The effects of pressure drops on the performance characteristics of the air standard Otto cycle are reported. The pressure drops are assumed as constant values independent of the engine size. It has been shown that the pressure drops to about 60% of the maximum pressure in the ideal cycle (Curto-Risso et al., 2008). Three different models are studied: constant pressure model, reversible adiabatic expansion model and polytropic expansion model. The findings of this study show that, at this level of pressure drop, the maximum efficiency of the Otto cycle is reduced by 15% approximately based on the constant pressure model. The combined effect of pressure drop with other modes of irreversibility, for example, internal irreversibility and heat leaks, could reduce the maximum efficiency into very low values (approximately 30%). The reversible adiabatic model predicts reduction of 13% in efficiency at 40% pressure drop levels but at the price of zero power production. On the other hand, the polytropic expansion model predicts 40% reduction in efficiency for the same level of pressure drop (40%). All three models show that the power output is very sensitive to pressure drop.
Finite time thermodynamics (FTT) is a nonequilibrium theory. Its aim is to provide performance bounds and extremes for irreversible thermodynamic processes [
The method of FTT with the method of optimal control theory has been applied to determine the optimal piston trajectory for successively idealized models of the Otto cycle [
Different effects have been studied on the standard air Otto cycle.
FTT Bounds about the efficiency at maximum power production of an air standard Otto cycle were found under the effects of cylinder wall heat transfer [
The effects of engine speed on the characteristic performance of an air standard Otto cycle were analyzed [
Performance analyses of an irreversible Otto cycle were considered using finite time thermodynamics [
The temperature-dependent specific heat and isentropic efficiencies were considered, and there effects on the power output and on the thermal efficiency of an air standard Otto cycle were studied [
The effect of the variable specific heat ratio on the performance of on endoreversible Otto cycle was studied [
The effects of cylinder wall heat transfer and global losses were lumped in a friction-like term on performance of different cycles (Diesel, Otto, Atkinson, and Brayton) [
Theoretical and simulated models for an irreversible Otto cycle were developed [
Cyclic variations in combustion, inside Otto engine, accounting for partial burning and misfire are extensively considered by Heywood [
In this study, the effect of pressure drop on the performance analysis of an air standard cycle is considered.
The paper is arranged as follows: in Section
Consider the air standard Otto cycle with two isentropic branches (compression and expansion) and with two constant volume heat addition and rejection (see Figure
Schematics of the air standard Otto cycle with different modes of irreversibility: cycle 1→2s→3→4s→1 represents the ideal Otto cycle; pressure drop is represented by points 1′, 1′′, 3′, and 3′′; isentropic losses are represented by points 2 and 4, and heat leak is represented by the heat leak coefficient
The thermodynamic properties along the isentropic branches are related via the following equations.
The thermodynamics along the constant volume branches are related according the following relation:
The pressure at point 3′ is defined as follows:
Similarly, the pressure at point 1′ is defined as follows:
Using definitions (
The isentropic efficiencies are defined as follows.
The isentropic compression efficiency is given by the following definition:
In this model the pressure drop at point 3 reduces the maximum temperature to
The assumption of this model is that the working fluid expands following a polytropic branch with exponent
In this section typical values of thermodynamic properties are used. The heat engine is assumed to work between
The performance characteristics of the constant pressure model are summarized in Figures
Efficiency versus compression ratio is plotted for different values of loss coefficients (pressure drop at point 1—
Relative power output to its maximum value versus compression ratio is plotted for different values of loss coefficients (pressure drop at point 1—
Power output relative to its maximum value versus efficiency is plotted for different values of loss coefficients (pressure drop at point 1—
Schematics of the air standard Otto cycle with pressure drop from point 3 to 3′ and reversible adiabatic expansion and 3′
Figure
Figure
Figure
The performance characteristics of reversible adiabatic expansion model are summarized in Figure
Power output relative to its maximum value versus efficiency for the reversible adiabatic model. Plots are shown for different values of the pressure drop coefficient (
Figure
The performance characteristics of the polytropic expansion process are summarized in Figure
Power output relative to its maximum value versus efficiency for polytropic expansion model. Both efficiency and power are reduced drastically as a function of the pressure coefficient (
From the figure it is clear that both power and efficiency are very sensitive to the exponent
In this study the air standard Otto cycles were reconsidered to account for pressure drop. At first, different studies were reviewed. These studies considered different modes of losses including finite heat transfer rates, friction, heat leaks, internal irreversibility represented by the isentropic efficiencies, combustion efficiency, piston speed, and volumetric efficiency. The objective functions typically include maximizing power or maximizing efficiency. Some studies considered finding optimal paths leading to the maximum power or maximum efficiency of the Otto cycle. The pressure drop from simulations of realistic Otto cycle models was observed to be in the level of 60%.
Three different modeling assumptions are considered for the pressure drop: constant pressure model, reversible adiabatic expansion model, and polytropic expansion model.
The pressure drop as introduced in Section
Two other modes of losses are included in constant pressure model: internal irreversibility and heat leak. From Figures
The reversible adiabatic model showed mild reduction in the maximum efficiency, but at that point the power output vanishes.
The last model considered in this study predicts strong reduction in the maximum efficiency (22% for 20% pressure drop and 40% for 40% pressure drop).
All three models show that the net power output is reduced in stronger fashion than that of the efficiency. It is important to note that heat leak as modeled in the first model does not affect the net power output.