Gas Turbine Cycle Quiz

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Questions and Answers

What is the formula for calculating the work done by the compressor per unit of mass?

$rac{h_3 - h_4}{ ext{ṁ}}$

$rac{h_1 - h_2}{ ext{ṁ}}$

$rac{h_2 - h_1}{ ext{ṁ}}$ (correct)

$rac{h_4 - h_3}{ ext{ṁ}}$

Which equation represents the heat added to the cycle per unit of mass?

$rac{h_1 - h_3}{ ext{ṁ}}$

$rac{h_3 - h_2}{ ext{ṁ}}$ (correct)

$rac{h_2 - h_4}{ ext{ṁ}}$

$rac{h_4 - h_1}{ ext{ṁ}}$

What is the back-work ratio formula for the cycle?

$rac{h_3 - h_4}{h_2 - h_1}$

$rac{ ext{W}_c}{ ext{W}_t}$

$rac{h_3 - h_2}{h_4 - h_1}$

$rac{h_2 - h_1}{h_3 - h_4}$ (correct)

What is the typical back-work ratio for gas turbines?

66% Signup and view all the answers

What happens to the specific heats when considering irreversibilities in the cycle?

Their variation with temperature is ignored. Signup and view all the answers

What is typically true about the work input required by a gas turbine compressor compared to a vapor power plant pump?

It requires much greater work input. Signup and view all the answers

How is thermal efficiency of the cycle calculated?

$rac{h_3 - h_4 - h_2 - h_1}{h_3 - h_2}$ Signup and view all the answers

What is the significance of the average specific volume of gas in compressors versus liquids in pumps?

Gas has a larger specific volume, requiring more work. Signup and view all the answers

What happens to the steam production when the pinch point is lowered in a heat recovery steam generator (HRSG)?

Steam production increases. Signup and view all the answers

What is the optimum value for the pinch point in a heat recovery steam generator (HRSG)?

8-10°C Signup and view all the answers

How does a lower approach temperature in the economizer affect steam production?

It produces more steam due to flashing. Signup and view all the answers

What is the impact of a higher pinch point on the cost of heat exchangers?

It increases the need for larger heat exchange surface area. Signup and view all the answers

What is the role of gas turbines in the combined gas turbine-vapor power cycle?

To provide sufficient heat for the steam cycle. Signup and view all the answers

What does the area to the left of the compression curve in a p–v diagram represent?

The magnitude of the work per unit mass of the process Signup and view all the answers

Why is cooling gas during compression considered advantageous?

It reduces the work input requirement Signup and view all the answers

What role do intercoolers play in a multi-stage compressor system?

They cool the gas between compression stages to enhance efficiency Signup and view all the answers

In a two-stage compressor setup, what is the purpose of the constant-pressure cooling stage?

To reduce the temperature of the gas before further compression Signup and view all the answers

What is indicated by the shaded area on the p–v diagram in relation to intercooling?

Reduction in work achieved with intercooling Signup and view all the answers

What type of compression occurs in the absence of intercooling in a single-stage compressor?

Isentropic compression Signup and view all the answers

What is a significant challenge in achieving effective cooling during gas compression?

High heat transfer rates are difficult to achieve Signup and view all the answers

What optimization problem arises in multi-stage compressors with intercooling?

Determining the number of stages and operating conditions for intercoolers Signup and view all the answers

What is the outcome when the pressure ratio is increased in a gas turbine for a fixed turbine inlet temperature?

Net work output per cycle decreases after reaching a maximum. Signup and view all the answers

What is the typical range of pressure ratios for gas turbines in common designs?

11 to 16 Signup and view all the answers

What happens to the required mass flow rate when a cycle has a lower net work output per cycle?

It increases, requiring a larger system. Signup and view all the answers

What is the implication of friction in gas turbine components on the working fluid?

It causes pressure drops along with an increase in specific entropy. Signup and view all the answers

How does a larger enclosed area in cycle B benefit mass flow rates compared to cycle A?

It allows for greater net power outputs. Signup and view all the answers

In the derived equations for net work output, what variable primarily affects the performance of the gas turbine?

Temperature of the working fluid at various state points. Signup and view all the answers

If a cycle must increase its mass flow rate to maintain power output, what could be a potential downside?

It may lead to reduced efficiency. Signup and view all the answers

What is the significance of the equation provided for net work output in terms of system performance?

It captures the relationship between temperature differences and work output. Signup and view all the answers

What effect does increasing the heat transfer area have on temperature difference in the regenerator?

It decreases the temperature difference at all locations. Signup and view all the answers

What is the maximum theoretical value for the temperature Tx of the air exiting on the compressor side of the regenerator?

It approaches the turbine exhaust temperature T4 when operating reversibly. Signup and view all the answers

What happens to the regenerator effectiveness η_reg as heat transfer approaches reversibility?

η_reg tends to unity (100%). Signup and view all the answers

What typical range do regenerator effectiveness values normally fall within?

60% to 80% Signup and view all the answers

What is the consequence of increasing regenerator effectiveness beyond the typical range?

It requires a larger heat transfer area and increases equipment costs. Signup and view all the answers

What parameter is defined as the ratio of the actual enthalpy increase to the maximum theoretical enthalpy increase in a regenerator?

Regenerator effectiveness (η_reg). Signup and view all the answers

How does the requirement for a greater heat transfer area affect overall performance when increasing regenerator effectiveness?

It results in a significant frictional pressure drop. Signup and view all the answers

What primarily influences the decision to add a regenerator?

Economic considerations. Signup and view all the answers

What is the primary function of the diffuser in a turbojet engine?

To decelerate incoming air and increase pressure Signup and view all the answers

In a turbojet engine, what role does the turbine play?

It drives the compressor and auxiliary equipment Signup and view all the answers

What happens in the combustor of a turbojet engine?

Fuel is burned at constant pressure Signup and view all the answers

What is the effect of an afterburner in a turbojet engine?

It increases thrust by raising nozzle exit velocity Signup and view all the answers

Which process involves isentropic expansion in a turbojet engine?

Expansion through the turbine Signup and view all the answers

What does the T–s diagram represent in the ideal turbojet engine analysis?

Processes in terms of temperature and entropy Signup and view all the answers

What is the effect of isentropic compression on the air in a turbojet engine?

It increases the air temperature and pressure Signup and view all the answers

What occurs during the process of deceleration in the diffuser?

Static pressure rises due to ram effect Signup and view all the answers

Study Notes

Power Station Chapter 3: Gas Power Cycle

Gas turbines are often lighter and more compact than vapor power plants.
They are well-suited for transportation applications (e.g., planes, maritime power plants) thanks to their advantageous power output-to-weight ratio.
Gas turbines are frequently used for generating stationary power.

Brayton Cycle

Gas turbines typically operate on an open cycle.
Ambient air enters the compressor, increasing its temperature and pressure.
High-pressure air proceeds to the combustion chamber where fuel is burned at constant pressure.
The resulting high-temperature gases enter the turbine, expanding to atmospheric pressure while generating power.
Exhaust gases are expelled, not recirculated, classifying the cycle as open.
The open cycle can be modeled as a closed cycle using air-standard assumptions.
Air-standard analysis simplifies gas turbine study by treating air as an ideal gas and assuming combustion as a constant-pressure heat addition.

Evaluating Principal Work and Heat Transfers

Work and heat transfers at steady state are derived from control volume mass and energy balances.
Adiabatic turbine work (per unit mass) is h₃ - h₄.
Compressor work (per unit mass) is h₂ - h₁.
Heat added (per unit mass) is h₃ - h₂.
Heat rejected (per unit mass) is h₄ - h₁.
Thermal efficiency is (W_t/m - W_c/m) / (Q_in/m).
Back-work ratio = (W_c/m) / (W_t/m).
Specific enthalpies are readily obtained from ideal gas tables if temperatures are known.

Effect of Pressure Ratio on Performance

Thermal efficiency increases with increasing pressure ratio across the compressor.
Higher pressure ratios yield a higher average temperature of heat addition in the cycle, leading to improved thermal efficiency.

Gas Turbine Irreversibilities and Losses

Irreversibilities, such as frictional pressure drops in components, cause increases in specific entropy (a measure of disorder).
These losses result in pressure drops through heat exchangers.
While significant, these losses are usually secondary and often ignored in simplified analyses.

Gas Turbines with Regeneration

Regeneration utilizes heat from turbine exhaust to preheat air entering the combustion chamber.
This reduces the amount of fuel needed, increasing thermal efficiency.
The regenerator is a counterflow heat exchanger.
Regenerator effectiveness gauges its efficiency compared to a reversible regenerator.
A heat transfer from an external source is needed only to raise temperature from stage 𝑥 to 3, not entirely through 2 to 3 as in a non-regenerative system.

Gas Turbines with Reheat

Reheat improves network by allowing the combustion gases to be reheated at constant pressure before expanding through subsequent turbine sections.
This method increases the total work output even though additional heat addition is required.
The reheat cycle's total network is greater than a non-reheat cycle, but the resulting temperature at the turbine exit is higher, leading to potential enhancement of reheat.
Reheat is commonly used with regenerative cycles.
High reheat temperatures are limited by material limitations.

Gas Turbines with Compression with Intercooling

Intercooling reduces compressor work input by compressing the working fluid (air) in stages and cooling it between each compression stage.
This reduces the energy needed from the power plant to run the compressor stages.
Intercooling between compression stages results in lower work input than for the adiabatic compression process.

Regeneration, Reheat, and Intercooling

Simultaneous application of these technologies leads to a substantial performance improvement in gas turbines.

Gas Turbines for Aircraft Propulsion

Gas turbines are favored for aircraft propulsion due to their favorable power-to-weight ratio.
Turbojet engines, the simplest form, have a diffuser, gas generator, and nozzle.
The gas generator handles compression, combustion, and turbine.
Thrust results from expelling hot compressed gases at high velocity through the nozzle, creating a reaction.
Afterburners are added to some turboprops to boost thrust by injecting fuel into the turbine exhaust stream and burning it.

Turboprop vs. Turbofan

In turboprops, a significant part of the turbine's output drives a propeller, creating thrust.
In turbofans, most thrust comes from the high velocity exhaust gases exiting the nozzle.

Ramjet

Ramjets are simple turbine engines without compressors or turbines.
They rely on the ram effect of high-speed incoming air to generate sufficient pressure for combustion.
Useful for high-speed flight applications where prior air compression is already provided.

Combined Gas Turbine-Vapor Power Cycle

Combined cycles couple a gas turbine cycle (topping cycle) with a vapor cycle.
The high-temperature exhaust gases from the gas turbine preheat the air entering the vapor cycle.
This approach generally increases efficiency because of the high temperatures involved in the gas streams.
The temperature difference between the water and the higher temperature stream in the heat exchanger may be the limiting factor.

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Description

Test your knowledge on the gas turbine cycle concepts including work done by compressors, heat added, and back-work ratios. This quiz will cover essential formulas and typical values related to gas turbines, enhancing your understanding of thermodynamic cycles.