The amount of fresh air induced into the cylinder is the main parameter to be taken into account when developing the engine control laws. However, the instantaneous amount of induced air cannot be directly measured. Additionally, as the engine air ducting becomes more and more complex (high and low pressure exhaust gas recirculation, variable valve timing, pneumatic hybridization…), models used to develop engine control laws must be as predictive as possible. It has therefore been decided to use 1d aerodynamics simulation to provide accuracy to the control laws development and validation process. Commercial engine codes have been tested but did not give satisfactory results in terms of calculation time and flexibility. Additionally, in the case where no experimental data are available to determine valve discharge coefficient, simulation results were in total disagreement with the engine bench measurements. Therefore, it has been decided to develop a 1D simulation platform in order to comply with the control laws development needs. The study detailed in this paper is focused on the exhaust valve model.
One dimensional mathematical modeling of unsteady gas flow in pipe systems is based on the Euler's equations: continuity equation, momentum equation and energy equation. In order to solve cylinder inlet/outlet valve boundary conditions, a specific resolution of the Euler's equations needs to be implemented: the method of characteristics, modified to take into account the non-isentropicity of the valve flow process. This model has been successfully implemented into engine CAE codes at the early of the 80s, providing satisfying robustness and accuracy. The work shown in the paper is based on this model, and emphasis has been put on two main points:
At first, the equations and hypotheses introduced to build exhaust valve models have been reviewed. The paper develops classical quasistatic one-dimensional valve outflow models. Quasistatic model results are compared to steady state CFD results. The goal of this study is to determine which literature model provides the most accurate results when compared to multi-dimensional results, therefore limiting the need of a discharge coefficient. The idea is to get a ‘generic’ model in the case where no flow bench data are available.
Then the Method of Characteristics (MOC), as detailed in the literature, has been reviewed. While it is concluded that MOC provides a rigorous mathematical environment to solve valve boundary conditions, two weaknesses are identified: 1- Each exhaust valve model requires to build a specific resolution algorithm to deal with the MOC. 2-The iterative scheme applied to the MOC found in the literature is slow to converge. Additionally, when a Newton-Raphson algorithm is directly applied to the MOC, calculation divergence occurs.
In order to overcome these limitations, it is proposed to introduce the pressure ratio across the valve as the input of the MOC resolution scheme. Subsequent improvements are: 1- Pressure ratio causality allows to use pre-processed data maps as an universal interface between the exhaust valve model equations and the MOC scheme. Therefore, MOC convergence algorithm does not need to be modified for each valve model, providing more flexibility to the simulation tool. Additionally, if an experimental data map from valve flow bench is available, it can be used directly as a model input. 2- Pressure ratio causality allows to build a robust Newton-Raphson convergence scheme, using the MOC as a convergence criterion. Results from the proposed model will be compared to transient experimental data. It will be shown that results are in a good agreement with measurements, and that the convergence time is quicker than in the original MOC implementation.