Chapter 9: Vapor Power Systems

Transcription

1 Chapter 9: Vapor Power Systems Table of Contents Introduction... 2 Analyzing the Rankine Cycle... 4 Rankine Cycle Performance Parameters... 5 Ideal Rankine Cycle... 6 Example... 7 Rankine Cycle Including Isentropic Efficiencies... 8 Example... 9 Example Rankine Cycle Improvements Example Numerical Answers to Examples

2 Introduction Vapor power systems, or vapor power plants, convert a primary energy source into electricity by alternately vaporizing and condensing a working fluid (usually water). The Rankine cycle is the basic building block of vapor power systems. The primary energy source (e.g., fossil-fuel, nuclear, solar, or geothermal) supplies Q ", the energy needed to vaporize the working fluid in the boiler. The turbine power shaft is connected to an electric generator, which generates the electricity that is then transmitted and distributed to consumers via the electrical grid. For fossil-fueled vapor power plants, Q " is supplied by combustion of the fossil fuel (e.g., coal). 1 1 (Moran, Shapiro, Boettner, & Bailey, 2011) 2

3 For nuclear vapor power plants, Q " is supplied by a controlled nuclear reaction. 2 For solar power plants, Q " is supplied by collected and concentrated solar radiation. 3 2 (Moran, Shapiro, Boettner, & Bailey, 2011) 3 (Moran, Shapiro, Boettner, & Bailey, 2011) 3

4 For geothermal power plants, Q " is supplied by hot water and/or steam drawn from below the earth s surface. Of note, the working fluid in a geothermal power plant is an organic substance, such as isobutene, that has a lower boiling point than water. 4 Analyzing the Rankine Cycle We will analyze the components of the Rankine cycle by applying the 1 st Law to each device in the cycle (turbine, condenser, pump, boiler). For all devices we will assume steady state, steady flow (SSSF), onedimensional (1D) flow, uniform flow, and a quasiequilibrium process. We will also neglect any changes in kinetic and potential energy. 4 (Moran, Shapiro, Boettner, & Bailey, 2011) 4

5 Neglecting heat transfer with the surroundings, the rate at which work is developed per unit mass of vapor passing through the turbine is: W $%&'()* = W $%&'()* m = h. h 0 The sign of W $%&'()* will be positive, following our sign convention that work is positive when it is done by the system and on the surroundings. The only work interaction for the condenser is flow work. Therefore, the rate at which heat is transferred per unit mass of vapor passing through the condenser is: Q 12)3*)4*& = Q 12)3*)4*& m = h 5 h 0 = Q 6 The sign of Q 12)3*)4*& will be negative, following our sign convention that heat transfer is positive when heat is transferred to the system from the surroundings. Neglecting heat transfer with the surroundings, the rate at which work is developed per unit mass of vapor passing through the pump is: W 7%87 = W 7%87 m = h 5 h 9 The sign of W 7%87 will be negative, following our sign convention for work. The only work interaction for the boiler is flow work. Therefore, the rate at which heat is transferred per unit mass of vapor passing through the boiler is: Q '2(:*& = Q '2(:*& m = h. h 9 = Q " The sign of Q '2(:*& will be positive, following our sign convention for heat transfer. Rankine Cycle Performance Parameters The thermal efficiency of the Rankine cycle will be a comparison of what we get (the net work of the cycle) to what we have to pay (the heat supplied to the cycle). η = W $%&'()* + W 7%87 Q '2(:*& = h. h 0 + h 5 h 9 h. h 9 = 1 + h 5 h 0 h. h 9 The back work ratio compares the work required by the pump to the work developed by the turbine. bwr = W 7%87 W $%&'()* = h 5 h 9 h. h 0 5

6 Ideal Rankine Cycle An ideal Rankine cycle consists of four reversible processes. 1à2 2à3 3à4 4à1 Process Isentropic expansion through the turbine from saturated vapor to the condenser pressure Constant pressure heat rejection through the condenser to saturated liquid Isentropic compression through the pump Constant pressure heat addition through the boiler The pump work can be evaluated using the 1 st Law or by using the expression for mechanical work for steady-flow reversible processes, where changes in kinetic and potential energy have been neglected. W m &*A = 2%$ vdp () The specific volume of the fluid flowing through the pump is approximately constant. Therefore, pump work can be approximated as: W 7%87 m &*A v 5 p 9 p 5 6

7 Example Water is the working fluid in an ideal Rankine cycle. The condenser pressure is 6 kpa. The boiler pressure is 10 MPa. Find the thermal efficiency of the cycle and compare to Carnot cycle efficiency. 7

8 Rankine Cycle Including Isentropic Efficiencies Analysis of an ideal Rankine cycle assumed all processes operated reversibly. We can also analyze Rankine cycles when given isentropic efficiencies of the turbine and of the pump. The thermal efficiency of a Rankine cycle including isentropic efficiencies of the turbine and of the pump can be calculated by: η = h. h 0 + h 5 h 9 h. h 9 = η $%&'()* h. h 04 + h 5 h 94 η 7%87 h. h 9 = η $%&'()* h. h 04 + v 5 p 5 p 9 η 7%87 h. h 9 8

9 Example Steam is the working fluid in a Rankine cycle. Superheated vapor enters the turbine at 10 MPa, 480 C. Condenser pressure is 6 kpa. The turbine and pump have isentropic efficiencies of 80% and 70%. Find the heat addition through the boiler (kj/kg), the thermal efficiency of the cycle, and the heat rejection through the condenser (kj/kg). 9

10 Example Water is the working fluid in a Rankine cycle. Superheated vapor enters the turbine at 10 MPa, 480 C with a mass flow rate of 7.8 kg/s and exits at 8 kpa. The isentropic efficiency of the turbine is 88% and the isentropic efficiency of the pump is 82%. Find the net power developed in kw and the thermal efficiency of the cycle. 10

11 Rankine Cycle Improvements Superheat and Reheat are two options for improving the thermal efficiency of a Rankine cycle. A Rankine cycle with superheat allows the turbine inlet to be superheated vapor rather than saturated vapor. A Rankine cycle with reheat includes a two-stage turbine. Steam expands through a first stage turbine (1à2), returns to the boiler to be reheated (2à3), and then expands through the second stage of the turbine (3à4) before moving through the compressor and pump. The thermal efficiency of the Rankine cycle with reheat is again a comparison of what we get (the net work of the cycle) to what we have to pay (the heat supplied to the cycle). For this η = h. h 0 + h 5 h 9 + h F h G h. h G + h 5 h 0 11

12 Example Steam at 10 MPa, 600 C enters the first-stage turbine of an ideal Rankine cycle with reheat. Steam leaves the reheat section of the boiler at 500 C. The condenser pressure is 6 kpa. The quality at the exit of the second-stage turbine is 90%. Find the thermal efficiency of the cycle and compare it to the Carnot efficiency. 12

13 Numerical Answers to Examples Page Answer(s) %, 47.1% kj/kg, 32.8%, 2120 kj/kg kw, 32% %, 64.5% 13