Titlebook: Vortex Ring Models; Ionut Danaila,Felix Kaplanski,Sergei S. Sazhin Book 2021 Springer Nature Switzerland AG 2021 Vortex rings.Direct numer

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Viscous Vortex Rings,ed asymptotic expansions. A comparison with experimental results and direct numerical simulations shows that the model describes well the integral quantities and provides a more accurate description of the vortex ring geometry than inviscid models.

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Confined Vortex Rings,enerated by a piston–cylinder mechanism. A simplified procedure for fitting experimental and numerical data with the predictions of the model is described. This opens the way for applying the model to realistic confined vortex rings in various applications.

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Applications of the Models,e regions of maximal vorticity, predicted by the generalised vortex ring model, are compared with the results of experimental studies of vortex ring-like structures in gasoline engine conditions. It is shown that most of the observed values of these velocities are compatible with the predictions of

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Formation Number of Vortex Rings,x ring from the injection slug. The model is based on the match of the slug-flow model describing the vortex generator and models for viscous vortex rings presented in this book. Theoretical predictions are compared to DNS results obtained for unconfined or confined vortex rings.

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Viscous Vortex Rings with Elliptical Cores,to describe numerical (DNS) vortex rings with elongated elliptic-shape cores. The fitting procedure, using normalised values of energy and circulation, is presented in detail. Theoretical estimates based on the new model are then compared to experimental and numerical results.

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The Vortex Ring Problem,sible Navier–Stokes equations of motion and the vorticity equation in three dimensions. We use the cylindrical coordinate system which best fits the geometry of the problem. We subsequently simplify the vorticity equation for axisymmetric flows, with or without swirl. We then characterise the struct

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Steady Inviscid Vortex Rings,tic models is a useful first exercise for anyone interested in the mathematical modelling of vortex rings. We first derive a fundamental solution to the vorticity equation using the Green function. This solution is then used to describe the circular vortex filament, characterised by an infinitely sm

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