PurposeThe purpose of this paper is to assess a phenomenological zero‐dimensional model (0‐D model) in order to evaluate both the in‐cylinder tumble motion and turbulence in high‐performance engine, focusing on the capability and sensitivity of the model.Design/methodology/approachThe study was performed using a four‐valve pentroof engine, testing two different intake ports. The first one was a conventional port and the second one was design in such a way to promote tumble. CFD simulations for admission and compression strokes under different engine conditions were carried out. Then, the in‐cylinder entrance mass and mean velocities from CFD were imposed as boundary conditions in the 0‐D model.FindingsMarked discrepancies between 0‐D model and CFD results were found. As expected, for the original port, CFD results displayed a poor tumble generation during the admission period. It was followed by a fast degradation of the tumble momentum along the compression stroke due to it was not dominant over the other two momentum components. 0‐D model overestimated the entrance‐tumble but underestimated the vortex degradation along the compression stroke, resulting in higher tumble predictions, thereby it is not recommended for low‐tumble engines. As for the modified port, 0‐D model assumptions were closer to the in‐cylinder flow field from CFD, but results underestimated the entrance‐tumble during the intake stroke and predicted excessive tumble at the end of the compression stroke. Summarizing, 0‐D model neither showed sensitivity to changes in the intake port because of the scarce information about the entrance‐flow field nor it was not suitable to evaluate the tumble degradation.Originality/valueThe limitations of the current model were highlighted, given possible guidelines in order to improve it.

Computational fluid dynamic (CFD) simulations and experimental steady flow tests (flow discharge, swirl, and tumble) were carried out to study the in-cylinder flow in a commercial four-valve spark ignition engine. The present investigation was aimed at analysing and controlling the generation of macro-vortex structures (swirl and tumble) during the inlet process. A comparative study of the most commonly employed tumble benches along with in-house design was performed, the last showing some advantages with respect to the others. The outcomes from the simulations were in agreement with experimental results. Mainly, the tumble generation rate was in general proportional to the valve lift. However, tumble was reduced drastically at medium valve lift due to a change in the vortex pattern. A stagnation zone was observed between inlet valves. CFD calculations successfully captured this tumble-fall effect, which was related to characteristic changes in the vortex pattern downstream of the inlet valves at medium valve lift. This affects tumble production without affecting the mass flowrate efficiency. Finally, at high valve lifts the tumble production and the vortex pattern were recovered. The capability of the cylinder head to induce swirl, tumble, or combined swirl-tumble by modifying the valve timing or by introducing adjustable flow deflectors was evaluated using CFD. Several valve timing strategies were analysed: some of them produced significant swirl, but introduced high mass flowrate losses. On the other hand, adjustable flow deflectors were shown to be an interesting alternative to induce swirltumble at low load and to improve tumble at high load.

Two-fluid models are central to the simulation of transport processes in two-phase homogenized systems. Even though this physical model has been widely accepted, an inherently nonhyperbolic and nonconservative ill-posed problem arises from the mathematical point of view. It has been demonstrated that this drawback occurs even for a very simplified model, i.e., an inviscid model with no interfacial terms. Much effort has been made to remedy this anomaly and in the literature two different types of approaches can be found. On one hand, extra terms with physical origin are added to model the interphase interaction, but even though this methodology seems to be realistic, several extra parameters arise from each added term with the associated difficulty in their estimation. On the other hand, mathematical based-work has been done to find a way to remove the complex eigenvalues obtained with two-fluid model equations. Preconditioned systems, characterized as a projection of the complex eigenvalues over the real axis, may be one of the choices. The aim of this paper is to introduce a simple and novel mathematical strategy based on the application of a preconditioning mass matrix that circumvents the drawback caused by the nonhyperbolic behavior of the original model. Although the mass and momentum conservation equations are modified, the target of this methodology is to present another way to reach a steady-state solution (using a time marching scheme), greatly valued by researchers in industrial process design. Attaining this goal is possible because only the temporal term is affected by the preconditioner. The obtained matrix has two parameters that correct the nonhyperbolic behavior of the model: the first one modifies the eigenvalues removing their imaginary part and the second one recovers the real part of the original eigenvalues. Besides the theoretical development of the preconditioning matrix, several numerical results are presented to show the validity of the method.