2.1 INTRODUCTION Power generation systems throughout the world are mainly based on theoretical cycles. The following context will discuss gas cycle, vapor cycle and their developments and the combined cycle.
2.1.1 The Ideal Cycle for Gas-Turbine Engines The Brayton cycle was first proposed by George Brayton for use in the reciprocating oil-burning engine that he developed around 1870. Today, it is used for gas turbines only where both the compression and expansion processes take place in rotating machinery. Gas turbines usually operate on an open cycle, as shown in Figure (2.1). Fresh air at ambient conditions is drawn into the compressor, where its temperature and pressure are raised. The high pressure air proceeds into the combustion chamber, where the fuel is burned at constant pressure. The resulting high-temperature gases then enter the turbine, where they expand to the atmospheric pressure while producing power. The exhaust gases leaving the turbine are thrown out (not recirculated), causing the cycle to be classified as an open cycle. The open gas-turbine cycle described above can be modeled as a closed cycle, as shown in Figure (2.2), by utilizing the air-standard assumptions. Here the compression and expansion processes remain the same, but the combustion process is replaced by a constant-pressure heat-addition process from an external source, and the exhaust process is replaced by a constant pressure heat-rejection process to the ambient air. The ideal cycle that the working fluid undergoes in this closed loop is the Brayton cycle, which is made up of four internally reversible processes:
Figure (2.3) T-S And P-V Diagrams For The Ideal Brayton Cycle (1- 2) Isentropic compression (in a compressor) (2- 3) Constant-pressure heat addition (3- 4) Isentropic expansion (in a turbine) (4-1) Constant-pressure heat rejection Notice that all four processes of the Brayton cycle are executed in steady flow devices; thus, they should be analyzed as steady-flow processes. When the changes in kinetic and potential energies are neglected, the energy balance for a steady-flow process can be expressed, on a unit–mass basis, as
𝒒𝒊𝒏−𝒒𝒐𝒖𝒕 + 𝒘𝒊𝒏−𝒘𝒐𝒖𝒕 =𝒉𝒆𝒙𝒊𝒕−𝒉𝒊𝒏𝒍𝒆𝒕 ( 1.1)
Therefore, heat transfers to and from the working fluid are 𝒒𝒊𝒏 =𝒉𝟑−𝒉𝟐= 𝒄𝒑(𝑻𝟑−𝑻𝟐) (1.2) and 𝒒𝒐𝒖𝒕=𝒉𝟒−𝒉𝟏= 𝒄𝒑(𝑻𝟒−𝑻𝟏) (1.3) Then the thermal efficiency of the ideal Brayton cycle air standard assumptions becomes: 𝜼𝒕𝒉,𝑩𝒓𝒂𝒚𝒕𝒐𝒏 =𝒘𝒏𝒆𝒕𝒒𝒊𝒏=𝟏−𝒒𝒐𝒖𝒕𝒒𝒊𝒏=𝟏−𝒄𝒑(𝑻𝟒−𝑻𝟏)𝒄𝒑(𝑻𝟑−𝑻𝟐)=𝟏−𝑻𝟏(𝑻𝟒𝑻𝟏 −𝟏)𝑻𝟐(𝑻𝟑𝑻𝟐 −𝟏) (1.4)
Processes 1-2 and 3-4 are isentropic, and P2 = P3 and P4 = P1. Thus, 𝑻𝟐𝑻𝟏 = 𝑷𝟐𝑷𝟏 (𝒌−𝟏)𝒌 = 𝑷𝟑𝑷𝟒 (𝒌−𝟏)𝒌 =𝑻𝟑𝑻𝟒 (1.5)
Substituting these equations into the thermal efficiency relation and simplifying give: 𝜼𝒕𝒉,𝑩𝒓𝒂𝒚𝒕𝒐𝒏= 𝟏−𝟏𝒓𝒑(𝒌−𝟏)𝒌 (1.6)
Where 𝒓𝒑=𝑷𝟐𝑷𝟏 is the pressure ratio and k is the specific heat ratio.
2.1.1 The Ideal Cycle for Gas-Turbine Engines The Brayton cycle was first proposed by George Brayton for use in the reciprocating oil-burning engine that he developed around 1870. Today, it is used for gas turbines only where both the compression and expansion processes take place in rotating machinery. Gas turbines usually operate on an open cycle, as shown in Figure (2.1). Fresh air at ambient conditions is drawn into the compressor, where its temperature and pressure are raised. The high pressure air proceeds into the combustion chamber, where the fuel is burned at constant pressure. The resulting high-temperature gases then enter the turbine, where they expand to the atmospheric pressure while producing power. The exhaust gases leaving the turbine are thrown out (not recirculated), causing the cycle to be classified as an open cycle. The open gas-turbine cycle described above can be modeled as a closed cycle, as shown in Figure (2.2), by utilizing the air-standard assumptions. Here the compression and expansion processes remain the same, but the combustion process is replaced by a constant-pressure heat-addition process from an external source, and the exhaust process is replaced by a constant pressure heat-rejection process to the ambient air. The ideal cycle that the working fluid undergoes in this closed loop is the Brayton cycle, which is made up of four internally reversible processes:
Figure (2.3) T-S And P-V Diagrams For The Ideal Brayton Cycle (1- 2) Isentropic compression (in a compressor) (2- 3) Constant-pressure heat addition (3- 4) Isentropic expansion (in a turbine) (4-1) Constant-pressure heat rejection Notice that all four processes of the Brayton cycle are executed in steady flow devices; thus, they should be analyzed as steady-flow processes. When the changes in kinetic and potential energies are neglected, the energy balance for a steady-flow process can be expressed, on a unit–mass basis, as
𝒒𝒊𝒏−𝒒𝒐𝒖𝒕 + 𝒘𝒊𝒏−𝒘𝒐𝒖𝒕 =𝒉𝒆𝒙𝒊𝒕−𝒉𝒊𝒏𝒍𝒆𝒕 ( 1.1)
Therefore, heat transfers to and from the working fluid are 𝒒𝒊𝒏 =𝒉𝟑−𝒉𝟐= 𝒄𝒑(𝑻𝟑−𝑻𝟐) (1.2) and 𝒒𝒐𝒖𝒕=𝒉𝟒−𝒉𝟏= 𝒄𝒑(𝑻𝟒−𝑻𝟏) (1.3) Then the thermal efficiency of the ideal Brayton cycle air standard assumptions becomes: 𝜼𝒕𝒉,𝑩𝒓𝒂𝒚𝒕𝒐𝒏 =𝒘𝒏𝒆𝒕𝒒𝒊𝒏=𝟏−𝒒𝒐𝒖𝒕𝒒𝒊𝒏=𝟏−𝒄𝒑(𝑻𝟒−𝑻𝟏)𝒄𝒑(𝑻𝟑−𝑻𝟐)=𝟏−𝑻𝟏(𝑻𝟒𝑻𝟏 −𝟏)𝑻𝟐(𝑻𝟑𝑻𝟐 −𝟏) (1.4)
Processes 1-2 and 3-4 are isentropic, and P2 = P3 and P4 = P1. Thus, 𝑻𝟐𝑻𝟏 = 𝑷𝟐𝑷𝟏 (𝒌−𝟏)𝒌 = 𝑷𝟑𝑷𝟒 (𝒌−𝟏)𝒌 =𝑻𝟑𝑻𝟒 (1.5)
Substituting these equations into the thermal efficiency relation and simplifying give: 𝜼𝒕𝒉,𝑩𝒓𝒂𝒚𝒕𝒐𝒏= 𝟏−𝟏𝒓𝒑(𝒌−𝟏)𝒌 (1.6)
Where 𝒓𝒑=𝑷𝟐𝑷𝟏 is the pressure ratio and k is the specific heat ratio.
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