One method proposed for reducing the pumping work in throttled spark-ignition engines is early intake valve closing (EIVC). The ideal cycle p-V diagram shown illustrates the concept. The EIVC cycle is...

One method proposed for reducing the pumping work in throttled spark-ignition engines is early intake valve closing (EIVC). The ideal cycle p-V diagram shown illustrates the concept. The EIVC cycle is 1-2-3-4-5-6-7-8-1 (the conventional throttled cycle is 1-2-3-4-5-6-7'-1). With EIVC, the inlet manifold is held at a pressure pi (which is higher than the normal engine intake pressure, p:), and the inlet valve is closed during the inlet stroke at 8. The trapped fresh charge and residual is then expanded to the normal cycle (lower) intake pressure, p:. You can assume that both cycles have the same mass of gas in the cylinder, temperature, and pressure at state 1 of the cycle.

(a) On a sketch of the intake and exhaust process p-V diagram, shade in the area that corresponds to the difference between the pumping work of the EIVC cycle and that of the normal cycle.

(b) What value of pi and V_EIVC
will give the maximum reduction in pumping work for the EIVC cycle.

(c) Derive an expression for this maximum difference in pumping work between the normal cycle and the EIVC cycle in terms of p_e, pf, V_c, and V_m. You can make the appropriate ideal cycle assumptions