Analysis of the structure of a mathematical model of a piston engine cycle

Abstract

The paper analyzes the structure of the mathematical model of a piston engine cycle and proposes a modified version of it, allowing determination of the optimum pressure p in the cylinder. For the analysis the authors used published results of other authors’ studies of work processes for piston engines, working on liquid fuels, and gave recommendations on usage of models for calculation and development of engines. In the considered mathematical model there are used cycle equations of: thermodynamic processes, energy balance, mass conservation, state and known empirical relationships. It is shown that four factors have major impact on changes of pressures p: current volume of the cylinder V; mass of the working body at gas exchange M; supply of heat released during combustion Qx and heat exchange with walls of intracylinder space Qw. The authors analyzed the influence of each of these factors on the change of pressure in a piston engine cylinder. Defining contribution of each of these factors on the pressure change of the working body in the cylinder will purposefully improve processes in a piston engine, providing not only environmental but also efficiency performance. Although the mathematical model is presented in quasi-stationary formulation, it provides the desired results in design studies, especially in fine-tuning engine to the required performance. When calculating the cycle the most important is accuracy of determination of the start of visible combustion (the beginning of heat supply to the working body by the crank angle φf), as well as determination of mixture ignition time delay (MID) τi. Position of the point by crankshaft angle φf relative to the TDC significantly affects indicator performance and cycle efficiency. Angle φf is an adjustment parameter, so its accepted value is included in the original data for calculation of the cycle. The complexity of considering of influence of various factors on the duration of mixture ignition delay led to a wide variety of empirical or semi-empirical formulas for calculation of MID τi, which significantly complicates their selection for a particular model. The analysis made for the structure, conditions and methods for the preparation of formulas for determination of τi (analyzed 19 semi-empirical and experimental formulas of various authors). The heat involved in the heat exchange between the working body and the walls of intracylinder space is calculated by the formula of Newton-Richman. Increments of pressure and temperature in the pipes are calculated in the exhaust and intake pipes. The described model of piston engine cycle was implemented in a package of piston engines and calculation softwares used in scientific research and educational process.