爱豆传媒

Objectives

• To investigate the range of applicability of currently available vortex ring models or their modifications for the analysis of vortex rings observed in direct injection gasoline engines.
• To perform theoretical and experimental study of vortex ring properties, including the conditions for their formation, for parameters typical for direct injection gasoline engines during homogeneous and stratified charge operation.
• To perform a detailed comparison between theoretical and experimental results. To investigate the feasibility of developing a vortex ring model, capable to predict properties of vortex rings in gasoline engines.

Model

A conventional laminar vortex ring model is generalised by assuming that the time dependence of the vortex ring thickness l is given by the relation l = at^b, where a is a positive number, and ¼ ≤ b ≤ ½. In the case when a = √(2ν), where ν is the laminar kinematic viscosity, and b = ½, the predictions of the generalised model are identical with the predictions of the conventional laminar model. In the case of b = ¼ some of its predictions are similar to the turbulent vortex ring models, assuming that the time dependent effective turbulent viscosity ν* is equal to ll' .

This generalisation is performed both in the case of a fixed vortex ring radius, R₀, and increasing vortex ring radius. In the latter case, the so called second Saffman's formula is modified. In the case of fixed R₀, the predicted vorticity distribution for short times shows a close agreement with a Gaussian form for all b and compares favourably with available experimental data. The time evolution of the location of the region of maximal vorticity and the region where the velocity of the fluid in the frame of reference moving with the vortex ring centroid is equal to zero, is analysed. It is noted that the locations of both regions depend upon b; the latter region being always further away from the vortex axis than the first one. It is shown that the axial velocities of the fluid in the first region are always greater than the axial velocities in the second region. Both velocities depend strongly upon b. Although the radial component of velocity in both of these regions is equal to zero, the location of both of these regions changes with time. This leads to the introduction of an effective radial velocity component; the latter case depends upon b. The predictions of the model are compared with the results of experimental measurements of vortex ring parameters reported in the literature.

Download the presentation Vortex Ring Models by Felix Kaplanski

A generalised vortex ring model is based on the assumption that the time dependence of the vortex ring thickness l is given by the relation atb, where a is an arbitrary positive number, and ¼ ≤ b ≤ ½ is suggested.

The predictions of the model were compared with the results of experimental studies of vortex rings in gasoline engine-like conditions with a high pressure (100 bar) G-DI injector and a low-pressure (3.5 bar) port fuel injector (PFI). The G-DI results have shown good agreement with the model. In contrast, the agreement of the PFI results with the model has been poor.