Consider the starting process of a compression ignition engi

Consider the starting process of a compression ignition engine with a compression ratio of 11. The air temperature at the beginning of the compression stroke is t_a. Assume both the fuel injection and combustion occurring right at the TDC. At the TDC, the combustion heat release rate (Q_f),the heat transfer rate from the gas to the cylinder wall (Q_h), and the cylinder friction-loss rate (Q_mf) may be calculated from_f = 2.0 times 10^12 middot m_f middot_hv middot e^-20100/T_GTDC Watts_h = h_TDC middot A_TDC middot ( 120/RPM)^0.8 (T_GRDC - T_w) Watts_mf = 1200 middot (RPM/120) middot (295/T_w)^0.8 Watts where m_f is the amount of fuel injected = 1.2 time 10^-4 kg, Q_hv he fuel heating value = 4.5 times 10^7 J/kg, h_TDC the heat transfer coefficient = 70 W/m^2 degreeC, A_TDC the heat transfer area = 0.05 m^2, T_GTDC and T_w ar the TDC combustion gas and cylinder wall temperatures in Kelvin. Assume the polytropic index n = 1.38 for the cylinder content and compression process. (a) Define the condition under which the engine can be started. (b) Determine whether the engine can be started at RPM = 100 and T_a = T_w = 278 K. (c) Determine the optimum cranking RPM for the engine at T_a = T_w = 280 K.

Solution

A) Qf = Qh+ Qmf (condition under which engine can be started )

solve to get desired conditions

B) solve if Qf> Qh + Qmf then engine can be started otherwise not

C) solve equation Qf = Qh +Qmf to get rpm putting the values given