This project aimed to investigate the applicability of a theoretical model for vortex rings, developed by Kaplanski and Rudi (2005), to the analysis of vortex rings observed in direct injection gasoline engines. The investigators also carried out a feasibility study on the further modification of this model, taking into account the effects of multiphase flow.
They also undertook further experimental investigation of vortex rings in these engines with particular emphasis on the essential parameter values required in order to develop the theoretical model. The project examined the theoretical predictions of vortex ring properties against the values of typical parameters for gasoline engines which will allowed a detailed comparison between the predictions of the model and experimental results to be made. Finally, the team investigated the feasibility of developing a vortex ring model, capable of predicting the properties of vortex rings in gasoline engines.
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 = atb, 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.
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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.
Professor Sergei Sazhin, Project Coordinator
Professor Morgan Heikal
Dr Steven Begg
Dr Felix Kaplanski