# Putting some numbers on the diesel engine

Diesel engines convert the chemical energy in fuel to mechanical energy. Energy is released in a series of combustions as fuel reacts with oxygen from the air. The chemical equation of diesel fuel combustion is 4 C12H23 +71 O2 –> 48 CO2 + 46 H­2O. Combustion reactions are spontaneous yielding a -∆G. The reaction goes from 71 moles of O2 gas to 48 moles of CO2 yielding a -∆S. Combustion reactions break bonds between the molecules signaling an exothermic reaction or -∆H.

To find the value of ∆G, we will use the values 50.1 kJ/mol for C12H23, 0 kJ/mol for O2, -393.5 kJ/mol for CO2, and -229 kJ/mol for H­2O. To solve for ∆G, we calculate 46(-229) + 48(-394) – 4(50.1) which equates to -29622 kJ, a -∆G for a spontaneous reaction. To find the value of ∆S, we can use the equation ∆G = ∆H – T∆S. Using the -56,000 kJ for  ∆H  from our prior blog post,-29622 kJ for ∆G, and the 483 K ignition temperature of diesel fuel we can calculate the ∆S. This equates to -54 kJ, a -∆S.

Steve Lynch

# Putting some numbers on the diesel engine

The ultimate goal of the diesel engine is to convert the potential energy of the diesel fuel into mechanical energy that moves the car forward.  It has already been explained that the combustion reaction of the diesel fuel is responsible for this.  The reaction is 4 C12H23 +71 O2 –> 48 CO2 + 46H­2O.  Of course there is more going on.  This is for the complete combustion of diesel, which does not actually happen.  There are other products that can include CO and unburned fuel.  When the reaction is not the complete combustion this results in the reaction yielding less energy.  This happens when there is a lack of oxygen so not all of the fuel can combust and can also be seen in a Bunsen burner.  For simplicities sake, we will assume the diesel fuel completely combusts.

The combustion of diesel fuel is clearly exothermic, which can be seen from the energy that is released as light and heat.  This means the change in enthalpy of the reaction has to be negative.  The change in enthalpy of a reaction is equal to the change in enthalpy of the products minus the change in enthalpy of the reactants.  With numbers that can easily be found on the internet or in the appendix of a chemistry book you can find the exact change in enthalpy for one mole of diesel fuel.  The heat of formation of diesel, oxygen, carbon dioxide, and water respectively are 6,700 kJ/mole (converted from kJ/kg and assuming the a molecular formula of C12H23), 0kJ/mole, -393.5 kJ/mole, and -242 kJ/mole.  If you multiply all of those numbers by the moles present and subtract reactants from products you get the change in enthalpy for the combustion of diesel.  It is 46 *(-242) + 48 * (-393.5) – 4 * (6,700) you get -56,000 kJ as the heat of formation for the combustion reaction for diesel.

Chris Pagliaro

# More on the Diesel Cycle and Thermal Efficiency

Thermal Efficiency is basically a performance measure of devices, such as diesel engines, that use thermal energy. It basically measures energy output over energy input. Because you can never get more energy than you put it, thermal efficiency will always be less than one.

Maximum diesel efficiency is dependent on the cut-off ratio and the compression ratio shown by the following equation:

nth=1-(1/rγ-1)(αγ-1/[γ(α-1)])

where nth is the thermal efficiency, α (alpha) is the cut-off ratio (V3/V2), r is the compression ratio (V1/V2), and γ is the ratio of the specific heats (Cp/Cv). This equation is based off of this graph that represents the idealized diesel cycle:

Gasses act ideal at high temperatures and low pressures.

The cycle can be summarized as follows. Work is put in at point one. As this happens, volume decreases and pressure increases. Basically, the pressure compresses the gas. The heat is put in increasing the volume of the gas, expanding it, at constant pressure. From there the pressure decreases as the volume increases due to expansion of the gas, releasing work that powers the engine. Then, pressure goes down at constant volume as heat is given off to return to the beginning of the cycle.

Higher thermal efficiency is not only more cost effective than lower thermal efficiency, but it yields a longer engine life. This is why diesel engines are becoming more popular, they last longer, and fuel is cheaper. This makes them perfect for heavy hauling trucks and now some companies are even making cars that have them that everyday people can use.

Eddie McClain

# Spontaneity and Efficiency

Diesel engines convert the chemical energy in fuel to mechanical energy which moves pistons up and down inside cylinders. The pistons are connected to the engine’s crankshaft, which changes their linear motion into the rotary motion needed to propel the vehicle’s wheels. Energy is released in a series of small explosions (combustion) as fuel reacts chemically with oxygen from the air. The chemical equation of diesel fuel combustion is as follows, C13H28 + 20O2 → 13CO2 +14H2O. Combustion reactions are spontaneous yielding a -∆G. The reaction goes from 20 moles of O2 gas to 13 moles of CO2 yielding a -∆S. Combustion reactions break bonds between the molecules signaling an exothermic reaction or -∆H.

German engineer Rudolf Diesel theorized that fuel could be made to ignite spontaneously if the air inside an engine’s cylinders became hot enough through compression because air heats up when it’s compressed. Achieving high temperatures meant producing much greater air compression than occurs in gasoline engines, but Diesel calculated that high compression should lead to high engine efficiency. Part of the reason is that compressing air concentrates fuel-burning oxygen. A fuel that has high energy content per gallon, like diesel fuel, should be able to react with most of the concentrated oxygen to deliver more punch per explosion, if it was injected into an engine’s cylinders at exactly the right time. Diesel’s calculations were correct. As a result, although diesel engines have seen vast improvements, the basic concept of the four-stroke diesel engine has remained virtually unchanged for over 100 years.

Steven Lynch

# Design Considerations in Diesel Engines

Diesel engines had to have several design considerations taken into account because of the chemical properties of the diesel fuel.  The engine had to be designed around the fuel and because of these chemical properties some considerations were made for the diesel engines.

In order to ignite the diesel engine the cylinder has to be very pressurized because there are no spark plugs.  This means that the engines have to be made stronger in order to not break under such high pressures.  This results in diesel engines being extremely heavy than gasoline engines and they are also much stronger as a result.

Another consideration with diesel engines is the byproducts they create.  There are two main byproducts made from the combustion of diesel fuel, carbon based soot and NOX, which is a nitrogen oxide that can have different amounts of oxygen depending on the conditions.  This is more of a problem with diesel engines than gasoline engines because of the way fuel is injected into the diesel engine.    While a car is accelerating there is a shortage of air in diesel engines, which yields unburned soot.

Generally when one is decreased, it results in an increase in the other.  As combustion temperatures go down, the amount of NOX created is much less, but that results in an increase in the production of soot.  A reduction in temperature can be accomplished this by injecting the fuel later during the combustion cycle.  However this is bad because if too much soot gets trapped in the oil, around a concentration 3-5%, that will results in increased wear on the engine.  There are also very strict regulations on the amount of soot that diesel engines can make which are enforced by the government.  To reduce the soot and NOX made  there are several filters in an engine that help reduce levels of these harmful compounds.  There is a diesel particulate filters which treats the exhaust of the engine after the combustion is complete.  This is much easier and cheaper than reducing NOX by selective catalyst reduction, however there are such strict regulations on the amount of soot that can be created; both are usually present in modern diesel engines.

Because of the different properties chemical properties of diesel fuel, different considerations were taken into account in the design of the diesel engine.  These are a few of the design considerations that were made.

Chris Pagliaro

# Problems With Viscosity of Diesel Fuel

Viscosity is a very important issue with diesel fuel. Viscosity is the resistance to deformities of a substance caused by stress. It is also described as how thick something is. The reason a substance, such as diesel has a higher viscosity in lower temperatures and a lower viscosity in higher temperatures is that in higher temperatures, more energy from heat is being added to the substance to break the bonds, or weaken the intermolecular forces. This makes something less viscos because the property of viscosity is due to intermolecular forces. The atoms with stronger intermolecular forces are pulling each other together making it harder to move through the substance macroscopically; this substance is thicker and more viscos.

This causes a problem with diesel fuel. In the winter time, when the temperature gets cold enough, diesel fuel becomes too viscos and will not ignite or pump. It will not ignite because diesel needs to be aerosolized to ignite. Simply, it must be easily turned into a gaseous material which is difficult to do if it is too viscos. Also it is too thick to pump throughout the engine. It is like trying to swim through honey, it would be very difficult.

Preheaters are used in diesel engines to get around the cold weather problem. This is used to heat the fuel during start up to make it less viscos so the car can start. They can only operate for a few seconds while the car is starting up. If they go for any longer they may burn out. This problem is now much easier to get around with computers that monitor things like that.

Eddie McClain

# Diesel Engine Cycle

The term “compression ignition” is typically used in technical literature to describe the modern engines commonly called “Diesel engines”. This is in contrast to “spark ignition” for the typical automobile gasoline engines that operate on a cycle derived from the Otto cycle. Rudolph Diesel patented the compression-ignition cycle which bears his name in the 1890s. The diesel internal combustion engine differs from the gasoline powered Otto cycle by using a higher compression of the fuel to ignite the fuel rather than using a spark plug (“compression ignition” rather than “spark ignition”).

In the diesel engine, air is compressed adiabatically with a compression ratio typically between 15 and 20. This compression raises the temperature to the ignition temperature of the fuel mixture which is formed by injecting fuel once the air is compressed. The ideal air-standard cycle is modeled as a reversible adiabatic compression followed by a constant pressure combustion process, then an adiabatic expansion as a power stroke and an isovolumetric exhaust. A new air charge is taken in at the end of the exhaust, as indicated by the processes a-e-a on the diagram. Since the compression and power strokes of this idealized cycle are adiabatic, the efficiency can be calculated from the constant pressure and constant volume processes. The input and output energies and the efficiency can be calculated from the temperatures and specific heats.

Diesel engines are more powerful and fuel-efficient than similar-sized gasoline engines (about 30-35% more fuel efficient). Today’s diesel vehicles are much improved over diesels of the past.

Steven Lynch