Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna 4.8. Atkinson Cycle: Atkinson cycle is an ideal cycle for Otto engine exhausting to a gas turbine. In this cycle the isentropic expansion (3-4) of an Otto cycle (1-2-3-4) is further allowed to proceed to the lowest cycle pressure so as to increase the work output. With this modification the cycle is known as Atkinson cycle. The cycle is shown on p-v and T-s diagrams in Fig.4.8. Processes involved are: Process 1-2: Reversible adiabatic compression (v1 to v2). Process 2-3: Constant volume heat addition. Process 3-4: Reversible adiabatic expansion (v3 to v4). Process 4-1: Constant pressure heat rejection. 3 2 4' 1 Volume (a) Indian Institute of Technology Madras 4 Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna 3 4' 2 4 1 Entropy (b) Fig.4.8. Atkinson cycle on p-v and T-s diagrams Thermal Efficiency: Heat supplied = C v ( T3 - T2 ) Heat rejected = Cp ( T4 - T1 ) Net workdone = C v ( T3 - T2 ) - Cp ( T4 - T1 ) ηth = C v ( T3 - T2 ) - Cp ( T4 - T1 ) C v ( T3 - T2 ) = 1- γ ( T4 - T1 ) Let, r = ( T3 - T2 ) v1 = CR v2 T2 = T1 r γ - 1 T3 P = 3 = rp = Pressure ratio T2 P2 Indian Institute of Technology Madras Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna T3 = T2 rp = T1 r γ - 1 rp ⎛P ⎞ T3 =⎜ 3⎟ T4 ⎝ P4 ⎠ γ -1 γ ⎛P ⎞ = ⎜ 3⎟ ⎝ P1 ⎠ γ -1 γ ⎛P P ⎞ = ⎜ 3. 2⎟ ⎝ P2 P1 ⎠ γ -1 γ ⎛ P ⎞ = ⎜ rp . 2 ⎟ ⎝ P1 ⎠ since, γ ⎛v ⎞ P2 = ⎜ 1 ⎟ = rγ P1 ⎝ v2 ⎠ and T4 = T3 γ -1 rp γ ηth Indian Institute of Technology Madras T1 rp r γ - 1 = γ -1 rp γ rγ - 1 = rγ - 1 1 ⎡ ⎤ ⎢ rγ - 1 ⎥ p ⎥ =1-γ ⎢ ⎢ rp - 1 r γ - 1 ⎥ ⎢ ⎥ ⎣ ⎦ ( ) 1 T1 rpγ γ -1 γ = γ -1 rp γ . r γ−1