Numerical Investigation of Droplet Properties of a Liquid Jet in Supersonic Crossflow

The atomization process of a liquid jet in supersonic crossflow with a Mach number of 1.94 was investigated numerically under the Eulerian-Lagrangian scheme. The droplet stripping process was calculated by the KH (Kelvin-Helmholtz) breakup model, and the secondary breakup due to the acceleration of shed droplets was calculated by the combination of the KH breakup model and the RT (Rayleigh-Taylor) breakup model. In our research, the existing KH-RT model was modified by optimizing the empirical constants incorporated in this model. Moreover, it was also found that the modified KH-RT breakup model is applied better to turbulent inflow of a liquid jet than laminar inflow concluded from the comparisons with experimental results. To validate the modified breakup model, three-dimensional spatial distribution and downstream distribution profiles of droplet properties of the liquid spray in the Ma = 1.94 airflow were successfully predicted in our simulations. Eventually, abundant numerical cases under different operational conditions were launched to investigate the correlations of SMD (Sauter Mean Diameter) with the nozzle diameter as well as the airflow Mach number, and at the same time, modified multivariate power functions were developed to describe the correlations.

A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games

A multi-step Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of spatially inhomogeneous evolutionary games, describing the evolution of a system of spatially distributed agents with strategies, or labels, whose payoff depends also on the current position of the agents. The scheme is Lagrangian, as it traces the evolution of position and labels along characteristics, and is a multi-step scheme, as it develops on the following two stages: First, the distribution of strategies or labels is updated according to a best performance criterion, and then, this is used by the agents to evolve their position. A general convergence result is provided in the space of probability measures. In the special cases of replicator-type systems and reversible Markov chains, variants of the scheme, where the explicit step in the evolution of the labels is replaced by an implicit one, are also considered and convergence results are provided.

Mean zonal flow driven by precession in planetary cores: numerical simulations with a semi-lagrangian scheme

<p>We revisit the generation of mean zonal flows in fluid planetary interiors subjected to precession.<br>The main effect of precession on a (nearly) spherical fluid envelope is to make the fluid rotate along an axis tilted with respect to the rotation axis of the solid mantle. This is the so-called "spin-over" response of the fluid.<br> also shows that a steady shear flow develops on top of the spin-over mode due to non-linear effects in the boundary layer equation.<br>This mean zonal shear flow has been studied theoretically and numerically by .</p><p>With faster computers and more efficient codes, we compute this flow down to very low viscosity and compare with the inviscid theory of Busse (1968).<br>In addition we investigate the width and the intensity of the detached shear layer, which is controlled by viscosity and therefore not present in the theory.</p><p>We also use this problem as a benchmark to assess the benefits of using a semi-lagrangian numerical scheme, where solid-body rotation is treated exactly.</p>