Internal Combustion Engines. Allan T. Kirkpatrick

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      (2.54)

      Rearranging, and if heat transfer during the intake stroke is neglected,

      (2.55)

      Since and ,

      (2.56)

      Solving for :

(2.57)

      Therefore, the enthalpy at the end of the intake stroke is not just the average of the initial and intake enthalpies, as would be the case for a steady flow situation, but also includes the flow work term.

      The equation for the enthalpy at the end of the intake stroke, Equation (2.57), can also be expressed in terms of the residual gas fraction, . From Equation (2.45),

(2.58)

      so

      (2.59)

      and from the ideal gas law,

(2.60)

Upon substitution of Equations (2.58) and (2.60) into Eq. (2.57),

      (2.61)

      If the reference enthalpy is chosen so that , then

      (2.62)

      For example, if 0.05, 0.5, 1.35, 320 K, and 1400 K, then 365 K.

      The volumetric efficiency of the inlet stroke for a gas cycle is given by

(2.63)

      During the intake process, the gas within the control volume does work since the piston is expanding the cylinder volume. During exhaust, work is done on the gas. The net effect during the intake and exhaust strokes is

      (2.64)

      The negative of that work is called pumping work since it is a loss of useful work for the throttled engine. The pumping mean effective pressure is defined as the pumping work per unit displacement volume:

      (2.65)

      The indicated mean effective pressure (imep) is defined as the work per unit displacement volume done by the gas during the compression and expansion stroke. The work per unit displacement volume required to pump the working fluid into and out of the engine during the intake and exhaust strokes is termed the pumping mean effective pressure (pmep). It is the sum of the pressure drops across flow restrictions during the intake and exhaust strokes, including intake system, valves, and the exhaust system.

      The following relations should be clear:

      (2.66)

(2.67)

      Four‐Stroke Otto Gas Cycle Analysis

      When we include the exhaust and intake strokes, we have two additional equations for the gas cycle analysis, the exhaust energy equation and the intake energy equation. The two unknown parameters in these equations are the residual gas fraction, , and the gas temperature at the end of the intake stroke, . When the residual gas fraction is taken into account, the energy addition, , is

      (2.68)

      where is the energy addition per unit mass of gas inducted.

The cycle input parameters in this four‐stroke gas cycle analysis are summarized in Table 2.2. Since it is difficult to solve these two equations algebraically, the solution is found by iteration, as shown in this section. Since is dependent on the residual gas fraction, , and the residual gas temperature, , we first need to estimate the values of and , then iterate through the cycle calculation repeatedly

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