A frequency modelling of the pressure waves in the inlet manifold of internal combustion engine

Abstract

The simulation of pressure waves in inlet and exhaust manifolds of internal combustion engines remains challenging. In this paper, a new model is presented in order to analyze these pressures waves without the use of a one-dimensional description of the system. It consists on studying the system using a frequency approach. In order to establish this model, a dynamic flow bench is used. The latter has been modified in order to generate waves in a gas which can be in motion or not. The inlet system is then characterized by its geometrical characteristics as well as the fluid characteristics. Indeed, the gas temperature and the gas velocity have a major impact on the fluid behaviour. The new model is then used in order to simulate the pressure waves into a 1-m pipe which is connected to a driven engine acting as a pulse generator. The experimental and the numerical results are in good agreement.

Introduction

In automotive applications, legislations on environmental protection limit emissions of pollutants as well as carbon dioxide. As a consequence, it is important to reduce the engine consumption and to optimize the combustion process. For spark-ignition engine, the air–gasoline mixture is characterized by a stoechiometric ratio. However, some components (like valves, compressor …) of internal combustion engines generate pressure waves which are propagated into the inlet and exhaust manifolds [1], [2], [3]. As a consequence, the engine performance and the volumetric efficiency can be impacted by this phenomenon [4], [5], [6], [7]. Furthermore, the combustion process can be different in each cylinder if the air mass flow is affected by unsteady flow phenomena. It is then necessary to develop computational tools capable of taking into account this kind of phenomenon and to associate them to internal combustion engine simulation codes [1], [8], [9].

Inlet and exhaust manifolds can be studied by a one-dimensional approach by solving the Euler equations [8], [9]. The gas dynamics flows equations are obtained by: the continuity equation, the momentum equation, and the energy equation [10]. These equations can be written in the following form:

$$\frac{\partial W}{\partial t}+\frac{\partial F(W)}{\partial x}=B$$

where the vectors W, F, and B are defined by:

$$W=\left[\begin{array}{c}\hfill \rho S\hfill \\ \hfill \rho \mathit{uS}\hfill \\ \hfill \rho (e+\frac{1}{2}{u}^2)S\hfill \end{array}\right]$$

$$F(W)=\left[\begin{array}{c}\hfill \rho \mathit{uS}\hfill \\ \hfill (p+\rho u^2)S\hfill \\ \hfill (e+\frac{1}{2}{u}^2+p{\rho }^{-1})\rho \mathit{uS}\hfill \end{array}\right]$$

$$B=\left[\begin{array}{c}\hfill 0\hfill \\ \hfill p\frac{\mathit{dS}}{\mathit{dx}}-\rho G\hfill \\ \hfill \rho \mathit{qeS}\hfill \end{array}\right]$$

In order to solve these gas dynamic equations, a numerical scheme is required. Historically, the first technique used was the method of characteristics [1]. It is based on the possibility to transform the set of equations with partial derivative terms into a set of equations with full derivative terms. However, this method is non-conservative. The increasing performance of computers gives the possibility to use finite difference schemes with a second order precision [11] and total variation diminishing (TVD) flux limiter algorithms [12]. For this kind of problem, the Harten–Lax–Leer scheme appears to be the best [2]. An inlet (or an exhaust) manifold is composed of pipes, volumes or specific components and the difficulty remains in defining the boundary conditions of the pipes. In this objective, experimental setup [13] or CFD codes are used [14], [15], [16]. The objective is to analyze the fluid flow around these boundaries in order to complete the one-dimensional description of the system. Finally, internal combustion engine simulation codes can be used in order to define the engine behaviour. The comparison between experimental results and numerical ones shows good agreements [15]. The computational time required by one-dimensional codes is acceptable today in order to determine the engine behaviour or to optimize an element of the engine [17]. However, the simulation times are very long due to the complex geometries of the inlet and exhaust systems in order to realize a real time simulation. In order to reduce the number of equations, the acoustic method can be employed [10], [18]: the fluid is considered to be non-viscous, isentropic, and only small disturbances of the thermodynamics variables are considered. With theses assumptions, a single equation describes the fluid evolution in the pipe elements. However, the number of equations remains important (it depends on the mesh refinement) and as a consequence the computational time is too high.

The analysis of the volumetric efficiency of an internal combustion engine can also be obtained by the means of a frequency analysis. In order to obtain a frequency spectrum of the pipe systems, different experimental techniques have been developed [19], [20], [21], [22]. The objective is then to establish a link between the volumetric efficiency and the pressure spectrum of the manifold. It appears that the pressure spectrum depends on the excitation amplitude (air mass floss or fluid velocity). As a consequence, it is interesting to establish a direct link between the pressure and the velocity by a simple model without a pipe meshing which gives the possibility to realize a real time calculation which takes into account of the pressure waves phenomenon.