A Common Mistake in the Current Thermodynamics of IC Engines
(Updated on 2018-1-7)
This article shows the PV diagram and the T-S diagram of Carnot cycle, Otto engine, and turbocharged Zhou Engine, and compares them. We found that: the isenthalpic expansion in the exhaust pipe of an Otto engine (or Diesel engine), which loses a lot mechanical work and reduce the thermal efficiency. A turbocharged Zhou Engine can avoid the isenthalpic expansion, to raise the thermal efficiency.
§1. Carnot Cycle
Fig.1 and fig.2 show the PV diagram and T-S diagram of a Carnot cycle.
In the fig.1 and fig.2 — The process a-b, is adiabatic compression, absorb mechanical work, and is isentropic process. The process b-c, is isothermal expansion, absorb heat and output mechanical work, is isothermal process. The process c-d, is adiabatic expansion, output mechanical work, and is isentropic process. The process d-a, is isothermal compression, releases heat and absorbs mechanical work, and is isothermal process.
This is a classic thermal cycle, is a close cycle. It is simple, clear, and correct. It is shown here as the reference of the below.
§2. Otto Engine
According to the following ideal gas basic formulas:
Here, we suppose — An Otto engine, its ambient temperature is 300K, ambient atmospheric pressure is 0.1013MPa, cylinder volume is Va, its compression ratio is 10, its temperature limit of combustion is 2500K, it is in an ideal cycle. This is an open cycle, which exchanges its working medium (air) outside.
We have calculated and then draw PV diagram in fig.3 and T-S diagram in fig.4.
In fig.3 and fig.4:
Point a: T=300, p=0.1013, V=1*Va, S=4818*Va;
Point b: T= 753.57, p= 2.5445, V=0.1*Va, S=4818*Va;
Point c: T=2500, p=8.4417, V=0.1*Va, S=5832*Va;
Point d: T=995.27, p=0.3361, V=Va, S=5832*Va;
Point f: T=995.27, p=0.1013, V=3.3176*Va, S=6236*Va 。
At point a, suction air. The process a-b, it is compression stroke, is adiabatic compression, and is isentropic compression. The process b-c, it is constant volume combustion, its entropy increasing, its temperature increasing. The process c-d, it is expansion stroke, is adiabatic expansion, is isentropic expansion. The process d-f (in blue line in the drawings), it is isenthalpic (or isothermal) expansion in the exhaust pipe, its entropy is increasing, it loses the huge (pressure) mechanical energy and leads to the transport work in the exhaust to reduce the thermal efficiency. Point f, it corresponds to the outlet of the exhaust pipe, from it the exhaust discharges to atmosphere.
Note: The process d-f (in blue line) of "entropy increasing", is carelessly neglected in many university textbooks and the writings about IC engine, please compare with https://en.wikipedia.org/wiki/Otto_cycle. This is a common mistake of the current thermodynamics of IC engines.
Likewise, this common mistake is also in the theory of Diesel engines.
According to the second law of thermodynamics, in all real cases, the entropy always increases and is irreversible. If the process d-f of "entropy increasing" exists, we irreversibly lose the related mechanical energy, no matter what we will do, even if we will recycle the waste heat. In other words, if we want to avoid losing the related mechanical energy, we must avoid the process d-f of "entropy increasing".
This mistake, neglecting of the process d-f, leads us to overvalue the ideal thermal efficiency of IC engine, please see “A common mistake in textbook of physics” (https://www.dhirubhai.net/pulse/common-mistake-textbook-physics-jihua-zhou ).
This mistake, neglecting of the process d-f, it has been an inertial thinking. It has ever been limiting our insight. It has ever lost our way to increase the thermal efficiency.
This mistake, neglecting the process d-f, it hides the huge wasted mechanical energy in the exhaust. The "turbocharged Zhou Engine" happens to avoid the process d-f of "entropy increasing", and recycle the huge mechanical energy, seeing the below §3.
Note, there should not have a line between point a and f in fig.4, Otto engine T-S diagram, because the working gas does not circular flow inside an Otto engine. This is the big difference from a Carnot cycle.
§3. Turbocharged Zhou Engine
Here, we extract the fig.5 and which data of “Turbocharged Zhou Engine” (https://www.dhirubhai.net/pulse/turbocharged-zhou-engine-jing-yuan-zhou ), calculate the entropies according to expression (2) above, and draw the PV diagram at this Fig.5, and draw the T-S diagram at this Fig.6.
In Fig.5 and Fig.6,
A: p=0.1013, V=V1, T=273.15, S=5205*V1
B: p=6.715, V=0.05*V1, T=905.3, S=5205*V1
C: p=18.544, V=0.05*V1, T=2500, S=6148*V1
D: p=0.1013, V=2.0658*V1, T=564.28, S=6148*V1
E: p=1.5, V=0.3013*V1, T=1218.8, S=6148*V1
F: p=0.5433, V=0.3013*V1, T=441.4, S=5205*V1
At point A, suction air. The process A-F-B, is adiabatic compression, and is isentropic compression; in which, the process A-F is inside a compressor, the process F-B is inside the cylinder of the Zhou Engine. The process B-C, it is constant volume combustion inside the cylinder of the Zhou Engine, its entropy increasing, its temperature increasing. The process C-E-D, is adiabatic expansion, is isentropic expansion; in which, the process C-E is inside the cylinder of the Zhou Engine, the process E-D is inside a turbine. Point D, it corresponds to the outlet of the exhaust pipe, from it the exhaust discharges to atmosphere. For more detail, please read “Turbocharged Zhou Engine”.
Note, there should not have a line between point A and D in fig.6, the T-S diagram of Turbocharged Zhou Engine, because the working gas does not circular flow inside an turbocharged Zhou Engine. This is the big difference from a Carnot cycle.
We can design a Zhou Engine best matching a turbine, to avoid the isenthalpic expansion inside the exhaust pipe, or to avoid the process d-f in §2, to obtain high thermal efficiency.
For more detail, please see “About Zhou Engine”.
Thanks Yogesh Kumar, tiecheng wang and Lawrence Willey, for their query and discussion.