Internal Combustion Engines. Allan T. Kirkpatrick

Figure 2.11 The exhaust stroke (4 to 5 to 6) illustrating residual mass.

The energy equation is

      (2.40)

      The work term is

      (2.41)

      and if the flow is assumed to be adiabatic, the first law becomes

      (2.42)

      or

      (2.43)

      (2.44)

Therefore, during an adiabatic exhaust stroke, the enthalpy and temperature of the exhaust gases remain constant as they leave the cylinder, and the enthalpy of the residual gas left in the cylinder clearance volume is constant. The residual gas fraction, , is the ratio of the residual gas mass, , in the cylinder at the end of the exhaust stroke (state 6) to the mass, , of the fuel–air mixture:

(2.45)

      Since

      (2.46)

      the residual fraction is

(2.47)

      With a compression ratio of 9, 101 kPa, 500 kPa, and 1.3, the residual fraction 0.035. Since heat transfer to the cylinder walls is neglected in this analysis, this analysis will underpredict the actual residual fraction. Typical values of the residual gas fraction, , are in the 0.03 to 0.12 range. The residual gas fraction is lower in Diesel cycle engines than in Otto cycle engines, due to the higher compression ratio in Diesel cycles.

      Intake Stroke

      There is a flow of a gas mixture into or out of the cylinder during the intake stroke when the intake valve is opened, depending on the relative pressure difference. As indicated in Figure 2.10, there are three different flow situations for the intake stroke, depending on the ratio of inlet to exhaust pressure. If the inlet pressure is less than the exhaust pressure, the engine is throttled. In this case there is flow from the cylinder into the intake port when the intake valve opens. In the initial portion of the intake stroke, the induced gas is primarily composed of combustion products that have previously flowed into the intake port. In the latter portion of the stroke, the mixture flowing in is fresh charge, undiluted by any combustion products.

      If the inlet pressure is greater than the exhaust pressure, the engine is said to be supercharged (turbocharging is a special case of supercharging in which a compressor driven by an exhaust turbine raises the pressure of atmospheric air delivered to an engine). In this case there is flow from the intake port into the engine until the pressure equilibrates. In actual engines, because of valve overlap, there may be a flow of fresh mixture from the inlet to the exhaust port, which can waste fuel and be a source of hydrocarbon exhaust emissions. The third case is when inlet and exhaust pressures are equal; the engine is then said to be unthrottled.

      Since the intake gas temperature is usually less than the residual gas temperature, the cylinder gas temperature at the end of the intake stroke will be greater than the intake temperature. In addition, if heat transfer is neglected, the flow across the intake valve, either from the intake manifold to the cylinder or the reverse, is at constant enthalpy.

The unsteady open‐system mass and energy equations for a control volume, i.e., the increasing cylinder volume, are used to determine the state of the fuel air mixture and residual gas combination at state 1, the end of the intake stroke. The net gas flow into the cylinder control volume has mass , enthalpy , and pressure . Again, at this level of modeling, as the piston moves downward, it is assumed that the cylinder pressure remains constant at the inlet pressure, .

      The initial state of the gas in the system at the beginning of the intake process is at state 6. For the overall process from state 6 to state 1 with the inlet flow at state , the open‐system conservation of mass equation is

      (2.48)

      The open‐system unsteady energy equation is

      (2.49)

      Integrating over the intake stroke from state 6 to state 1, where the work term accounts for the change in volume of the cylinder, and assuming ,

      (2.50)

      (2.51)

      (2.52)

      (2.53)

      Therefore,