Question

Consider a simple ideal Rankine cycle and an ideal regenerative Rankine cycle with one open feed water heater. The two cycles are very much alike, except the feed water in the regenerative cycle is heated by extracting some steam just before it enters the turbine. How would you compare the efficiencies of these two cycles?

Short answer

Short Answer: The ideal regenerative Rankine cycle with one open feed water heater has a higher efficiency compared to the simple ideal Rankine cycle. This is because the regenerative cycle incorporates an open feed water heater, which recovers some of the remaining heat of the steam extracted from the turbine. This reduces overall heat rejection in the condenser and requires less heat input in the boiler to produce the same work output, resulting in higher overall efficiency.

Step-by-step solution

Understand the simple ideal Rankine cycle

A simple ideal Rankine cycle consists of four main components: a boiler, a turbine, a condenser, and a feed pump. The process can be summarized in the following steps: 1. Water is pumped from the condenser to the boiler. 2. The water is heated and converted to steam in the boiler. 3. Steam from the boiler expands in the turbine, converting thermal energy into mechanical work. 4. The steam leaves the turbine and enters the condenser, where it is cooled and returns to the liquid state. 5. Condensed water is then pumped back to the boiler, and the cycle repeats.

Calculate the efficiency of the simple ideal Rankine cycle

To calculate the efficiency of the simple ideal Rankine cycle, we need to consider the work and heat transfers involved in the four main components. The efficiency is given by the formula: Efficiency = \(\frac{Work_{turbine} - Work_{pump}}{Heat_{input}}\) where \(Work_{turbine}\) is the work done by the turbine, \(Work_{pump}\) is the work required by the pump, and \(Heat_{input}\) is the heat input to the cycle (boiler).

Understand the ideal regenerative Rankine cycle with one open feed water heater

A regenerative Rankine cycle with one open feed water heater enhances the efficiency of the simple Rankine cycle. The main difference is the extraction of steam from the turbine before it enters the condenser, which is used to heat the feed water. This results in a higher temperature of the liquid water entering the boiler, increasing the overall efficiency of the cycle.

Calculate the efficiency of the ideal regenerative Rankine cycle

To calculate the efficiency of the ideal regenerative Rankine cycle, we need to consider the work and heat transfers involved in the four main components as well as the open feed water heater. The efficiency is given by the formula: Efficiency = \(\frac{Work_{turbine} - Work_{pump}}{Heat_{input}}\) Keep in mind that \(Work_{turbine}\), \(Work_{pump}\), and \(Heat_{input}\) will be different for the regenerative Rankine cycle compared to the simple Rankine cycle due to the feed water heating process.

Compare the efficiencies of the simple Rankine cycle and regenerative Rankine cycle

Since the simple Rankine cycle and the regenerative Rankine cycle differ only in the preheating of the feed water, the efficiency of the regenerative Rankine cycle can be expected to be higher. The reason is that the additional open feed water heater recovers some of the remaining heat of the steam extracted from the turbine, reducing the overall heat rejection in the condenser. Consequently, the regenerative Rankine cycle requires less heat input in the boiler to produce the same amount of work output, thus providing a higher overall efficiency.