In theory, the diesel engine is actually less efficient than a gasoline engine due to the thermodynamic cycle by which it operate. But in practice a diesel engine is more efficient than a gasoline engine, the main reason is the use of a higher compression ratio, and at part load, the lack of throttling. In practice the thermal cycle of the diesel also look very much like the cycle of the gasoline engine, more toward heat release at constant volume than at constant pressure.
The modern diesel engine is direct injected and the combustion occur in two stages. When the fuel injection starts before TDC a small part of the fuel will vaporise due to the compression heat, and the longer the ignition delay is, the more fuel will have had time to vaporise. This fuel will mix with the air inside the cylinder and will burn rapidly when ignited. This is the premixed burning in a diesel engine and since the heat release rate (J/deg) is very high it will result in a pressure spike and the knocking engine sound of a diesel engine. When the load, but also engine speed is increased the ignition delay will become shorter and the pressure spike will disappear.
The second phase of diesel engine combustion occur with a diffusion flame. Unlike a direct injected gasoline engine the fuel injection isn't completed before the combustion starts, no, the injection continue during the burn. The injector nozzle inject liquid fuel, a small diesel usually have around 5 sprays per injector, which vaporise and oxidize when it comes into contact with air. If you haven't seen this on an in cylinder video, it looks like having 5 very small flame throwers in the cylinder. Inside the plume the mixture is rich, which cause the formation of soot, and at the outside the mixture is lean, causing the formation of nitrous oxides. This is shown in the picture below.
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In a gasoline engine the combustion speed is dependant on the engine speed. Higher engine speed means more turbulence, which means a higher combustion speed. In the gasoline engine, the result is that the combustion can be done at about the same duration in crankshaft degrees independent on engine speed (only the ignition delay increase with speed). This is not the case with the diesel, where the duration of the combustion becomes longer and longer when the engine speed increases. The result is that the maximum cylinder pressure, pmax, occur later and later in the power stroke. With a gasoline engine you want pmax to occur at around 17 degrees after top dead center, and the ignition advance is set to achieve that if possible. If the ignition is retarded we get less torque, a lower efficiency and a higher exhaust temperature. The same thing will happen if we run a gasoline engine lean as that would result in a slower burn. This is also what is happening to the diesel at high engine speeds. So, the engine speed is kept down with diesels.
Diesel engines always operate with lean fuel mixtures, and the load is also controlled by adjusting the amount of fuel injected as opposed to air as with the gasoline engine. The diesel also have a smoke limit somewhere around lambda 1.3, use richer fuel mixtures than that and the engine will start to produce visible smoke while the exhaust temperature increase.
High injection pressures, as high as 2400 bar, are mainly used to prevent soot, important in itself but also important if an EGR system should be possible to use. Supercritical fuel injection is studied as a possible next step.
It is often said that diesels produce more torque than gasoline engines. They don't. Compare a diesel engine on equal grounds, that is, equal displacement and boost pressure, and they will produce about the same amount of torque. The diesel will however in such a comparison produce much less power. The reason diesels often produce more torque than a gasoline engine is either due to a greater displacement or a higher boost pressure. Since a diesel can't knock it can use very high boost pressures to compensate for what it lacks in engine speed. But high boost pressures combined with a high compression ratio also result in very high peak cylinder pressures. A naturally aspiranted engine producing 100 hp/l such as several BMW engine, see peak pressures in the order of 90 bar, a F1 engine 110 bar or so and a downsized turbo engine such as the VW TSI 120 bar. A diesel with 100 hp/l operate with peak pressures in the order or 190 bar, roughly twice that of the gasoline engine with similar specific output. For a production engine that translates into a roughly 20% weight handicap since the engine must be reinforced to handle this king of pressures.
Diesel fuel contain 42.5 MJ/kg and has a specific gravity of 820-845 kg/m3. Premium gasoline contain more energy, 43.5 MJ/kg, but has a lower density of 720-745 kg/m3. Overall, this gives diesel roughly 10% more energy ona volume basis. Scandinavian diesel, or more specifically, Swedish MK1 diesel have a reduced aromatics content to make the fuel cleaner, that result in a less dense fuel at 810 kg/m3 but it also has a higher energy content of 43.2 MJ/kg.
For a diesel engine to be possible in F1 which require a compact lightweight package, it would probably be forced to operate with a low compression ratio by diesel engine standards and with a very high boost pressure. Since the engine would be forced to produce the same output as the competition, but at a much lower engine speed, it would also put high demands on the drivetrain.