Optimizing piston velocity profile for maximum work output from a generalized radiative law Diesel engine

A Diesel cycle engine with internal and external irreversibilities of finite combustion rate of the fuel, friction and heat leakage is investigated in this paper. The heat transfer between the working fluid and the environment outside the cylinder obeys generalized radiative heat transfer law [ $q\alpha \Delta \left(T^n\right)$ ]. Under the conditions of the fixed total cycle time and fuel consumed per cycle, the optimal piston motion trajectories for maximizing the work output per cycle of the cases with unconstrained and constrained piston accelerations are derived on each stroke by applying optimal control theory. The optimal distribution of the total cycle time among the strokes is also obtained. The optimal piston motion along the power stroke with constrained acceleration consists of three segments including the initial motion delay, the middle motion and the final maximum deceleration segments. Numerical examples for the case with the radiative heat transfer law [ $q\alpha \Delta \left(T^4\right)$ ] and constrained acceleration are provided, and the obtained results are also compared with those obtained with Newtonian [ $q\alpha \Delta \left(T\right)$ ] and linear phenomenological [ $q\alpha \Delta \left(T^{-1}\right)$ ] heat transfer laws. The results show that optimizing the piston motion for the case with the radiative heat transfer law can improve both the net work output per cycle and the net efficiency of the standard engine by more than 7%, and heat transfer laws have significant effects on the optimal piston motion trajectory for maximum work output.