Internal combustion engine heat release calculation using single-zone and CFD 3D numerical models

International Journal of Energy and Environmental Engineering https://doi.org/10.1007/s40095-018-0265-9 ORIGINAL RESEARCH Internal combustion engine heat release calculation using single‑zone and CFD 3D numerical models S. Mauro1 · R. Şener2 · M. Z. Gül2 · R. Lanzafame1 · M. Messina1 · S. Brusca3 Received: 30 October 2017 / Accepted: 12 February 2018 © The Author(s) 2018. This article is an open access publication Abstract The present study deals with a comparative evaluation of a single-zone (SZ) thermodynamic model and a 3D computational fluid dynamics (CFD) model for heat release calculation in internal combustion engines. The first law, SZ, model is based on the first law of thermodynamics. This model is characterized by a very simplified modeling of the combustion phenomenon allowing for a great simplicity in the mathematical formulation and very low computational time. The CFD 3D models, instead, are able to solve the chemistry of the combustion process, the interaction between turbulence and flame propagation, the heat exchange with walls and the dissociation and re-association of chemical species. They provide a high spatial resolution of the combustion chamber as well. Nevertheless, the computation requirements of CFD models are enormously larger than the SZ techniques. However, the SZ model needs accurate experimental in-cylinder pressure data for initializing the heat release calculation. Therefore, the main objective of an SZ model is to evaluate the heat release, which is very difficult to measure in experiments, starting from the knowledge of the in-cylinder pressure data. Nevertheless, the great simplicity of the SZ numerical formulation has a margin of uncertainty which cannot be known a priori. The objective of this paper was, therefore, to evaluate the level of accuracy and reliability of the SZ model comparing the results with those obtained with a CFD 3D model. The CFD model was developed and validated using cooperative fuel research (CFR) engine experimental in-cylinder pressure data. The CFR engine was fueled with 2,2,4-trimethylpentane, at a rotational speed of 600 r/ min, an equivalence ratio equal to 1 and a volumetric compression ratio of 5.8. The analysis demonstrates that, considering the simplicity and speed of the SZ model, the heat release calculation is sufficiently accurate and thus can be used for a first investigation of the combustion process. Keywords Internal combustion engines · Heat release · Single zone model · CFD combustion modeling List of symbols SOI Start of ignition TDC Top dead center IVC Intake valve closing Qhr Gross heat release k Specific heat ratio T Temperature * S. Mauro 1 Department of Civil Engineering and Architecture, University of Catania, Viale A. Doria, 6, 95125 Catania, Italy 2 Mechanical Engineering Department, Faculty of Engineering, Marmara University, Kadikoy, 34722 Istanbul, Turkey 3 Department of Engineering, University of Messina, Contrada Di Dio, 98166 Messina, Italy p Pressure V Volume Qw Heat exchanged with wall Us Internal sensible energy W Work due to piston motion m Mass trapped cv Specific heat at constant volume cp Specific heat at constant pressure Nu Nusselt number Re Reynolds number b Reynolds exponent for thermal exchange correlation n Engine rotational speed C1, C2 Calibration constants w Characteristic charge velocity up Average piston velocity pm Pressure of the motored cycle p0, V0, T0 Reference pressure, temperature and volume 13 Vol.:(0123456789) International Journal of Energy and Environmental Engineering ϕ Equivalence ratio B Bore y+ Non-dimensional distance from wall mb Mass burned mu Mass unburned kb, ku Burned and unburned specific heat ratios θ Crank angle ρ Density Introduction The complex task of improving internal combustion engines (ICEs), which have reached a higher degree of sophistication, can be achieved with a combination of experiments and numerical models [1]. Essentially, two main distinct categories of numerical models have been developed for ICE studies. These are thermodynamic and fluid dynamic models. In the thermodynamic models, the conservation of mass and energy is used for evaluating the closed cylinder system using the first law of thermodynamics. In these models, the thermodynamic system can be considered either as a single zone (SZ) or as a multi-zone. When the system is considered multi-zone, the first law of thermodynamics is applied to each of the zones while, in SZ models, the entire cylinder (Fig. 1) is the unique domain where the first law is solved. The mathematical equations, in general, form a set of ordinary differential equations with an independent variable, which is the time or the crank angle [2]. The heat transfer through the walls plays an important role in engine combustion, performance and emission characteristics [3, 4]. This is due to the fact that the wall temperatures are considerably lower than the maximum temperature of the burned gases inside the cylinder. For this reason, the heat transfer must be taken into account for an accurate modeling of the engine operative conditions [2]. Several thermodynamics models have been developed during the last few years, because of the great importance of ̇ spark plug ̇w . W Fig. 1  Control volume of the CFR engine combustion chamber in a single-zone model 13 the heat release evaluation. The first simple models needed only in-cylinder pressure data but presented a great disadvantage: the assumption of a constant value for the polytrophic exponent [5]. Gatowski et al. developed a simple and quite accurate SZ model [6] which was further optimized for a charge with high swirl motion by Cheung and Heywood [7]. The thermodynamics model, developed in a previous work by the authors [10], is a SZ model which takes into account the variability of the specific heats [k = k(T)] and the heat exchange between gas and cylinder walls. In this way, both gross and net heat release can easily be calculated. The fluid dynamic models, also known as computational fluid dynamics (CFD) models, are inherently unsteady, tridimensional models and are based on the conservation of mass, chemical species, momentum, and energy at any location within the engine cylinder domain. Thus, the CFD models solve the Navier–Stokes equations, and the general transport equations for each physical quantity. As is widely known, CFD models are based on numerical iterative techniques which lead to a set of equations filtered in time, named RANS equations, or in space, named LES equations. This is done in order to take into account the viscous stresses in a discretized computational domain that covers the whole cylinder volume [8]. Both time and spatial coordinates are considered independent variables, so a full spatial and temporal resolution of the properties of the gas inside the cylinder is possible [2]. In this way, the physics of the combustion process and, specifically, the f (...truncated)