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The aim of this study is numerical investigation of a evaporating and non-reacting diesel spray operating in a high pressure and high temperature constant volume combustion chamber, as an essential step in simulation of liquid fuels combustion. To this end, the impact of droplets diameter distribution on estimating two critical characteristic parameter i.e. liquid and vapor penetration lengths is studied using the open-source OpenFOAM code. In order to determine droplets diameter distribution effect, three different distribution ranging from 0.25-100 micron is chosen and the liquid and vapor penetration lengths are individually calculated for each distribution. The results are validated against the experimental data published by Sandia National Laboratory. The results show while the droplets diameter distribution has a remarkable effect on the predicted value of the liquid length, so that leads to overestimate liquid penetration lengths up to more than two times; its effect on the vapor length prediction is negligible. Also assuming a nozzle diameter distribution leads to non-physically increase in the value of liquid length. This non-physically prediction may lead to misleading prediction of spray impingement to piston and the cylinder walls resulting an error in unburnt hydrocarbons concentration as well as the engine efficiency estimation.

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Prediction of spray droplet diameter distribution depends on the various parameters such as physical properties, fluid velocity, and discharge environment and injector geometry. The stage of forming droplets has a great variety in size and therefore will be predictable with a statistical approach. The maximum entropy principle is one of the most popular and best ways to predict the spray droplet size distribution along with the conservation equations. Due to some drawbacks in this model, the predicted results do not match well with the experimental data. It is suggested to improve the available energy source in the MEP model equation by numerical solution of flow inside the injector based on the CFD technique. This will enhance the calculation accuracy of the turbulent kinetic energy of the output spray. In fact, by using this sub-model in the maximum entropy model, the prediction accuracy of the spray characteristics is improved. Also, the requirement of the maximum entropy model to the experimental data as inputs has been reduced. By the present coupled model, the effect of spray upstream on the droplet size distribution can be considered with a good accuracy. The results show a close agreement with the available experimental data.