Reheating Explanation in Gas Turbines

Reheating is a process used in gas turbine cycles to improve the performance, particularly the work output. It involves taking the exhaust gas from the first stage turbine, passing it through another combustion chamber (or heat exchanger) to increase its temperature again, and then expanding it in a second turbine stage.

Impact on Turbine Work Output

The primary goal of reheating is to extract more work from the expanding gas. After the first turbine stage, the gas is still at a relatively high pressure and temperature. By reheating it, its enthalpy increases, allowing it to expand further and perform more work in the second turbine stage. Therefore, the total turbine work output increases.

Effect on Compressor Work

The compressor work is determined by the pressure ratio and the mass flow rate of the air entering the compressor. The reheating process itself occurs after the compression stage and does not directly change the work required by the compressor. Thus, the compressor work input remains essentially constant.

Work Ratio Analysis

The work ratio (WR) in a thermodynamic cycle is defined as the ratio of the net work output (or turbine work output) to the compressor work input.

For a gas turbine cycle:

$$ WR = \frac{\text{Turbine Work Output}}{\text{Compressor Work Input}} $$

Since reheating increases the turbine work output while the compressor work input stays the same, the work ratio is bound to increase.

$$ WR_{\text{reheat}} > WR_{\text{no reheat}} $$

Thermal Efficiency Considerations

Thermal efficiency ($\eta_{th}$) is calculated as the ratio of the net work output to the total heat input:

$$ \eta_{th} = \frac{\text{Net Work Output}}{\text{Total Heat Input}} = \frac{\text{Turbine Work Output} - \text{Compressor Work Input}}{\text{Heat Input in Combustor} + \text{Heat Input during Reheating}} $$

While reheating increases the turbine work output (and thus net work output), it also requires additional heat input ($Q_{\text{reheat}}$) in the second combustion stage. Whether the thermal efficiency increases or decreases depends on the magnitude of the increase in net work compared to the increase in heat input.

In many practical scenarios, the additional heat input required for reheating might be proportionally larger than the increase in net work output, especially if there are pressure losses associated with the reheating process or if the reheating temperature is not optimally chosen. This can lead to a decrease in the overall thermal efficiency of the cycle.

Combined Effects of Reheating

Based on the analysis:

• Reheating increases the total work done by the turbine.
• Compressor work remains unchanged.
• Consequently, the work ratio increases.
• However, the additional heat required for reheating can sometimes lead to a decrease in thermal efficiency, as the increase in heat input may outweigh the gains in net work output.

Therefore, reheating results in an increase in the work ratio but can lead to a decrease in thermal efficiency.