All four components associated with the Rankine cycle (the pump, boiler, turbine, and condenser) are steady-flow devices, and thus all four processes that make up the Rankine cycle can be analyzed as steady-flow processes. The kinetic and potential energy changes of the steam are usually small relative to the work and heat transfer terms and are therefore usually neglected. Then the steady-flow energy equation per unit mass of steam reduces to 𝒒𝒊𝒏−𝒒𝒐𝒖𝒕 + 𝒘𝒊𝒏−𝒘𝒐𝒖𝒕 =𝒉𝒆−𝒉𝒊 (kJ/kg) (1.9) The boiler and the condenser do not involve any work, and the pump and the turbine are assumed to be isentropic. Then the conservation of energy relation for each device can be expressed as follows: Pump (q = 0): 𝒘𝒑𝒖𝒎𝒑,𝒊𝒏=𝒉𝟐−𝒉𝟏 (1.10) or 𝒘𝒑𝒖𝒎𝒑,𝒊𝒏=𝒗(𝑷𝟐−𝑷𝟏) (1.11) Where 𝒉𝟏=𝒉𝒇 @ 𝑷𝟏 and 𝒗≅𝒗𝟏=𝒗𝒇 @ 𝑷𝟏 Boiler (w = 0): 𝒒𝒊𝒏=𝒉𝟑−𝒉𝟐 (1.12) Turbine (q = 0): 𝒘𝒕𝒖𝒓𝒃,𝒐𝒖𝒕=𝒉𝟑−𝒉𝟒 (1.13) Condenser (w = 0): 𝒒𝒐𝒖𝒕=𝒉𝟒−𝒉𝟏 (1.14) The thermal efficiency of the Rankine cycle is determined from
𝜼𝒕𝒉=𝒘𝒏𝒆𝒕𝒒𝒊𝒏=𝟏−𝒒𝒐𝒖𝒕𝒒𝒊𝒏 (1.15) Where 𝒘𝒏𝒆𝒕=𝒒𝒊𝒏−𝒒𝒐𝒖𝒕=𝒘𝒕𝒖𝒓𝒃,𝒐𝒖𝒕−𝒘𝒑𝒖𝒎𝒑,𝒊𝒏 (1.16)
2.2.3 Deviation of Actual Vapor Power Cycles From Idealized Ones The actual vapor power cycle differs from the ideal Rankine cycle, as illustrated in Figure (2.6a), as a result of irreversibility in various components. Fluid friction and heat loss to the surroundings are the two common sources of irreversibility. Fluid friction causes pressure drops in the boiler, the condenser, and the piping between various components. As a result, steam leaves the boiler at a somewhat lower pressure. Also, the pressure at the turbine inlet is somewhat lower than that at the boiler exit due to the pressure drop in the connecting pipes. The pressure drop in the condenser is usually very small. To compensate for these pressure drops, the water must be pumped to a sufficiently higher pressure than the ideal cycle calls for. This requires a larger pump and larger work input to the pump. The other major source of irreversibility is the heat loss from the steam to the surroundings as the steam flows through various components. To maintain the same level of net work output, more heat needs to be transferred to the steam in the boiler to compensate for these undesired heat losses. As a result, cycle efficiency decreases. Of particular importance are the irreversibility occurring within the pump and the turbine. A pump requires a greater work input, and a turbine produces a smaller work output as a result of irreversibility. Under ideal conditions, the flow through these devices is isentropic. The deviation of actual pumps and turbines from the isentropic ones can be accounted for by utilizing isentropic efficiencies, defined as
𝜼𝑷=𝒘𝒔𝒘𝒂=𝒉𝟐𝒔−𝒉𝟏𝒉𝟐𝒂−𝒉𝟏 (1.17) and 𝜼𝑻=𝒘𝒂𝒘𝒔=𝒉𝟑−𝒉𝟒𝒂𝒉𝟑−𝒉𝟒𝒔 (1.18) Where states 1a and 4a are the actual exit states of the pump and the turbine, respectively, and 1s and 4s are the corresponding states for the isentropic case Figure (2.6b).
Figure (2.6) (A) Deviation Of Actual Vapor Power Cycle From The Ideal Rankine Cycle. (B) The Effect Of Pump And Turbine Irreversibility On The Ideal Rankine Cycle
Other factors also need to be considered in the analysis of actual vapor power cycles. In actual condensers, for example, the liquid is usually sub-cooled to prevent the onset of cavitation, the rapid vaporization and condensation of the fluid at the low-pressure side of the pump impeller, which may damage it. Additional losses occur at the bearings between the moving parts as a result of friction. Steam that leaks out during the cycle and air that leaks into the condenser represent two other sources of loss. Finally, the power consumed by the auxiliary equipment such as fans that supply air to the furnace should also be considered in evaluating the overall performance of power plants.
𝜼𝒕𝒉=𝒘𝒏𝒆𝒕𝒒𝒊𝒏=𝟏−𝒒𝒐𝒖𝒕𝒒𝒊𝒏 (1.15) Where 𝒘𝒏𝒆𝒕=𝒒𝒊𝒏−𝒒𝒐𝒖𝒕=𝒘𝒕𝒖𝒓𝒃,𝒐𝒖𝒕−𝒘𝒑𝒖𝒎𝒑,𝒊𝒏 (1.16)
2.2.3 Deviation of Actual Vapor Power Cycles From Idealized Ones The actual vapor power cycle differs from the ideal Rankine cycle, as illustrated in Figure (2.6a), as a result of irreversibility in various components. Fluid friction and heat loss to the surroundings are the two common sources of irreversibility. Fluid friction causes pressure drops in the boiler, the condenser, and the piping between various components. As a result, steam leaves the boiler at a somewhat lower pressure. Also, the pressure at the turbine inlet is somewhat lower than that at the boiler exit due to the pressure drop in the connecting pipes. The pressure drop in the condenser is usually very small. To compensate for these pressure drops, the water must be pumped to a sufficiently higher pressure than the ideal cycle calls for. This requires a larger pump and larger work input to the pump. The other major source of irreversibility is the heat loss from the steam to the surroundings as the steam flows through various components. To maintain the same level of net work output, more heat needs to be transferred to the steam in the boiler to compensate for these undesired heat losses. As a result, cycle efficiency decreases. Of particular importance are the irreversibility occurring within the pump and the turbine. A pump requires a greater work input, and a turbine produces a smaller work output as a result of irreversibility. Under ideal conditions, the flow through these devices is isentropic. The deviation of actual pumps and turbines from the isentropic ones can be accounted for by utilizing isentropic efficiencies, defined as
𝜼𝑷=𝒘𝒔𝒘𝒂=𝒉𝟐𝒔−𝒉𝟏𝒉𝟐𝒂−𝒉𝟏 (1.17) and 𝜼𝑻=𝒘𝒂𝒘𝒔=𝒉𝟑−𝒉𝟒𝒂𝒉𝟑−𝒉𝟒𝒔 (1.18) Where states 1a and 4a are the actual exit states of the pump and the turbine, respectively, and 1s and 4s are the corresponding states for the isentropic case Figure (2.6b).
Figure (2.6) (A) Deviation Of Actual Vapor Power Cycle From The Ideal Rankine Cycle. (B) The Effect Of Pump And Turbine Irreversibility On The Ideal Rankine Cycle
Other factors also need to be considered in the analysis of actual vapor power cycles. In actual condensers, for example, the liquid is usually sub-cooled to prevent the onset of cavitation, the rapid vaporization and condensation of the fluid at the low-pressure side of the pump impeller, which may damage it. Additional losses occur at the bearings between the moving parts as a result of friction. Steam that leaks out during the cycle and air that leaks into the condenser represent two other sources of loss. Finally, the power consumed by the auxiliary equipment such as fans that supply air to the furnace should also be considered in evaluating the overall performance of power plants.
ليست هناك تعليقات:
إرسال تعليق