Answer Happy

98-Mar-B5 May 2015 Page 7 of 19 QUESTION 5 GAS TURBINE BLADES Refer to the Examination Paper Attachments Page 13 Acacia and Port Rex Power Stations and Page 14 Gas Turbine Velocity Diagram, Each power station has three units. Each unit has a nominal output of 60 MW and is powered by twin back to back gas turbines driving common electrical generator. The diagram on Page 13 is for one gas turbine only while the specifications are for both gas turbines combined. The net power output and exhaust gas flow rate as given must therefore be divided by two for the purposes of this question. Consider conditions on the power turbine (free turbine with N3 rotor) at peak load. The power turbine has the following approximate blade dimensions for the first stage: Blade tip diameter 1500 mm Blade root (hub) diameter 1050 mm Stator blade inlet angle do 30° Stator blade exit angle at 60° Rotor blade inlet angle B, 30° Rotor blade exit angle B2 60° The exhaust gas has parameters slightly different from those of cold air, so use the following values for its specific heat: Cp = 1.148 kJ/kg°C Cv = 0.861 kJ/kg °C Based on these dimensions and conditions for the first stage and, assuming that the gas flow conditions are the same for the second and third stages of the power turbine, determine the following: (a) Mean blade velocity (velocity at mid-height of blades). (b) The velocity diagram for the first stage of the turbine drawn to scale as recommended below. (c) Relative and absolute gas velocities from the velocity diagram (d) Power turbine output based on gas velocities and gas mass flow rate. (e) Power turbine output based on actual temperature change and gas flow rate. Difference between answers to (d) and (e) above and specified value and comment on any discrepancy. (0) Note: The scale drawing should be to a large enough scale for accurate measurements (a scale of 10 m/s = 4 mm is suggested). While calculation of velocities by trigonometric ratios is acceptable it is longer and more time consuming. [ 10 marks ]
98-Mar-B5 May 2015 Page 13 of 19 QUESTION 5 ACACIA AND PORT REX POWER STATIONS GAS GENERATOR SECTION FREE TURBINE SECTION EXHAUST GAS DISCHARGE N3 ROTOR NOSE CONE -ROTOR STAGE STATOR STAGE NI ROTOR N2 ROTOR HIT! mm 2. 1... Lesnada HII LI ... COMPRESSOR FREE TORBINE INLET POWER SHAFT COUPLING EXHAUST Technical Specifications Peak Load Base Load Net Output (kW) Heat Rate (kJ/kWh) Speed - N1 Rotor (rev/min) Speed - N2 Rotor (rev/min) Speed - Power Turbine (rev/min) Temperature - Gas Generator Turbine Inlet (C) Temperature - Power Turbine Inlet (°C) Temperature - Power Turbine Exhaust (°C) Exhaust Gas Flow Rate (kg/s) Gas Generator Pressure Ratio 60 860 11 791 6 805 8 395 3 000 1 077 682 483 278 14.1 57 100 11 887 6 640 8 320 3 000 1 043 657 467 272 13.6 N1 Low Speed Compressor and Turbine N2 High Speed Compressor and Turbine Inlet Air Conditions 15°C
98-Mar-B5 May 2015 Page 14 of 19 QUESTION 5 GAS TURBINE VELOCITY DIAGRAM do Stator (Fixed) Blade Row CA 01 W1 U Rotor (Moving) Blade Row a2 W2 U U Blade velocity C Rotor blade absolute inlet velocity w, Rotor blade relative inlet velocity C2 Rotor blade absolute outlet velocity W2 Rotor blade relative outlet velocity Cy Stator blade absolute outlet velocity