Calculation document. Introduction

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1 Introduction This calculation document supports the engine designs of Engine incorporated by project team 2A2O. Engine incorporated designed three different engines. This document contains an overview of the excel sheets of the three possible designs under three different conditions: during take off, at 9000 feet under hot day conditions and during cruise conditions. The following calculations are made: efficiencies thrust specific fuel consumption, pressure loss in the combustion, the range and thrust values. First of all, an overview of the different components are given in an abbreviation list (1). Secondly, a stage overview is given (2). This overview is necessary to get an understandable idea over the formulas given in chapter three (3). The formulas, that are given, are used by the made of the calculations. The formulas are followed by the standard atmosphere and specifications of the engine (4). Finally an overview is given of the three different engines (5,6,7). Group 2A2O Amsterdam, November,

2 1. Abbreviation list P (MSL) = Pressure on Mean Seal Level m core engine= Mass of air flowing through the core engine P atm = Atmosphere pressure P02c= Pressure behind the low pressure compressor T (MSL) = Temperature on Mean Sea Level P03= Pressure behind the high pressure compressor T atm = Atmosphere temperature T'0'2c= Theorectical temperature behind the low pressure compressor π lpc = Low pressure ratio T02c= Actual temperature behind the low pressure compressor π total = Total pressure ratio T'0'3= Theorectical temperature behind the high pressure compressor EGT = Exhaust Gas Temperature T03= Actual temperature behind the high pressure compressor C axial = Speed of air in the inlet (T04 T04.9)= Actual temperature behind the high pressure turbine FPR = Fan Pressure Ratio (T04.9 T05)= Actual temperature behind the low pressure turbine BPR = By Pass Ratio TIT=T04= Temperature behind the burner m air total = Total mass of air per second T'4.9= Theoretical temperature behind the high pressure turbine m fuel = Fuel mass per second T05= Actual temperature behind the low pressure turbine γ gas = Gas Poisson exponent T'05= Theoretical temperature behind the low pressure turbine γ air = Air Poisson exponent P04= Pressure behind the burner Cp gas = Gas specific heat P04.9= Pressure behind the high pressure turbine Cp air = Air specific heat P05= Pressure behind the low pressure turbine Rs = Specific gas constant P critical= Critical pressure Ho = Lower heat value T08= Theoretical temperature behind the exhaust of the core engine ρ (MSL) = Density on Mean Sea Level C8= Airspeed behind the exhaust of the core engine ρ atm = Density atmosphere F hot core= Forward force caused by the core engine D fan = Diameter fan F thrust total= Total forward force caused by the engine D cone = Diameter cone η thermal= Thermal efficiency TAS = True Air Speed η thermodynamic= Thermodynamic efficiency C sound = Speed of sound η propulsion= Propulsion efficiency M = Mach η total= Total efficiency Group 2A2O Amsterdam, November,

3 m fan = Mass of air flowing through the by pass η fan = Fan efficiency T01= Temperature behind the inlet & before the fan η jetfan = Jet fan efficiency P01= Pressure behind the inlet & before the fan η lpc = Low pressure compressor efficiency P02= Pressure behind the fan η hpc = High pressure compressor efficiency T0'2= Theoretic temperature behind the fan η lpt = Low pressure turbine efficiency T02= Actual temperature behind the fan η hpt = High pressure turbine efficiency p2.8=p critical= Critical pressure η mech = Mechanical efficiency T2.8= Actual temperature behind the bypass nozzle η jet = η pn = Propelling nozzle efficiency C2.8= Airspeed behind the bypass nozzle η burner = Burner efficiency F fan cold= Forward force caused by the fan TSFC = Thrust Specific Fuel Consumption F fan cold= Forward force caused by the fan P internal= This is the internal power Group 2A2O Amsterdam, November,

4 2. Engine stages overview Group 2A2O Amsterdam, November,

5 3. Formula overview a. Fan calculation =Isentropic inlet efficiency =Actual fan inlet temperature =Theoretical fan inlet temperature =Ambient temperature Percentage (%) (1) =Ram inlet efficiency =Ambient pressure =Inlet pressure =Fan inlet pressure Percentage (%) (2) Pascal (P) Pascal (P) Pascal (P) =Theoretical fan outlet temperature = Fan inlet temperature =Fan pressure ratio = Laplace constant (3) Joule per Kilogram Kelvin (KJ/[Kg*K]) =Fan efficiency =Fan inlet temperature = Theoretical fan outlet temperature =Actual fan outlet temperature Percentage(%) (4) = Fan outlet pressure = Fan inlet pressure = Fan pressure ratio Pascal (P) (5) Pascal (P) Pascal (P) b. Core engine calculation = Compressor ratio = Pressure after compression stage = Pressure before compression stage Pascal (P) Pascal (P) (6) =Dynamic ratio = Temperature before compression (7) Group 2A2O Amsterdam, November,

6 =Temperature after compression = Theoretical compressor outlet temperature = Compressor ratio =Compressor inlet temperature (8) Low pressure compressor efficiency (LPC) LPC inlet temperature Actual LPC outlet Temperature Theoretical LPC outlet temperature (9) High pressure compressor efficiency (HPC) LPC outlet temperature Actual HPC outlet Temperature Theoretical HPC outlet temperature (10) = Low pressure turbine (LPT) efficiency = Turbine Inlet temperature (TIT) = Actual turbine outlet temperature = Theoretical turbine outlet temperature (11) = High pressure turbine (LPT) efficiency = Turbine Inlet temperature (TIT) = Actual turbine outlet temperature = Theoretical turbine outlet temperature (12) = Fan nozzle efficiency =Fan nozzle inlet temperature = Fan nozzle outlet temperature =Theoretical fan nozzle outlet temperature (13) = Core nozzle efficiency =Core nozzle inlet temperature = Core nozzle outlet temperature (14) Group 2A2O Amsterdam, November,

7 =Theoretical core nozzle outlet temperature 2 1 = Critical pressure =Pressure at exhaust = Laplace constant Pascal (P) (15) Pascal (P) Joule per Kilogram Kelvin (J/[Kg*K]) = Exhaust pressure = Critical pressure = Gas constant = Critical temperature Pascal (P) (16) Pascal (P) Joule per Kilogram Kelvin (J/[Kg*K]) c. Results calculation Thermal efficiency 1 1 =Thermal efficiency =Pressure ratio = Laplace constant Joule per Kilogram Kelvin (KJ/[Kg*K]) (17) Thermodynamic efficiency / 1 /. 1 1 /. Thermodynamic efficiency = Dynamic ratio = Compression ratio / = Low and high pressure turbine efficiency / = Low and high pressure compressor efficiency (18) Propulsion efficiency 2 =Jet velocity = Pressure constant = Nozzle temperature =Surrounding temperature Metres per second (m/s) (19) Joule per Kilogram Kelvin (J/[Kg*K]) Group 2A2O Amsterdam, November,

8 2 1 = Propulsion efficiency = Jet exhaust speed = Engine inlet speed Percentage (%) (20) Metres per second (m/s) Metres per second (m/s) Propulsion Fan thrust Mass flow Fan exhaust velocity Inlet speed Newtons per kilograms per second (21) (N/kg/s) Kilograms per second (Kg/s) Metres per second (M/s) Metres per second (m/s) Core thrust Mass flow core exhaust velocity Inlet speed Newtons per kilograms per second (N/kg/s) (22) Kilograms per second (Kg/s) Metres per second (M/s) Metres per second (m/s) = Total thrust = Fan thrust = Core thrust Newtons per kilograms per second (N/kg/s) (23) Newtons per kilograms per second (N/kg/s) Newtons per kilograms per second (N/kg/s) Group 2A2O Amsterdam, November,

9 Fuel consumption = Mass flow of the air = Pressure constant of the air. = Combustion chamber inlet temperature =Mass flow of the fuel = Combustion factor = Pressure constant of the fuel. = Combustion chamber outlet temperature (24) Kilograms per(21) second (Kg/s) Joule per Kilogram Kelvin (J/[Kg*K]) Kilograms per second (Kg/s) Joule per Kilogram Kelvin (J/[Kg*K]) Thrust + = Thrust = Mass flow = Exhaust velocity = Inlet velocity = Area exhaust nozzle = Exhaust pressure = Ambient pressure Newtons per kilograms per second (N/kg/s) (25) Kilograms per second (Kg/s) Metres per second (m/s) Metres per second (m/s) Square meters (M 2 ) Pascal (P) Pascal (P) d. Range R overall * H 0 * L / D * Ln( TOW ) MLW g *1.852 R = Range H 0 = Combustion factor L = Lift D = Drag TOW = Take Off Weight MLW = Maximum Landing Weight g = Gravity factor Nautical mile (NM) (26) Joule per Kilogram Kelvin (J/Kg*K) KiloNewton (kn) KiloNewton (kn) Kilograms (kg) Kilograms (kg) 9,81 m/s² Group 2A2O Amsterdam, November,

10 4. Standard atmosphere and engine specifications Standard inputs Calculated inputs P (MSL) 1,01325 bar Efficiencies: P atm 1,01325 bar η fan 0,9 T (MSL) 288 Kelvin η jetfan 0,95 T atm 15 Celsius η lpc 0,95 π lpc 1,73 η hpc 0,95 π total 15,8 η lpt 0,96 Exhaust Gas Temperature (EGT) 1123,00 Kelvin η hpt 0,96 Max EGT value 1123,00 Kelvin η mech 0,99 C axial 210 m/s η jet = η pn 0,9 N1 115 % η burner 0,98 Max N1 115 % Fan Pressure Ratio (FPR) 1,6 By Pass Ratio (BPR) 3,04 m air total 233,10 kg/s m fuel 1,28 kg/s Pressure loss in burner 4,30 % γ gas 1,33 γ air 1,4 Cp gas 1147 J/KgK Cp air 1005 J/KgK Rs 287 J/KgK T atm 288 Kelvin Ho kj/kg ρ (MSL) 1,2259 Kg/m3 ρ atm 1,2259 Kg/m3 Group 2A2O Amsterdam, November,

11 D fan 1,176 m D cone 0,3193 m τ totaal 0,9 TAS 120 kts = 61,73 m/s τ λ 4,84 τ c 2,22 a = c sound 340,17 m/s M 0,18 Estimated alt. (ISA)(+/ 1500ft/500m) 0 ft = 0 m g 9,81 m/s² Group 2A2O Amsterdam, November,

12 5. Design 1 Low gas emission engine Group 2A2O Amsterdam, November,

13 Take off conditions F thrust total= 76696,02 Newton F thrust total= 76,70 kn F thrust total= 17220,59 lbs η thermal= 0,55 η thermodynamic= 0,50 η propulsion= 0,26 η total= 0,13 Thrust Specific Fuel Consumption= 0,0600 Kg/Nh Thrust Specific Fuel Consumption= 0,6001 lb/lbh P internal= 27275,73 kw Percentage cold thrust of total thrust= 62,61 % Percentage hot thrust of total thrust= 37,39 % Range & Endurance: Lift= 55,00 kn Drag= 1,00 KN Take off weight= 97996,69 lbs = 44450,00 kg landing weight= 87998,60 lbs = 39915,00 kg Range= 1785,17 NM Endurance= 14,88 Hour Group 2A2O Amsterdam, November,

14 9000 feet hot day conditions F thrust total= 53204,31 Newton F thrust total= 53,20 kn F thrust total= 11945,99 lbs η thermal= 0,55 η thermodynamic= 0,49 η propulsion= 0,25 η total= 0,12 Thrust Specific Fuel Consumption= 0,0558 Kg/Nh Thrust Specific Fuel Consumption= 0,5578 lb/lbh P internal= 17407,51 kw Percentage cold thrust of total thrust= 64,25 % Percentage hot thrust of total thrust= 35,75 % Range & Endurance: Lift= 55,00 kn Drag= 1,00 KN Take off weight= 97996,69 lbs = 44450,00 kg landing weight= 87998,60 lbs = 39915,00 kg Range= 1747,28 NM Endurance= 14,56 Hour Group 2A2O Amsterdam, November,

15 Cruise conditions F thrust total= 14386,22 Newton F thrust total= 14,39 kn F thrust total= 3230,14 lbs η thermal= 0,55 η thermodynamic= 0,50 η propulsion= 0,55 η total= 0,28 Thrust Specific Fuel Consumption= 0,1049 Kg/Nh Thrust Specific Fuel Consumption= 1,0488 lb/lbh P internal= 9093,55 kw Percentage cold thrust of total thrust= 50,51 % Percentage hot thrust of total thrust= 49,49 % Range & Endurance: Lift= 25,00 kn Drag= 1,00 KN Take off weight= 97996,69 lbs = 44450,00 kg landing weight= 87998,60 lbs = 39915,00 kg Range= 1769,95 NM Endurance= 5,53 Hour Group 2A2O Amsterdam, November,

16 6. Design 2 Noise reduced engine Group 2A2O Amsterdam, November,

17 Take off conditions F thrust total= 62004,01 Newton F thrust total= 62,00 kn F thrust total= 13921,79 lbs η thermal= 0,55 η thermodynamic= 0,47 η propulsion= 0,32 η total= 0,15 Thrust Specific Fuel Consumption= 0,0382 Kg/Nh Thrust Specific Fuel Consumption= 0,3818 lb/lbh P internal= 13356,40 kw Percentage cold thrust of total thrust= 80,55 % Percentage hot thrust of total thrust= 19,45 % Range & Endurance: Lift= 55,00 kn Drag= 1,00 KN Take off weight= 97996,69 lbs = 44450,00 kg landing weight= 87998,60 lbs = 39915,00 kg Range= 2093,35 NM Endurance= 17,44 Hour Group 2A2O Amsterdam, November,

18 9000 feet hot day conditions F thrust total= 30395,60 Newton F thrust total= 30,40 kn F thrust total= 6824,74 lbs η thermal= 0,55 η thermodynamic= 0,46 η propulsion= 0,36 η total= 0,14 Thrust Specific Fuel Consumption= 0,0488 Kg/Nh Thrust Specific Fuel Consumption= 0,4881 lb/lbh P internal= 8160,54 kw Percentage cold thrust of total thrust= 94,39 % Percentage hot thrust of total thrust= 5,61 % Range & Endurance: Lift= 55,00 Newton Drag= 1,00 Newton Take off weight= 97996,69 lbs = 44450,00 kg landing weight= 87998,60 lbs = 39915,00 kg Range= 1978,92 NM Endurance= 16,49 Hour Group 2A2O Amsterdam, November,

19 Cruise conditions F thrust total= 12126,72 Newton F thrust total= 12,13 kn F thrust total= 2722,82 lbs η thermal= 0,55 η thermodynamic= 0,49 η propulsion= 0,63 η total= 0,31 Thrust Specific Fuel Consumption= 0,0671 Kg/Nh Thrust Specific Fuel Consumption= 0,6708 lb/lbh P internal= 4760,39 kw Percentage cold thrust of total thrust= 62,32 % Percentage hot thrust of total thrust= 37,68 % Range & Endurance: Lift= 25,00 kn Drag= 1,00 KN Take off weight= 97996,69 lbs = 44450,00 kg landing weight= 87998,60 lbs = 39915,00 kg Range= 1956,58 NM Endurance= 6,11 Hour Group 2A2O Amsterdam, November,

20 7. Design 3 Low fuel consumption engine Group 2A2O Amsterdam, November,

21 Take off conditions F thrust total= 75091,95 Newton F thrust total= 75,09 kn F thrust total= 16860,42 lbs η thermal= 0,55 η thermodynamic= 0,50 η propulsion= 0,26 η total= 0,13 Thrust Specific Fuel Consumption= 0,0545 Kg/Nh Thrust Specific Fuel Consumption= 0,5445 lb/lbh P internal= 24232,60 kw Percentage cold thrust of total thrust= 66,10 % Percentage hot thrust of total thrust= 33,90 % Range & Endurance: Lift= 55,00 kn Drag= 1,00 KN Take off weight= 97996,69 lbs = 44450,00 kg landing weight= 87998,60 lbs = 39915,00 kg Range= 1821,80 NM Endurance= 15,18 Hour Group 2A2O Amsterdam, November,

22 9000 feet hot day conditions F thrust total= 52194,40 Newton F thrust total= 52,19 kn F thrust total= 11719,23 lbs η thermal= 0,55 η thermodynamic= 0,49 η propulsion= 0,26 η total= 0,13 Thrust Specific Fuel Consumption= 0,0505 Kg/Nh Thrust Specific Fuel Consumption= 0,5052 lb/lbh P internal= 15465,24 kw Percentage cold thrust of total thrust= 67,69 % Percentage hot thrust of total thrust= 32,31 % Range & Endurance: Lift= 55,00 kn Drag= 1,00 KN Take off weight= 97996,69 lbs = 44450,00 kg landing weight= 87998,60 lbs = 39915,00 kg Range= 1779,97 NM Endurance= 14,83 Hour Group 2A2O Amsterdam, November,

23 Cruise conditions F thrust total= 13833,69 Newton F thrust total= 13,83 kn F thrust total= 3106,08 lbs η thermal= 0,55 η thermodynamic= 0,50 η propulsion= 0,56 η total= 0,28 Thrust Specific Fuel Consumption= 0,0969 Kg/Nh Thrust Specific Fuel Consumption= 0,9690 lb/lbh P internal= 8079,12 kw Percentage cold thrust of total thrust= 54,29 % Percentage hot thrust of total thrust= 45,71 % Range & Endurance: Lift= 25,00 kn Drag= 1,00 KN Take off weight= 97996,69 lbs = 44450,00 kg landing weight= 87998,60 lbs = 39915,00 kg Range= 1806,68 NM Endurance= 5,65 Hour Group 2A2O Amsterdam, November,

SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT

SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT B.Tech. [SEM IV (ME-41,42,43,44,45 & 46)] QUIZ TEST-2 (Session: 2012-13) APPLIED THERMODYNAMICS (EME-401) Q.1) In a gas turbine installation air is