Fuel-Air Modeling of Brayton Cycle P M V Subbarao Professor Mechanical Engineering Department Exact Modeling of Cycle is a first step for Energy Conservation…..

Brayton Cycle for Power Generation

Isentropic Compression Process For a infinitesimal compression process:

Properties of Gases GasC0C0 C1C1 C2C2 C3C3 Air Methane CO Steam O2O N2N

 cpcp cvcv

P2P2 P 1 +dP P 1 +2dP P 1 +3dP P 1 +(n-1)dP dT 1 dT 2 dT n

Explicit Method: For an infinitesimal compression from p 1 :

Explicit Method: For another infinitesimal compression from p+dp: For another infinitesimal compression from p+2dP:

For another infinitesimal compression from p+idP:

Irreversible Compression Process

For a infinitesimal compression process: Any adiabatic process from p to p+dp: For an irreversible adiabatic process: For a reversible adiabatic process:

For an irreversible adiabatic compression:

For small pressure ratio:  comp,∞ Polytropic efficiency

For Irreversible Adiabatic Compression

For an infinitesimal irreversible compression from p+idP: Aerodynamic performance of a compressor can be characterized by polytropic efficiency.

Gas Turbine Combustor : Modeling Methods

Brayton Cycle for Power Generation Natural Resource

Basics of Combustor

Combustors Heat input (through Natural Resources) to the gas turbine Brayton cycle is provided by a combustor. The combustor accepts air from the compressor and delivers it at an elevated temperature to the turbine. A combustor is a direct fired air heater in which fuel is burned almost stoichiometrically. The compressor discharges at least three times the stoichiometric air. Only one third participates in combustion.

First Law Analysis of Furnace:SSSF dm C.V. = 0 dt dE C.V. = 0 dt Conservation of Mass: m comp. air + m fuel - m fluegas = 0 First Laws for SG in SSSF Mode:  m in (h + ½ V 2 +gZ) in =  m fluegas (h + ½ V 2 +gZ) fluegas Temperature of flue gas will be very high. Turbine materials cannot withstand such a high temperature. More Dilution air is required. m fuel m compressed air m fluegas

Performance of Combustor Combustor efficiency is a measure of combustion completeness.

The loss of pressure in combustor (p 3 <p 2 ) is a major problem. The total pressure loss is usually in the range of 2 – 8% of p 2. The pressure loss leads to decrease in efficiency and power output. This in turn affects the size and weight of the engine. Combustion Terms Reference Velocity: The theoretical velocity for flow of combustor inlet air through an area equal to the minimum cross section of the combustor casing. (20 – 40 m/s). Profile Factor: The ratio between the maximum exit temperature and the average exit temperature.

Length Scaling An estimate of the size of main burner is required during the engines preliminary design. The cross sectional area can be easily determined using velocity constraints. The length calculations require scaling laws. The length of a main burner is primarily based on the distance required for combustion to come to near completion. Residence time t res in main burner is given by

Combustion Design Considerations Cross Sectional Area: The combustor cross section is determined by a reference velocity appropriate for the particular turbine. Another basis for selecting a combustor cross section comes from thermal loading for unit cross section. Length: Combustor length must be sufficient to provide for flame stabilization. The typical value of the length – to – diameter ratio for liner ranges from three to six. Ratios for casing ranges from two – to – four. Wobbe Number: Wobbe number is an indicator of the characteristics and stability of the combustion process. Pressure Drop: The minimum pressure drop is upto 4%. Volumetric Heat Release Rate: The heat-release rate is proportional to combustion pressure. Actual space required for combustion varies with pressure to the 1.8 power.

Contemporary Main Burners Engine Type TF39 Annular TF41 Cannular J79 Cannular JT9D Annular F100 Annular T63 Can Air Flow (kg/sec) Fuel Flow (K/hr) Length (m) Diameter (m) P (kPa) T comb o C

Modeling of Actual Combustion

Modeling of Combustion C X H Y S Z +  4.76 (X+Y/4+Z) AIR + Moisture in Air + Moisture in fuel → P CO 2 +Q H 2 O +R SO 2 + T N 2 + U O 2 + V CO Exhaust gases: P CO 2 +QH2O+R SO 2 + T N 2 + U O 2 + V CO kmols. Excess air coefficient : . Volume fraction = mole fraction. Volume fraction of CO 2 : x 1 = P * 100 /(P+R + T + U + V) Volume fraction of CO : x 2 = VCO * 100 /(P +R + T + U + V) Volume fraction of SO 2 : x 3 = R * 100 /(P +R + T + U + V) Volume fraction of O 2 : x 4 = U * 100 /(P +R + T + U + V) Volume fraction of N 2 : x 5 = T * 100 /(P +R + T + U + V) These are dry gas volume fractions. Emission measurement devices indicate only Dry gas volume fractions.

Emission Standards 15% oxygen is recommended in exhaust. NO x upto 150 ppm. SO 2 upto 150 ppm. CO upto 500 ppm. HC upto 75 ppm. Volume fractions of above are neglected for the calculation of specific heat flue gas.

Specific Heat of flue gas:

For a given mass flow rate of fuel and air, the temperature of the exhaust can be calculated using above formula. If mass flow rates of fuel and air are known. Guess approximate value of specific heat of flue gas. Calculate T 3. Calculate c p,flue gase. Re calculate T 3. Repeat till the value of T 3 is converged.

For an infinitesimal expansion from p+idp: Evaluation of Polytropic efficiency,  turb, .

Global Cycle Parameters Actual Power Input to Compressor: Rate of Heat Input in Combustion Chamber: Actual Power Output of Turbine: Net Power Output of Plant: