7 Consider a 475 MW steam power plant that operates on a sim

7. Consider a 475 MW steam power plant that operates on a simple ideal rankine cycle. Steam enters the trubine at 10 MPa and 800 degrees Celsius. It is cooled in a condenser at a pressure of 20 kPa.

a. Determine the Enthalpy of the Steam at the Turbine Exit?

b. The Pump Work (Required for the Cycle)?

c. Enthalpy of Steam (KJ/Kg) at each Step in the Rankine Cycle?

d. Thermal Efficiency of the Cycle?

e. Mass Flow Rate of the Steam?

Steam C. wsnder a NTS MW steam powwer plant that operates on a of 20 kra. enters the twit une at to Mrn and snor c at a Cons sled in a co Hint e the Problem: state 1 aR tung Conden Refore Enterins Sara d r, 20 kPa set State 2 (ENIing usmp Ret te Entertng Compressed Liquid State 3 atsiting let vee intenng Tustine): superheated vapor T3 S00 C and 13 10.0 MPa State 4 (Exiting Tuttane Refore Entering condenser: P. 20 kra A) Determine the enthalpy otthe steam at the turbinc csit pimenal tor l\'attal Credit) a. List each s in the ideal Rankine Tower Cycle component b. Draw a sketch of the 1dea cycle each What are the pr perties of the steam after it exits e. the boiler before it enters the turbine? the turbine? d. What are the known properties steam after it exits of the e. What is the quality of the steam when it exits the turbine? f What is the equation for the enthalpy of the steam? g. What is the enthalpy of the steam at the turbine exit? Bo Ihepump work Irequi tional for Partial Credit) exits the a. What are the properties of the water as it condenser and before it enters the pump? b. What are the known properties of the water as it exits the pump before it enters the boiler? c What is the equation for the pump work [J/kg d. What is the pump work required for the cycle? he Rankin (Optional for Partial Credit) a. What is the energy equation (1st law) on the pump? b. What is the specific enthalpw, hilkl/kgl, h kJ/kgl, of the water entering and exiting the pump? c. What is the specific enthalpy h, kj/kgl from Part A for the steam leaving the boiler and entering the turbine? d. What is the specific enthalpy h, J/kgl from Part A for the steam leaving the turbine and entering the condenser? (Continued on Next Page)

Solution

given 475MW steam power plant,condenser pressure = 20 kPa

a) for steam which enters the turbine at 10Mpa and 800⁰C,from steam tables,

h = 4104.40 kJ/kg ,s = 7.3967 kJ/(kg·K).

it is given ideal rankine cycle,so entropy of steam at turbine exit = 7.3967 kJ/(kg·K)

let steam quality at turbine exit = x, from steam tables at 20 kPa ,s_f = 0.8313 kJ/(kg·K),sg=7.9090 kJ/(kg·K),

h_f = 251.31 kJ/kg ,hg = 2609.96 kJ/kg

7.3967 = (1-x)*0.8313+x*7.909 from this equation x = 0.927

enthalpy of steam at turbine exit = (1-0.927)*251.31+0.927*2609.96 = 2437.78 kJ/kg

b) pump work = change in pressure * specific volume of Saturated liquid at 20kPa

= (10*1000000-20000)*0.001017 = 10.149 kJ/kg

c) enthalpy of steam at turbine inlet = 4104.40 kJ/kg (from steam table)

enthalpy of steam at turbine exit = 2437.78 kJ/kg (solved in part a)

enthalpy at pump inlet = 251.31 kJ/kg (since it is a ideal rankine cycle,its value is equal to enthalpy of sat liquid from steam table)

enthalpy at pump outlet = enthalpy at boiler in = 251.31+ 10.149 = 261.459 kJ/kg

d)cycle thermal efficiency = (turbine work output - pump work input)/(heat input)

= (4104.4-2437.78-10.149)/(4104.4-261.459) = 0.431

e) (turbine work output - pump work input)*mass flow rate os steam = 475000 kW

mass flow rate os steam = 475000/(4104.4-2437.78-10.149) = 286.754 Kg/s