To address the various aspects of the Rankine cycle with reheat and regeneration, we'll follow a structured approach to sketch the T-s diagram, calculate the thermal efficiency, determine the mass flow rate, and analyze the effects and improvements.
1. T-s Diagram
The T-s diagram for the Rankine cycle with reheat and regeneration typically involves the following key states:
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State 1: Water entering the high-pressure turbine (15 MPa, 600°C)
State 2: Steam exiting the high-pressure turbine and entering the reheater (1 MPa, partial expansion)
State 3: Steam exiting the reheater and entering the low-pressure turbine (550°C, 1 MPa)
State 4: Steam exiting the low-pressure turbine and entering the condenser (10 kPa)
State 5: Water leaving the condenser and entering the feedwater heater (0.5 MPa, 25°C)
State 6: Water exiting the feedwater heater and entering the pump (0.5 MPa)
State 7: Water exiting the pump and entering the high-pressure boiler (15 MPa)
Sketch: Plot temperature (T) on the vertical axis and entropy (s) on the horizontal axis. The cycle will show
High-pressure (15 MPa) with a high temperature (600°C) in the rightmost part of the diagram.
Expansion and reheating followed by further expansion to lower pressures.
A line sloping downwards as the steam condenses at the condenser.
The feedwater heating process, which increases temperature while maintaining pressure
2. Thermal Efficiency Calculation
To find the thermal efficiency, we need to calculate the enthalpies at all key points. We'll use steam tables and isentropic efficiency for this.
Steps:
Enthalpy at State 1 (h1):
Given: 15 MPa, 600°C. Use steam tables for this condition.
Enthalpy at State 2 (h2):
• Partial expansion to 1 MPa. Determine the enthalpy using steam tables or the isentropic process equation if you have the entropy values.
• Calculate using isentropic efficiency for the turbine if needed.
Enthalpy at State 3 (h3):
Given: 550°C, 1 MPa (after reheating). Use steam tables for this condition.
Enthalpy at State 4 (h4):
At 10 kPa. Use steam tables to determine the enthalpy.
Enthalpy at State 5 (h5)
After condensation, water enters the feedwater heater. It’s usually near saturation temperature at this pressure (0.5 MPa).
Enthalpy at State 6 (h6):
Enthalpy of water exiting the feedwater heater (assumed to be close to liquid at 0.5 MPa).
Enthalpy at State 7 (h7):
After pump compression, use the pump efficiency to find the increase in enthalpy.
Using these enthalpies, the thermal efficiency () of the cycle can be calculated using:
Where:• Heat Input = h1−h7
3. Mass Flow Rate Calculation
To find the mass flow rate () required to generate 100 MW:
steam is calculated using the enthalpy values.4. Effect of Reheat and Regeneration
Comparison:
A cycle with reheat generally has higher efficiency than a simple Rankine cycle because reheating increases the average temperature of heat addition.
Regeneration reduces the heat required in the boiler by preheating the feedwater, thus improving efficiency.
5. Energy Destruction Analysis
Energy destruction (exergy loss) in each component can be evaluated by calculating the difference between the actual work and ideal work, considering the temperature of the environment (25°C).
Components:
Boiler: Loss due to irreversibilities and temperature difference.
Turbine: Loss due to non-ideal expansion (isentropic efficiency).
Reheater: Loss due to temperature difference in reheating.
Feedwater Heater: Loss due to temperature difference in heating.
Condenser: Loss due to temperature difference in condensation.
The component with the most significant temperature difference to the environment or the lowest efficiency contributes most to the energy destruction.
6. Improvement Proposal
Proposal: Implement a combined cycle with a gas turbine (Combined Cycle Gas Turbine - CCGT).
Justification:
By utilizing the waste heat from a gas turbine to preheat the feedwater, you can increase the efficiency of the Rankine cycle.
This approach improves overall thermal efficiency by utilizing waste heat that would otherwise be lost.
This strategy leverages the high temperature and pressure of the gas turbine exhaust to provide additional heat for the Rankine cycle, effectively increasing its efficiency.
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