## L

-60 -30 0 30 60 90 -60 -30 0 30 60 90 Crank angle (deg)

-60 -30 0 30 60 90 -60 -30 0 30 60 90 Crank angle (deg)

Figure 1.19 Fuel burning rates in a Dl truck diesel engine under variable load/speed conditions (Watson and Marzouk)

sition, for the case of simultaneous inflow and outflow. The magnitude of these mass flow increments dmm and dmex is a function of the instantaneous flow rates m,„ and mex which in turn are functions of the geometric characteristics of the inlet and exhaust valves (or ports, when appropriate), of the state of the gas entering or leaving and the available pressure difference across the valves (or ports). In most high speed engines and many medium and slow speed engines, the inlet and exhaust manifold pressure, p[m and pcm are subject to substantial cyclic pressure fluctuations which leads to further complications in that the change of state of the gases in the inlet and exhaust manifolds has to be calculated by further step-by-step procedures. For this purpose two techniques are available:

(a) the so-called filling and emptying technique which treats the manifolds as having a uniform state at any one instant24.

(b) wave action calculations, usually by the method of characteristics25 in which the manifold state is evaluated on the basis of complex pressure waves propagating from the inlet or exhaust valves and subject to repeated partial reflection and transmission at branches, junctions, etc.

For the purposes of this chapter the inlet and exhaust manifold pressure pim and pem will be assumed to be known.

1.6.2.1 Generalized calculation procedure (Figure 1.20)

The equations governing the most general case of simultaneous inflow, dmm, and outflow, dmex, are as follows:

(Replacing eqn (1.42) for the closed period and assuming perfect

Figure 1.20 Simplified system for filling and emptying

mixing of the incoming mass increment dmt„ and the cylinder charge mcyl)

Equation ( 1.50) in turn enables the change in composition of the cylinder charge to be calculated since, for the incoming air d(mcylCVcyi Tcyi) + dQL +pdVcyl change of internal J®3' pison energy of cylinder loss work charge dm n1 i'pnn T,,„ + (//?/,.y i 'p j TCy\ — 0

incoming enthalpy leaving enthalpy

where CVcy| is the mean specific heat at constant volume of the cylinder gases (eqn (1.32b)) expressed on a unit mass and not a molar basis. The conversion is easily effected via eqn (1.20), the mass basis being more appropriate since inflows and outflows are invariably calculated on a mass basis.

Cpim is the mean specific heat at constant pressure of the incoming gases (usually air), again on a mass basis. CPcyl is the mean specific heat at constant pressure of the cylinder

(= Rcyi + C„ ,) characterizing the enthalpy of the leaving gas.

(b) Equation of state for semi-perfect gases

This is again expressed on a mass rather than a molar basis (see eqn (1.33e)) in the form pdV+Vdp = d(mcyi#cy|7*cyi)

= RcyiTcyidmcyi + mcyiRcyldTcyl + mcylTcyl dRcy, (1.49)

The gas constant Rcyl is expressed on a unit mass basis and replaces the universal molar gas constant G, where

0 0