Diesel Cycle Thermal Efficiency
Diesel Cycle Thermal Efficiency
The air-standard Diesel cycle models compression-ignition engines, which compress air alone to a high ratio before injecting fuel that burns at roughly constant pressure — unlike the Otto cycle's constant-volume combustion — and this difference is captured in the cutoff ratio, the volume expansion that occurs during combustion itself. Diesel engines run much higher compression ratios than gasoline engines specifically because Diesel-cycle efficiency keeps rising with compression ratio without the knock limitations gasoline faces, which is a major reason diesel engines are inherently more fuel-efficient than spark-ignition engines of similar size.
The air-standard Diesel efficiency is eta = 1 - (1/r^(k-1))·((rc^k - 1)/(k·(rc-1))), where r is the compression ratio and rc is the cutoff ratio, both dimensionless. where r is the compression ratio, rc is the cutoff ratio (volume ratio during constant-pressure combustion), and k is the ratio of specific heats of the air.
Inputs
r_comp := 18=18
r_cut := 2=2
k_d := 1.4=1.4
This bracketed term corrects the simple compression-ratio efficiency for the fact that Diesel combustion happens over a finite volume expansion rather than instantaneously, which costs some of the efficiency gain that high compression alone would otherwise give.
eta_diesel := 1 - (1/r_comp^(k_d-1))·((r_cut^k_d - 1)/(k_d·(r_cut-1)))=0.63
Results
The result, around 63%, is a typical ideal air-standard efficiency for a diesel engine at this compression ratio — noticeably higher than a gasoline engine's ideal Otto-cycle efficiency at a compression ratio gasoline could not reach without knocking. Real diesel engines deliver considerably less than this ideal number, commonly in the 35–45% brake thermal efficiency range, because of friction, heat transfer, and non-ideal combustion the air-standard model ignores. A larger cutoff ratio (more fuel injected, longer constant-pressure burn) always reduces efficiency relative to the equivalent Otto cycle at the same compression ratio, which is why partial-load diesel operation (short injection, small rc) is more thermally efficient than full-load operation.
Assumptions & limitations
- Ideal air-standard cycle: no friction, heat transfer, or combustion losses.
- Working fluid treated as air with constant specific heats.
- Combustion idealized as constant-pressure heat addition.
- No account of actual injection timing, turbocharging, or real fuel-air chemistry.