Thermal Efficiency for Dual Cycle

The thermal efficiency for a dual cycle is:

Diesel Cycle – Diesel Engine

A dual cycle, or limited pressure cycle, is a thermodynamic cycle that combines the Otto cycle and the Diesel cycle. In the dual cycle, combustion occurs partly at constant volume and partly at constant pressure. It can be used to describe internal combustion engines. The pressure-volume diagrams of actual internal combustion engines are not described well by the Otto and Diesel cycles. An air standard cycle that can be made to approximate the pressure variations more closely is the air-standard dual cycle. A more capable approach would be to model the combustion process in both Otto and Diesel engines as a combination of two heat-transfer processes, one isochoric process, and one isobaric process.

Compared to an Otto cycle, which assumes an instantaneous heat addition (isochoric heat addition), heat is added partly at constant volume and partly at constant pressure in a dual cycle. Therefore the advantage is that more time is available for the fuel to combust completely. On the other hand, the use of a dual cycle is slightly more complex. The thermal efficiency lies between Otto and Diesel cycle.

The dual cycle combines the Otto cycle and the Diesel cycle.. There is an Otto engine in this picture, which is ignited by a spark plug instead of compression itself.

Four stroke engine - Otto engine — Four-stroke engine – Otto engine
Source: wikipedia.org, Own work of Zephyris, CC BY-SA 3.0

Thermal Efficiency for Dual Cycle

In general, the thermal efficiency, η_th, of any heat engine is defined as the ratio of the work it does, W, to the heat input at the high temperature, Q_H.

The thermal efficiency, η_th, represents the fraction of heat, Q_H, converted to work. Since energy is conserved according to the first law of thermodynamics and energy cannot be converted to work completely, the heat input, Q_H, must equal the work done, W, plus the heat that must be dissipated as waste heat Q_C into the environment. Therefore we can rewrite the formula for thermal efficiency as:

Therefore the heat added and rejected are given by:

Q_add-1 = mc_v (T₃ – T₂)

Q_add-2 = mc_p (T₄ – T₃)

Q_out = mc_v (T₅ – T₁)

Therefore the thermal efficiency for a dual cycle is:

Efficiency of Engines in Transportation

In the middle of the twentieth century, a typical steam locomotive had a thermal efficiency of about 6%. That means for every 100 MJ of coal burned, 6 MJ of mechanical power were produced.
A typical gasoline automotive engine operates at around 25% to 30% of thermal efficiency. About 70-75% is rejected as waste heat without being converted into useful work, i.e., work delivered to wheels.
A typical diesel automotive engine operates at around 30% to 35%. In general, engines using the Diesel cycle are usually more efficient.
In 2014, new regulations were introduced for Formula 1 cars. These motorsport regulations have pushed teams to develop highly efficient power units. According to Mercedes, their power unit is now achieving more than 45% and close to 50% thermal efficiency, i.e., 45 – 50% of the potential energy in the fuel is delivered to wheels.
The diesel engine has the highest thermal efficiency of any practical combustion engine. Low-speed diesel engines (as used in ships) can have a thermal efficiency that exceeds 50%. The largest diesel engine in the world peaks at 51.7%.

References:

Nuclear and Reactor Physics:

J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
Kenneth S. Krane. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN: 978-0471805533
G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

Other References:

Diesel Engine – Car Recycling

See above:

Thermodynamic Cycles