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# gas turbine

gas turbine

gas turbine

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### gas turbine

1. 1. Idealized Brayton cycle 1 2 3 4 1 2 3 4
2. 2. Idealized Brayton cycle
3. 3. The ideal gas turbine cycle equations 𝑊 𝑐 = ℎ1 − ℎ2 𝑊𝑡 = ℎ3 − ℎ4 𝑊𝑛𝑒𝑡 = 𝑊𝑡 − 𝑊 𝑐 𝑄𝑖𝑛 = ℎ3 − ℎ2 𝑄𝑜𝑢𝑡 = ℎ4 − ℎ1 𝜂𝑡ℎ = 𝑊𝑛𝑒𝑡 𝑄𝑖𝑛 𝑃2 𝑃1 = 𝑇2 𝑇1 𝑘 𝑘−1 𝑃3 𝑃4 = 𝑇3 𝑇4 𝑘 𝑘−1
4. 4. Example 1 compressor Turbine Combustion chamber Heat Exchanger Input 1 Air Pressure : 0.1 [MPa] Temperature : 15 [c] 1 2 3 4 output 2 Air Pressure : 1.0 [MPa] Temperature : ? output 3 Air + exhaust gas Pressure : ? Temperature : 1100 [c] output 4 Air + exhaust gas Pressure : 0.1 [MPa] Temperature : 15 [c] 𝑄𝑖𝑛 =? 𝑄𝑜𝑢𝑡 =? 𝑊 𝑐 =? 𝑊𝑡 =? 𝑊𝑛𝑒𝑡 =? 𝜂𝑡ℎ =?
5. 5. EES Program for Example 1 p[1] = 0.1 t[1]=288 h[1]=Enthalpy(Air,t=t[1]) s[1]=Entropy(Air,t=t[1],p=p[1]) p[2]=1 p[2]=p[3] p[1]=p[4] t[2]=t[1]*((p[2]/p[1])^0.286) h[2]=Enthalpy(Air,t=t[2]) s[2]=Entropy(Air,t=t[2],p=p[2]) t[3]=1373 h[3]=Enthalpy(Air,t=t[3]) s[3]=Entropy(Air,t=t[3],p=p[3]) t[4]=t[3]*((p[4]/p[3])^0.286) h[4]=Enthalpy(Air,t=t[4]) s[4]=Entropy(Air,t=t[4],p=p[4]) w_c =h[2]-h[1] w_t =h[3]-h[4] Q_in =h[3]-h[2] Q_out =h[4]-h[1] w_net =w_t -w_c eta_th=(w_net /Q_in)
6. 6. Program Result
7. 7. The actual cycle of the Brayton cycle
8. 8. The actual gas turbine cycle equations 𝑊 𝑐 = ℎ1 − ℎ2 𝑊𝑡 = ℎ3 − ℎ4 𝑊𝑛𝑒𝑡 = 𝑊𝑡 − 𝑊 𝑐 𝑄𝑖𝑛 = ℎ3 − ℎ2 𝑄𝑜𝑢𝑡 = ℎ4 − ℎ1 𝜂𝑡ℎ = 𝑊𝑛𝑒𝑡 𝑄𝑖𝑛 𝑇2𝑠 𝑇1 = 𝑃2 𝑃1 𝑘−1 𝑘 𝜂𝐶 = ℎ2𝑠 − ℎ1 ℎ2 − ℎ1 𝜂𝑡 = ℎ3 − ℎ4 ℎ3 − ℎ4𝑠 𝑇3 𝑇4𝑠 = 𝑃3 𝑃4 𝑘−1 𝑘
9. 9. Example 2 compressor Turbine Combustion chamber Heat Exchanger Input 1 Air Pressure : 0.1 [MPa] Temperature : 15 [c] 1 2 3 4 output 2 Air Pressure : 1.0 [MPa] Temperature : ? output 3 Air + exhaust gas Pressure : ? Temperature : 1100 [c] output 4 Air + exhaust gas Pressure : 0.1 [MPa] Temperature : ? 𝑄𝑖𝑛 =? 𝑄𝑜𝑢𝑡 =? 𝑊 𝑐 =? 𝑊𝑡 =? 𝑊𝑛𝑒𝑡 =? 𝜂𝑡ℎ =? 𝜂𝑐 = 80% 𝜂𝑡 = 85% 𝑃2 − 𝑃3 = 15 [𝑘𝑝𝑎]
10. 10. p[1] = 0.1 t[1]=288 h[1]=Enthalpy(Air,t=t[1]) s[1]=Entropy(Air,t=t[1],p=p[1]) p[2]=1 t_2s=t[1]*((p[2]/p[1])^0.286) eta_c=0.80 eta_c=(t_2s-t[1])/(t[2]-t[1]) s_sc=s[1] h_sc=enthalpy(air,p=p[2],s=s_sc) eta_c=(h_sc-h[1])/(h[2]-h[1]) p[3]=p[2]-0.015 p[4]=p[1] t[3]=1373 t_4s=t[3]/((p[3]/p[4])^0.286) s[3]=Entropy(Air,t=t[3],p=p[3]) s_st=s[3] h_st=enthalpy(air,p=p[4],s=s_st) eta_t=0.85 eta_t=(t[3]-t[4])/(t[3]-t_4s) h[3]=Enthalpy(Air,t=t[3]) eta_t=(h[3]-h[4])/(h[3]-h_st) w_c =h[2]-h[1] w_t =h[3]-h[4] Q_in =h[3]-h[2] Q_out =h[4]-h[1] w_net =w_t -w_c eta_th=(w_net /Q_in) EES Program for Example 2
11. 11. Program Result
12. 12. comparing results
13. 13. References 1- Wikiwand.com / Accessed 10 July 2017 2- Powergen.gepower.com / Accessed 10 July 2017 3- Siemens.com/ Accessed 10 July 2017 4-Van Wylen Thermodynamics book