Attached are two identical single-shaft gas turbines V94.2. One of them, GT1, has an output power 5 MW greater than GT2. Upon investigation, it was observed that the radial gap (clearance) of the first compressor blades in GT2 is larger than in GT1. I am looking to grasp the theoretical understanding behind this difference. Can you provide the formula for gas turbine output power and mass flow rate of air? Furthermore, is there a relationship or formula between the compressor radial clearance and mass flow rate? Any advice with formulas would be greatly appreciated. Please note that the radial clearance information is displayed in the attached image, excluding the 1st stage.
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The power output of a gas turbine is directly proportional to the mass flow rate of air given by the formula, P=ηmCp(T3-T4), where P is the power output, η is the efficiency, m is mass flow rate of air, Cp is the specific heat at constant pressure, and T3, T4 are the inlet and outlet temperatures of the gas. This states that more the mass flow rate of air, higher is the power output. The compressor radial clearance plays a significant role in the performance of the gas turbine. If the radial clearance of the compressor is more, it provides more space for the air flow leading to a decreased velocity of air at the outlet. This reduction in outlet air velocity may lead to a decrease in the mass flow rate of air, resulting in a lower power output. While I don't have an exact formula linking radial clearance to mass flow rate, I hope this explanation helps you understand the relationship between them. More clearance generally causes greater leakage, lowering efficiency, and thereby reducing power output.
The output power of a gas turbine is directly proportional to the mass flow rate of air. A larger radial clearance in the compressor blades tends to decrease the mass flow rate due to increased leakages. As a result, less compressed air is available for combustion, which in turn reduces the turbine's output power. A key formula related to this is the Brayton cycle efficiency η = 1 - (1/compression ratio^(γ-1)), where γ represents the heat capacity ratio. Understanding this might clarify the issue you’re dealing with - a smaller clearance leads to higher compression ratios, hence more efficiency. However, linking radial clearance to mass flow rate would need further research and complex computational fluid dynamic modeling, as multiple parameters are interlinked.
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Answer: Answer: The difference in output power might be linked to variations in compressor blade clearances, as observed in GT1 and GT2.
Answer: Answer: Yes, there are formulas available to calculate gas turbine output power and mass flow rate of air. These formulas can help in understanding the performance differences between the turbines.
Answer: Answer: There might be a relationship between compressor radial clearance and mass flow rate in gas turbines, as the clearances can affect the efficiency and performance of the compressor blades. Formulas related to this relationship may help in analyzing the discrepancies observed in GT1 and GT2.
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