., Breyer, C. and Engelhard, M., 2016, March. The Impact of Cost Dynamics of Lithium-Ion Batteries on the Economics of Hybrid PV-Battery-Gas Turbine Plants and the Consequences for Competitiveness of Coal and Natural Gas-Fired Power Plants. In 10th International Renewable Energy Storage Conference, DAŒssel-dorf.

González-Díaz, A., Alcaráz-Calderón, A.M., González-Díaz, M.O., Méndez-Aranda, Á., Lucquiaud, M. and González-Santaló, J.M., 2017. Effect of the ambient conditions on gas turbine combined cycle power plants with post-combustion CO 2 capture. Energy.

Shukla, A.K. and Singh, O., 2017. Thermodynamic Investigation of parameters affecting the Execution of Steam Injected Cooled Gas Turbine based Combined Cycle Power Plant with Vapor Absorption Inlet Air Cooling. Applied Thermal Engineering.