Reduced models for flows in IC-engines

The finite response time of the turbocharger is the most notable effect of transient operation on a turbocharged diesel engine. To fulfill future emission requirements, high amounts of transient EGR will be required even though after-treatment devices are being used. This implies that advanced turbocharger systems have to be introduced to enable high boost pressure with improved or at least maintained response time. The increased amount of tuneable parameters from the more advanced turbocharging system will make it difficult and expensive to optimise the engine experimentally. Therefore, the wish is to optimise the engine design using numerical tools. This requires predictive models for the gas exchange system and its components, i.e. the turbocharger, the manifolds and the cylinder with its valves. The results have shown that engine simulation tools based on tabulated data from measurements can qualitatively predict the engine's performance and be used as a first step in engine design. However, these models have to be calibrated extensively in order to reflect the engine performance quantitatively. The objective of this research is therefore to find a modelling approach for the gas exchange system and its components that are more predictive than the tools used, but still computationally effective enough to be suited for engine simulations. The thesis contains a summary of on-engine experimental results as well as some One-Dimensional (1D) simulations. Since the 1D modelling approach has limited range of validity and applicability, we have considered two approaches for reducing the full Three-Dimensional (3D) governing equations, which are a set of Partial Differential Equations (PDE), in a systematic manner. The first approach is based on a numerical length scale analysis of the different terms in the governing equations after changing the coordinate system with one coordinate aligned with the flow path. By retaining the most important terms or neglecting the (significantly) smallest terms, different reductions may be attained, which in their simplest form may look like the boundary layer equations. The results for a double bent pipe, used to illustrate the approach, show that the most significant component of the viscous terms is the radial component, which is in the order of two magnitudes larger than the axial and azimuthal components. The convective terms are all in the same order of magnitude, whereas the radial component is of significant importance in the bends of the pipe due to centrifugal forces, and the azimuthal component after the second bend due to a swirling motion. For the flow in a straight pipe, the approach would give the same model as the common 1D simulation tool. However, for pipes with a more general shape, the approach is superior as it allows for a rational reduction of the governing equations. The main limitation of the approach is for flow situations that do not have a dominating flow direction. Under such conditions the a priori and/or the a posteriori analysis would reveal that the reduction is inconsistent. Thus, the approach implies maintained efficiency, but with improved (and assessable) accuracy as compared to the common 1D simulation tool. The second approach is based on the Galerkin projection of the governing equations projected onto Proper Orthogonal Decomposition (POD) modes. These POD modes are computed for the flow in a given geometry obtained through Large Eddy Simulations (LES). The Galerkin projection results in a system of Ordinary Differential Equations (ODE) for the time-dependent coefficients of the 3D POD modes. The results show that the method is best suited for flows with strong coherent structures. However, the system of ODEs may be inherently unstable (depending on the number of modes used in the simulation) and modelling errors grow with each time-step. This limitation may be remedied by numerically preventing any exponential growth. The approach can also be extended into a combined Galerkin (ODE) - LES (PDE) approach by replacing several steps of the LES by the same amount of time steps with the reduced model. It should be pointed out that this approach can provide the full 3D flow field in contrast to space reduced models (e.g. the common 1D tool) and thereby handle more complex flows with high degree of computational efficiency. To summarize, the thesis demonstrates new possibilities of obtaining reduced models suited for engine simulations based on 3D CFD. With this application in mind, these tools are novel and their evaluation and assessment should be extended to other components of the gas exchange system.QC 2011092