Question

Consider a power plant with water as the working fluid that operates on a Rankine cycle. It has a net power output of 40 MW. Superheated steam enters the turbine at 8 MPa and 600°C (h = 3642 kJ/kg; s = 7.0206 kJ/kg K) and is cooled in the condenser at a pressure of 10 kPa by running cooling water from a lake through the tubes of the condenser. The isentropic efficiency of the turbine is 85%. The pump has an isentropic efficiency of 100%.

(a) Show the cycle on a T-s diagram (a right schematic is fine - you do not need to calculate the temperatures at each point);
(b) Determine the work done by the turbine and the pump in KJ/kg;
(c) the mass flow rate of water used by the power plant;
(d) the thermal efficiency of the cycle;
(e) the back work ratio

Answer 1

Answer 2

A detailed solution is given in the image. Hope it's helpful.

Answer 3

Given data :

• Net workdone in the cycle, = 40 MW
• Turbine inlet pressure, = 8 MPa
• Turbine inlet temperature = 600°C
• Condenser pressure, = 10 kPa
• Efficiency of Turbine, = 85 %
• Efficiency of pump, = 100 %

(a) T-S diagram of Rankine Cycle

(b) Workdone by Turbine and Pump

• Workdone by Turbine

As per given data,

= 3642 kJ/kg

= 7.0206 kJ/kg K

Now, Let dryness fraction at point 2 ( Outlet of turbine ) is X.

Also, process 1-2 is isentropic expansion process. So, entropy at point 1 and point 2 will be same.

Now, entropy at point 2 is given by,

Where,   = Specific entropy of saturated liquid at 10 kPa pressure

= 0.6492 kJ/kg K ( from steam table for saturated water : pressure table )

   = Specific entropy of saturated vapour at 10 kPa pressure

= 8.1501 kJ/kg K ( from steam table for saturated water : pressure table )

So,

Now for isentropic process, 1-2 ,

So,   

So,   

Now, specific enthalpy at point 2 can be given by,

Where, = specific enthalpy of saturated liquid at 10 kPa pressure

= 191.81 kJ/kg ( from steam table for saturated water : pressure table )

   = specific enthalpy of saturated vapour at 10 kPa pressure

= 2584.6 kJ/kg ( from steam table for saturated water : pressure table )

So,

Now, Workdone by Turbine can be given by,

  

So,   

Now, efficiency of Turbine is 85 %. So, Actual workdone by turbine,

SO, workdone by turbine per kg of steam is 1205.0544 kJ/kg.

• Work consumed by Pump

Now, work consumed by pump can be found by,

  

Where, = specific volume of saturated liquid at 10 kPa

= 0.001010 ( from steam table for saturated water : Pressure table )

  

So,  

Now, Efficiency of pump is 100 %. So, actual work consumption by pump,

So, Work consumed by the pump per kg of water is 8.0699 kJ/kg.

(C) Mass flowrate of water

Let mass flowrate of water in the cycle is kg/s .

So, total work done by the turbine,

And total work consumption by the pump,

So, Net workdone in the Cycel,

So,

So,

So,

So, mass flowrate of water in the cycle is 33.4173 kg/s .

(d)  Thermal efficiency of Cycle

Thermal efficiency of the cycle can be given by,

Where, = heat supplied to the water in the boiler =   

Where, = Specific enthalpy of water at Pump outlet ( kJ/kg )

Now, Pump work per kg of water can also be given by,

  

Where, = = specific enthalpy of saturated liquid at 10 kPa pressure

= 191.81 kJ/kg ( from steam table for saturated water : pressure table )

So,

So,  

So, heat supplied per kg of water in the boiler,

So, Total heat supplied to the water in the turbine,

So,  

Now, efficiency of cycle,

  

So, Thermal efficiency of the Cycle is 34.775 % .

(e) Back work ratio

Back work ratio is given by,

So,

So, backwork ratio of the cycle is 0.0066967.

  

Note : Please do ask in comment if you have any doubt. Thank you.

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