Diesel Cycle - Ideal Cycle for Compression-ignition Engines

Isentropic Compression (1-2) Click to View Movie (25.0 kB)		The only difference between ideal Otto cycle and ideal Diesel cycle is the heat addition process. Instead of constant volume heat addition process in SI engine, heat is added to the air in the Diesel engine at constant pressure. The four processes are: 1-2 Isentropic compression 2-3 Constant pressure heat addition 3-4 Isentropic expansion 4-1 Constant volume heat rejection
Constant Pressure Heat Addition (2-3) Click to View Movie (45 kB) Isentropic Expansion (3-4) Click to View Movie (29 kB) Constant Volume Heat Rejection (4-1) Click to View Movie (35 kB)		Noting that the ideal Diesel cycle is executed in a closed system and the working fluid is air according to the air-standard assumption. Also, changes in kinetic and potential energies are negligible. No heat transfer is involved in the two isentropic processes. The energy balances for these two processes are:       -w12 = u2 - u1       -w34 = u4 - u3 w12 is negative since work is needed to compress the air in the cylinder and w34 is positive since air does work to the surroundings during its expansion. In the constant pressure heat addition process, air is expanded to keep the pressure as constant during the heat addition. The expansion work equals       w23 = P2(v3 - v2) The energy balances for this process is:       q23 = u3 - u2 + w23 = h3 - h2 In the constant volume heat rejection process, no work interaction is involved since no volume change occurs. The energy balances for this process is:           q41 = u1 - u4 q23 is positive since heat is added to the air and q41 is negative since heat is rejected to the surroundings during this process. For the whole cycle, the energy balance can be determined by adding the energy balance of its four processes. That is,       q23 + q41 - w12 - w34 = 0
		The thermal efficiency of an ideal Otto cycle is       ηth,Diesel = wnet/qin According to the analysis above, the net work output is       wnet = w34 + w12 = q23 + q41       qin = q23       ηth, Diesel = 1+ q41/q23 Under the cold air-standard assumption, the thermal efficiency of an ideal Diesel cycle is
		In order to simplify the above equation, the cutoff ratio rc is defined as rc = v3/v2 Process 1-2 and process 3-4 are isentropic. Thus,        The thermal efficiency relation reduces to

Thermodynamics(Auto cycle, Diesel cycle,Brayton cycle,Gay-Lussac's Law,Efficiency of Heat Engine formulas)

Thermodynamics is a branch of physics which deals with the energy and work of a system. It was born in the 19th century as scientists were first discovering how to build and operate steam engines. Thermodynamics deals only with the large scale response of a system which we can observe and measure in experiments. As aerodynamicists, we are most interested in the thermodynamics of propulsion systems and high speed flows. On this page we consider the thermodynamics of a four-stroke internal combustion engine. Today, most general aviation or private airplanes are powered by internal combustion (IC) engines, much like the engine in your family automobile.
There are two main parts to engine operation: the mechanical operation of the engine parts, and the thermodynamics through which the engine produces work and power. On this page we discuss the basic thermodynamic equations that allow you to design and predict engine performance.
In an internal combustion engine, fuel and air are ignited inside a cylinder. The hot exhaust pushes a piston which is connected to a crankshaft to produce power. The burning of fuel is not a continuous process, but occurs very quickly at regular time intervals. Between ignitions, the engine parts move in a repeated sequence called a cycle. The engine is called a four stroke engine because there are four movements, or strokes, of the piston during one cycle.
On the figure we show a plot of pressure versus gas volume throughout one cycle. We have broken the cycle into six numbered stages based on the mechanical operation of the engine. For the ideal four stroke engine, the intake stroke (1-2) and exhaust stroke (6-1) are done at constant pressure and do not contribute to the generation of power by the engine. During the compression stroke (2-3), work is done on the gas by the piston. If we assume that no heat enters the gas during the compression, we know the relations between the change in volume and the change in pressure and temperature from our solutions of the entropy equation for a gas. We call the ratio of the volume at the beginning of compression to the volume at the end of compression the compression ratio, r. Then
p3 / p2 = r ^ gamma
T3 / T2 = r ^ (gamma - 1)
where p is the pressure, T is the temperature, and gamma is the ratio of specific heats. During the combustion process (3-4), the volume is held constant and heat is released. The change in temperature is given by
T4 = T3 + f * Q /cv
where Q is the heat released per pound of fuel which depends on the fuel,f is the fuel/air ratio for combustion which depends on several factors associated with the design and temperature in the combustion chamber, and cv is the specific heat at constant volume. From the equation of state, we know that:
p4 = p3 * (T4 /T3)
During the power stroke (4-5), work is done by the gas on the piston. The expansion ratio is the reciprocal of the compression ratio and we can use the same relations used during the compression stroke:
p5 / p4 = r ^ (-gamma)
T5 / T4 = r ^ (1 - gamma)
Between stage 5 and stage 6, residual heat is transferred to the surroundings so that the temperature and pressure return to the initial conditions of stage 1 (or 2).
During the cycle, work is done on the gas by the piston between stages 2 and 3. Work is done by the gas on the piston between stages 4 and 5. The difference between the work done by the gas and the work done on the gas is shown in yellow and is the work produced by the cycle. We can calculate the work by determining the area enclosed by the cycle on the p-V diagram. But since the processes 2-3 and 4-5 are curves, this is a difficult calculation. We can also evaluate the work W by the difference of the heat into the gas minus the heat rejected by the gas. Knowing the temperatures, this is an easier calculation.
W = cv * [(T4 - T3) - (T5 - T2)]
The work times the rate of the cycle (cycles per second cps) is equal to the power P produced by the engine.
P = W * cps

On this page we have shown an ideal Otto cycle in which there is no heat entering (or leaving) the gas during the compression and power strokes, no friction losses, and instantaneous burning occurring at constant volume. In reality, the ideal cycle does not occur and there are many losses associated with each process. These losses are normally accounted for by efficiency factors which multiply and modify the ideal result. For a real cycle, the shape of the p-V diagram is similar to the ideal, but the area (work) is always less than the ideal value.

Diesel Cycle

Rudolph Diesel
	Rudolph Diesel was born in Paris of Bavarian parents in 1858. As a budding mechanical engineer at the Technical University in Munich, he became fascinated by the 2nd law of thermodynamics and the maximum efficiency of a Carnot process and attempted to improve the existing thermal engines of the day on the basis of purely theoretical considerations. His first prototype engine was built in 1893, a year after he applied for his initial patent, but it wasn't until the third prototype was built in 1897 that theory was put into practice with the first 'Diesel' engine.
Diesel Cycle Operation
The Diesel cycle is the cycle used in the Diesel (compression-ignition) engine. In this cycle the heat is transferred to the working fluid at constant pressure. The process corresponds to the injection and burning of the fuel in the actual engine. The cycle in an internal combustion engine consists of induction, compression, power and exhaust strokes.
Run Diesel Cycle Animation
	Induction Stroke The induction stroke in a Diesel engine is used to draw in a new volume of charge air into the cylinder. As the power generated in an engine is dependent on the quantity of fuel burnt during combustion and that in turn is determined by the volume of air (oxygen) present, most diesel engines use turbochargers to force air into the cylinder during the induction stroke. From a theoretical perspective, each of the strokes in the cycle complete at Top Dead Centre (TDC) or Bottom Dead Centre (BDC), but in practicality, in order to overcome mechanical valve delays and the inertia of the new charge air, and to take advantage of the momentum of the exhaust gases, each of the strokes invariably begin and end outside the 0, 180, 360, 540 and 720 (0) degree crank positions (see valve timing chart).
	Compression Stroke The compression stroke begins as the inlet valve closes and the piston is driven upwards in the cylinder bore by the momentum of the crankshaft and flywheel. The purpose of the compression stroke in a Diesel engine is to raise the temperature of the charge air to the point where fuel injected into the cylinder spontaneously ignites. In this cycle, the separation of fuel from the charge air eliminates problems with auto-ignition and therefore allows Diesel engines to operate at much higher compression ratios than those currently in production with the Otto Cycle.
	Compression Ignition Compression ignition takes place when the fuel from the high pressure fuel injector spontaneously ignites in the cylinder. In the theoretical cycle, fuel is injected at TDC, but as there is a finite time for the fuel to ignite (ignition lag) in practical engines, fuel is injected into the cylinder before the piston reaches TDC to ensure that maximum power can be achieved. This is synonymous with automatic spark ignition advance used in Otto cycle engines.
	Power Stroke The power stroke begins as the injected fuel spontaneously ignites with the air in the cylinder. As the rapidly burning mixture attempts to expand within the cylinder walls, it generates a high pressure which forces the piston down the cylinder bore. The linear motion of the piston is converted into rotary motion through the crankshaft. The rotational energy is imparted as momentum to the flywheel which not only provides power for the end use, but also overcomes the work of compression and mechanical losses incurred in the cycle (valve opening and closing, alternator, fuel injector pump, water pump, etc.).
	Exhaust Stroke The exhaust stroke is as critical to the smooth and efficient operation of the engine as that of induction. As the name suggests, it's the stroke during which the gases formed during combustion are ejected from the cylinder. This needs to be as complete a process as possible, as any remaining gases displace an equivalent volume of the new charge air and leads to a reduction in the maximum possible power.
	Exhaust and Inlet Valve Overlap Exhaust and inlet valve overlap is the transition between the exhaust and inlet strokes and is a practical necessity for the efficient running of any internal combustion engine. Given the constraints imposed by the operation of mechanical valves and the inertia of the air in the inlet manifold, it is necessary to begin opening the inlet valve before the piston reaches Top Dead Centre (TDC) on the exhaust stroke. Likewise, in order to effectively remove all of the combustion gases, the exhaust valve remains open until after TDC. Thus, there is a point in each full cycle when both exhaust and inlet valves are open. The number of degrees over which this occurs and the proportional split across TDC is very much dependent on the engine design and the speed at which it operates.