Question

In: Mechanical Engineering

I have absolutely no idea how to attempt this. You work for a power station design...

I have absolutely no idea how to attempt this.

You work for a power station design company and have a client who has a fairly loose specification for a steam powered plant. You are required to design a steam power plant cycle that can achieve a cycle thermal efficiency of at least 20%. Assume that any used turbines have isentropic efficiencies of 80% and any pumps have isentropic efficiencies of 65%. The maximum pressure allowed for the cycle is 50 bar and minimum pressure allowed is 1 bar. You have total discretion to assume the temperatures, pressures and any other variable you deem necessary unless stated above, though assumptions need to be of sensible values that are justified given current engineering technology. Your brief summary report should include as a minimum the following;

1- Discuss the advantages and disadvantages of your chosen cycle and compare it to alternative cycles using bullet points.

2- System diagram (Block diagram) and T-s diagrams with labeled states and temperature, pressure, enthalpy, and entropy information for your design. This should also include explanation of your design.

3- Sample calculations for enthalpy difference of turbine stage of your selected cycle.

Solutions

Expert Solution

Design criteria for our cycle:

  • Thermal efficiency > 20%.
  • Turbine isentropic efficiency = 80% = 0.80
  • Pump isentropic efficiency = 65% = 0.65
  • Boiler pressure = 50 Bar
  • Condenser pressure = 1 Bar

We shall make use of RANKINE CYCLE for the power production.

Assumptions:

  • In ideal case, the steam exiting the turbine is saturated vapor condition.
  • Water enters the pump in a saturated liquid state.

Net work done = Turbine work - Pump work.

Saturated properties of steam at boiler and condenser pressure:

Now, from the above TS chart, s2' = s1 = sg at condenser pressure = 7.359 kJ/kgK

But, we know,

where

  • sg = sg at boiler pressure = 5.973 kJ/kgK
  • C = Specific heat of vapor = 2.01 kJ/kgK
  • T1 = temp at state 1 = ?
  • T(sat) = Saturated temp at boiler pressure = 264 C = 537 K

Now, h2' = hg at condenser pressure = 2675.102 kJ/kg

And  

where

  • hg = hg at boiler pressure = 2793.74 kJ/kg
  • C = Specific heat of vapor = 2.01 kJ/kgK
  • T1 = 1158.667 C
  • T(sat) = Saturated temp at boiler pressure = 264 C

But we are given the isentropic efficiency of turbine.

where

  • = 0.80
  • h1 = 4592.022 kJ/kg
  • h2 = ?
  • h2' = 2675.102 kJ/kg

Now, the corresponding temperature is (temp at which the steam enters the condenser) = T2 = ?

where

  • hg = hg at condenser pressure = 2675.102 kJ/kg
  • C = Specific heat of vapor = 2.01 kJ/kgK
  • T2 = ?
  • T(sat) = Saturated temp at condenser pressure = 99.61 C

Now, h3 = hf at condenser pressure = 417.4 kJ/kg

And ideal pump work can be written as

where

  • vf = vf at condenser pressure = 0.001043 m3/kg
  • P(boiler) = 50 Bar = 5000 kPa
  • P(condenser) = 1 Bar = 100 kPa

T3 = saturation temperature at condenser pressure = 99.61 C

But we are given the isentropic efficiency of pump.

where

  • = 0.65
  • ideal work = 5.1107 kJ/kg
  • Actual work = ?

So, h4' = ideal work + h3 = 5.1107 + 417.4 = 422.5107 kJ/kg

And, h4 = actual work + h3 = 7.8626 + 417.7 = 425.2626 kJ/kg

Now, net work = turbine work - pump work

where

  • h1 = 4592.022 kJ/kg
  • h2 = 3058.486 kJ/kg
  • h3 = 417.4 kJ/kg
  • h4 = 425.2626 kJ/kg

--------------------------------------------------------------

Now, heat supplied = Q = (h1 - h4) = (4592.022 - 425.2626) = 4166.7594 kJ/kg

So, thermal efficiency of the cycle =

So, the cycle is 36.62 % thermally efficient.

-------------------------------------------------------------

Salient points of choosing this cycle over other cycles:

We have chosen the Rankine Cycle for this purpose. A few advantages of Rankine cycle are:

  • The medium (waer) is readily available.
  • The medium is non-toxic in nature.
  • Water has a very high specific heat capacity.
  • Water has low viscosity and thus, less frictional losses.

A few disadvantages are:

  • If we add multi-stage expansion, then te process becomes very expensive.
  • Expansion has to begin in the superheated area annd thus a lot of heat is wasted. Also, after expansion, the dryness fraction must be carefully kept under control and recommended above 0.9.

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Took me more than an hour and a half. Kindly upvote if you are satisfied with my efforts. :)


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