The Lenoir cycle is an idealized
thermodynamic cycle
A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventu ...
often used to model a
pulse jet engine
300px, Diagram of a pulsejet
A pulsejet engine (or pulse jet) is a type of jet engine in which combustion occurs in pulses. A pulsejet engine can be made with few or no moving parts, and is capable of running statically (i.e. it does not need ...
. It is based on the operation of an engine patented by
Jean Joseph Etienne Lenoir in 1860. This engine is often thought of as the first commercially produced
internal combustion engine
An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal co ...
. The absence of any compression process in the design leads to lower
thermal efficiency
In thermodynamics, the thermal efficiency (\eta_) is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, steam turbine, steam engine, boiler, furnace, refrigerator, ACs etc.
For a he ...
than the more well known
Otto cycle
An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.
The Otto cycle is a description of what happ ...
and
Diesel cycle
The Diesel cycle is a combustion process of a reciprocating internal combustion engine. In it, fuel is ignited by heat generated during the compression of air in the combustion chamber, into which fuel is then injected. This is in contrast to ign ...
.
The cycle
In the cycle, an
ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
undergoes
:1–2: Constant volume (
isochoric
Isochoric may refer to:
*cell-transitive, in geometry
*isochoric process
In thermodynamics, an isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which ...
) heat addition;
:2–3:
Isentropic
In thermodynamics, an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no net transfer of heat or matter. Such an idealized process ...
expansion;
:3–1: Constant pressure (
isobaric
Isobar may refer to:
* Isobar (meteorology), a line connecting points of equal atmospheric pressure reduced to sea level on the maps.
* Isobaric process
In thermodynamics, an isobaric process is a type of thermodynamic process in which the pr ...
) heat rejection.
The expansion process is
isentropic
In thermodynamics, an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no net transfer of heat or matter. Such an idealized process ...
and hence involves no heat interaction. Energy is absorbed as heat during the isochoric heating and rejected as work during the isentropic expansion.
Waste heat
Waste heat is heat that is produced by a machine, or other process that uses energy, as a byproduct of doing work. All such processes give off some waste heat as a fundamental result of the laws of thermodynamics. Waste heat has lower utility ...
is rejected during the isobaric cooling which consumes some work.
Constant volume heat addition (1–2)
In the ideal gas version of the traditional Lenoir cycle, the first stage (1–2) involves the addition of heat in a constant volume manner. This results in the following for the first law of thermodynamics:
There is no work during the process because the volume is held constant:
and from the definition of constant volume specific heats for an ideal gas:
Where ''R'' is the ideal gas constant and ''γ'' is the ratio of specific heats (approximately 287 J/(kg·K) and 1.4 for air respectively). The pressure after the heat addition can be calculated from the ideal gas law:
Isentropic expansion (2–3)
The second stage (2–3) involves a reversible adiabatic expansion of the fluid back to its original pressure. It can be determined for an isentropic process that the second law of thermodynamics results in the following:
Where
for this specific cycle. The first law of thermodynamics results in the following for this expansion process:
because for an adiabatic process:
Constant pressure heat rejection (3–1)
The final stage (3–1) involves a constant pressure heat rejection back to the original state. From the first law of thermodynamics we find:
.
From the definition of work:
, we recover the following for the heat rejected during this process:
.
As a result, we can determine the heat rejected as follows:
.
For an ideal gas,
.
Efficiency
The overall efficiency of the cycle is determined by the total work over the heat input, which for a Lenoir cycle equals
:
Note that we gain work during the expansion process but lose some during the heat rejection process.
Alternatively, the first law of thermodynamics can be used to put the efficiency in terms of the heat absorbed and heat rejected,
:
Utilizing that, for the isobaric process, , and for the adiabatic process, , the efficiency can be put in terms of the
compression ratio
The compression ratio is the ratio between the volume of the cylinder and combustion chamber in an internal combustion engine at their maximum and minimum values.
A fundamental specification for such engines, it is measured two ways: the stati ...
,
:
where is defined to be . Comparing this to the Otto cycle's efficiency graphically, it can be seen that the Otto cycle is more efficient at a given compression ratio. Alternatively, using the relationship given by process 2–3, the efficiency can be put in terms of , the
pressure ratio,
:
Cycle diagrams
References
{{Thermodynamic cycles, state=uncollapsed
Thermodynamic cycles
Belgian inventions