Question

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?

Short answer

Answer: The primary effects are: (a) An increase in net work output (b) A decrease in back work ratio (c) An increase in thermal efficiency (d) A decrease in heat rejected

Step-by-step solution

1. Impact of multistage compression with intercooling

Multistage compression with intercooling reduces the overall work input required for the compression process. This is because the intercooling process cools the air before it enters the next compression stage, which requires less work input. The overall effect is a decrease in the work input for compression.

2. Impact of multistage expansion with reheating

Multistage expansion with reheating increases the overall work output of the expansion process. Reheating the air before it enters the next expansion stage allows the air to produce more work, thus increasing the work output. The overall effect is an increase in the work output for expansion.

3. Impact of regeneration

Regeneration transfers heat from the exhaust gas to the compressed air before it enters the combustion chamber. This preheating process reduces the heat added to the cycle, thus reducing the overall heat input. The overall effect is a decrease in the heat input for the cycle. Now, we can analyze the modified cycle parameters as follows:

(a) Net work output

The net work output is given by the difference between the work output from the expansion process and the work input for the compression process. As we saw previously, the expansion work output increases, and the compression work input decreases due to the modifications. Therefore, the net work output increases.

(b) Back work ratio

The back work ratio is defined as the ratio of the work input for the compression process to the work output from the expansion process. Since the compression work input decreases and the expansion work output increases with the modifications, the back work ratio decreases.

(c) Thermal efficiency

Thermal efficiency is defined as the ratio of the net work output to the heat input. As the net work output increases and the heat input decreases due to regeneration, the thermal efficiency increases.

(d) Heat rejected

Heat rejected is defined as the difference between the heat input and the net work output. Since the net work output increases and the heat input decreases due to regeneration, the heat rejected decreases. In conclusion, incorporating multistage compression with intercooling, multistage expansion with reheating, and regeneration in a simple ideal Brayton cycle results in: (a) An increase in net work output (b) A decrease in back work ratio (c) An increase in thermal efficiency (d) A decrease in heat rejected

Key concepts

Multistage Compression with Intercooling

The concept of multistage compression with intercooling plays a critical role in enhancing the performance of gas turbine cycles, such as the Brayton cycle. By dividing the compression process into multiple stages and cooling the air between stages, the required work input for compression is significantly reduced. This is because cooling the air reduces its volume, making the subsequent compression require less energy.

Understanding the mechanics of this process is vital for grasping the overall efficiency improvements in the Brayton cycle. When air is compressed, its temperature increases due to the work done on it. If this hot air were to be compressed further without cooling, it would require more energy and become even hotter. With intercooling, after each compression stage, the air is cooled to a lower temperature before entering the next stage. This not only saves energy but also prevents temperature from reaching excessively high levels that could lead to material fatigue or other technical challenges.

Overall, multistage compression with intercooling leads to a lower required work input, which in turn increases the efficiency and output of the Brayton cycle engines.

Multistage Expansion with Reheating

Just as intercooling benefits the compression portion of the Brayton cycle, multistage expansion with reheating substantially improves the expansion part. In this modification, after the working fluid (such as air or gas) expands and performs work in one turbine stage, it is reheated before entering a subsequent stage of expansion.

This reheating step ensures that the fluid enters the next turbine stage at a higher temperature, which allows for more efficient expansion and more work to be done. The rationale behind reheating is similar to intercooling in reverse; by expanding the gas in stages and reheating it in between, the turbine's efficiency is improved because a consistently higher energy level is maintained throughout the process.

Therefore, extension of the expansion process over several stages, with reheating in between, enhances the work output of a Brayton cycle gas turbine. This is a key factor in the increase of the net power output mentioned in the exercise solution above.

Regeneration in Thermodynamics

Regeneration in thermodynamics is a powerful method to improve the thermal efficiency of heat engines. In the context of the Brayton cycle, it involves capturing waste heat from the exhaust and using it to preheat the compressed air before it enters the combustion chamber. This effectively decreases the amount of heat necessary to reach the desired turbine inlet temperature.

The regeneration process reduces the energy that would otherwise be wasted and, as a consequence, decreases the cycle's heat input. This process not only conserves energy but also contributes to a lower fuel consumption, thereby increasing the cycle's thermal efficiency. The regenerator acts as a heat exchanger and is a critical component for achieving higher efficiency in power plants and aircraft engines utilizing the Brayton cycle.

By incorporating regeneration, the cycle becomes more economical and environmentally friendly due to the reduced fuel requirements. This modification also leads to a decrease in the amount of heat rejected to the environment, as less excess heat is produced.

Thermal Efficiency

Thermal efficiency is a measure of the performance of a heat engine and is defined by the ratio of work output to heat input. In other words, it is an indication of how well an engine converts heat from fuel into useful work. The concept of thermal efficiency is pivotal in understanding how modifications like intercooling, reheating, and regeneration improve the Brayton cycle.

An increase in thermal efficiency, as achieved through these modifications, means that less fuel is required to perform the same amount of work. This improvement is due to the combined effects of reduced work input during compression (thanks to intercooling), increased work output during expansion (due to reheating), and a decrease in heat input necessitated by the cycle (as a result of regeneration).

This enhancement in thermal efficiency is critical for industries relying on gas turbines, as it leads to significant fuel savings and lower operational costs, making it a cornerstone for sustainable and cost-effective energy production.

Back Work Ratio

The back work ratio is a term used in thermodynamics to describe the proportion of energy used for the compression phase relative to the energy produced during the expansion phase of a cycle. It is an important indicator of the effectiveness of a gas turbine engine. A lower back work ratio indicates that a smaller percentage of the turbine's output is being used to drive the compressor and, consequently, more of the work produced is available for output or other uses.

With the enhancements discussed such as multistage compression with intercooling and multistage expansion with reheating, the back work ratio of the Brayton cycle decreases. This is because the work required for compressing the working fluid is reduced and the work generated from expansion is increased. A decrease in the back work ratio implies that the engine is becoming more efficient; less work is spent compressing the air, which means more work is left over for output, be it electrical generation or propulsion.

In the context of the modifications made to the Brayton cycle, a decrease in back work ratio suggests a more efficient cycle with enhanced net power output, thereby portraying a clear advantage of the discussed modifications to the overall performance of the cycle.