The optimal path of piston motion for Otto cycle with linear phenomenological heat transfer law

Abstract

An Otto cycle engine with internal and external irreversibilities of friction and heat leakage, in which the heat transfer between the working fluid and the environment obeys linear phenomenological heat transfer law [q ∝ Δ(T −1 )], is studied in this paper. The optimal piston motion trajectory for maximizing the work output per cycle is derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston trajectories for the cases of with and without piston acceleration constraint on each stroke and the optimal distribution of the total cycle time among the strokes. The optimal piston motion with acceleration constraint for each stroke consists of three segments, including initial maximum acceleration and final maximum deceleration boundary segments, respectively. Numerical examples for optimal configuration are provided, and the obtained results are compared with those obtained with Newton's heat transfer law [q ∝ Δ(T )]. The results also show that optimizing the piston motion can improve power and efficiency of the engine by more than 9%. This is primarily due to the decrease in heat leakage loss on the initial portion of the power stroke.linear phenomenological heat transfer law, Otto cycle, maximum work output, optimal piston trajectory, finite time thermodynamics, generalized thermodynamic optimization

Progress in Finite Time Thermodynamic Studies for Internal Combustion Engine Cycles

“…Considering the influences of convective-radiative HTA (q « ∆(T) + ∆(T 4 )), Burzler and Hoffman [274,275] derived the OPM in compression and power strokes of a four stroke Diesel engine with MP as the OPB when the WF was non-ideal. Fixing total cycle time and fuel consumed per cycle, Xia et al [276] investigated the OPM trajectory of an Otto cycle engine for MW when HTA between WF and the environment obeys a linear phenomenological HTA (q « ∆(T´1)), and found that work output and efficiency could improve by more than 9% after optimizing the piston motion. Xia et al [277] and Chen et al [278] applied the finite combustion rate model in [259], derived the OPM trajectories of irreversible Diesel cycle engine for MW when HTA between WF and the environment obeys a linear phenomenological HTA [277] and generalized radiative HTA [278], respectively, and examined the influence of HTA on the OPM trajectories.…”

“…Using the heat engine models established in [257,258,272,276], Ge [84] obtained the OPM trajectories of an Otto cycle for MEG which was generated by FL, HTL and pressure drop loss, as well as for MEF, respectively, when the HTA obeys generalized radiative HTA, and the results obtained included the OPM trajectories for MEG [272,289] and MEF with linear phenomenological HTA [272] and radiative HTA [289]. The OPM trajectories on power strokes of an irreversible Otto cycle for MEG and MEF when HTA obeys generalized radiative HTA are determined by following differential equations [84]:…”

“…According to [84,257,258,272,276,289], the conventional piston motion of irreversible Otto cycle is determined by:…”

Constructal optimization of discrete and continuous-variable cross-section conducting path based on entransy dissipation rate minimization

“…Based on irreversible thermodynamics, some scholars used finite-time thermodynamics (FTT) or entropy generation minimization (EGM) [18][19][20][21][22][23][24][25][26][27][28][29][30] to optimize the heat transfer process, which was also called thermodynamic optimization. The entropy generation minimization is a heat transfer optimization aiming at exergy lost minimization, but the heat transfer mostly focuses on the heat transfer regularity and its transfer speed, not the exergy lost.…”

Constructal optimization of a vertical insulating wall based on a complex objective combining heat flow and strength

“…to search the optimal internal structure, external shape and time rhythm of one thing by taking performance maximization as an objective with given global constraints [2][3][4][5][6][7][8]17]. And the researches, which combine entransy dissipation extremum principle and finite time thermodynamics [55][56][57][58][59][60][61][62][63][64][65][66][67] with constructal theory [1-17, , are the new directions of this field.…”