The air-standard Atkinson cycle consists of the following four thermodynamic processes: 1-2 adiabatic and reversible compression,...

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The air-standard Atkinson cycle consists of the following four thermodynamic processes: 1-2 adiabatic and reversible compression, 2-3 constant volume heat addition, 3-4 adiabatic and reversible expansion, 4-1 constant pressure heat rejection. Note that the expansion ratio rex = v4/v3 is significantly larger than the volumetric compression ratio r = v/v2. In a real, spark-ignition, reciprocating piston engine, the Atkinson cycle can be realized by means of a special linkage or by clever control of the valves. This type of engine is useful in hybrid powertrains. a) Draw the cycle both on a P-vand a T - s diagram. The thermal efficiency can be expressed as: Wnet Qin - Qout mc,(T3 T2) mcp (T4 - T) nth Qin Qin mc, (T3 - T) b) Show that the thermal efficiency can be written in the following form: 1 nth = 1 { }, where the term in the { } brackets is a function of T4/T1, T3/T2 and the isentropic index k. c) Show that: T4 Tex T1 rv d) Find an expression for 12 in terms of rex, r and k. T e) Write an expression for th in terms of Tex, r, and k. Tv f) Is such a cycle more efficient that one operating on the air-stander Otto cycle. Give arguments. P 3 b) 2 S S 1 thermal efficiency is defined as 3 4 2 4 P = constant 1 - WIN_MC (T3-T2) mp (T4 T) mCy (T3-T2) nth = Qin Here k is the specific heat ratio between Cp and C nth = WIN Qin k = Cp = k* Cy MCV (T3 - T) - m(k * Cy) (T4 - T) mCy (T3-T2) The air-standard Atkinson cycle consists of the following four thermodynamic processes: 1-2 adiabatic and reversible compression, 2-3 constant volume heat addition, 3-4 adiabatic and reversible expansion, 4-1 constant pressure heat rejection. Note that the expansion ratio rex = v4/v3 is significantly larger than the volumetric compression ratio r = v/v2. In a real, spark-ignition, reciprocating piston engine, the Atkinson cycle can be realized by means of a special linkage or by clever control of the valves. This type of engine is useful in hybrid powertrains. a) Draw the cycle both on a P-vand a T - s diagram. The thermal efficiency can be expressed as: Wnet Qin - Qout mc,(T3 T2) mcp (T4 - T) nth Qin Qin mc, (T3 - T) b) Show that the thermal efficiency can be written in the following form: 1 nth = 1 { }, where the term in the { } brackets is a function of T4/T1, T3/T2 and the isentropic index k. c) Show that: T4 Tex T1 rv d) Find an expression for 12 in terms of rex, r and k. T e) Write an expression for th in terms of Tex, r, and k. Tv f) Is such a cycle more efficient that one operating on the air-stander Otto cycle. Give arguments. P 3 b) 2 S S 1 thermal efficiency is defined as 3 4 2 4 P = constant 1 - WIN_MC (T3-T2) mp (T4 T) mCy (T3-T2) nth = Qin Here k is the specific heat ratio between Cp and C nth = WIN Qin k = Cp = k* Cy MCV (T3 - T) - m(k * Cy) (T4 - T) mCy (T3-T2)