The schematic for the crevice model is given in Figure 9.1: Schematic diagram of the crevice volumes and planes used in the model , which reproduces Figure 15 of Namazian and Heywood [62] .

The flow between regions 1 through 5 is pressure driven. In the model the pressure in region 1 is defined to be equal to the cylinder pressure, and zone 5 is at atmospheric pressure. The continuity equations, which give expressions for the pressure in zones 2, 3, and 4, are given in equation (6) of Namazian and Heywood [62] , and are reproduced here for completeness.

Figure 9.1: Schematic diagram of the crevice volumes and planes used in the model

(9–1)

(9–2)

(9–3)

where the subscript ‘o’ refers to a reference condition such as the one at intake valve closing, m is mass, p is pressure, t is time, and the double subscript means the flow from the first to the second number. For example, in Equation 9–1 , the 12 subscript refers to mass flow from region 1 above the top ring to region 2 behind the first ring.

To determine the mass flow rates in equations, two types of flow conditions are used in the theory: isothermal and isentropic. They are used in the following situations: