Estimation of exhaust gas aerodynamic force on the variable geometry turbocharger actuator: 1D flow model approach Fayez Shakil Ahmed a , Salah Laghrouche a,⇑ , Adeel Mehmood b , Mohammed El Bagdouri a a Laboratoire IRTES-SET, Université de Technologie de Belfort-Montbèliard (UTBM), Belfort, France b Laboratoire MIPS, Université de Haute Alsace (UHA), Mulhouse, France article info Article history: Received 11 November 2013 Accepted 29 March 2014 Keywords: Diesel engine Exhaust aerodynamic force Variable turbine geometry 1D flow modeling abstract This paper provides a reliable tool for simulating the effects of exhaust gas flow through the variable turbine geometry section of a variable geometry turbocharger (VGT), on flow control mechanism. The main objective is to estimate the resistive aerodynamic force exerted by the flow upon the variable geom- etry vanes and the controlling actuator, in order to improve the control of vane angles. To achieve this, a 1D model of the exhaust flow is developed using Navier–Stokes equations. As the flow characteristics depend upon the volute geometry, impeller blade force and the existing viscous friction, the related source terms (losses) are also included in the model. In order to guarantee stability, an implicit numerical solver has been developed for the resolution of the Navier–Stokes problem. The resulting simulation tool has been validated through comparison with experimentally obtained values of turbine inlet pressure and the aerodynamic force as measured at the actuator shaft. The simulator shows good compliance with experimental results. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Fuel economy and reduction in exhaust emission levels are the major challenges of today’s automobile industry [1,2]. These challenges translate directly onto technological improvements in vehicles. Coupled between the intake and exhaust, turbochargers have a direct influence on the engine’s performance in terms of both, the fuel efficiency and emission quality [3]. Yet the perfor- mance of the turbochargers themselves is usually calculated through empiric methods such as interpolation of characteristic maps. These maps differ from each other for different class of turbochargers and they must be adapted, requiring expensive tests on specialized rigs [4–6]. The information in these maps is limited to static flow characteristics at the outlets, making it impossible to determine the effects of flow inside the turbocharger. This is specially critical for the turbine section, of Variable Geometry Turbochargers (VGTs), as static characteristic maps provide no information about the effect of flow on the variable geometry vanes. In reality, the geometry of a VGT turbine inlet is determined by the angle of vanes at the inlet, which are controlled by an actuator. As these vanes regulate the quantity of exhaust flow and its angle of incidence on the impeller, they are subjected to a significant resistive force by the exhaust gas. Estimation of this aerodynamic force on the vanes and its effect on the VGT actuator requires exhaust flow modeling inside the turbine as well. While the task appears daunting, it has now become absolutely necessary for VGT control at levels of precision that are compatible with the energy efficiency requirement of today. In the literature review, such models can be found for multistage compressors and turbines used in the heavy industry [7,8], based on wave energy conversion [9]. Analytical and lumped volume (0D) models are simple but not accurate [10]. In the auto- motive industry, such models are discussed only to estimate the exhaust pressure by considering engine dynamics, i.e. engine speed and load or turbocharger speed [11–13]. Other methods involve the lumped volume approach where the turbocharger is consid- ered as an object with single constant volume [14,15]. The drawback of this approach is that we require turbocharger maps for further analysis and the quantities like air density and flow rate are not available. On the contrary 2D or 3D models are too complex to be solved by numerical analysis in real-time for control objec- tives [16–18]. Therefore, 1D models of the air flow through a turbocharger have received more attention of researchers. The existing 1D models deal mostly with fixed geometry compressors and turbochargers [19]. The modeling of aerodynamic forces is also limited to impellers [20,21]. As the role of aerodynamic forces on variable geometry vanes cannot be neglected in VGTs [22], it is important to obtain accurate yet computationally simple http://dx.doi.org/10.1016/j.enconman.2014.03.080 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +33 612832335. E-mail addresses: fayez-shakil.ahmed@utbm.fr (F.S. Ahmed), salah. laghrouche@utbm.fr (S. Laghrouche), adeel.mehmood@uha.fr (A. Mehmood). Energy Conversion and Management 84 (2014) 436–447 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman