THE IDEAL HEAT ENGINE

Of All Heat Engines, Rudolf Diesel's Can Yield The Best Fuel Economy Because It Is Based On Carnot

Heat Engine Theory
A heat engine converts part of the heat energy into mechanical work.

In 1824, Sadi Carnot wrote:   Since every re-establishment of equilibrium in the caloric may be the cause of the production of motive power, every re-establishment of equilibrium which shall be accomplished without production of this power should be considered as an actual loss.   Now, very little reflection would show that all change of temperature which is not due to a change of volume of the bodies can be only a useless re-establishment of equilibrium in the caloric.   The necessary condition of the maximum is, then, that in the bodies employed to realize the motive power of heat there should not occur any change of temperature which may not be due to a change of volume.   Reciprocally, every time that this condition is fulfilled the maximum will be attained.   This principle should never be lost sight of in the construction of heat engines; it is its fundamental basis.   If it cannot be strictly observed, it should at least be departed from as little as possible.   [Emphasis in the original.]

Carnot observed that the maximum work available per unit of water descending down a waterfall is fixed by its height.   He reasoned that the same would be true of heat; that 100% of the heat would be converted to work if the expanding body continued to expand until its temperature was absolute zero.   If expansion of the body stops before absolute zero, then the maximum fraction of heat that can be converted into mechanical work is the Carnot efficiency, which depends only on cycle temperatures:

where absolute zero is the numeral 0.   (Practical bodies such as gases eventually stop expanding and shrink due to liquefaction well above absolute zero.)

Necessaries
Understanding the advantages of programmable fuel injection requires a few auxiliary details about heat engines.

1. Working fluid:   modern parlance for Carnot's archaic "body employed to realize the motive power of heat."
   
   
   R. Diesel's original analysis used the perfect gas law, pV = mRT, for air as the working fluid which is valid since temperature stays well above its critical temperature, -223F.   Despite the burning of fuel, the properties of just air can still be used for calculations throughout the entire cycle with little numerical error.   This is due to the large ratio of air to chemical species added by combusting small quantities of highly energetic fuels such as hydrocarbons.   The error of this approximation increases as fuel heating value decreases.
   
   
2. The direction of heat transfer is only from hot toward cold.   (This statement ignores statistical mechanics.)
   
   
3. In an internal combustion engine, heat is transferred at high temperature into the working fluid.   Part of that energy is converted into work while the remainder must be rejected as unusable waste heat because expansion stops at low temperature, not absolute zero.
   
   
4. The rate and amount of heat transfer are each proportional to the temperature difference.   Escape of high temperature heat out of the working fluid lowers fuel economy, which makes this a critical defect in the operating principle(s) of existing engines, especially gasoline engines.
   
   
5. Engine cycle:   one complete sequence of engine piston / cylinder processes.
   
   
   In the sense used here, a real engine cycle consists of four piston strokes; intake, compression, power, and exhaust.   The intake and exhaust strokes refresh the working fluid for each cycle by completing the removal of unusable waste heat and restoring the level of oxygen.   The compression and power strokes are the focus of the cycle of four thermodynamic processes discussed below.
   
   
6. Thermodynamic cycle:   one complete sequence of thermodynamic processes.
   
   
   Thermodynamic processes both a) transfer heat and b) convert heat into work through changes in temperature, pressure, and volume of the working fluid.   Each cycle must reject unusable, waste heat to return the working fluid to its initial state.

Most Efficient Heat Engine
Before his book was published in 1892, Rudolf Diesel had set out to improve the steam engine, which featured an external combustion boiler and a notoriously poor thermal efficiency of 12-13% even in the most advanced, triple-expansion steam engines.   (The efficiency defect of an external combustion boiler still exists in steam turbine-generator power plants, whether they burn coal, oil, natural gas, or uranium.   The thermal efficiency of power plants used to charge electric cars would limit the total cycle efficiency of these cars to little or no better than that of an ordinary diesel engine.)

After considering ammonia as a more superheated vapor working fluid to avoid the tendency to condense he arrived at air, which eliminates boiler heat losses by permitting internal combustion.   In his own words, the three main points for designing a heat engine that can almost attain Carnot efficiency are:

1. Production of the highest temperature of the cycle (temperature of combustion), not by and during combustion, but before and independently of it, entirely by compression of ordinary air.
   
   
2. ...The combustible is added in such a way, that no increase in temperature of the gases, consequent upon the process of combustion, takes place, .... After ignition, combustion should not be left to itself, but be regulated by an external arrangement, maintaining the right proportion between the pressures, volumes, and temperatures.
   
   
3. Correct choice of the proper weight of air ... in proportion to the heat value ... of the combustible...

In sum:   transfer heat at a constant high temperature into the working fluid.   Or, restated:   depending on its heat value, inject fuel at a rate, after it autoignites and burns, to maintain the air at the high temperature to which it was raised by compression.   For efficiency approaching the Carnot maximum theoretical limit within a real heat engine, Diesel suggested the following thermodynamic cycle.   The letters A, B, C, and D refer to the real engine cycle while the numerals 1, 2, 3, and 4 refer to the thermodynamic processes for the constant temperature cycle on the right of the comparison diagram.

• Engine cycle piston stroke A:   fresh air intake.   The expended gas working fluid of the previous cycle is replaced.
  
  
• Engine cycle piston stroke B:   compression stroke.
  
  
  1. Thermodynamic cycle process 1:   transfer unusable, waste heat out of the working fluid by compressing the air at constant low temperature.   The work put into the air exactly equals the heat transferred out as the compressed air is cooled at the temperature of the intake air.
     
     
  2. Thermodynamic cycle process 2:   continue compressing the air but without rejecting heat until the air temperature is above the auto-ignition point of the selected fuel.   The temperature of the air rises from low to high.
     
     
• Engine cycle piston stroke C:   power stroke, or work output stroke.
  
  
  3. Thermodynamic cycle process 3:   transfer heat into the working fluid by "admitting the combustible gradually" at constant high temperature.   Restated, rate shape the injected fuel profile such that the temperature of the working fluid is not raised or lowered but stays the same as the heat is added by combustion of the fuel.   The heat transferred at constant high temperature into the gas by the combustion of the fuel exactly equals the work output as the gas expands while absorbing heat.   The rate at which a fuel is injected depends on its heating value.
     
     
  4. Thermodynamic cycle process 4:   continue expanding the gas but without rejecting heat until the gas cools to its initial temperature.   The temperature of the gas falls from high to low.
     
     
• Engine cycle piston stroke D:   exhaust stroke.   Expended gas working fluid is expelled.