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How does regeneration affect the efficiency of a Brayton cycle, and how does it accomplish it?

Short Answer

Expert verified
Answer: Regeneration affects the efficiency of a Brayton cycle by increasing it. This is achieved by preheating the air entering the compressor using the exhaust gases from the turbine, which reduces the amount of heat required from the external source and improves the overall efficiency of the cycle.

Step by step solution

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1. Understanding the Brayton Cycle

The Brayton cycle consists of four processes: adiabatic compression, constant pressure heating, adiabatic expansion, and constant pressure cooling. The working fluid (air) enters the compressor, where its pressure increases. It then receives heat from an external source and expands in an adiabatic turbine. The exhaust gases from the turbine are cooled before being mixed with fresh air and entering the compressor again.
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2. Brayton Cycle Efficiency

The efficiency of a Brayton cycle can be expressed as: η = 1 - \frac{T1(T3 - T2)}{T2(T3 - T1)} Here, η is the cycle efficiency, T1 is the temperature at the entry to the compressor, T2 is the temperature at the exit of the compressor, and T3 is the temperature at the exit of the turbine.
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3. Regeneration in Brayton Cycle

Regeneration is a process that improves the efficiency of the Brayton cycle by preheating the air before it enters the compressor. The exhaust gases from the turbine are used to heat the incoming air in a heat exchanger called a regenerator or recuperator. By transferring heat from the exhaust gas to the incoming air, the amount of heat required from the external source is reduced, and the overall efficiency of the cycle is increased.
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4. Effect of Regeneration on Efficiency

The efficiency of a regenerative Brayton cycle can be expressed as: η_r = 1 - \frac{T1(T3 - T2)}{T2(T3 - T1_r)} Where T1_r is the temperature at the entry to the compressor after regeneration. Since T1_r is higher than T1 (due to preheating), the denominator of the fraction will be greater in the case of a regenerative Brayton cycle. As a result, the overall efficiency (η_r) will be higher. In conclusion, regeneration affects the efficiency of a Brayton cycle by increasing it, which is achieved by preheating the air entering the compressor using the exhaust gases from the turbine. This reduces the amount of heat required from the external source and improves the overall efficiency of the cycle.

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Most popular questions from this chapter

An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is \(95 \mathrm{kPa}\) and \(20^{\circ} \mathrm{C}\). If the maximum temperature in the cycle is not to exceed \(2200 \mathrm{K}\) determine \((a)\) the thermal efficiency and \((b)\) the mean effective pressure. Assume constant specific heats for air at room temperature.

A gas-turbine power plant operates on a simple Brayton cycle with air as the working fluid. The air enters the turbine at 120 psia and \(2000 \mathrm{R}\) and leaves at 15 psia and \(1200 \mathrm{R} .\) Heat is rejected to the surroundings at a rate of 6400 \(\mathrm{Btu} / \mathrm{s},\) and air flows through the cycle at a rate of \(40 \mathrm{lbm} / \mathrm{s}\) Assuming the turbine to be isentropic and the compresssor to have an isentropic efficiency of 80 percent, determine the net power output of the plant. Account for the variation of specific heats with temperature.

A simple ideal Brayton cycle is modified to incorporate multistage compression with intercooling, multistage expansion with reheating, and regeneration without changing the pressure limits of the cycle. As a result of these modifications, (a) Does the net work output increase, decrease, or remain the same? (b) Does the back work ratio increase, decrease, or remain the same? \((c) \quad\) Does the thermal efficiency increase, decrease, or remain the same? (d) Does the heat rejected increase, decrease, or remain the same?

Consider the ideal regenerative Brayton cycle. Determine the pressure ratio that maximizes the thermal efficiency of the cycle and compare this value with the pressure ratio that maximizes the cycle net work. For the same maximumto- minimum temperature ratios, explain why the pressure ratio for maximum efficiency is less than the pressure ratio for maximum work.

Air at \(7^{\circ} \mathrm{C}\) enters a turbojet engine at a rate of \(16 \mathrm{kg} / \mathrm{s}\) and at a velocity of \(300 \mathrm{m} / \mathrm{s}\) (relative to the engine). Air is heated in the combustion chamber at a rate \(15,000 \mathrm{kJ} / \mathrm{s}\) and it leaves the engine at \(427^{\circ} \mathrm{C}\). Determine the thrust produced by this turbojet engine. (Hint: Choose the entire engine as your control volume.

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