In the diesel engines, the processes of ignition and combustion start when air is drawn into the cylinder on the downward stroke, during the next stroke, the air charge compressed to a final pressure (= 35 − 50) bar with a final temperature of about 900 - 1000 K. Then fuel is injected by means of a pressure jet atomizer in the form of a fine spray shortly before the end of the compression stroke. After the elapse of the ignition delay, ignition occurs and combustion results at about the compression stroke. At this point pressure may exceed 70 bar and temperature may reach 2800 K. Energy release continues as work is done during the downward expansion stroke. The pressure-crank angle diagram (Figure 1), the compression and combustion process can be divided into three broad stages, to analyze what is actually happening. When the injector starts to inject fuel into the combustion chamber there will be some time elapse before the fuel droplets reach the temperature of ignition. This is represented by the distance, when this takes place, most of the fuel injected during the first stage ignites spontaneously, causing an abrupt pressure rise. The rest of the fuel injected during stage 3 is burnt as soon as it enters the combustion chamber. During the first stage, the fuel is sprayed into the hot air in the cylinder, the fuel droplets are heated up and then vaporized, mixing will take place and hence the mixture will be at this point ignitable, and ready to burn after the ignition lag has elapsed. In the second stage, the fuel injected and prepared for combustion in the first stage now begins to burn and thus causing a very rapid pressure rise, resulting from the sudden burning of the prepared fuel accumulated during the delay period. This is known as knock in diesel engines. In the third stage the burning of the prepared first stage mixture is completed and the burning of the fuel injected in the second and third stages occurs. During this stage the conditions are controlled by the mixing of the rest of the fuel injected with air. From the above, the combustion process can be seen as two portions, physical and chemical portions. During the physical portion of the above processes, fuel injection, fuel jet disintegration, air penetration by liquid fuel, fuel evaporation and mixing of the evaporated fuel with air take place, where in the chemical portion, pre-ignition reactions will take place, which are responsible for generating the required pre-flame oxidation of the hydrocarbons (the liquid fuel) to release energy.

The ignition delay period is universally defined as that time interval extending from the start of injection to the onset combustion. This ignition delay will cause an increase in temperature inside combustion chamber of diesel engines before

combustion commences and consequently, will cause pressure to increase, which will lead to undesirable autoigniton. This will result in knock phenomenon which is a very high speed pressure waves (shock waves) that may cause a failure of piston walls and piston rings. When fuel first injected it start to atomize, then evaporates, these process govern the physical delay. After that fuel then mixes with the hot air in the cylinder where chemical reaction commences relatively slowly, which governs the chemical delay in the ignition process. The reaction then rapidly accelerates until “ignition” occurs. An important fact that must be considered in analyzing that ignition delay is the start of injection and the combustion in the cylinder. The start of injection is usually taken as the time when the injector needle lifts off its seat, which is normally determined by a needle-lift indicator. On the other hand, the combustion process is rather more complicated as it is an unsteady three-dimensional process and depends on other parameters such as the fuel, combustion chamber, fuel-injection system, and the operating conditions of a particular diesel engine, such as, late injection timing and low engine speed (rpm) which may also cause ignition delay.

The injection parameters include injection timing, injection pressure, and injection quantity. However, when injection starts early in the engine cycle, it will cause the delay period to be longer because initially pressure and temperature are low and longer time will be required for the pressure and temperature to reach the desired level for ignition. However, if the injection starts late (closer to the TDC), pressure and temperature are initially slightly higher and decrease due to the piston motion. Injection pressure will influence the velocity, drop size and the rate of injection, the effect will depend on the injector nozzle type and the geometry. However, experiments by [8] have shown that none of these factors has a significant effects on the delay, increasing injection pressure at normal operating conditions, will produce only modest decrease in the delay period. The amount of fuel injected have no significant effect on the ignition delay at normal operating conditions, however under engine starting condition, the delay increases with the increase of injection quantity. This is due to the lower temperature associated with increased evaporation for more amount of fuel injected.

However at the starting conditions (speed of engine, compression temperature are low) the effect becomes more important [1] , due to the higher rates of evaporation and mixing associated with swirl. On other hand, the chemical characteristics of the diesel fuel play an important role and hence a strong impact on the ignition delays. The most important factor is the cetane number, as this indicates how readily the fuel self-ignition. Fuels with high cetane number will reduce the ignition delay compared to fuels with low cetane number. A good research has been made [7] , which studies the ignition and combustion characteristics of the principle hydrocarbons found in diesel fuels, and made a better understanding of the relationships between fuel composition and its combustion behavior under divers conditions of utilization. Many investigators have interpreted the starting points of combustion [1] [2] [3] [4] [5] . However, most of them have considered combustion to occur at the point of measurable pressure rise owing to energy release [3] . Others have adapted alternative ways including the start of rapid temperature rise, the point of detectable light emission, and the point of measurable free radical concentration. An important factor that had to be considered in processing the collected file data, is to be aware of the actual starting point of injection. This value is estimated by tracing the injection. More informative details about ignition delay periods in diesel engines can be found in [12] .

In the present research, theoretical approach is used via a program written in MATLAB [13] , to compute the ignition delay in (ms) for a diesel engine at different operation conditions, by taking different pressures, temperatures, with different compression ratios (rc1:16, rc2:18, rc3:20), different fuel types (CAN = 40, CNB = 50) with different engine speeds such as [1000, 1500, 2100, 2800, 4500, 5500] (rpm). There are some assumptions that have been made as the injection timing taken at top dead center (TDC) and 0.12 m stroke length. The ignition delay in crank angle will be calculated 300 times at different operation conditions as mentioned previously. First, the mean piston speed will be calculated 6 times depend on engine speeds [1000, 1500, 2100, 2800, 4500 and 5500]. Then, the activation energy will be calculated 3 times with each compression ratio (rc1:16, rc2:18, rc3:20) ; the inlet temperature at (TDC) will be calculated 6 times at rc1:16, Also will be calculated 6 times at rc2:18, also will be calculated at rc3:20. and the inlet pressure at (TDC) will be calculated 6 times at rc1:16, Also will be calculated 6 times at rc2:18 and will be calculated at rc3:20, the ignition delay in millisecond could be calculated.

At the present time, there is no simple complete model of ignition delay. However, an empirical formula, developed by [5] , including assumptions for all equations, to estimate the period of ignition delay in diesel engine has shown to give good agreement for different engines.

where, is the ignition delay in crank angle degrees, P is the pressure in bars, and S_p is the mean piston speed m/s, is the mean piston speed (m/s), R = Universal gas constant (KJ/kmol K), E_A is activation energy, where, is the ignition delay in crank angle degrees, P is the pressure in bars, and S_p is the mean piston speed m/s,

T_TDC = Temperature in K,

P_TDC = Pressure in bar,

Ignition delay in millisecond, and

With the same values mentioned previously, the program will take it as input values as: Stroke length (L) = 0.12 m, polytrophic index (n) =1.4.

Temperatures (T) = [T1 = 15, T2 = 20, T3 = 25, T4 = 30, T5 = 35, T6 = 40];

Pressures (P) = [P1 = 1, P2 = 1.3, P3 =1.5, P4 = 1.7, P5 = 2.1, P6 = 2.5];

Engine speeds (N) = [N1 = 1000, N2 = 1500, N3 = 2100, N4 = 2800, N5 = 4500, N6 = 5500];

Compression Ratios (rc) = [rc1 = 16 rc2 = 18 rc3 = 20];

Cetane number (CN) = [CAN = 40, CNB = 50].