On the 0D – 3D Modelling Procedure for the Filling Analysis of the Lubrication System of Internal Combustion Engines

The paper focuses on the development of a predictive numerical tool for the assessment of the filling performance of engine lubrication systems. Filling analyzes are typically carried out by means of multi-phase 3-D CFD models but, despite allowing detailed and reliable results, they require very demanding computational requirements. On this basis, a procedure for the lumped parameter modelling of the fluid domain is proposed, allowing the discretization of complex systems that cannot be straightforwardly attributable to elementary submodels. The presented criteria are then applied to the lubrication system of a heavy-duty engine, for which the filling of the circuit plays a fundamental role. Different temperature conditions are simulated, and the predictive capabilities of the numerical model are presented in terms of flow pattern and filling time of the circuit branches. The same simulations are also carried out by means of a 3-D CFD model, permitting a result comparison. The comparative analysis concerns both the overall distribution of the lubricant over time, and the local phenomena within the oil domain, in order to assess the approximation of the lumped parameter approach with respect to the more accurate three-dimensional models.

INFINITE COMBINATORICS PLAIN AND SIMPLE

We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly broaden this framework by developing the corresponding technique for countably closed models of size continuum. The applications range from various theorems on paradoxical decompositions of the plane, to coloring sparse set systems, results on graph chromatic number and constructions from point-set topology. Our main purpose is to demonstrate the ease and wide applicability of this method in a form accessible to anyone with a basic background in set theory and logic.

Rich families and elementary submodels

We compare two methods of proving separable reduction theorems in functional analysis — the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with elementary submodels and the converse is true in spaces with fundamental minimal system and in spaces of density ℵ1. We do not know whether the converse is true in general. We apply our results to show that a projectional skeleton may be without loss of generality indexed by ranges of its projections.