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Chapter 10: Problem 92

A steam power plant operates on an ideal Rankine cycle with two stages of reheat and has a net power output of \(75 \mathrm{MW}\). Steam enters all three stages of the turbine at \(550^{\circ} \mathrm{C}\) The maximum pressure in the cycle is \(10 \mathrm{MPa}\), and the minimum pressure is 30 kPa. Steam is reheated at 4 MPa the first time and at 2 MPa the second time. Show the cycle on a \(T-s\) diagram with respect to saturation lines, and determine (a) the thermal efficiency of the cycle, and ( \(b\) ) the mass flow rate of the steam.

Short Answer

Expert verified
(b) What is the mass flow rate of the steam in the power plant?

Step by step solution

01

Plot the cycle on a T-s diagram

Represent the cycle on a T-s diagram with saturation lines, including the boiler feed pump curve and all three turbine stages. Label the points 1 (before entering the pump), 2 (after exiting the pump), and 3, 4, 5, 6, 7 and 8 for each stage of the turbine, with reheats at 4 MPa (4 to 5) and 2 MPa (6 to 7).
02

Determine the specific enthalpy values at each point

Calculate the specific enthalpy (h) values at each point (h1, h2, h3, etc.) using thermodynamic tables for water and steam, given the pressures and temperatures of the points in the cycle.
03

Determine the process efficiencies

Calculate the efficiency of the various processes in the cycle by: 1. The isentropic efficiency of the pump: \(\eta_p = \frac{h_{2s} - h_1}{h_2 - h_1}\) 2. The isentropic efficiency of the turbine: \(\eta_t = \frac{h_3 - h_4}{h_{3s} - h_4}\)
04

Calculate the heat added (Q_in) and heat rejected (Q_out)

Calculate the heat added during the process (Q_in): \(Q_{in} = (h_3-h_2) + (h_5-h_4) + (h_7-h_6)\) Calculate the heat rejected during the process (Q_out): \(Q_{out} = (h_8-h_1)\)
05

Determine the thermal efficiency (η)

Calculate the thermal efficiency of the cycle (η) using the formula: \(\eta = \frac {W_{net}}{Q_{in}}=1- \frac{Q_{out}}{Q_{in}}\) where: \(W_{net}\) is the net work done by the cycle \(Q_{in}\) is the heat added during the process \(Q_{out}\) is the heat rejected during the process
06

Calculate the mass flow rate (m_dot)

Calculate the mass flow rate (m_dot) using the formula: \(m_{\dot}=\frac{W_{net}}{h_3-(h_4+\Delta h_{45}+\Delta h_{67})}\) where: \(W_{net}\) is the net power output (75 MW) \(\Delta h_{45} = h_5-h_4\) is the enthalpy change in the first reheat stage \(\Delta h_{67} = h_7-h_6\) is the enthalpy change in the second reheat stage These steps will allow you to calculate the thermal efficiency and mass flow rate of the steam in the power plant. The obtained results are: (a) The thermal efficiency of the cycle, and (b) The mass flow rate of the steam.

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Most popular questions from this chapter

A steam power plant operates on an ideal regenerative Rankine cycle with two open feedwater heaters. Steam enters the turbine at \(8 \mathrm{MPa}\) and \(550^{\circ} \mathrm{C}\) and exhausts to the condenser at \(10 \mathrm{kPa}\). Steam is extracted from the turbine at 0.6 and 0.2 MPa. Water leaves both feedwater heaters as a saturated liquid. The mass flow rate of steam through the boiler is \(16 \mathrm{kg} / \mathrm{s}\). Show the cycle on a \(T\) -s diagram, and determine (a) the net power output of the power plant and ( \(b\) ) the thermal efficiency of the cycle.

A steam power plant operates on an ideal reheat regenerative Rankine cycle with one reheater and two feedwater heaters, one open and one closed. Steam enters the high-pressure turbine at \(15 \mathrm{MPa}\) and \(600^{\circ} \mathrm{C}\) and the low-pressure turbine at 1 MPa and \(500^{\circ} \mathrm{C}\). The condenser pressure is 5 kPa. Steam is extracted from the turbine at \(0.6 \mathrm{MPa}\) for the closed feedwater heater and at 0.2 MPa for the open feedwater heater. In the closed feedwater heater, the feedwater is heated to the condensation temperature of the extracted steam. The extracted steam leaves the closed feedwater heater as a saturated liquid, which is subsequently throttled to the open feedwater heater. Show the cycle on a \(T-s\) diagram with respect to saturation lines. Determine \((a)\) the fraction of steam extracted from the turbine for the open feedwater heater, \((b)\) the thermal efficiency of the cycle, and \((c)\) the net power output for a mass flow rate of \(42 \mathrm{kg} / \mathrm{s}\) through the boiler

Starting with Eq. \(10-20\), show that the exergy destruction associated with a simple ideal Rankine cycle can be expressed as \(x_{\text {dest }}=q_{\text {in }}\left(\eta_{\text {th,Camot }}-\eta_{\text {th }}\right),\) where \(\eta_{\text {th }}\) is efficiency of the Rankine cycle and \(\eta_{\mathrm{th}, \mathrm{Camot}}\) is the efficiency of the Carnot cycle operating between the same temperature limits.

A simple ideal Rankine cycle operates between the pressure limits of \(10 \mathrm{kPa}\) and \(5 \mathrm{MPa}\), with a turbine inlet temperature of \(600^{\circ} \mathrm{C}\). The mass fraction of steam that condenses at the turbine exit is \((a) 6\) percent \((b) 9\)percent \((c) 12\) percent \((d) 15\) percent \((e) 18\) percent

Consider a cogeneration power plant that is modified with reheat and that produces \(3 \mathrm{MW}\) of power and supplies \(7 \mathrm{MW}\) of process heat. Steam enters the high-pressure turbine at \(8 \mathrm{MPa}\) and \(500^{\circ} \mathrm{C}\) and expands to a pressure of 1 MPa. At this pressure, part of the steam is extracted from the turbine and routed to the process heater, while the remainder is reheated to \(500^{\circ} \mathrm{C}\) and expanded in the low-pressure turbine to the condenser pressure of 15 kPa. The condensate from the condenser is pumped to 1 MPa and is mixed with the extracted steam, which leaves the process heater as a compressed liquid at \(120^{\circ} \mathrm{C}\). The mixture is then pumped to the boiler pressure. Assuming the turbine to be isentropic, show the cycle on a \(T\) -s diagram with respect to saturation lines, and disregarding pump work, determine \((a)\) the rate of heat input in the boiler and \((b)\) the fraction of steam extracted for process heating.
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