Thermal Engineering

Thermal Efficiency of Rankine Cycle

In general the thermal efficiency, η_th, of any heat engine is defined as the ratio of the work it does, W, to the heat input at the high temperature, Q_H.

The thermal efficiency, η_th, represents the fraction of heat, Q_H, that is converted to work. Since energy is conserved according to the first law of thermodynamics and energy cannot be be converted to work completely, the heat input, Q_H, must equal the work done, W, plus the heat that must be dissipated as waste heat Q_C into the environment. Therefore we can rewrite the formula for thermal efficiency as:

This is very useful formula, but here we express the thermal efficiency using the first law in terms of enthalpy.

Typically most of nuclear power plants operates multi-stage condensing steam turbines. In these turbines the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure; 6 MPa; 275.6°C) from a steam generator and exhaust it to moisture separator-reheater (point D). The steam must be reheated in order to avoid damages that could be caused to blades of steam turbine by low quality steam. The reheater heats the steam (point D) and then the steam is directed to the low-pressure stage of steam turbine, where expands (point E to F). The exhausted steam then condenses in the condenser and it is at a pressure well below atmospheric (absolute pressure of 0.008 MPa), and is in a partially condensed state (point F), typically of a quality near 90%.

In this case, steam generators, steam turbine, condensers and feedwater pumps constitute a heat engine, that is subject to the efficiency limitations imposed by the second law of thermodynamics. In ideal case (no friction, reversible processes, perfect design), this heat engine would have a Carnot efficiency of

= 1 – T_cold/T_hot = 1 – 315/549 = 42.6%

where the temperature of the hot reservoir is 275.6°C (548.7K), the temperature of the cold reservoir is 41.5°C (314.7K). But the nuclear power plant is the real heat engine, in which thermodynamic processes are somehow irreversible. They are not done infinitely slowly. In real devices (such as turbines, pumps, and compressors) a mechanical friction and heat losses cause further efficiency losses.

To calculate the thermal efficiency of the simplest Rankine cycle (without reheating) engineers use the first law of thermodynamics in terms of enthalpy rather than in terms of internal energy.

The first law in terms of enthalpy is:

dH = dQ + Vdp

In this equation the term Vdp is a flow process work. This work,  Vdp, is used for open flow systems like a turbine or a pump in which there is a “dp”, i.e. change in pressure. There are no changes in control volume. As can be seen, this form of the law simplifies the description of energy transfer. At constant pressure, the enthalpy change equals the energy transferred from the environment through heating:

Isobaric process (Vdp = 0):

dH = dQ     →     Q = H₂ – H₁

At constant entropy, i.e. in isentropic process, the enthalpy change equals the flow process work done on or by the system:

Isentropic process (dQ = 0):

dH = Vdp     →     W = H₂ – H₁

It is obvious, it will be very useful in analysis of both thermodynamic cycles used in power engineering, i.e. in Brayton cycle and Rankine cycle.

The enthalpy can be made into an intensive, or specific, variable by dividing by the mass. Engineers use the specific enthalpy in thermodynamic analysis more than the enthalpy itself. It is tabulated in the steam tables along with specific volume and specific internal energy. The thermal efficiency of such simple Rankine cycle and in terms of specific enthalpies would be:

It is very simple equation and for determination of the thermal efficiency you can use data from steam tables.

In modern nuclear power plants the overall thermal efficiency is about one-third (33%), so 3000 MWth of thermal power from the fission reaction is needed to generate 1000 MWe of electrical power. The reason lies in relatively low steam temperature (6 MPa; 275.6°C). Higher efficiencies can be attained by increasing the temperature of the steam. But this requires an increase in pressures inside boilers or steam generators. However, metallurgical considerations place an upper limits on such pressures. In comparison to other energy sources the thermal efficiency of 33% is not much. But it must be noted that nuclear power plants are much more complex than fossil fuel power plants and it is much easier to burn fossil fuel ,than to generate energy from nuclear fuel. Sub-critical fossil fuel power plants, that are operated under critical pressure (i.e. lower than 22.1 MPa), can achieve 36–40% efficiency.

Causes of Inefficiency

As was discussed, an efficiency can range between 0 and 1. Each heat engine is somehow inefficient. This inefficiency can be attributed to three causes.

• Irreversibility of Processes. There is an overall theoretical upper limit to the efficiency of conversion of heat to work in any heat engine. This upper limit is called the Carnot efficiency. According to the Carnot principle, no engine can be more efficient than a reversible engine (a Carnot heat engine) operating between the same high temperature and low temperature reservoirs. For example, when the hot reservoir have T_hot of 400°C (673K) and T_cold of about 20°C (293K), the maximum (ideal) efficiency will be: = 1 – T_cold/T_hot = 1 – 293/673 = 56%. But all real thermodynamic processes are somehow irreversible. They are not done infinitely slowly. Therefore, heat engines must have lower efficiencies than limits on their efficiency due to the inherent irreversibility of the heat engine cycle they use.
• Presence of Friction and Heat Losses. In real thermodynamic systems or in real heat engines, a part of the overall cycle inefficiency is due to the losses by the individual components. In real devices (such as turbines, pumps, and compressors) a mechanical friction, heat losses and losses in the combustion process cause further efficiency losses.
• Design Inefficiency. Finally, last and also important source of inefficiencies is from the compromises made by engineers when designing a heat engine (e.g. power plant). They must consider cost and other factors in the design and operation of the cycle. As an example consider a design of the condenser in the thermal power plants.  Ideally the steam exhausted into the condenser would have no subcooling. But real condensers are designed to subcool the liquid by a few degrees of Celsius in order to avoid the suction cavitation in the condensate pumps. But, this subcooling increases the inefficiency of the cycle, because more energy is needed to reheat the water.

Thermal Efficiency Improvement – Rankine Cycle

There are several methods, how can be the thermal efficiency of the Rankine cycle improved. Assuming that the maximum temperature is limited by the pressure inside the reactor pressure vessel, these methods are:

Isentropic Efficiency – Turbine, Pump

In previous chapters we assumed that the steam expansion is isentropic and therefore we used T_4,is  as the outlet temperature of the gas. These assumptions are only applicable with ideal cycles.

Most steady-flow devices (turbines, compressors, nozzles) operate under adiabatic conditions, but they are not truly isentropic but are rather idealized as isentropic for calculation purposes. We define parameters η_T,  η_P, η_N, as a ratio of real work done by device to work by device when operated under isentropic conditions (in case of turbine). This ratio is known as the Isentropic Turbine/Pump/Nozzle Efficiency. These parameters describe how efficiently a turbine, compressor or nozzle approximates a corresponding isentropic device. This parameter reduces the overall efficiency and work output. For turbines, the value of η_T is typically 0.7 to 0.9 (70–90%).

See also: Isentropic Process

See also:

Rankine Cycle

Comparison of Actual and Ideal Diesel Cycles

 

In this article it is shown an ideal Diesel cycle in which there are a lot of assumptions differs from actual Diesel cycle. The main differences between the actual and ideal Diesel engine appear in the figure. In reality, the ideal cycle does not occur and there are many losses associated with each process. For an actual cycle, the shape of the pV diagram is similar to the ideal, but the area (work) enclosed by the pV diagram is always less than the ideal value. The ideal Diesel cycle is based on the following assumptions:

• Closed cycle: The largest difference between the two diagrams is the simplification of the intake and exhaust strokes in the ideal cycle. In the exhaust stroke, heat Q_out is ejected to the environment (in a real engine, the gas leaves the engine and is replaced by a new mixture of air and fuel).
• Isobaric heat addition. In real engines the heat addition is never isobaric.
• No heat transfer
  • Compression – The gas is compressed adiabatically from state 1 to state 2. In real engines, there are always some inefficiencies that reduce the thermal efficiency.
  • Expansion. The gas expands adiabatically from state 3 to state 4.
• Complete combustion of the mixture.
• No pumping work. Pumping work is the difference between the work done during exhaust stroke and the work done during intake stroke. In real cycles, there is a pressure difference between exhaust and inlet pressures.
• No blowdown loss. Blowdown loss is caused by the early opening of exhaust valves. This results in a loss of work output during expansion stroke.
• No blow-by loss. The blow-by loss is caused by the leakage of compressed gases through piston rings and other crevices.
• No frictional losses.

These simplifying assumptions and losses lead to the fact that the enclosed area (work) of the pV diagram for an actual engine is significantly smaller than the size of the area (work) enclosed by the pV diagram of the ideal cycle. In other words, the ideal engine cycle will overestimate the net work and, if the engines run at the same speed, greater power produced by the actual engine by around 20% (similarly as in the case of Otto engine).

See also:

Diesel Cycle

Diesel Cycle – Problem with Solution

Diesel Cycle – Problem with Solution

Let assume the Diesel cycle, which is the one of most common thermodynamic cycles that can be found in automobile engines. One of key parameters of such engines is the change in volumes between top dead center (TDC) to bottom dead center (BDC). The ratio of these volumes (V₁ / V₂) is known as the compression ratio. Also the cut-off ratio V₃/V₂, which is the ratio of volumes at the end and start of the combustion phase.

In this example let assume the Diesel cycle with compression ratio of CR = 20 : 1 and cut-off ratio α = 2. The air is at 100 kPa = 1 bar, 20 °C (293 K), and the volume of the chamber is 500 cm³ prior to the compression stroke.

• Specific heat capacity at constant pressure of air at atmospheric pressure and room temperature: c_p = 1.01 kJ/kgK.
• Specific heat capacity at constant volume of air at atmospheric pressure and room temperature: c_v = 0.718 kJ/kgK.
• κ = c_p/c_v = 1.4

Calculate:

1. the mass of intake air
2. the temperature T₂
3. the pressure p₂
4. the temperature T₃
5. the amount of heat added by burning of fuel-air mixture
6. the thermal efficiency of this cycle
7. the MEP

Solution:

1)

At the beginning of calculations we have to determine the amount of gas in the cylinder before the compression stroke. Using the ideal gas law, we can find the mass:

pV = mR_specificT

where:

• p is the absolute pressure of the gas
• m is the mass of substance
• T is the absolute temperature
• V is the volume
• R_specific is the specific gas constant, equal to the universal gas constant divided by the molar mass (M) of the gas or mixture. For dry air R_specific = 287.1 J.kg^-1.K^-1.

Therefore

m = p₁V₁/R_specificT₁ = (100000 × 500×10^-6 )/(287.1 × 293) = 5.95×10^-4 kg

2)

In this problem all volumes are known:

• V₁ = V₄ = V_max = 500×10^-6 m³ (0.5l)
• V₂ = V_min = V_max / CR = 25 ×10^-6 m³

Note that (V_max – V_min) x number of cylinders = total engine displacement

Since the process is adiabatic, we can use the following p, V, T relation for adiabatic processes:

thus

T₂ = T₁ . CR^{κ – 1} = 293 . 20^0.4 = 971 K

3)

Again, we can use the ideal gas law to find the pressure at the end of the compression stroke as:

p₂ = mR_specificT₂ / V₂ = 5.95×10^-4 x 287.1 x 971 / 25 ×10^-6 = 6635000 Pa = 66.35 bar

4)

Since process 2 → 3 occurs at constant pressure, the ideal gas equation of state gives

T₃ = (V₃/V₂) x T₂ = 1942 K

To calculate the amount of heat added by burning of fuel-air mixture, Q_add, we have to use the first law of thermodynamics for isobaric process, which states:

Q_add = mc_p (T₃ – T₂) = 5.95×10^-4 x 1010 x 971 = 583.5 J

5)

Thermal efficiency for this Diesel cycle:

As was derived in the previous section, the thermal efficiency of Diesel cycle is a function of the compression ratio, the cut-off ratio and κ:

where

• η_Diesel is the maximum thermal efficiency of a Diesel cycle
• α is the cut-off ration V₃/V₂ (i.e. the ratio of volumes at the end and start of the combustion phase)
• CR is the compression ratio
• κ = c_p/c_v = 1.4

For this example:

η_Diesel = 0.6467 = 64.7%

6)

The MEP was defined as:

It this equation the displacement volume is equal to V_max – V_min. The net work for one cycle can be calculated using the heat added and the thermal efficiency:

W_net = Q_add . η_Otto = 583.5 x 0.6467 = 377.3 J

MEP = 377.3 / (500×10^-6 – 25 ×10^-6) = 794.3 kPa = 7.943 bar

See also:

Diesel Cycle

Thermal Efficiency for Diesel Cycle

Since Carnot’s principle states that no engine can be more efficient than a reversible engine (a Carnot heat engine) operating between the same high temperature and low temperature reservoirs, the Diesel engine must have lower efficiency than the Carnot efficiency. A typical diesel automotive engine operates at around 30% to 35% of thermal efficiency. About 65-70% is rejected as waste heat without being converted into useful work, i.e. work delivered to wheels. In general, engines using the Diesel cycle are usually more efficient, than engines using the Otto cycle. The diesel engine has the highest thermal efficiency of any practical combustion engine. Low-speed diesel engines (as used in ships) can have a thermal efficiency that exceeds 50%. The largest diesel engine in the world peaks at 51.7%.

In general the thermal efficiency, η_th, of any heat engine is defined as the ratio of the work it does, W, to the heat input at the high temperature, Q_H.

The thermal efficiency, η_th, represents the fraction of heat, Q_H, that is converted to work. Since energy is conserved according to the first law of thermodynamics and energy cannot be be converted to work completely, the heat input, Q_H, must equal the work done, W, plus the heat that must be dissipated as waste heat Q_C into the environment. Therefore we can rewrite the formula for thermal efficiency as:

The heat absorbed occurs during combustion of fuel-air mixture, when the spark occurs, roughly at constant volume. Since during an isochoric process there is no work done by or on the system, the first law of thermodynamics dictates ∆U = ∆Q. Therefore the heat added and rejected are given by:

Q_add = mc_p (T₃ – T₂)

Q_out = mc_v (T₄ – T₁)

Substituting these expressions for the heat added and rejected in the expression for thermal efficiency yields:

This equation can be rearranged to the form with the compression ratio and the cut-off ratio. Thermal efficiency for Diesel cycle:

where

• η_Diesel is the maximum thermal efficiency of a Diesel cycle
• α is the cut-off ration V₃/V₂ (i.e. the ratio of volumes at the end and start of the combustion phase)
• CR is the compression ratio
• κ = c_p/c_v = 1.4

It is very useful conclusion, because it is desirable to achieve a high compression ratio to extract more mechanical energy from a given mass of the fuel. As we have concluded in previous section the air-standard Otto cycle thermal efficiency is also a function of compression ratio and κ.

When we compare these to formulae, it can be seen that for a given compression ratio (CR), the Otto cycle will be more efficient than the Diesel cycle . But diesel engines are usually be more efficient since they are able to operate at higher compression ratios.

In ordinary Otto engines the compression ratio has its limits. The compression ratio in a gasoline-powered engine will usually not be much higher than 10:1. Higher compression ratios will make gasoline engines subject to engine knocking, caused by autoignition an unburned mixture, if lower octane-rated fuel is used. In diesel engines there is minimal risk of autoignition of the fuel, because diesel engines are compression-ignition engines and there is no fuel in the cylinder at the beginning of the compression stroke.

See also: Diesel Cycle – Problem with Solution

See also: Compression Ratio

See also:

Diesel Cycle

Diesel Cycle – Diesel Engine

Dual cycle, or limited pressure cycle, is a thermodynamic cycle that combines the Otto cycle and the Diesel cycle. In the dual cycle, combustion occurs partly at constant volume and partly at constant pressure. It can be used to describe internal combustion engines. The pressure–volume diagrams of actual internal combustion engines are not described well by the Otto and Diesel cycles. An air standard cycle that can be made to approximate the pressure variations more closely is the air-standard dual cycle. A more capable approach would be to model the combustion process in both Otto and Diesel engines as a combination of two heat-transfer processes, one isochoric process and one isobaric process.

In comparison to an Otto cycle, which assumes an instantaneous heat addition (isochoric heat addition), in a dual cycle heat is added partly at constant volume and partly at constant pressure. Therefore the advantage is that more time is available for the fuel to completely combust. On the other hand the use of a dual cycle is slightly more complex. The thermal efficiency lies between Otto and Diesel cycle.

Dual Cycle – Processes

In a dual cycle, the system executing the cycle undergoes a series of five processes: two isentropic (reversible adiabatic) processes alternated with two isochoric process and one isobaric process:

• 

  Isentropic compression (compression stroke) – The gas is compressed adiabatically from state 1 to state 2, as the piston moves from intake valve closing point (1) to top dead center. The surroundings do work on the gas, increasing its internal energy (temperature) and compressing it. On the other hand the entropy remains unchanged. The changes in volumes and its ratio (V₁ / V₂) is known as the compression ratio. The compression ratio is smaller than the expansion ratio.

• Isochoric compression (ignition phase) – In this phase (between state 2 and state 3) there is a constant-volume (the piston is at rest ) heat transfer to the air from an external source while the piston is at rest at top dead center. This process is similar to the isochoric process in the Otto cycle. It is intended to represent the ignition of the fuel–air mixture injected into the chamber and the subsequent rapid burning. The pressure rises and the ratio (P₃ / P₂) is known as the “explosion ratio”.
• Isobaric expansion (power stroke) – In this phase (between state 3 and state 4) there is a constant-pressure (idealized model) heat transfer to the air from an external source (combustion of the fuel) while the piston is moving toward the V₄. During the constant pressure process, energy enters the system as heat Q_add, and a part of work is done by moving piston.
• Isentropic expansion (power stroke) – The gas expands adiabatically from state 4 to state 5, as the piston moves from  V₃ to bottom dead center. The gas does work on the surroundings (piston) and loses an amount of internal energy equal to the work that leaves the system. Again the entropy remains unchanged.
• Isochoric decompression (exhaust stroke) – In this phase the cycle completes by a constant-volume process in which heat is rejected from the air while the piston is at bottom dead center. The working gas pressure drops instantaneously from point 5 to point 1. The exhaust valve opens at point 5. The exhaust stroke is directly after this decompression. As the piston moves from bottom dead center (point 1) to top dead center (point 0) with the exhaust valve opened, the gaseous mixture is vented to the atmosphere and the process starts anew.

During the Dual cycle, work is done on the gas by the piston between states 1 and 2 (isentropic compression). Work is done by the gas on the piston between stages 2 and 3 (isobaric heat addition) and between stages 2 and 3 (isentropic expansion). The difference between the work done by the gas and the work done on the gas is the net work produced by the cycle and it corresponds to the area enclosed by the cycle curve. The work produced by the cycle times the rate of the cycle (cycles per second) is equal to the power produced by the Diesel engine.

Isentropic Process

An isentropic process is a thermodynamic process, in which the entropy of the fluid or gas remains constant. It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter. It is a reversible adiabatic process. The assumption of no heat transfer is very important, since we can use the adiabatic approximation only in very rapid processes.

Isentropic Process and the First Law

For a closed system, we can write the first law of thermodynamics in terms of enthalpy:

dH = dQ + Vdp

or

dH = TdS + Vdp

Isentropic process (dQ = 0):

dH = Vdp     →     W = H₂ – H₁     →     H₂ – H₁ = C_p (T₂ – T₁)    (for ideal gas)

Isentropic Process of the Ideal Gas

The isentropic process (a special case of adiabatic process) can be expressed with the ideal gas law as:

pV^κ = constant

or

p₁V₁^κ = p₂V₂^κ

in which κ = c_p/c_v is the ratio of the specific heats (or heat capacities) for the gas. One for constant pressure (c_p) and one for constant volume (c_v). Note that, this ratio κ  = c_p/c_v is a factor in determining the speed of sound in a gas and other adiabatic processes.

Isochoric Process

An isochoric process is a thermodynamic process, in which the volume of the closed system remains constant (V = const). It describes the behavior of gas inside the container, that cannot be deformed. Since the volume remains constant, the heat transfer into or out of the system does not the p∆V work, but only changes the internal energy (the temperature) of the system.

Isochoric Process and the First Law

The classical form of the first law of thermodynamics is the following equation:

dU = dQ – dW

In this equation dW is equal to dW = pdV and is known as the boundary work. Then:

dU = dQ  – pdV

In isochoric process and the ideal gas, all of heat added to the system will be used to increase the internal energy.

Isochoric process (pdV = 0):

dU = dQ    (for ideal gas)

dU = 0 = Q – W    →     W = Q      (for ideal gas)

Isochoric Process of the Ideal Gas

The isochoric process can be expressed with the ideal gas law as:

or

On a p-V diagram, the process occurs along a horizontal line that has the equation V = constant.

See also: Guy-Lussac’s Law

Isobaric Process

An isobaric process is a thermodynamic process, in which the pressure of the system remains constant (p = const). The heat transfer into or out of the system does work, but also changes the internal energy of the system.

Since there are changes in internal energy (dU) and changes in system volume (∆V), engineers often use the enthalpy of the system, which is defined as:

H = U + pV

Isobaric Process and the First Law

The classical form of the first law of thermodynamics is the following equation:

dU = dQ – dW

In this equation dW is equal to dW = pdV and is known as the boundary work. In an isobaric process and the ideal gas, part of heat added to the system will be used to do work and part of heat added will increase the internal energy (increase the temperature). Therefore it is convenient to use the enthalpy instead of the internal energy.

Isobaric process (Vdp = 0):

dH = dQ → Q = H₂– H₁

At constant entropy, i.e. in isentropic process, the enthalpy change equals the flow process work done on or by the system.

Isobaric Process of the Ideal Gas

The isobaric process can be expressed with the ideal gas law as:

or

On a p-V diagram, the process occurs along a horizontal line (called an isobar) that has the equation p = constant.

See also: Charles’s Law

Thermal Efficiency for Dual Cycle

In general the thermal efficiency, η_th, of any heat engine is defined as the ratio of the work it does, W, to the heat input at the high temperature, Q_H.

The thermal efficiency, η_th, represents the fraction of heat, Q_H, that is converted to work. Since energy is conserved according to the first law of thermodynamics and energy cannot be be converted to work completely, the heat input, Q_H, must equal the work done, W, plus the heat that must be dissipated as waste heat Q_C into the environment. Therefore we can rewrite the formula for thermal efficiency as:

Therefore the heat added and rejected are given by:

Q_add-1 = mc_v (T₃ – T₂)

Q_add-2 = mc_p (T₄ – T₃)

Q_out = mc_v (T₅ – T₁)

Therefore the thermal efficiency for a dual cycle is:

See also:

Thermodynamic Cycles

Diesel Cycle – Diesel Engine

Dual cycle, or limited pressure cycle, is a thermodynamic cycle that combines the Otto cycle and the Diesel cycle. In the dual cycle, combustion occurs partly at constant volume and partly at constant pressure. It can be used to describe internal combustion engines. The pressure–volume diagrams of actual internal combustion engines are not described well by the Otto and Diesel cycles. An air standard cycle that can be made to approximate the pressure variations more closely is the air-standard dual cycle. A more capable approach would be to model the combustion process in both Otto and Diesel engines as a combination of two heat-transfer processes, one isochoric process and one isobaric process.

In comparison to an Otto cycle, which assumes an instantaneous heat addition (isochoric heat addition), in a dual cycle heat is added partly at constant volume and partly at constant pressure. Therefore the advantage is that more time is available for the fuel to completely combust. On the other hand the use of a dual cycle is slightly more complex. The thermal efficiency lies between Otto and Diesel cycle.

Thermal Efficiency for Dual Cycle

In general the thermal efficiency, η_th, of any heat engine is defined as the ratio of the work it does, W, to the heat input at the high temperature, Q_H.

The thermal efficiency, η_th, represents the fraction of heat, Q_H, that is converted to work. Since energy is conserved according to the first law of thermodynamics and energy cannot be be converted to work completely, the heat input, Q_H, must equal the work done, W, plus the heat that must be dissipated as waste heat Q_C into the environment. Therefore we can rewrite the formula for thermal efficiency as:

Therefore the heat added and rejected are given by:

Q_add-1 = mc_v (T₃ – T₂)

Q_add-2 = mc_p (T₄ – T₃)

Q_out = mc_v (T₅ – T₁)

Therefore the thermal efficiency for a dual cycle is:

See also:

Thermodynamic Cycles

Brayton Cycle – Turbine Engine

In 1872, an American engineer, George Bailey Brayton advanced the study of heat engines by patenting a constant pressure internal combustion engine, initially using vaporized gas but later using liquid fuels such as kerosene. This heat engine is known as “Brayton’s Ready Motor”. It means, the original Brayton engine used a piston compressor and piston expander instead of a gas turbine and gas compressor.

Today, modern gas turbine engines and airbreathing jet engines are also a constant-pressure heat engines, therefore we describe their thermodynamics by the Brayton cycle. In general, the Brayton cycle describes the workings of a constant-pressure heat engine.

It is the one of most common thermodynamic cycles that can be found in gas turbine power plants or in airplanes. In contrast to Carnot cycle, the Brayton cycle does not execute isothermal processes, because these must be performed very slowly. In an ideal Brayton cycle, the system executing the cycle undergoes a series of four processes: two isentropic (reversible adiabatic) processes alternated with two isobaric processes.

Since Carnot’s principle states that no engine can be more efficient than a reversible engine (a Carnot heat engine) operating between the same high temperature and low temperature reservoirs, a gas turbine based on the Brayton cycle must have lower efficiency than the Carnot efficiency.

A large single-cycle gas turbine typically produces for example 300 megawatts of electric power and has 35–40% thermal efficiency. Modern Combined Cycle Gas Turbine (CCGT) plants, in which the thermodynamic cycle of consists of two power plant cycles (e.g. the Brayton cycle and the Rankine cycle), can achieve a thermal efficiency of around 55%.

Types of Gas Turbines

In general, heat engines and also gas turbines are categorized according to a combustion location as:

• Turbines with internal combustion. Most gas turbines are internal combustion engines. In these turbines the high temperature is achieved by burning the fuel-air mixture in the combustion chamber.
• Turbines with external combustion.  In these turbines, a heat exchanger is usually used and only clean medium with no combustion products travels through the power turbine. Since the turbine blades are not subjected to combustion products, much lower quality (and therefore cheaper) fuels are able to be used. These turbines have usually lower thermal efficiency than turbines with internal combustion.

Types of Brayton Cycle

Open Brayton Cycle (keywords)

Since most gas turbines are based on the Brayton cycle with internal combustion (e.g. jet engines), they are based on the open Brayton cycle. In this cycle, air from the ambient atmosphere is compressed to a higher pressure and temperature by the compressor. In the combustion chamber, air is heated further by burning the fuel-air mixture in the air flow. Combustion products and gases expand in the turbine either to near atmospheric pressure (engines producing mechanical energy or electrical energy) or to a pressure required by the jet engines. The open Brayton cycle means that the gases are discharged directly into the atmosphere.

Closed Brayton Cycle

In a closed Brayton cycle working medium (e.g. helium) recirculates in the loop and the gas expelled from the turbine is reintroduced into the compressor.  In these turbines, a heat exchanger (external combustion) is usually used and only clean medium with no combustion products travels through the power turbine. The closed Brayton cycle is used, for example, in closed-cycle gas turbine and high-temperature gas cooled reactors.

Reverse Brayton Cycle – Brayton Refrigeration Cycle

A Brayton cycle that is driven in reverse direction is known as the reverse Brayton cycle. Its purpose is to move heat from colder to hotter body, rather than produce work. In compliance with the second law of thermodynamics, Heat cannot spontaneously flow from cold system to hot system without external work being performed on the system. Heat can flow from colder to hotter body, but only when forced by an external work. This is exactly what refrigerators and heat pumps accomplish. These are driven by electric motors requiring work from their surroundings to operate. One of possible cycles is a reverse Brayton cycle, which is similar to the ordinary Brayton cycle but it is driven in reverse, via net work input. This cycle is also known as the gas refrigeration cycle or Bell Coleman cycle. This type of cycle is widely used in jet aircrafts for air conditioning systems using air from the engine compressors. It is also widely used in the LNG industry where the largest reverse Brayton cycle is for subcooling LNG using 86 MW of power from a gas turbine-driven compressor and nitrogen refrigerant.

Brayton Cycle – Processes

In a closed ideal Brayton cycle, the system executing the cycle undergoes a series of four processes: two isentropic (reversible adiabatic) processes alternated with two isobaric processes:

• 

  Isentropic compression (compression in a compressor) – The working gas (e.g. helium) is compressed adiabatically from state 1 to state 2 by the compressor (usually an axial-flow compressor). The surroundings do work on the gas, increasing its internal energy (temperature) and compressing it (increasing its pressure). On the other hand the entropy remains unchanged. The work required for the compressor is given by W_C = H₂ – H₁.

• Isobaric heat addition (in a heat exchanger) – In this phase (between state 2 and state 3) there is a constant-pressure heat transfer to the gas from an external source, since the chamber is open to flow in and out. In an open ideal Brayton cycle, the compressed air then runs through a combustion chamber, where fuel is burned and air or another medium is heated (2 → 3). It is a constant-pressure process, since the chamber is open to flow in and out. The net heat added is given by Q_add = H₃ – H₂
• Isentropic expansion (expansion in a turbine) – The compressed and heated gas expands adiabatically from state 3 to state 4 in a turbine. The gas does work on the surroundings (blades of the turbine) and loses an amount of internal energy equal to the work that leaves the system. The work done by turbine is given by W_T = H₄ – H₃. Again the entropy remains unchanged.
• Isobaric heat rejection (in a heat exchanger) – In this phase the cycle completes by a constant-pressure process in which heat is rejected from the gas. The working gas temperature drops from point 4 to point 1. The net heat rejected is given by Q_re = H₄ – H₁

During a Brayton cycle, work is done on the gas by the compressor between states 1 and 2 (isentropic compression). Work is done by the gas in the turbine between stages 3 and 4 (isentropic expansion). The difference between the work done by the gas and the work done on the gas is the net work produced by the cycle and it corresponds to the area enclosed by the cycle curve (in pV diagram).

As can be seen, it is convenient to use enthalpy or specific enthalpy and to express the first law in terms of enthalpy in analysis of this thermodynamic cycle. This form of the law simplifies the description of energy transfer. At constant pressure, the enthalpy change equals the energy transferred from the environment through heating:

Isobaric process (Vdp = 0):

dH = dQ     →     Q = H₂ – H₁

At constant entropy, i.e. in isentropic process, the enthalpy change equals the flow process work done on or by the system:

Isentropic process (dQ = 0):

dH = Vdp     →     W = H₂ – H₁

See also: Why power engineers use enthalpy? Answer: dH = dQ + Vdp

Isentropic Process

An isentropic process is a thermodynamic process, in which the entropy of the fluid or gas remains constant. It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter. It is a reversible adiabatic process. The assumption of no heat transfer is very important, since we can use the adiabatic approximation only in very rapid processes.

Isentropic Process and the First Law

For a closed system, we can write the first law of thermodynamics in terms of enthalpy:

dH = dQ + Vdp

or

dH = TdS + Vdp

Isentropic process (dQ = 0):

dH = Vdp     →     W = H₂ – H₁     →     H₂ – H₁ = C_p (T₂ – T₁)    (for ideal gas)

Isentropic Process of the Ideal Gas

The isentropic process (a special case of adiabatic process) can be expressed with the ideal gas law as:

pV^κ = constant

or

p₁V₁^κ = p₂V₂^κ

in which κ = c_p/c_v is the ratio of the specific heats (or heat capacities) for the gas. One for constant pressure (c_p) and one for constant volume (c_v). Note that, this ratio κ  = c_p/c_v is a factor in determining the speed of sound in a gas and other adiabatic processes.

Isobaric Process

An isobaric process is a thermodynamic process, in which the pressure of the system remains constant (p = const). The heat transfer into or out of the system does work, but also changes the internal energy of the system.

Since there are changes in internal energy (dU) and changes in system volume (∆V), engineers often use the enthalpy of the system, which is defined as:

H = U + pV

Isobaric Process and the First Law

The classical form of the first law of thermodynamics is the following equation:

dU = dQ – dW

In this equation dW is equal to dW = pdV and is known as the boundary work. In an isobaric process and the ideal gas, part of heat added to the system will be used to do work and part of heat added will increase the internal energy (increase the temperature). Therefore it is convenient to use the enthalpy instead of the internal energy.

Isobaric process (Vdp = 0):

dH = dQ → Q = H₂– H₁

At constant entropy, i.e. in isentropic process, the enthalpy change equals the flow process work done on or by the system.

Isobaric Process of the Ideal Gas

The isobaric process can be expressed with the ideal gas law as:

or

On a p-V diagram, the process occurs along a horizontal line (called an isobar) that has the equation p = constant.

See also: Charles’s Law

Brayton Cycle – pV, Ts diagram

The Brayton cycle is often plotted on a pressure volume diagram (pV diagram) and on a temperature-entropy diagram (Ts diagram).

When plotted on a pressure volume diagram, the isobaric processes follow the isobaric lines for the gas (the horizontal lines), adiabatic processes move between these horizontal lines and the area bounded by the complete cycle path represents the total work that can be done during one cycle.

The temperature-entropy diagram (Ts diagram) in which the thermodynamic state is specified by a point on a graph with specific entropy (s) as the horizontal axis and absolute temperature (T) as the vertical axis. Ts diagrams are a useful and common tool, particularly because it helps to visualize the heat transfer during a process. For reversible (ideal) processes, the area under the T-s curve of a process is the heat transferred to the system during that process.

Thermal Efficiency of Brayton Cycle

In general the thermal efficiency, η_th, of any heat engine is defined as the ratio of the work it does, W, to the heat input at the high temperature, Q_H.

The thermal efficiency, η_th, represents the fraction of heat, Q_H, that is converted to work. Since energy is conserved according to the first law of thermodynamics and energy cannot be be converted to work completely, the heat input, Q_H, must equal the work done, W, plus the heat that must be dissipated as waste heat Q_C into the environment. Therefore we can rewrite the formula for thermal efficiency as:

This is very useful formula, but here we express the thermal efficiency using the first law in terms of enthalpy.

To calculate the thermal efficiency of the Brayton cycle (single compressor and single turbine) engineers use the first law of thermodynamics in terms of enthalpy rather than in terms of internal energy.

The first law in terms of enthalpy is:

dH = dQ + Vdp

In this equation the term Vdp is a flow process work. This work,  Vdp, is used for open flow systems like a turbine or a pump in which there is a “dp”, i.e. change in pressure. There are no changes in control volume. As can be seen, this form of the law simplifies the description of energy transfer.

There are expressions in terms of more familiar variables such as temperature and pressure:

dH = C_pdT + V(1-αT)dp

Where C_p is the heat capacity at constant pressure and α is the coefficient of (cubic) thermal expansion. For ideal gas αT = 1 and therefore:

dH = C_pdT

At constant pressure, the enthalpy change equals the energy transferred from the environment through heating:

Isobaric process (Vdp = 0):

dH = dQ     →     Q = H₃ – H₂   →   H₃ – H₂ = C_p (T₃ – T₂)

At constant entropy, i.e. in isentropic process, the enthalpy change equals the flow process work done on or by the system:

Isentropic process (dQ = 0):

dH = Vdp     →     W = H₄ – H₃     →     H₄ – H₃ = C_p (T₄ – T₃)

The enthalpy can be made into an intensive, or specific, variable by dividing by the mass. Engineers use the specific enthalpy in thermodynamic analysis more than the enthalpy itself.

Now, let assume the ideal Brayton cycle that describes the workings of a constant pressure heat engine. Modern gas turbine engines and airbreathing jet engines also follow the Brayton cycle. This cycle consist of four thermodynamic processes:

1. 

   isentropic compression – ambient air is drawn into the compressor, where it is pressurized (1 → 2). The work required for the compressor is given by W_C = H₂ – H₁.

2. isobaric heat addition – the compressed air then runs through a combustion chamber, where fuel is burned and air or another medium is heated (2 → 3). It is a constant-pressure process, since the chamber is open to flow in and out. The net heat added is given by Q_add = H₃ – H₂
3. isentropic expansion – the heated, pressurized air then expands on turbine, gives up its energy. The work done by turbine is given by W_T = H₄ – H₃
4. isobaric heat rejection – the residual heat must be rejected in order to close the cycle. The net heat rejected is given by Q_re = H₄ – H₁

As can be seen, we can fully describe and calculate such cycles (similarly for Rankine cycle) using enthalpies.

The thermal efficiency of such simple Brayton cycle, for ideal gas and in terms of specific enthalpies can now be expressed in terms of the temperatures:

where

• W_T the work done by the gas in the turbine
• W_C the work done on the gas in the compressor
• c_p is the heat capacity ratio

Pressure Ratio – Brayton Cycle – Gas Turbine

The thermal efficiency in terms of the compressor pressure ratio (PR = p₂/p₁), which is the parameter commonly used:

In general, increasing the pressure ratio is the most direct way to increase the overall thermal efficiency of a Brayton cycle, because the cycle approaches the Carnot cycle.

According to Carnot’s principle higher efficiencies can be attained by increasing the temperature of the gas.

But there are also limits on the pressure ratios that can be used in the cycle. The highest temperature in the cycle occurs at the end of the combustion process, and it is limited by the maximum temperature that the turbine blades can withstand. As usual, metallurgical considerations (about 1700 K) place an upper limits on thermal efficiency.

Consider the effect of compressor pressure ratio on thermal efficiency when the turbine inlet temperature is restricted to the maximum allowable temperature. There are two Ts diagrams of Brayton cycles having the same turbine inlet temperature but different compressor pressure ratios on the picture. As can be seen for a fixed-turbine inlet temperature, the net work output per cycle (W_net = W_T – W_C) decreases with the pressure ratio (Cycle A). But the Cycle A has the greater efficiency.

On the other hand, the Cycle B has a larger net work output per cycle (enclosed area in the diagram) and thus the greater net work developed per unit of mass flow. The work produced by the cycle times a mass flow rate through the cycle is equal to the power output produced by the gas turbine.

Therefore with less work output per cycle (Cycle A), a larger mass flow rate (thus a larger system) is needed to maintain the same power output, which may not be economical. This is the key consideration in design of gas turbine, since here engineers must balance the thermal efficiency and the compactness. In most common designs, the pressure ratio of a gas turbine ranges from about 11 to 16.

Thermal Efficiency Improvement – Brayton Cycle

There are several methods, how can be the thermal efficiency of the Brayton cycle improved. Assuming that the maximum temperature is limited by metallurgical consideration, these methods are:

Increasing pressure ratio

In general, increasing the pressure ratio is the most direct way to increase the overall thermal efficiency of a Brayton cycle, since the thermodynamic efficiency is primarily dependent on the pressure ratio, PR.

As was discussed, increasing the pressure ratio increases the compressor discharge temperature. Since the turbine inlet temperature is limited by the maximum temperature that the turbine blades can withstand, the pressure ration influences the heat amount that can be added to the flow. Moreover with an increase of the pressure ratio, the diameter of the compressor blades becomes progressively smaller in higher pressure stages of the compressor. Because the gap between the blades and the engine casing increases in size as a percentage of the compressor blade height as the blades get smaller in diameter, a greater percentage of the compressed air can leak back past the blades in higher pressure stages. This causes a leak back and in result it decreases the isentropic compressor efficiency (will be discussed later). Finally, from the formula for the thermal efficiency in term of pressure ratio can be seen, there is smaller gain as the pressure ratio increases (due to the exponent).

Heat regeneration

Significant increases in the thermal efficiency of gas turbine power plants can be achieved through reducing the amount of fuel that must be burned in the combustion chamber. This can be done by transferring heat from the turbine exhaust gas, which is normally well above the ambient temperature, to the compressor discharge air flow known as heat regeneration. Especially at a low or moderate pressure ratio, there is a high temperature increase in the combustion chamber and the turbine exhaust gas might still contain significant amount of heat at higher temperature than the compressor outlet gas (after the last compression stage but before the combustor). For this purpose a heat exchanger called a regenerator is used. Sometimes engineers use the term economiser that are heat exchangers intended to reduce energy consumption, especially in case of preheating of a fluid.

This heat regenerator allows the air exiting the compressor to be preheated before it enters the combustion chamber, thereby reducing the amount of fuel that must be burned in the combustor. This form of heat recycling is only possible if the gas turbine is run with low pressure ratio.

As was stated the temperature difference between turbine outlet and compressor outlet is crucial and determines the amount of heat that can be recovered. In case of negative difference (i.e. T₂ > T₄), the heat regeneration is not possible. There are two main ways, how to change this difference:

• to increase the turbine outlet temperature (T₄) through reheat of the flow during expansion phase (i.e. use of a multistage turbine with a reheat combustor or with a reheater)
• to decrease the compressor outlet temperature (T₂) through intercooling of the flow during compression phase (i.e. use of a multistage compressor with an intercooler)

Therefore reheat and intercooling are complementary with heat regeneration. By itself, they would not necessarily increase the thermal efficiency, however, when intercooling or reheat is used in conjunction with heat regeneration, a significant increase in thermal efficiency can be achieved.

It must be noted, transferring heat from the turbine outlet to the compressor inlet would reduce efficiency, as hotter inlet air means more volume, thus more work for the compressor. Engineers must also take into consideration pressure losses generated by the heat exchanger that slightly reduce the power of the gas turbine.

Regeneration vs. Recuperation of Heat

In general, the heat exchangers used in regeneration may be classified as either regenerators or recuperators.

• Regenerator is a type of heat exchanger where heat from the hot fluid is intermittently stored in a thermal storage medium before it is transferred to the cold fluid. It has a single flow path in which the hot and cold fluids alternately pass through.

• Recuperator is a type of heat exchanger has separate flow paths for each fluid along their own passages and heat is transferred through the separating walls. Recuperators (e.g. economisers) are often used in power engineering, to increase the overall efficiency of thermodynamic cycles. For example, in a gas turbine engine. The recuperator transfers some of the waste heat in the exhaust to the compressed air, thus preheating it before entering the combustion chamber. Many recuperators are designed as counterflow heat exchangers.

Reheat - Reheaters

As was discussed, the maximum temperature is limited by metallurgical consideration, but in order to deliver more of the heat at a temperature close to the peak of the cycle the gas can be reheated in a reheater. This involves splitting the turbine, i.e. use of a multistage turbine with a reheat combustor or with a reheater. High pressure and low pressure stages of the turbine may be on the same shaft to drive a common generator, but they will have separate cases. With a reheater, the flow is extracted after a partial expansion (point a), run back through the heat exchanger to heat it back up to the peak temperature (point b), and then passed to the lower pressure stage of the turbine. The expansion then completed in this stage from point b to point 4.

With this arrangement the net work per unit of mass flow can be increased. Despite the increase in net work with reheat, the cycle thermal efficiency would not necessarily increase because a greater total heat addition would be required. On the other hand, the temperature at the exit of the turbine (low pressure stage) is higher with reheat than without reheat, so there is the potential for heat regeneration. Therefore reheat and regeneration are complementary, they are used usually together in order to increase the thermal efficiency of gas turbine.

Compression with Intercooling

Significant increases in the thermal efficiency of gas turbine power plants can be achieved also through intercooling. Intercooling can be applied between compressor stages to reduce compression work, W_C, hence increasing overall power of the gas turbine.

For this purpose a heat exchanger known as an intercooler is usually used between stages of a multi-stage compression process. In general, intercoolers are heat exchangers that are used in many applications, including air compressors, air conditioners, refrigerators, and gas turbines. Intercoolers are widely known also in automotive use as a turbocharger or supercharger, but here they increase intake air charge density, hence the power of an engine.

In gas turbine power plant the thermal efficiency is of the highest importance and intercooling with heat regeneration are widely used. This involves splitting the compressor, i.e. use of a multistage compressor with an intercooler or intercoolers. High pressure and low pressure stages of the compressor may be on the same shaft even with turbine or a generator, but it is not a rule. With an intercooler, the flow is extracted after a partial compression (point c), run through the heat exchanger (intercooler) to cool it to the ambient temperature (point d), and then passed to the high stage of compressor. The compression is then completed in the second compressor from point d to point 2.

With this arrangement the net work per unit of mass flow (↑W_net = W_T – ↓W_C) can be increased by reducing the compression work (↓W_C).  Despite the increase in net work with intercooling, the cycle thermal efficiency would not necessarily increase because the temperature of the air entering the combustor would be reduced and a greater total heat addition would be required to achieve the desired turbine inlet temperature. On the other hand, the temperature at the exit of the compressor (high pressure stage) is lower with intercooling than without intercooling, so there is the potential for heat regeneration (Q_regen increases). Note that, the heat regeneration requires lower compressor outlet temperature than the turbine outlet temperature (simply due to 2nd law) and this temperature difference determines the amount of heat available for heat regeneration.

Therefore reheat and intercooling are complementary with heat regeneration. By itself, they would not necessarily increase the thermal efficiency, however, when intercooling or reheat is used in conjunction with heat regeneration, a significant increase in thermal efficiency can be achieved.

Some large compressors with higher pressure ratio have several stages of compression with intercooling between stages. Engineers must also take into consideration pressure losses generated by all heat exchangers that slightly increase compression work. The certain gas turbine design (the number of intercoolers, reheaters and regenerators) is an engineering problem and depends on certain purpose of the gas turbine.

Reheat, Intercooling and Regeneration  in Brayton Cycle

As was discussed reheat and intercooling are complementary with heat regeneration. By itself, they would not necessarily increase the thermal efficiency, however, when intercooling or reheat is used in conjunction with heat regeneration, a significant increase in thermal efficiency can be achieved and the net work output is also increased. This requires a gas turbine with two stages of compression and two turbine stages.

Isentropic Efficiency – Turbine, Compressor

Most steady-flow devices (turbines, compressors, nozzles) operate under adiabatic conditions, but they are not truly isentropic but are rather idealized as isentropic for calculation purposes. We define parameters η_T,  η_C, η_N, as a ratio of real work done by device to work by device when operated under isentropic conditions (in case of turbine). This ratio is known as the Isentropic Turbine/Compressor/Nozzle Efficiency.

See also: Irreversibility of Natural Processes

These parameters describe how efficiently a turbine, compressor or nozzle approximates a corresponding isentropic device. This parameter reduces the overall efficiency and work output. For turbines, the value of η_T is typically 0.7 to 0.9 (70–90%).

Brayton Cycle – Problem with Solution

Let assume the closed Brayton cycle, which is the one of most common thermodynamic cycles that can be found in modern gas turbine engines. In this case assume a helium gas turbine with single compressor and single turbine arrangement. One of key parameters of such engines is the maximum turbine inlet temperature and the compressor pressure ratio (PR = p₂/p₁) which determines the thermal efficiency of such engine.

In this turbine the high-pressure stage receives gas (point 3 at the figure) from a heat exchanger:

• p₃ = 6.7 MPa;
• T₃ = 1190 K (917°C))
• the isentropic turbine efficiency is η_T = 0.91 (91%)

and exhaust it to another heat exchanger, where the outlet pressure is (point 4):

• p₄ = 2.78 MPa
• T_4,is = ?

Thus the compressor pressure ratio is equal to PR = 2.41.  Moreover we know, that the compressor receives gas (point 1) at the figure:

• p₁ = 2.78 MPa;
• T₁ = 299 K (26°C)
• the isentropic compressor efficiency η_K = 0.87 (87%).

The heat capacity ratio, , for helium is equal to =c_p/c_v=1.66

Calculate:

1. the heat added by the heat exchanger (between 2 → 3)
2. the compressor outlet temperature of the gas (T_2,is)
3. the real work done on this compressor, when the isentropic compressor efficiency is η_K = 0.87 (87%)
4. the turbine outlet temperature of the gas (T_4,is)
5. the real work done by this turbine, when the isentropic turbine efficiency is η_T = 0.91 (91%)
6. the thermal efficiency of this cycle

Solution:

1) + 2)

From the first law of thermodynamics, the net heat added is given by Q_add,ex = H₃ – H₂ [kJ] or Q_add = C_p.(T₃-T_2s), but in this case we do not know the temperature (T_2s) at the outlet of the compressor. We will solve this problem in intensive variables. We have to rewrite the previous equation (to include η_K) using the term (+h₁ – h₁) to:

Q_add = h₃ – h₂ = h₃ – h₁ – (h_2s – h₁)/η_K  [kJ/kg]

Q_add = c_p(T₃-T₁) – (c_p(T_2s-T₁)/η_K)

Then we will calculate the temperature, T_2s, using p, V, T Relation (from Ideal Gas Law) for adiabatic process between (1 → 2).

In this equation the factor for helium is equal to =c_p/c_v=1.66. From the previous equation follows that the compressor outlet temperature, T_2s, is:

Q_add = c_p(T₃-T₁) – (c_p(T_2s-T₁)/η_K) = 5200.(1190 – 299) – 5200.(424-299)/0.87 = 4.633 MJ/kg – 0.747 MJ/kg = 3.886 MJ/kg

3)

The work done on the gas by the compressor in the isentropic compression process is:

W_C,s = c_p (T_2s – T₁) = 5200 x (424 – 299) = 0.650 MJ/kg

The real work done on the gas by the compressor in the adiabatic compression is then:

W_C,real = c_p (T_2s – T₁). η_C = 5200 x (424 – 299) / 0.87 = 0.747 MJ/kg

4)

The turbine outlet temperature of the gas, T_4,is, can be calculated using the same p, V, T Relation as in 2) but between states 3 and 4:

From the previous equation follows that the outlet temperature of the gas, T_4,is, is:

5)

The work done by gas turbine in the isentropic expansion is then:

W_T,s = c_p (T₃ – T_4s) = 5200 x (1190 – 839) = 1.825 MJ/kg

The real work done by gas turbine in the adiabatic expansion is then:

W_T,real = c_p (T₃ – T_4s) . η_T = 5200 x (1190 – 839) x 0.91 = 1.661 MJ/kg

6)

As was derived in the previous section, the thermal efficiency of an ideal Brayton cycle is a function of pressure ratio and κ:

therefore

η_th = 0.295 = 29.5%

The thermal efficiency can be also calculated using the work and the heat (without η_K):

η_th,s = (W_T,s – W_C,s) / Q_add,s = (1.825 – 0.650) / 3.983  =  0.295 = 29.5%

Finally, the thermal efficiency including isentropic turbine/compressor efficiency is:

η_th,real = (W_T,real – W_C,real) / Q_add = (1.661 – 0.747) / 3.886  =  0.235 = 23.5%

See also:

Thermodynamic Cycles

Brayton Cycle – Turbine Engine

In 1872, an American engineer, George Bailey Brayton advanced the study of heat engines by patenting a constant pressure internal combustion engine, initially using vaporized gas but later using liquid fuels such as kerosene. This heat engine is known as “Brayton’s Ready Motor”. It means, the original Brayton engine used a piston compressor and piston expander instead of a gas turbine and gas compressor.

Today, modern gas turbine engines and airbreathing jet engines are also a constant-pressure heat engines, therefore we describe their thermodynamics by the Brayton cycle. In general, the Brayton cycle describes the workings of a constant-pressure heat engine.

It is the one of most common thermodynamic cycles that can be found in gas turbine power plants or in airplanes. In contrast to Carnot cycle, the Brayton cycle does not execute isothermal processes, because these must be performed very slowly. In an ideal Brayton cycle, the system executing the cycle undergoes a series of four processes: two isentropic (reversible adiabatic) processes alternated with two isobaric processes.

Since Carnot’s principle states that no engine can be more efficient than a reversible engine (a Carnot heat engine) operating between the same high temperature and low temperature reservoirs, a gas turbine based on the Brayton cycle must have lower efficiency than the Carnot efficiency.

A large single-cycle gas turbine typically produces for example 300 megawatts of electric power and has 35–40% thermal efficiency. Modern Combined Cycle Gas Turbine (CCGT) plants, in which the thermodynamic cycle of consists of two power plant cycles (e.g. the Brayton cycle and the Rankine cycle), can achieve a thermal efficiency of around 55%.

Types of Brayton Cycle

Open Brayton Cycle (keywords)

Since most gas turbines are based on the Brayton cycle with internal combustion (e.g. jet engines), they are based on the open Brayton cycle. In this cycle, air from the ambient atmosphere is compressed to a higher pressure and temperature by the compressor. In the combustion chamber, air is heated further by burning the fuel-air mixture in the air flow. Combustion products and gases expand in the turbine either to near atmospheric pressure (engines producing mechanical energy or electrical energy) or to a pressure required by the jet engines. The open Brayton cycle means that the gases are discharged directly into the atmosphere.

Closed Brayton Cycle

In a closed Brayton cycle working medium (e.g. helium) recirculates in the loop and the gas expelled from the turbine is reintroduced into the compressor.  In these turbines, a heat exchanger (external combustion) is usually used and only clean medium with no combustion products travels through the power turbine. The closed Brayton cycle is used, for example, in closed-cycle gas turbine and high-temperature gas cooled reactors.

Reverse Brayton Cycle – Brayton Refrigeration Cycle

A Brayton cycle that is driven in reverse direction is known as the reverse Brayton cycle. Its purpose is to move heat from colder to hotter body, rather than produce work. In compliance with the second law of thermodynamics, Heat cannot spontaneously flow from cold system to hot system without external work being performed on the system. Heat can flow from colder to hotter body, but only when forced by an external work. This is exactly what refrigerators and heat pumps accomplish. These are driven by electric motors requiring work from their surroundings to operate. One of possible cycles is a reverse Brayton cycle, which is similar to the ordinary Brayton cycle but it is driven in reverse, via net work input. This cycle is also known as the gas refrigeration cycle or Bell Coleman cycle. This type of cycle is widely used in jet aircrafts for air conditioning systems using air from the engine compressors. It is also widely used in the LNG industry where the largest reverse Brayton cycle is for subcooling LNG using 86 MW of power from a gas turbine-driven compressor and nitrogen refrigerant.

Brayton Cycle – Processes

In a closed ideal Brayton cycle, the system executing the cycle undergoes a series of four processes: two isentropic (reversible adiabatic) processes alternated with two isobaric processes:

• 

  Isentropic compression (compression in a compressor) – The working gas (e.g. helium) is compressed adiabatically from state 1 to state 2 by the compressor (usually an axial-flow compressor). The surroundings do work on the gas, increasing its internal energy (temperature) and compressing it (increasing its pressure). On the other hand the entropy remains unchanged. The work required for the compressor is given by W_C = H₂ – H₁.

• Isobaric heat addition (in a heat exchanger) – In this phase (between state 2 and state 3) there is a constant-pressure heat transfer to the gas from an external source, since the chamber is open to flow in and out. In an open ideal Brayton cycle, the compressed air then runs through a combustion chamber, where fuel is burned and air or another medium is heated (2 → 3). It is a constant-pressure process, since the chamber is open to flow in and out. The net heat added is given by Q_add = H₃ – H₂
• Isentropic expansion (expansion in a turbine) – The compressed and heated gas expands adiabatically from state 3 to state 4 in a turbine. The gas does work on the surroundings (blades of the turbine) and loses an amount of internal energy equal to the work that leaves the system. The work done by turbine is given by W_T = H₄ – H₃. Again the entropy remains unchanged.
• Isobaric heat rejection (in a heat exchanger) – In this phase the cycle completes by a constant-pressure process in which heat is rejected from the gas. The working gas temperature drops from point 4 to point 1. The net heat rejected is given by Q_re = H₄ – H₁

During a Brayton cycle, work is done on the gas by the compressor between states 1 and 2 (isentropic compression). Work is done by the gas in the turbine between stages 3 and 4 (isentropic expansion). The difference between the work done by the gas and the work done on the gas is the net work produced by the cycle and it corresponds to the area enclosed by the cycle curve (in pV diagram).

As can be seen, it is convenient to use enthalpy or specific enthalpy and to express the first law in terms of enthalpy in analysis of this thermodynamic cycle. This form of the law simplifies the description of energy transfer. At constant pressure, the enthalpy change equals the energy transferred from the environment through heating:

Isobaric process (Vdp = 0):

dH = dQ     →     Q = H₂ – H₁

At constant entropy, i.e. in isentropic process, the enthalpy change equals the flow process work done on or by the system:

Isentropic process (dQ = 0):

dH = Vdp     →     W = H₂ – H₁

See also: Why power engineers use enthalpy? Answer: dH = dQ + Vdp

Isentropic Process

An isentropic process is a thermodynamic process, in which the entropy of the fluid or gas remains constant. It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter. It is a reversible adiabatic process. The assumption of no heat transfer is very important, since we can use the adiabatic approximation only in very rapid processes.

Isentropic Process and the First Law

For a closed system, we can write the first law of thermodynamics in terms of enthalpy:

dH = dQ + Vdp

or

dH = TdS + Vdp

Isentropic process (dQ = 0):

dH = Vdp     →     W = H₂ – H₁     →     H₂ – H₁ = C_p (T₂ – T₁)    (for ideal gas)

Isentropic Process of the Ideal Gas

The isentropic process (a special case of adiabatic process) can be expressed with the ideal gas law as:

pV^κ = constant

or

p₁V₁^κ = p₂V₂^κ

in which κ = c_p/c_v is the ratio of the specific heats (or heat capacities) for the gas. One for constant pressure (c_p) and one for constant volume (c_v). Note that, this ratio κ  = c_p/c_v is a factor in determining the speed of sound in a gas and other adiabatic processes.

Isobaric Process

An isobaric process is a thermodynamic process, in which the pressure of the system remains constant (p = const). The heat transfer into or out of the system does work, but also changes the internal energy of the system.

Since there are changes in internal energy (dU) and changes in system volume (∆V), engineers often use the enthalpy of the system, which is defined as:

H = U + pV

Isobaric Process and the First Law

The classical form of the first law of thermodynamics is the following equation:

dU = dQ – dW

In this equation dW is equal to dW = pdV and is known as the boundary work. In an isobaric process and the ideal gas, part of heat added to the system will be used to do work and part of heat added will increase the internal energy (increase the temperature). Therefore it is convenient to use the enthalpy instead of the internal energy.

Isobaric process (Vdp = 0):

dH = dQ → Q = H₂– H₁

At constant entropy, i.e. in isentropic process, the enthalpy change equals the flow process work done on or by the system.

Isobaric Process of the Ideal Gas

The isobaric process can be expressed with the ideal gas law as:

or

On a p-V diagram, the process occurs along a horizontal line (called an isobar) that has the equation p = constant.

See also: Charles’s Law

Brayton Cycle – pV, Ts diagram

The Brayton cycle is often plotted on a pressure volume diagram (pV diagram) and on a temperature-entropy diagram (Ts diagram).

When plotted on a pressure volume diagram, the isobaric processes follow the isobaric lines for the gas (the horizontal lines), adiabatic processes move between these horizontal lines and the area bounded by the complete cycle path represents the total work that can be done during one cycle.

The temperature-entropy diagram (Ts diagram) in which the thermodynamic state is specified by a point on a graph with specific entropy (s) as the horizontal axis and absolute temperature (T) as the vertical axis. Ts diagrams are a useful and common tool, particularly because it helps to visualize the heat transfer during a process. For reversible (ideal) processes, the area under the T-s curve of a process is the heat transferred to the system during that process.

Thermal Efficiency of Brayton Cycle

In general the thermal efficiency, η_th, of any heat engine is defined as the ratio of the work it does, W, to the heat input at the high temperature, Q_H.

The thermal efficiency, η_th, represents the fraction of heat, Q_H, that is converted to work. Since energy is conserved according to the first law of thermodynamics and energy cannot be be converted to work completely, the heat input, Q_H, must equal the work done, W, plus the heat that must be dissipated as waste heat Q_C into the environment. Therefore we can rewrite the formula for thermal efficiency as:

This is very useful formula, but here we express the thermal efficiency using the first law in terms of enthalpy.

To calculate the thermal efficiency of the Brayton cycle (single compressor and single turbine) engineers use the first law of thermodynamics in terms of enthalpy rather than in terms of internal energy.

The first law in terms of enthalpy is:

dH = dQ + Vdp

In this equation the term Vdp is a flow process work. This work,  Vdp, is used for open flow systems like a turbine or a pump in which there is a “dp”, i.e. change in pressure. There are no changes in control volume. As can be seen, this form of the law simplifies the description of energy transfer.

There are expressions in terms of more familiar variables such as temperature and pressure:

dH = C_pdT + V(1-αT)dp

Where C_p is the heat capacity at constant pressure and α is the coefficient of (cubic) thermal expansion. For ideal gas αT = 1 and therefore:

dH = C_pdT

At constant pressure, the enthalpy change equals the energy transferred from the environment through heating:

Isobaric process (Vdp = 0):

dH = dQ     →     Q = H₃ – H₂   →   H₃ – H₂ = C_p (T₃ – T₂)

At constant entropy, i.e. in isentropic process, the enthalpy change equals the flow process work done on or by the system:

Isentropic process (dQ = 0):

dH = Vdp     →     W = H₄ – H₃     →     H₄ – H₃ = C_p (T₄ – T₃)

The enthalpy can be made into an intensive, or specific, variable by dividing by the mass. Engineers use the specific enthalpy in thermodynamic analysis more than the enthalpy itself.

Now, let assume the ideal Brayton cycle that describes the workings of a constant pressure heat engine. Modern gas turbine engines and airbreathing jet engines also follow the Brayton cycle. This cycle consist of four thermodynamic processes:

1. 

   isentropic compression – ambient air is drawn into the compressor, where it is pressurized (1 → 2). The work required for the compressor is given by W_C = H₂ – H₁.

2. isobaric heat addition – the compressed air then runs through a combustion chamber, where fuel is burned and air or another medium is heated (2 → 3). It is a constant-pressure process, since the chamber is open to flow in and out. The net heat added is given by Q_add = H₃ – H₂
3. isentropic expansion – the heated, pressurized air then expands on turbine, gives up its energy. The work done by turbine is given by W_T = H₄ – H₃
4. isobaric heat rejection – the residual heat must be rejected in order to close the cycle. The net heat rejected is given by Q_re = H₄ – H₁

As can be seen, we can fully describe and calculate such cycles (similarly for Rankine cycle) using enthalpies.

The thermal efficiency of such simple Brayton cycle, for ideal gas and in terms of specific enthalpies can now be expressed in terms of the temperatures:

where

• W_T the work done by the gas in the turbine
• W_C the work done on the gas in the compressor
• c_p is the heat capacity ratio

Pressure Ratio – Brayton Cycle – Gas Turbine

The thermal efficiency in terms of the compressor pressure ratio (PR = p₂/p₁), which is the parameter commonly used:

In general, increasing the pressure ratio is the most direct way to increase the overall thermal efficiency of a Brayton cycle, because the cycle approaches the Carnot cycle.

According to Carnot’s principle higher efficiencies can be attained by increasing the temperature of the gas.

But there are also limits on the pressure ratios that can be used in the cycle. The highest temperature in the cycle occurs at the end of the combustion process, and it is limited by the maximum temperature that the turbine blades can withstand. As usual, metallurgical considerations (about 1700 K) place an upper limits on thermal efficiency.

Consider the effect of compressor pressure ratio on thermal efficiency when the turbine inlet temperature is restricted to the maximum allowable temperature. There are two Ts diagrams of Brayton cycles having the same turbine inlet temperature but different compressor pressure ratios on the picture. As can be seen for a fixed-turbine inlet temperature, the net work output per cycle (W_net = W_T – W_C) decreases with the pressure ratio (Cycle A). But the Cycle A has the greater efficiency.

On the other hand, the Cycle B has a larger net work output per cycle (enclosed area in the diagram) and thus the greater net work developed per unit of mass flow. The work produced by the cycle times a mass flow rate through the cycle is equal to the power output produced by the gas turbine.

Therefore with less work output per cycle (Cycle A), a larger mass flow rate (thus a larger system) is needed to maintain the same power output, which may not be economical. This is the key consideration in design of gas turbine, since here engineers must balance the thermal efficiency and the compactness. In most common designs, the pressure ratio of a gas turbine ranges from about 11 to 16.

Thermal Efficiency Improvement – Brayton Cycle

There are several methods, how can be the thermal efficiency of the Brayton cycle improved. Assuming that the maximum temperature is limited by metallurgical consideration, these methods are:

Increasing pressure ratio

In general, increasing the pressure ratio is the most direct way to increase the overall thermal efficiency of a Brayton cycle, since the thermodynamic efficiency is primarily dependent on the pressure ratio, PR.

As was discussed, increasing the pressure ratio increases the compressor discharge temperature. Since the turbine inlet temperature is limited by the maximum temperature that the turbine blades can withstand, the pressure ration influences the heat amount that can be added to the flow. Moreover with an increase of the pressure ratio, the diameter of the compressor blades becomes progressively smaller in higher pressure stages of the compressor. Because the gap between the blades and the engine casing increases in size as a percentage of the compressor blade height as the blades get smaller in diameter, a greater percentage of the compressed air can leak back past the blades in higher pressure stages. This causes a leak back and in result it decreases the isentropic compressor efficiency (will be discussed later). Finally, from the formula for the thermal efficiency in term of pressure ratio can be seen, there is smaller gain as the pressure ratio increases (due to the exponent).

Heat regeneration

Significant increases in the thermal efficiency of gas turbine power plants can be achieved through reducing the amount of fuel that must be burned in the combustion chamber. This can be done by transferring heat from the turbine exhaust gas, which is normally well above the ambient temperature, to the compressor discharge air flow known as heat regeneration. Especially at a low or moderate pressure ratio, there is a high temperature increase in the combustion chamber and the turbine exhaust gas might still contain significant amount of heat at higher temperature than the compressor outlet gas (after the last compression stage but before the combustor). For this purpose a heat exchanger called a regenerator is used. Sometimes engineers use the term economiser that are heat exchangers intended to reduce energy consumption, especially in case of preheating of a fluid.

This heat regenerator allows the air exiting the compressor to be preheated before it enters the combustion chamber, thereby reducing the amount of fuel that must be burned in the combustor. This form of heat recycling is only possible if the gas turbine is run with low pressure ratio.

As was stated the temperature difference between turbine outlet and compressor outlet is crucial and determines the amount of heat that can be recovered. In case of negative difference (i.e. T₂ > T₄), the heat regeneration is not possible. There are two main ways, how to change this difference:

• to increase the turbine outlet temperature (T₄) through reheat of the flow during expansion phase (i.e. use of a multistage turbine with a reheat combustor or with a reheater)
• to decrease the compressor outlet temperature (T₂) through intercooling of the flow during compression phase (i.e. use of a multistage compressor with an intercooler)

Therefore reheat and intercooling are complementary with heat regeneration. By itself, they would not necessarily increase the thermal efficiency, however, when intercooling or reheat is used in conjunction with heat regeneration, a significant increase in thermal efficiency can be achieved.

It must be noted, transferring heat from the turbine outlet to the compressor inlet would reduce efficiency, as hotter inlet air means more volume, thus more work for the compressor. Engineers must also take into consideration pressure losses generated by the heat exchanger that slightly reduce the power of the gas turbine.

Regeneration vs. Recuperation of Heat

In general, the heat exchangers used in regeneration may be classified as either regenerators or recuperators.

• Regenerator is a type of heat exchanger where heat from the hot fluid is intermittently stored in a thermal storage medium before it is transferred to the cold fluid. It has a single flow path in which the hot and cold fluids alternately pass through.

• Recuperator is a type of heat exchanger has separate flow paths for each fluid along their own passages and heat is transferred through the separating walls. Recuperators (e.g. economisers) are often used in power engineering, to increase the overall efficiency of thermodynamic cycles. For example, in a gas turbine engine. The recuperator transfers some of the waste heat in the exhaust to the compressed air, thus preheating it before entering the combustion chamber. Many recuperators are designed as counterflow heat exchangers.

Reheat - Reheaters

As was discussed, the maximum temperature is limited by metallurgical consideration, but in order to deliver more of the heat at a temperature close to the peak of the cycle the gas can be reheated in a reheater. This involves splitting the turbine, i.e. use of a multistage turbine with a reheat combustor or with a reheater. High pressure and low pressure stages of the turbine may be on the same shaft to drive a common generator, but they will have separate cases. With a reheater, the flow is extracted after a partial expansion (point a), run back through the heat exchanger to heat it back up to the peak temperature (point b), and then passed to the lower pressure stage of the turbine. The expansion then completed in this stage from point b to point 4.

With this arrangement the net work per unit of mass flow can be increased. Despite the increase in net work with reheat, the cycle thermal efficiency would not necessarily increase because a greater total heat addition would be required. On the other hand, the temperature at the exit of the turbine (low pressure stage) is higher with reheat than without reheat, so there is the potential for heat regeneration. Therefore reheat and regeneration are complementary, they are used usually together in order to increase the thermal efficiency of gas turbine.

Compression with Intercooling

Significant increases in the thermal efficiency of gas turbine power plants can be achieved also through intercooling. Intercooling can be applied between compressor stages to reduce compression work, W_C, hence increasing overall power of the gas turbine.

For this purpose a heat exchanger known as an intercooler is usually used between stages of a multi-stage compression process. In general, intercoolers are heat exchangers that are used in many applications, including air compressors, air conditioners, refrigerators, and gas turbines. Intercoolers are widely known also in automotive use as a turbocharger or supercharger, but here they increase intake air charge density, hence the power of an engine.

In gas turbine power plant the thermal efficiency is of the highest importance and intercooling with heat regeneration are widely used. This involves splitting the compressor, i.e. use of a multistage compressor with an intercooler or intercoolers. High pressure and low pressure stages of the compressor may be on the same shaft even with turbine or a generator, but it is not a rule. With an intercooler, the flow is extracted after a partial compression (point c), run through the heat exchanger (intercooler) to cool it to the ambient temperature (point d), and then passed to the high stage of compressor. The compression is then completed in the second compressor from point d to point 2.

With this arrangement the net work per unit of mass flow (↑W_net = W_T – ↓W_C) can be increased by reducing the compression work (↓W_C).  Despite the increase in net work with intercooling, the cycle thermal efficiency would not necessarily increase because the temperature of the air entering the combustor would be reduced and a greater total heat addition would be required to achieve the desired turbine inlet temperature. On the other hand, the temperature at the exit of the compressor (high pressure stage) is lower with intercooling than without intercooling, so there is the potential for heat regeneration (Q_regen increases). Note that, the heat regeneration requires lower compressor outlet temperature than the turbine outlet temperature (simply due to 2nd law) and this temperature difference determines the amount of heat available for heat regeneration.

Therefore reheat and intercooling are complementary with heat regeneration. By itself, they would not necessarily increase the thermal efficiency, however, when intercooling or reheat is used in conjunction with heat regeneration, a significant increase in thermal efficiency can be achieved.

Some large compressors with higher pressure ratio have several stages of compression with intercooling between stages. Engineers must also take into consideration pressure losses generated by all heat exchangers that slightly increase compression work. The certain gas turbine design (the number of intercoolers, reheaters and regenerators) is an engineering problem and depends on certain purpose of the gas turbine.

Reheat, Intercooling and Regeneration  in Brayton Cycle

As was discussed reheat and intercooling are complementary with heat regeneration. By itself, they would not necessarily increase the thermal efficiency, however, when intercooling or reheat is used in conjunction with heat regeneration, a significant increase in thermal efficiency can be achieved and the net work output is also increased. This requires a gas turbine with two stages of compression and two turbine stages.

Isentropic Efficiency – Turbine, Compressor

Most steady-flow devices (turbines, compressors, nozzles) operate under adiabatic conditions, but they are not truly isentropic but are rather idealized as isentropic for calculation purposes. We define parameters η_T,  η_C, η_N, as a ratio of real work done by device to work by device when operated under isentropic conditions (in case of turbine). This ratio is known as the Isentropic Turbine/Compressor/Nozzle Efficiency.

See also: Irreversibility of Natural Processes

These parameters describe how efficiently a turbine, compressor or nozzle approximates a corresponding isentropic device. This parameter reduces the overall efficiency and work output. For turbines, the value of η_T is typically 0.7 to 0.9 (70–90%).

See also:

Brayton Cycle

Brayton Cycle – Turbine Engine

In 1872, an American engineer, George Bailey Brayton advanced the study of heat engines by patenting a constant pressure internal combustion engine, initially using vaporized gas but later using liquid fuels such as kerosene. This heat engine is known as “Brayton’s Ready Motor”. It means, the original Brayton engine used a piston compressor and piston expander instead of a gas turbine and gas compressor.

Today, modern gas turbine engines and airbreathing jet engines are also a constant-pressure heat engines, therefore we describe their thermodynamics by the Brayton cycle. In general, the Brayton cycle describes the workings of a constant-pressure heat engine.

It is the one of most common thermodynamic cycles that can be found in gas turbine power plants or in airplanes. In contrast to Carnot cycle, the Brayton cycle does not execute isothermal processes, because these must be performed very slowly. In an ideal Brayton cycle, the system executing the cycle undergoes a series of four processes: two isentropic (reversible adiabatic) processes alternated with two isobaric processes.

Since Carnot’s principle states that no engine can be more efficient than a reversible engine (a Carnot heat engine) operating between the same high temperature and low temperature reservoirs, a gas turbine based on the Brayton cycle must have lower efficiency than the Carnot efficiency.

A large single-cycle gas turbine typically produces for example 300 megawatts of electric power and has 35–40% thermal efficiency. Modern Combined Cycle Gas Turbine (CCGT) plants, in which the thermodynamic cycle of consists of two power plant cycles (e.g. the Brayton cycle and the Rankine cycle), can achieve a thermal efficiency of around 55%.

Ericsson Cycle

The Ericsson cycle is named after a Swedish-American inventor John Ericsson, who designed and built many unique heat engines based on various thermodynamic cycles. He is credited with inventing two unique heat engine cycles and developing practical engines based on these cycles.

His first thermodynamic cycle “the first Ericsson cycle” is now called the “Brayton cycle”, in fact it is the closed Brayton cycle, which is commonly applied to modern closed cycle gas turbine engines.

Brayton Cycle vs Ericsson Cycle

The second Ericsson cycle is what is now called the Ericsson cycle. The second Ericsson cycle is similar to the Brayton cycle, but uses external heat and incorporates the multiple use of an intercooling and reheat. In fact, it is like a Brayton cycle with an infinite number of reheat and intercooler stages in the cycle. Compared to the Brayton cycle which uses adiabatic compression and expansion, an ideal Ericsson cycle consists of isothermal compression and expansion processes, combined with isobaric heat regeneration between them. Applying intercooling, heat regeneration and sequential combustion significantly increases thermal efficiency of a turbine, in fact, the thermal efficiency of the ideal Ericsson cycle equals to the Carnot efficiency.

See also:

Brayton Cycle

Brayton Cycle – Turbine Engine

In 1872, an American engineer, George Bailey Brayton advanced the study of heat engines by patenting a constant pressure internal combustion engine, initially using vaporized gas but later using liquid fuels such as kerosene. This heat engine is known as “Brayton’s Ready Motor”. It means, the original Brayton engine used a piston compressor and piston expander instead of a gas turbine and gas compressor.

Today, modern gas turbine engines and airbreathing jet engines are also a constant-pressure heat engines, therefore we describe their thermodynamics by the Brayton cycle. In general, the Brayton cycle describes the workings of a constant-pressure heat engine.

It is the one of most common thermodynamic cycles that can be found in gas turbine power plants or in airplanes. In contrast to Carnot cycle, the Brayton cycle does not execute isothermal processes, because these must be performed very slowly. In an ideal Brayton cycle, the system executing the cycle undergoes a series of four processes: two isentropic (reversible adiabatic) processes alternated with two isobaric processes.

Since Carnot’s principle states that no engine can be more efficient than a reversible engine (a Carnot heat engine) operating between the same high temperature and low temperature reservoirs, a gas turbine based on the Brayton cycle must have lower efficiency than the Carnot efficiency.

A large single-cycle gas turbine typically produces for example 300 megawatts of electric power and has 35–40% thermal efficiency. Modern Combined Cycle Gas Turbine (CCGT) plants, in which the thermodynamic cycle of consists of two power plant cycles (e.g. the Brayton cycle and the Rankine cycle), can achieve a thermal efficiency of around 55%.

Types of Brayton Cycle

Types of Brayton Cycle

Open Brayton Cycle (keywords)

Since most gas turbines are based on the Brayton cycle with internal combustion (e.g. jet engines), they are based on the open Brayton cycle. In this cycle, air from the ambient atmosphere is compressed to a higher pressure and temperature by the compressor. In the combustion chamber, air is heated further by burning the fuel-air mixture in the air flow. Combustion products and gases expand in the turbine either to near atmospheric pressure (engines producing mechanical energy or electrical energy) or to a pressure required by the jet engines. The open Brayton cycle means that the gases are discharged directly into the atmosphere.

Closed Brayton Cycle

In a closed Brayton cycle working medium (e.g. helium) recirculates in the loop and the gas expelled from the turbine is reintroduced into the compressor.  In these turbines, a heat exchanger (external combustion) is usually used and only clean medium with no combustion products travels through the power turbine. The closed Brayton cycle is used, for example, in closed-cycle gas turbine and high-temperature gas cooled reactors.

Reverse Brayton Cycle – Brayton Refrigeration Cycle

A Brayton cycle that is driven in reverse direction is known as the reverse Brayton cycle. Its purpose is to move heat from colder to hotter body, rather than produce work. In compliance with the second law of thermodynamics, Heat cannot spontaneously flow from cold system to hot system without external work being performed on the system. Heat can flow from colder to hotter body, but only when forced by an external work. This is exactly what refrigerators and heat pumps accomplish. These are driven by electric motors requiring work from their surroundings to operate. One of possible cycles is a reverse Brayton cycle, which is similar to the ordinary Brayton cycle but it is driven in reverse, via net work input. This cycle is also known as the gas refrigeration cycle or Bell Coleman cycle. This type of cycle is widely used in jet aircrafts for air conditioning systems using air from the engine compressors. It is also widely used in the LNG industry where the largest reverse Brayton cycle is for subcooling LNG using 86 MW of power from a gas turbine-driven compressor and nitrogen refrigerant.

Types of Gas Turbines

In general, heat engines and also gas turbines are categorized according to a combustion location as:

• Turbines with internal combustion. Most gas turbines are internal combustion engines. In these turbines the high temperature is achieved by burning the fuel-air mixture in the combustion chamber.
• Turbines with external combustion.  In these turbines, a heat exchanger is usually used and only clean medium with no combustion products travels through the power turbine. Since the turbine blades are not subjected to combustion products, much lower quality (and therefore cheaper) fuels are able to be used. These turbines have usually lower thermal efficiency than turbines with internal combustion.

See also:

Brayton Cycle