Schneider, L. (2009)
A Concise Moment Method for Unsteady Polydisperse Sprays.
Technische Universität Darmstadt
Dissertation, Erstveröffentlichung

Kurzbeschreibung (Abstract)

This body of research deals with the mathematical and numerical description of unsteady polydisperse sprays. The superior objective is to simulate the behaviour of combustion engines with higher accuracy but lower computational costs. The main spray phenomena in this type of processes are the primary and secondary breakup of the fuel jet, collision and evaporation of droplets, and acceleration or deceleration of droplets due to drag forces. The purpose of the spray is to distribute the fuel in the combustion chamber such that the fuel/air mixture ignites at controllable locations and times. Errors in the modelling of just one of the above spray phenomena can spread and even amplify as the combustion simulation proceeds. This occurs due to the strong coupling between the processes involved. Although the behaviour of technical sprays can be captured accurately with direct numerical simulation it is not applied as the computational workload would be extraordinary. Instead, methods such as Lagrange and Euler methods are used to describe the spray behaviour by approximating a solution to the kinetic spray equation, a partial differential equation for the distribution function of droplets. Although the Lagrange method captures the full complexity of this equation, it is computationally very expensive to use it for unsteady flows that have a high mass loading of droplets. The computational performance of Euler methods is independent of the unsteadiness and mass loading. However, Euler methods require further development as most of them assume the velocity distribution of droplets to be mono-modal and use presumed size distributions to describe the polydisperse character of sprays. These assumptions are not justified for technical sprays as they lead to spurious droplet concentrations at crossing points of fuel jets and inaccurate evaporation rates. In this thesis a concise Euler method is proposed that resolves the above problems of the classical Euler methods. The kinetic spray equation is transformed into moment equations that are closed by assuming the droplet distribution function to have a specific form. However, it still takes into account the spatial and temporal changes of dispersion in size and velocity space. All numerical algorithms follow from this specification. In the choice of the mathematical and numerical model, care was taken in modelling the mass transfer between droplets and gas. It is a key feature in combustion engines because it determines the fuel/air mass fraction. To assess the abilities of the method it was extensively tested in steady and unsteady, one- and two-dimensional configurations in which a polydisperse spray was splashed, evaporated or effected by a Stokes drag force. The tests were organised in such a way that crossing of two or more spray distributions was always included and bi- or multi-modal velocity distributions were present. The comparison of the results with highly resolved Lagrangian calculations demonstrates that the polydisperse character of sprays and the crossing of spray jets can be captured accurately.

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