*Gas Turbine CyclesLecture 01

Air standard cyclesAir standard cycles refers to thermodynamic cycle with certain assumptions so as to use the principles of thermodynamics conveniently. AssumptionsAir is the working fluid and behaves as a perfect gasMass and composition of the working fluid will not change in the cycleProcesses are reversibleSpecific heat capacity of the working fluid does not change

Otto Cycle*

Otto cycle (air standard)Spark Ignition (SI) engines are based on this cycle

Otto cycle

Otto cycleConsider process 1 2 Consider process 3 4 231

Otto cycleFrom equations 2 and 3From equation 1

Otto cycle efficiency vs. compression ratiog= 1.2g= 1.4

Mean effective pressure (MEP)- Otto cycle - is the mean pressure which is developed in the cylinder and can be measured. Defined as the ratio of net work done to the displacement of volume of the piston.

Mean effective pressure (MEP)- Otto cycle

Mean effective pressure (MEP)- Otto cycle Consider process 1 2

*Terminology : Reciprocating Engine volume swept out by the piston when it moves from TDC to BDC is called the displacement volume. distance from TDC to BDC is called strokeThe piston is said to be at the top dead center (TDC) when it has moved to a position where the cylinder volume is minimum. This volume is called a clearance volume.

Spark Ignition vs Compression IgnitionSpark-ignition engines: mixture of fuel and air are ignited by a spark plug.

Compression ignition engines: Air is compressed to high enough pressure and temperature that combustion occurs spontaneously when fuel is injected.

Diesel Cycle*

Air-Standard Diesel Cycle The Air-Standard Diesel Cycle is the ideal cycle that approximates the compression ignition engine i.e.Compression Ignition (CI) engines are based on this cycle

Process Description 1-2 Isentropic Compression 2-3 Constant Pressure Heat Addition 3-4 Isentropic Expansion 4-1 Constant Volume Heat Rejection

Diesel cycle

Diesel cycleProcess 1 - 2Process 2 - 3123

Diesel cycleProcess 3 - 44

Diesel cycleSubstituting for all Ts in equation 1.

Diesel cycle efficiency vs. compression ratior =2g = 1.4

Brayton cycle*

*ELEMENTS OF SIMPLE GAS TURBINE POWERPLANTS

*ELEMENTS OF SIMPLE GAS TURBINE POWERPLANTSThe simple gas turbine power plant mainly consists of a gas turbine coupled to a rotary type air compressor and combustion chamber which is placed between the compressor and turbine in the fuel circuit.

Auxiliaries, such as cooling fan, water pumps, etc. and the generator itself, are also driven by the turbine.

Other auxiliaries are starting device, lubrication system, duct system, etc.

A modified plant may have in addition to the above, an inter-cooler, a regenerator and a reheater

*Flow diagram Gas turbine power plant

Gas turbine cycleGas-turbines usually operate on an open cycleAcompressortakes in fresh ambient air (state 1), compresses it to a higher temperature and pressure (state 2).Fuel and the higher pressure air from compressor are sent to a combustion chamber, where fuel is burned at constant pressure. The resulting high temperature gases are sent to a turbine (state 3).The high temperature gases expand to the ambient pressure (state 4) in theturbineand produce power.The exhaust gases leave the turbine.

Brayton cycleBy using the air-standard assumptions, replacing the combustion process by a constant pressure heat addition process, and replacing the exhaust discharging process by a constant pressure heat rejection process, the open cycle described above can be modeled as a closed cycle, called ideal Brayton cycle.

*Open Cycle Gas Turbine50 70 % of turbine powerPressure ratio: usually about 15, but up to 40 and moreTurbine inlet temperature (TIT): 900 - 1700CTurbine exit temperature (TET): 400 - 600CPower: 100 kW 300 MWExhaust

*Closed Cycle Gas Turbine2134Working fluid circulates in a closed circuit and does not cause corrosion or erosionAny fuel, nuclear or solar energy can be used

The ideal Brayton cycle is made up of four internally reversible processes.1-2 Isentropic compression 2-3 Constant pressure heat addition3- 4 Isentropic expansion 4-1 Constant pressure heat rejection

Brayton cycleSteady Flow Energy Equation

Efficiency of Brayton Cycle1

Efficiency of Brayton CycleConsider process 1 2, Isentropic compressionConsider process 3 4, Isentropic expansion

Efficiency of Brayton CycleFrom equations 2 and 3:Substituting equations 2, 3 and 4 in equation 1

*Work ratio

*Equation shows that the work ratio increases in direct proportion to the ratio T3 /T1 and inversely with a power of the pressure ratio.

On the other hand, thermal efficiency equation shows that thermal efficiency increases with increased pressure ratio.

*Compressor work:w12 = - (h2 h1 ) = -Cp(T2 T1)

Heat supplied during the cycle:q23 = (h3 h2) = Cp(T3 T2)

Summary of EquationsTurbine work:w34 = (h3 h4) = Cp(T3 T4)Work ratioEfficiency

*Isentropic efficiency

Performance of turbines/compressors are measured by isentropic efficiencies.

The actual work input to the compressor is more and the actual work output from the turbine is more because of irreversibility.Isentropic efficiencies involve a comparison between the actual performance of a device and the performance that would be achieved under idealized circumstances for the same inlet state and the same exit pressure.

Isentropic efficiency - TurbineThe desired output from a turbine is the work output. Hence, the definition of isentropic efficiency of a turbine is the ratio of the actual work output of the turbine to the work output of the turbine if the turbine undergoes an isentropic process between the same inlet and exit pressures.

The isentropic efficiency of turbine can be written as

h1= enthalpy at the inleth2a= enthalpy of actual process at the exith2s= enthalpy of isentropic process at the exit

Isentropic efficiency - compressorThe isentropic efficiency of a compressor or pump is defined as the ratio of the work input to anisentropic process, to the work input to the actual process between the same inlet and exit pressures.

The isentropic efficiency of compressor can be written as

h1= enthalpy at the inleth2a= enthalpy of actual process at the exith2s= enthalpy of isentropic process at the exit

*The Back Work Ratio

Therefore, the turbine used in gas-turbine power plants are larger than those used in steam power plants of the same net power output, P.

Usually more than half of the turbine work output is used to drive the compressor.

*Deviation of Actual Gas-Turbine Cycles from Idealized Ones Pressure dropIsentropic efficiency

Example 1A four stroke SI engine has the compression ratio of 6 and swept volume of 0.15m3. Pressure and temperature at the beginning of compression are 98kPa and 60oC respectively. Heat supplied in the cycle is 150kJ. cp = 1kJ/kgK, cv = 0.71kJ/kgKDetermine the pressure , volume and temperature at all main state pointsEfficiencyMean effective pressure

Example 2An ideal diesel cycle using air as working fluid has a compression ratio of 16 and a cut off ratio of 2. The intake conditions are 100kPa, 20oC, and 2000cm3.Determine Temperature and pressure at the end of each processNet work outputThermal efficiencyMean effective pressurecp = 1.0045kJ/kgK, cv 0.7175kJ/kgK

Example 3In an air standard Brayton cycle the minimum and maximum temperature are 300K and 1200K respectively. The pressure ratio is 10. Find out temperatures after compression and expansion Calculate the compressor and turbine work, each in kJ/kg of air, and thermal efficiency of the cycle.

Example 4A gas turbine receives air at 1bar, 300K and compresses it adiabatically to 6.2bar. The isentropic efficiency of compressor is 0.88. The fuel has a heating value of 44186kJ/kg and the fuel air ratio is 0.017kg fuel/kg of air. The turbine efficiency is 0.9. Calculate the work of turbine and compressor per kg of air compressed and the thermal efficiency.For products of combustion cp = 1.147kJ/kgK, g = 1.33.For air cp = 1.005kJ/kgK, g = 1.4.

*

The ideal air-standard Brayton cycle operates with air entering the compressor at 95 kPa, 22oC. The pressure ratio rp is 6:1 and the air leaves the heat addition process at 1100 K. Determine the compressor work the turbine work per unit mass flow, the cycle efficiency, the back work ratio, and compare the compressor exit temperature to the turbine exit temperature.

Assume constant properties.

Example 5

Example 6

In a gas turbine plant, working on the Brayton cycle, helium at 30 C and 22 bar is compressed to a pressure of 64 bar and then heated to a temperature of 1200 C. After expansion in the turbine, the gas is cooled to initial pressure and temperature.Assume the following:Isentropic efficiency of the compressor 0.85Isentropic efficiency of the turbine 0.8Pressure loss in the combustion chamber 1.2 barPressure loss in the cooler 0.5 barSpecific heat (Cp) of the products of combustion is the same as that of helium and it is equal to 5.1926 kJ/kg K. Ratio of specific heats of helium 1.667Determine the following;Temperature at the end of compression and expansion.Heat supplied, heat rejected and the net work per kg of helium.Thermal efficiency of the plantFlow rate of helium required to give an output of 12 MW.

*The Mean Effective Pressure (Indicated mean effective pressure IMEP) - is the mean pressure which is developed in the cylinder and can be measured

*Mean effective pressure

= (Net work for one cycle) / (displacement volume*The piston is said to be at the top dead center (TDC) when it has moved to a position where the cylinder volume is minimum. This volume is called a clearance volume. The piston is said to be at the bottom dead center (BDC) when it has moved to a position where the cylinder volume is maximum. The volume swept out by the piston when it moves from TDC to BDC is called the displacement volume. The distance from TDC to BDC is called stroke.The bore of the cylinder is its diameter.

*CI engines - Preferred for applications requiring large power and high fuel efficiency (trucks and buses, locomotives and ships). Difference between Actual Diesel and the Otto Engines: Otto EngineHomogenous mixture of fuel and air formed in the carburetor is supplied to engine cylinder. Ignition is initiated by means of an electric spark plugPower output is controlled by varying the mass of fuel-air mixture by means of a throttle valve in the carburetor. Diesel EngineNo carburetor is used. Air alone is supplied to the engine cylinder. Fuel is injected directly into the engine cylinder at the end of compression stroke by means of a fuel injector. Fuel-air mixture is heterogeneous. No spark plug is used. Compression ratio is high and the high temperature of air ignites fuel. No throttle value is used. Power output is controlled only by means of the mass of fuel injected by the fuel injector.

*Variation of diesel cycle efficiency with compression ratio for varying cutoff ratios is given.**Most of the currently available gas turbine systems operate on the open Brayton cycle where a compressor takes in air from the atmosphere and derives it at increased pressure to the combustor. This is also called Joule cycle when irreversibilities are ignored. The air temperature is also increased due to compression.

Older and smaller units operate at a pressure ratio in the range of 15:1, while the newer and larger units operate at pressure ratios approaching 30:1.

Looking at this figure, the air is delivered through a diffuser to a constant-pressure combustion chamber, where fuel is injected and burned. Combustion takes place with high excess air and the exhaust gases exit the combustor at high temperature and with oxygen concentrations of up to 15-16%. The highest temperature of the cycle appears at this point; with current technology this is about 1300C.

The high pressure and high temperature exhaust gases enter the gas turbine and produce mechanical work to drive the compressor and the load. The exhaust gases leave the turbine at a considerable temperature (450-600C), which makes high-temperature heat recovery ideal. The produced steam can have high pressure and temperature. This makes it appropriate not only for thermal processes but also for driving a steam turbine thus producing additional power. *In the closed-cycle system, the working fluid is usually helium or air and it circulates in a closed circuit. It is heated in a heat exchanger before entering the turbine, and it is cooled down after the exit of the turbine releasing useful heat. This way the working fluid remains clean and it does not cause corrosion or erosion. Source of heat can be the external combustion of any fuel. Nuclear energy or solar energy can also be used. *