Internal Combustion Engines. Allan T. Kirkpatrick

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2.23 Cumulative work and heat/mass loss for Example 2.6.

      Compression Ignition Energy Release

In this section we use a dual Wiebe function to model the energy release of the two phases of compression ignition. Diesel combustion has a premixed and a diffusion phase. The first phase is premixed combustion resulting from the leading edge of the fuel jet mixing and then rapidly reacting with the cylinder air. The second phase is a diffusion flame in which the remaining injected fuel mixes and reacts with the cylinder air more slowly. The rate of combustion in a diffusion flame is limited by the rate at which the fuel can be mixed with the cylinder air.

The dual Wiebe equation, Equation (2.72), with seven parameters (Miyamoto et al. 1985) is restated here:

(2.107)

      The subscripts and refer to the premixed and diffusion controlled combustion phases, respectively. The parameter is a nondimensional efficiency factor, and are the burning duration for each phase, and are the overall integrated energy release values for each phase, and and are the nondimensional shape factors for each phase.

      The parameters are selected from correlation of experimental data. Miyamoto et al. (1985), for the specific direct (DI) and indirect injection (IDI) diesel engines tested in their experiments, reported that three parameters, , , and , were essentially independent of engine speed, load, fuel type, and injection timing. The fitted values of these parameters are 6.9, 4, 1.5 (DI) or 1.9 (IDI), and = +7.

      The injection process begins at the start of injection and has a duration of . The ignition delay in compression engines is the crank angle duration between the start of injection and the start of ignition. The determination of the ignition delay is covered in Chapter 7. The two energy release terms and and the diffusion burn duration were found to depend on , the energy of the fuel injected during the ignition delay , and the energy of the injected fuel .

      The injected fuel total energy is

      (2.108)

      Assuming that the fuel injection profile is top‐hat, can be expressed as a fraction of the injection duration ,

      (2.109)

(2.110)

      (2.111)

      The diffusion burn duration was found to correlate linearly with , the diffusion energy release per kmol of air (MJ/):

(2.112)

      The above equations are solved in the MATLAB® program CIHeatRelease.m which is listed in the Appendix. The inlet conditions , engine geometry, diesel fuel properties, and fuel injector timing are inputs to the program. The program first calculates the ignition delay and the and parameters using Equations (2.110) – (2.112), then calculates the energy release (J/deg) during the compression and expansion strokes using Equation (2.107), starting at bottom dead center = –180). The use of the program is detailed in the following example.

      Example 2.7 Compression Ignition Energy Release

A direct injection (DI) diesel engine has a bore and stroke of 165 mm, compression ratio of 18, and operates at 1500 rpm. Its equivalence ratio is 0.7, and residual fraction is 0.05. The inlet manifold temperature and pressure

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