Question

Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the cycle is modified with regeneration that involves one open feedwater heater (select the correct statement per unit mass of steam flowing through the boiler), \((a)\) the turbine work output will decrease. \((b)\) the amount of heat rejected will increase. \((c)\) the cycle thermal efficiency will decrease. \((d)\) the quality of steam at turbine exit will decrease. \((e)\) the amount of heat input will increase.

Short answer

Short Answer: None of the given statements are correct. The introduction of an open feedwater heater in a simple ideal Rankine cycle will result in an increase in turbine work output, a decrease in heat rejection, an increase in cycle thermal efficiency, an increase in the quality of steam at the turbine exit, and a decrease in the amount of heat input.

Step-by-step solution

Statement (a): Turbine work output will decrease

By introducing a feedwater heater, the temperature of the feedwater entering the boiler increases, which in turn means the steam generated will have a higher enthalpy. When the high-enthalpy steam expands through the turbine, it will generate more work. Therefore, the turbine work output will actually increase, not decrease. So, this statement is incorrect.

Statement (b): Amount of heat rejected will increase

The feedwater heater reduces the amount of heat required in the boiler to produce steam, which also means that the amount of heat rejected in the condenser will decrease. Since the amount of heat rejected is decreasing, this statement is incorrect.

Statement (c): Cycle thermal efficiency will decrease

Since the turbine work output is increasing and the amount of heat input is decreasing because of the feedwater heater's addition, the overall cycle thermal efficiency (defined as the ratio of net work output to heat input) will increase. Therefore, this statement is also incorrect.

Statement (d): Quality of steam at turbine exit will decrease

The quality of steam at the turbine exit (defined as the ratio of the mass of vapor phase to the total mixture) generally increases with the addition of a feedwater heater. This is because the dryness fraction of the steam at the turbine exit increases, making it less likely for liquid droplets to form, which can cause erosion and damage to turbine blades. Hence, this statement is incorrect.

Statement (e): Amount of heat input will increase

The main purpose of the feedwater heater is to utilize the excess heat from the cycle (from extracted steam) to preheat the feedwater before entering the boiler. This significantly reduces the amount of heat required in the boiler to produce steam. Therefore, the amount of heat input will decrease, not increase. As a result, this statement is also incorrect. Based on the detailed analysis of each statement, none of the options are correct. There is no correct statement in the given options.