Internal Combustion Engines. Allan T. Kirkpatrick

target="_blank" rel="nofollow" href="#fb3_img_img_07f464d0-cd1b-52a7-96c5-5819c0ff47c3.png" alt="images"/>, and the exhaust stroke temperature decrease, , of an engine that operates on the ideal four‐stroke Otto cycle. The engine is throttled with an inlet pressure of 50 kPa and has an inlet temperature of 300 K. The exhaust pressure is 100 kPa. The compression ratio, 10. Assume an energy addition of 2500 kJ/ and 1.3. Plot the volumetric efficiency, net thermal efficiency, and residual fraction as a function of the intake/exhaust pressure ratio for .

      Solution

      The program input portion of FourStrokeOtto.m is shown below.

       four-stroke Otto cycle model Input parameters: Ti = 300; inlet temperature (K) Pi = 50; inlet pressure (kPa) Pe = 100; exhaust pressure (kPa r = 10; compression ratio qin = 2500; energy addition, kJ/kg (gas) R = 0.287; gas constant (kJ/kg K) f = 0.05; guess value of residual fraction f Tr = 1000; guess value of exhaust temp (K) tol = 0.001; convergence tolerance ....

For the above conditions, as shown in Tables 2.3 and 2.4, the computation indicates that the intake stroke temperature rise, , is about 45 K, and the exhaust blowdown temperature decrease, , is about 280 K. The volumetric efficiency, , the net thermal efficiency, , and the residual fraction, 0.053.

Table 2.3 State Variables for Four‐Stroke Example 2.3

State	1	2	3	4
Pressure (kPa):	50.0	997.6	4582.6	229.7
Temperature (K):	345.3	688.9	3164.3	1585.9

Table 2.4 Computed Performance Parameters for Four‐Stroke Example 2.3

Residual Fraction	=	0.053
Net Imep (kPa)		612.0
Ideal Thermal Efficiency	=	0.499
Net Thermal Efficiency	=	0.461
Exhaust Temperature (K)		1309.0
Volumetric Efficiency	=	0.91

      Volumetric efficiency for Example 2.3. Residual fraction for Example 2.3.

The volumetric efficiency, Equation (2.63), the residual fraction, Equation (2.47), and the net thermal efficiency (Equation (2.67)) are plotted in Figures 2.13, and 2.14, respectively, as a function of the intake/exhaust pressure ratio.

      Comment: As the pressure ratio increases, the volumetric efficiency and thermal efficiency increase, and the residual fraction decreases. The dependence of the volumetric efficiency on compression ratio is reversed for the throttled and supercharged conditions. In addition, the residual gas fraction increases. The increase in residual fraction is due to the decrease in the intake mass relative to the residual mass as the intake pressure is decreased.

      Net thermal efficiency for Example 2.3.

2.8 Finite Energy Release

      Spark‐Ignition Energy Release

In the ideal Otto and Diesel cycles the fuel is assumed to burn at rates that result in constant volume top dead center combustion, or constant pressure combustion, respectively. Actual engine pressure and temperature profile data do not match these simple models, and more realistic modeling, such as a finite energy release model, is required. A finite energy release model is a differential equation model of an engine cycle in which the energy addition is specified as a function of the crank angle. It is also known as a model, since it is a function only of crank angle, and not a function of the combustion chamber geometry.

      Energy release models can address questions that the simple gas cycle models cannot. If one wants to know about the effect of spark timing or heat and mass transfer on engine work and efficiency, an energy release model is required. Also, if heat transfer is included, as is done in Chapter 11, then the state changes for the compression and expansion processes are no longer isentropic, and cannot be expressed as simple algebraic equations.

A typical cumulative mass fraction burned, i.e., fraction of fuel energy released, curve for a spark‐ignition engine is shown in Figure 2.15. The figure plots the cumulative mass fraction burned Скачать книгу