A frequency modelling of the pressure waves in the inlet manifold of internal combustion engine David Chalet a,⇑ , Alexandre Mahe a , Jérôme Migaud b , Jean-François Hetet a a Internal Combustion Engine Team, Laboratory of Fluid Mechanics – UMR CNRS 6598, Ecole Centrale de Nantes, BP 92101 44321 Nantes, France b Advanced Development, Mann+Hummel France, 53061 Laval, France article info Article history: Received 31 January 2011 Received in revised form 8 March 2011 Accepted 25 March 2011 Available online 12 April 2011 Keywords: Gas dynamics Pressure waves Compressible flow Internal combustion engine Frequency analysis 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 fre- quency approach. In order to establish this model, a dynamic flow bench is used. The latter has been mod- ified 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 tem- perature 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. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction In automotive applications, legislations on environmental pro- tection 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 inter- nal combustion engines generate pressure waves which are prop- agated into the inlet and exhaust manifolds [1–3]. As a consequence, the engine performance and the volumetric effi- ciency can be impacted by this phenomenon [4–7]. 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 ac- count 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-dimen- sional approach by solving the Euler equations [8,9]. The gas dynamics flows equations are obtained by: the continuity equa- tion, the momentum equation, and the energy equation [10]. These equations can be written in the following form: @W @t þ @F ðWÞ @x ¼ B ð1Þ where the vectors W, F, and B are defined by: W ¼ qS quS qðe þ 1 2 u 2 ÞS 2 6 4 3 7 5 ð2Þ F ðWÞ¼ quS ðp þ qu 2 ÞS ðe þ 1 2 u 2 þ pq 1 ÞquS 2 6 4 3 7 5 ð3Þ B ¼ 0 p dS dx  qG qqeS 2 6 4 3 7 5 ð4Þ 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 com- puters 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 ex- haust) manifold is composed of pipes, volumes or specific compo- nents and the difficulty remains in defining the boundary conditions of the pipes. In this objective, experimental setup [13] or CFD codes are used [14–16]. The objective is to analyze 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.03.036 ⇑ Corresponding author. Tel.: +33 2 40 37 16 53; fax: +33 2 40 37 25 56. E-mail address: David.Chalet@ec-nantes.fr (D. Chalet). Applied Energy 88 (2011) 2988–2994 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy