Question

For a specified pressure ratio, why does multistage compression with intercooling decrease the compressor work, and multistage expansion with reheating increase the turbine work?

Short answer

Answer: Multistage compression with intercooling decreases compressor work because the introduction of intercooling between compression stages reduces the gas temperature, making it easier to compress in the next stage. On the other hand, multistage expansion with reheating increases turbine work by maintaining higher gas temperatures throughout the expansion process, which directly affects the work generated during the expansion.

Step-by-step solution

Understand Multistage Compression with Intercooling

Multistage compression is used to increase the efficiency of compressors by reducing the work required to compress a gas. Intercooling is a process where a cooling mechanism is introduced between consecutive compression stages to remove heat generated during compression. The purpose of intercooling is to reduce the temperature of the gas entering the next compression stage, which in turn reduces the work required for the next compression stage.

Explain why Multistage Compression with Intercooling decreases Compressor Work

When intercooling is introduced between the stages of compression, it reduces the temperature of the gas. As a result, the gas volume decreases, making it easier to compress in the next stage. By reducing the gas temperature at each stage, multistage compression with intercooling effectively decreases the overall work required for compression. To understand this better, let's consider the work required to compress a gas isentropically (without heat transfer) as per the equation: \(W_{compressor} = \int_{V_1}^{V_2} PdV\) where \(W_{compressor}\) is the work required, and \(V_1\) and \(V_2\) are the initial and final volumes, respectively. By reducing the gas temperature, intercooling decreases the final volume \(V_2\), consequently reducing the work required for compression.

Understand Multistage Expansion with Reheating

In multistage expansion, the gas turbine is divided into multiple stages, with each stage expanding the gas partially. Reheating is a process where heat is added to the gas between expansion stages to increase its temperature. This helps to maintain higher gas temperatures throughout the expansion stages, which leads to an increase in the turbine work.

Explain why Multistage Expansion with Reheating increases Turbine Work

In a gas turbine, the work generated during the expansion process is directly proportional to the gas temperature. \(W_{turbine} = \int_{V_1}^{V_2} PdV\) In a multistage expansion process with reheating, the gas temperature is increased between the expansion stages, which helps maintain a higher gas temperature throughout the expansion process. As a result, the work generated during the expansion process is increased, leading to an overall increase in the turbine work. In conclusion, the use of multistage compression with intercooling reduces the work required for compression by reducing gas temperatures between compression stages, while multistage expansion with reheating increases turbine work by maintaining higher gas temperatures throughout the expansion process.