Engine Cycles

Engine cycle analysis

When it comes to the analysis of engine cycles, there are four stages. These include intake, compression, combustion, and exhaust. Each stage is shown in Figure 1 below which describes a four-stroke diesel engine or petrol engine. It is worth mentioning the main individual components in an engine cylinder. A cylinder is where the combustion takes place. A piston is a cylinder inside the engine which is connected to a rod that is used to move the piston vertically inside the engine cylinder in a gas-tight fit. There are two valves at the top of the cylinder, an intake valve and an exhaust valve, and a fuel injector or spark plug between the two valves.

Fig. 1. Four-stroke engine cycle

In petrol or diesel engines each vertical movement of the piston either upwards or downwards is called a stroke. Hence in four-stroke engines, the piston does 4 total upward and downward movements in total which are usually divided into four different stages to complete an engine cycle.

Engine Cycles Analysis: Intake Stroke

The first stroke is the intake stroke. In an intake stroke, the piston travels down the cylinder from the upper maximum position to the lower minimum position. Premixed air and fuel are suctioned into the cylinder via the open inlet valves increasing the volume inside the cylinder. The pressure in the cylinder remains constant, approximately below atmospheric pressure.

Engine Cycles Analysis: Compression

At this point, the valves are closed. The piston now moves upwards from the minimum vertical position to the maximum position decreasing the volume and increasing the pressure inside the cylinder. The mixture is compressed towards a spark plug. Work is done on the air during compression. This is the second stroke.

It is vital that the spark occurs right before the end of the stroke so that the mixture has had enough to reach the top of its stroke, thereby allowing maximum pressure to operate on the descending piston. The heated fuel powers the turbine and then is injected into the combustion chamber where it is burned.

Engine Cycles Analysis: Combustion

Due to high pressure near the top maximum position towards the end of the second stroke, the temperature of the mixture is increased and the mixture is ignited by a spark from the spark plug. The volume remains almost constant during this stage. This is the last step of the second stroke.

Engine Cycles Analysis: Expansion

The high pressure from the expanded gases forces the piston to move downwards. Work is done by the expanding gases. The exhaust valve opens at the minimum position, and the pressure reduces to nearly atmospheric. This is the third stroke.

Engine Cycles Analysis: Exhaust

The piston moves upwards expelling the burnt gases through the open exhaust valve while the pressure in the cylinder remains at just above atmospheric pressure. This is the fourth and last stroke of an engine cycle. The cycle then is repeated.

The heat or engine cycles basically add and reject energy in the form of heat during the combustion and exhaust stages, while work is done by the compression and expansion stages.

Two types of cycles for petrol and diesel engines

There are two types of engines. Diesel and petrol engines operate according to different theoretical engine cycles, the diesel cycle, and the Otto cycle respectively.

The ideal or theoretical Otto cycle described above is the principle at which the petrol engine operates. It assumes the following conditions:

• Intake is isobaric(0-1).

• Compression is reversible and adiabatic (1-2).

• Combustion (heat addition) is isochoric (2-3).

• Expansion is reversible and adiabatic (3-4).

• Exhaust (heat rejection) is isochoric (4-1).

The ideal Otto cycle can also describe the four strokes in using a thermodynamic pressure vs volume graph. This is shown in the figure below where the four strokes are described with numbers from 1 to 4 referring to the four sequential strokes completing one engine cycle. The constant volume and constant pressure processes are shown.

Fig. 2. Ideal Otto cycle

The ideal or theoretical diesel cycle is the principle at which the diesel engine operates. It can be described assumes the following conditions:

• Intake is isobaric (0-1).

• Compression is adiabatic (1–2).

• Combustion (heat addition) is isobaric (2–3).

• Expansion is adiabatic (3–4).

• Exhaust (heat rejection) is isochoric ( 4–1).

Fig. 3. Ideal diesel cycle - StudySmarter Originals

An indicating Otto cycle of a real petrol engine and diesel engine obtained using a pressure sensor in the cylinder and a transducer whose output depends on the angular position of the crankshaft is shown in the figure below.

Fig. 4. Left: Indicating diesel Engine, right: Indicating petrol engine

It can be seen from these figures above that they are not the same as the theoretical cycle figures. This is because the thermodynamic processes that take place in internal combustion are not as assumed in the theoretical cycles. The combustion and expansion stages are not constant in terms of volume and pressure as assumed. They are also not reversible in real life as it is assumed in theoretical conditions.

There are also other engine cycles besides the Otto and Diesel cycle which include the Carnot cycle, Brayton cycle, and the Rankine cycle. The most efficient cycle is the Carnot cycle and the least efficient cycle is the diesel engine cycle.

Equations for engine cycles

The above figures can be used for comparison with the ideal cycles, but also to find the work done on the gas during compression by estimating the area underneath the compression curve, and the work done by the expansion of the gas by estimating the area measured in m² underneath the expansion curve.

Thus the net work done by the air in one cycle is given by the area underneath the closed-loop on the p-V diagram. If the work done is divided by the time for one cycle, the indicated power is obtained as shown in the equation below where n_s is the number of cycles per second, n_cylinders is the number of cylinders in an engine. P_i is the indicated power developed by the combustion of fuel in the combustion chamber.

\[P_i[W] = Area \cdot n_s \cdot n_{cylinders}\]

Some of the chemical energy will be lost due to friction hence the output power of the engine will be less than the indicated power. Hence the output power P_out is equal to the indicated power P_i subtracting the frictional power P_f as shown below.

\[P_{out}[W] = P_i - P_f\]

Also, the output power P_out can also be calculated using the torque of the output shaft T and the angular velocity ω. Hence, the maximum power is the input power achieved from the chemical energy of the fuel.

\[P_{out} [W] = T[Nm] \cdot \omega [rad/s]\]

This can be calculated using the listed formulas where P_in is the input power generated from the chemical energy input, m_f is the fuel flow rate and c_f is the calorific value of the fuel.

\[P_{in}[MW] = c_f[MJ/kg] \cdot m_f[kg/s]\]

The theoretical efficiency of an ideal cycle can be found using the equation below, where η is the overall efficiency, r_n is the compression ratio. Thermal η_th and mechanical efficiencies η_m can also be found using the equations below. The efficiencies vary with the load of the engine.

\[\eta = 1 - \frac{1}{r_n^{0.4}} \quad \eta_o = \frac{P_{out}}{P_{in}} \quad \eta_m = \frac{P_{out}}{P_i} \quad \eta_{th} = \frac{P_i}{P_{in}}\]

where \(r_n = \frac{\text{Max volume at bottom stroke}}{\text{Min volume at top stroke}}\)