A simple gas turbine burns biogas from an anaerobic digestor (Figure 1): Air- Compressor Fuel- Combustor...

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A simple gas turbine burns biogas from an anaerobic digestor (Figure 1): Air- Compressor Fuel- Combustor W Turbine Wnet Exhaust T 2s 2 Figure 1: Gas turbine schematic (left) and thermodynamic cycle (right). In the thermodynamic cycle, black solid lines correspond to isentropic compression or expansion (1 to 2s and 3 to 4s); red lines correspond to the (assumed) real cycle through points 1,2,3,4; dashed lines indicate constant pressure. The biogas is scrubbed of CO before being burned and can be assumed to be entirely composed of methane. The gas turbine has the following parameters: Compressor pressure ratio: 25 Air enters the compressor at 1 bar and 298 K. Turbine exhaust pressure: 1.1 bar Compressor isentropic efficiency: 85% Turbine isentropic efficiency: 90% S 4s 4 You may assume: There is no pressure loss in the combustion chamber. Combustion is complete, there is no dissociation. Air consists of gases in the ratio of 1 mole of oxygen to 3.76 moles of nitrogen. Fuel enters the combustion chamber at 298 K, and the work required to compress the fuel is negligible. You may assume for all mixtures that the specific heat at constant pressure is cp =1.2 kJ/kg-K and a ratio of specific heats Y=Cp/Cv=1.4 Use the following data for the molar formation enthalpies referenced to a temperature of 298 K as hf,i (298 K): hof, CH4 = -70 MJ/kmol hf,co2 = -400 MJ/kmol hof,N2 = hf,02 = 0 MJ/kmol hf,H20 = -240 MJ/kmol (in gaseous state) Note that during an isentropic compression or expansion, TP(1-y)/y is constant. Please respond to the questions below. You may wish to re-consult lecture 3 where a very similar cycle analysis was done, see slides starting "real cycles". We also do a more complex case in tutorial 8. Determine the lower calorific fuel of the methane fuel, in MJ/kg. 50.6 Turbine blades can only withstand a certain inlet temperature, which is determined by the air to fuel ratio. Determine the minimum allowable air-to-fuel ratio (in kg air/kg fuel) that will result in a turbine entry temperature that is less than 1760 K. A simple gas turbine burns biogas from an anaerobic digestor (Figure 1): Air- Compressor Fuel- Combustor W Turbine Wnet Exhaust T 2s 2 Figure 1: Gas turbine schematic (left) and thermodynamic cycle (right). In the thermodynamic cycle, black solid lines correspond to isentropic compression or expansion (1 to 2s and 3 to 4s); red lines correspond to the (assumed) real cycle through points 1,2,3,4; dashed lines indicate constant pressure. The biogas is scrubbed of CO before being burned and can be assumed to be entirely composed of methane. The gas turbine has the following parameters: Compressor pressure ratio: 25 Air enters the compressor at 1 bar and 298 K. Turbine exhaust pressure: 1.1 bar Compressor isentropic efficiency: 85% Turbine isentropic efficiency: 90% S 4s 4 You may assume: There is no pressure loss in the combustion chamber. Combustion is complete, there is no dissociation. Air consists of gases in the ratio of 1 mole of oxygen to 3.76 moles of nitrogen. Fuel enters the combustion chamber at 298 K, and the work required to compress the fuel is negligible. You may assume for all mixtures that the specific heat at constant pressure is cp =1.2 kJ/kg-K and a ratio of specific heats Y=Cp/Cv=1.4 Use the following data for the molar formation enthalpies referenced to a temperature of 298 K as hf,i (298 K): hof, CH4 = -70 MJ/kmol hf,co2 = -400 MJ/kmol hof,N2 = hf,02 = 0 MJ/kmol hf,H20 = -240 MJ/kmol (in gaseous state) Note that during an isentropic compression or expansion, TP(1-y)/y is constant. Please respond to the questions below. You may wish to re-consult lecture 3 where a very similar cycle analysis was done, see slides starting "real cycles". We also do a more complex case in tutorial 8. Determine the lower calorific fuel of the methane fuel, in MJ/kg. 50.6 Turbine blades can only withstand a certain inlet temperature, which is determined by the air to fuel ratio. Determine the minimum allowable air-to-fuel ratio (in kg air/kg fuel) that will result in a turbine entry temperature that is less than 1760 K.