Internal Combustion Engines. Allan T. Kirkpatrick

      results in the following four ordinary differential equations for pressure, work, heat loss, and cylinder mass as a function of crank angle.

(2.106)

      The above four linear equations are solved numerically in the Matlab® program FiniteHeatMassLoss.m, which is listed in the Appendix. The program is a finite energy release program that can be used to compute the performance of an engine and includes both heat and mass transfer. The engine performance is computed by numerically integrating Equations (2.106) for the pressure, work, heat loss, and cylinder gas mass as a function of crank angle. The integration starts at bottom dead center = −180), with initial inlet conditions given. The integration proceeds degree by degree to top dead center and back to bottom dead center. Once the pressure and other terms are computed as a function of crank angle, the overall cycle parameters of net work, thermal efficiency, and imep are also computed. The use of the program is detailed in the following example.

      Example 2.6 Finite Energy Release with Heat and Mass Loss

      A single cylinder engine operates at rpm with a compression ratio , bore m, and stroke m. The cylinder wall heat transfer coefficient W/‐K, the cylinder wall temperature K, and the mass transfer parameter is . The initial cylinder pressure, , at bottom dead center is 1 bar, with a temperature at bottom dead center of 300 K. The heat addition, = 1190 J, and the combustion duration is constant at 40 degrees. Assume that the ideal gas specific heat ratio is 1.4.

      1 What is displacement volume , the volume at bottom dead center, , and the dimensionless heat addition ?

      2 Calculate the nondimensional parameters , and .

      3 Plot the effect of changing the start of energy release from −50 to +20 atdc on the thermal efficiency and imep of the engine.

      Solution

      1 The parameters , , and are:

      2 and , and are

      3 The engine parameters are entered into the FiniteHeatMassLoss.m program as shown below.function [ ] = FiniteHeatMassLoss( ) Gas cycle heat release code with heat and mass transfer thetas = -20; start of heat release (deg) thetad = 40; duration of heat release (deg) Neng = 1910; engine speed (rev/min) r =10; compression ratio b=0.10; bore (m) s=0.0675; stroke (m) gamma = 1.4; gas const Q = 20.; dimensionless heat release ht = 500; heat transfer coefficient (W/m^2-K) T_1 = 300; bottom dead center temperature (K) P_1 = 100; pressure at bdc (kPa) T_w = 360; cylinder wall temp (K) aw = 5; Wiebe parameter a nw = 3; Wiebe exponent n c = 0.8; mass loss coeff ...

The results are presented in Figures 2.21 and 2.22, and representative thermodynamic parameters are compared with the simple energy release computation with no heat or mass loss in Table 2.5. With the heat and mass transfer included, maximum efficiency is reduced from 0.60 to 0.52, and the maximum nondimensional imep is reduced from 13.24 to 11.55.

The cumulative work and heat/mass transfer loss is plotted in Figure 2.23 as a function of crank angle for the optimum case of −20. The cumulative work is initially negative due to the piston compression, and becomes positive on the expansion stroke. The heat transfer loss is very small during compression, indicating a nearly isentropic compression process, and is somewhat linear during the expansion process.

      The general dependence of the efficiency and imep on the start of energy release is very similar for both cases, as the optimum start of ignition remains at approximately 20 btdc, and the peak pressure crank angle remains at +11 atdc. Experimentally, the optimum ignition timing, which gives maximum imep is measured on a brake dynamometer, and indicates the maximum brake torque (MBT) for a given throttle position. MBT timing is discussed in more detail in Chapter 13.

Figure 2.21 Thermal efficiency vs. start of energy release for Examples 2.5 and 2.6.

Figure 2.22 Imep vs. start of energy release for Examples 2.5 and 2.6.

Table 2.5 Comparison of Energy Release Models with and without heat/mass transfer loss at = −20 and = 40

	w/o heat & mass loss	w/ heat & mass loss
	87.77	85.31