The design of an air to fuel ratio (AFR) control system is substantially facilitated by a suitable mathematical model of the mixture formation process. Such a model has to be a compromise between short simulation times and good prediction capabilities.
Well-known simple “linear” wall-wetting models are easy to use but require substantial calibration time to experimentally determine the operating point dependent model parameters. Full 3D simulations of all physical effects are still computationally not tractable. In this work a control oriented mathematical model of the mixture formation phenomena has been built, which tries to find a middle way between these two extremes. Computation times for one engine cycle are less than half a minute on a standard Pentium-PC. Nevertheless, the model is able to predict nonlinear effects that cannot be described by conventional wall-wetting models.
Only one cylinder with the inlet port and injector, combustion chamber and exhaust port with UEGO sensor is considered. The model of the gas exchange is based on given pressures in the inlet and exhaust system. Both engine ports are modeled as spatially discretized 1D systems, i.e., a one-dimensional temperature and concentration distribution along the port axis is assumed. Fuel is modeled as a blend of six hydrocarbons with different volatilities. They represent the characteristic components of an average gasoline. Accordingly, the gas phase consists of vapors of these hydrocarbons, air and burned mixture. The gas velocity field in the inlet port is based on published results of 3D numerical simulations. Droplets are injected into this field and 2D droplet trajectories are assumed. The injector is characterized by the droplet size and spatial distribution, by the opening and closing time and by the droplet starting velocity. Evaporation and secondary break-up of droplets are also included. Droplets can impinge onto the inlet port walls or enter the combustion chamber. Several impingement surfaces on the port walls and on the valve back face model the fuel film behavior. The model includes film evaporation and flow between the surfaces or into the combustion chamber.
The model was verified experimentally on a Ford Zetec 2,0 l 16 V EPFI engine. In this paper only results on warmed-up engine conditions are reported. The electronic control unit was bypassed in order to gain full control over all engine inputs. Step changes of fuel quantity, injection timing and throttle valve were carried out at a constant engine speed. Inlet and exhaust pressures and injection signal were recorded and then used for simulations. AFR responses were recorded by the UEGO sensor and later compared with simulations. A good agreement was reached.
The model enables the investigation of the mixture formation phenomena, which are not easy to measure. The most important feature of the model is the ability to predict the dynamic behavior of the mixture formation process. Since the model is not limited to small perturbations around a nominal operating point it can be used to derive nonlinear (wide-range) control strategies, e.g., to compensate for wall-wetting effects during large transients. This will firstly enhance the emission control performance and secondly reduce calibration time since less experimental data is needed to adapt the model to a specific engine.