Search Results

In this paper, a new solution method is presented to study the effect of wave propagation in engine manifolds, which includes solving one-dimensional models for compressible flow of air. Velocity, pressure, and density profiles are found by solving a system of non-linear Partial Differential Equations (PDEs) in space and time derived from Euler’s equations. The 1D model includes frictional losses, area change, and heat transfer. The solution is traditionally found by utilizing the Method of Characteristics and applying finite difference solutions to the resulting system of ordinary differential equations (ODEs) over a discretized grid. In this work, orthogonal collocation is used to solve the system of ODEs that is defined along the characteristic curves. Orthogonal polynomials are utilized to approximate velocity, pressure, sound speed, and the characteristic curves along which the system of PDEs reduce to a system of ODEs.

A real-time control-oriented mean value engine plant model that includes engine thermals and cold starts is developed for a Toyota Prius 2015 plug-in hybrid engine in Modelica and MapleSim and validated experimentally. The model consists of an engine block model, intake and exhaust manifold models, and a throttle model. An advantage of the engine block model is the ability to compute the frictional Mean Effective Pressure during engine cold starts from calculated air, oil, and coolant temperatures at various locations in the engine block. Traditionally, engine thermals are modelled utilizing thermal resistances and capacitors. The proposed model utilizes linear graph theory with terminal equations to study the topology of the different components that affect engine thermals, including engine head, liner, coolant, and oil sump.