Gas turbines

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Content – Energy sources

Gas turbines
A gas turbine is an internal combustion engine. Simplified, it has a rotating compressor coupled to a turbine, with a combustion chamber in between.

Principle
Atmospheric air flows through the compressor that raises the pressure.

Igniting and burning the fuel that is added to the combustion chamber, add energy to the gas. The combustion generates a high-temperature flow and high pressure. The gas enters the turbine, expands down to the exhaust pressure (atmospheric) and temperature, rotating the shaft and therby producing work. The turbine shaft work is used to drive the upstream compressor and the electric generator that may be coupled to the shaft. If the energy is not used for shaft work it will generate high temperature and/or high velocity exhaust gases.

Design
The design of the gas turbine is determined by the purpose; shaft output or temperature/thrust.

If the purpose is to generate shaft output (ie to drive a generator or a propeller) one will strive to obtain exit pressures as close to the entry pressure as possible, however some exit pressure is necessary to expel the exhaust gases.

Simplified gas turbine – Shaft output (turboprop)

If the purpose is to provide a jet stream (ie an airplane jet engine) then the only energy that is extracted through the shaft is the energy to drive the compressor and utilities. The remaining high pressure and high temperature gases are accelerated through the turbine to provide the desired jet stream.

Simplified gas turbine – Jet stream (turbofan)

The gases undergo (ideal) three thermodynamic processes: isentropic compression, isobaric (constant pressure) combustion and isentropic expansion.

In practical terms the processes are somewhat different; the compression is not adiabatic since, due to friction and turbulens the temperature rise is greater than a rise corresponding to adiabatic compression. Actually the process is polytropic and the polytropic index would be in the range 1,45 – 1,6.

Similarely the gas after expansion through the turbine also, due to friction, has a higher temperature than adiabatic expansion. The expansion also really is a polytropic process.

Compressor blade-tip speed determines the maximum pressure ratios that can be obtained by the turbine and the compressor. This is a limiting factor to the power and efficiency that can be obtained. Therefore small diameter turbines need to have a relatively high rpm compared to larger diameter turbines.

Many stationary plants for electrical power generation are ”Combined Cycle Power Plants” (CCPP)- These plants have increased thermal efficieny, compared to single cycle plants since they also utilise the remaining temperature of the exhaust gases for power generation.

In a typical combined cycle power plant using natural gas as fuel gas, (typically Methane – CH4) the temperature of the heated gas from the combustion chamber is more than 1200 oC entering the turbine. After expansion through the turbine the gas temperature would be around 600 oC. The exhaust gas will then (of a CCPP) be lead into a steam boiler, for heat recovery and generation of steam. The heat recovery system will in many plants include a NOx reduction plant taking the NOx emissions down to a lower level (for the most efficient plants down to 5ppm).

The high-pressure steam is then lead into a high-pressure steam turbine, back to the steam boiler for re-heating and into the medium and low-pressure sections of the steam turbine. Finally the steam goes into the condenser for cooling and condensation and then back to the steam boiler for re-use.

The energy from the steam is converted into kinetic energy by rotation of the damp turbine shaft, which then may be utilised for generation of electricasl power together with the kinetic energy from the gas turbine shaft.

The most efficient Combined cycle power plants convert close to 60% of the energy of the fuel gas into electrical power.

Combined cycle power plant (click on image to view larger version)

Formulas

Thermal efficiency (Joule process):

$\eta_0 = 1 - \dfrac{T_4-T_1}{T_3-T_2}$

η0 = (Theoretical/ideal thermal efficiency)
T1 = Temperature at beginning of compression
T2= Temperature after isentropic compression
T3 = Temperature after combustion at beginning of expansion
T= Temperature after isentropic expansion

$\eta_i = 1 - \dfrac{W_i}{Q_{appl.}}$

ηi = Indicated thermal efficiency
Wi= Indicated work
Qappl.= Applied energy

ηi always is less than η0 , the actual temperature raise in the compressor is larger and the actual temperature drop in the turbine is less than for a theoretical process (adiabatic).

The work (W) during compression or expansion can be expressed as the difference in energy (enthalpy) before and after the change (compression /expansion).

$W = c_p \Delta t$

W = Work (J)
c= Specific heat Capacity (at constant pressure) (J/KgoK)
Δt = Temperature difference (before and after compression/expansion) (oK)

To quantify the losses due to friction in the turbine and the compressor, the efficiency factors ηc (compressor) and η(turbine) are established.

$\eta_C = \cfrac{Temperature-increase (adiabatic-compression)}{Temperature-increase(actual-compression)}$

Normally in the range 0,75 – 0,9

$\eta_C = \dfrac{Temperature drop (actual-expansion)}{Temperature drop (adiabatic-expansion)}$

Normally in the range 0,85 – 0,9

Available work for the ideal (theoretical) process is expressed:

W0 = Wt0 – WC0

Wt0 = Work turbine
WC0 = Work compressor

The indicated work is then:

Wi = Wti – WCi = Wt0ηT – WCiηC

Some of the indicated work (Wi) will not be available at the shaft since it is used to overcome mechanical losses and for operation of auxiliary systems (injection pumps lubrication pumps etc).
The remaining work is available as effective work at the output shaft (We)

ηe = ηi ηm

ηe = Effectiv (actual) efficiency factor
ηm = Mechanical effieciency factor

For a gas turbine ηm is relatively high compared to other heat machines, due to its simple construction.

For a simple single cycle gas turbine ηe (no heat exchanger, intercooler of after burners) would be in the range 0,15 – 0,25

Fuel consumption and power

$\eta_e = \dfrac{1}{f_eh_g}$

ηe = Effectiv (actual) efficiency factor
fe = Effective specific fuel consumption (Kg/J)
hg = Higher heating Value for the fuel (J/Kg)

$f_e = \dfrac{1}{h_g\eta_e}(kg/J)$

$m_f = f_eP_e = \dfrac{m_a}{\lambda(\dfrac{L}{B})_r}(kg/s)$

$P_e = \dfrac{m_a}{f_e\lambda(\cfrac{L}{B})_r}=\dfrac{m_a\eta_eh_g}{f_e\lambda(\dfrac{L}{B})_r}$

Pe= Actual power (at the shaft) (W)
mf = Fuel consumption (mass, fuel)
fe= Effective specific fuel consumption (Kg/J)
ma = Air consumtion (Kg)
λ = Air index (related to air consumption)
$(\cfrac{L}{B})_r$
= Theoretical Air- fuel relationship, related to chemical reaction equation (“reaction equivalent”) (Kg/Kg)