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Transient heating of an evaporating droplet

机译：蒸发液滴的瞬时加热

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摘要

Two new solutions to the heat conduction equation, describing transient heating of an evaporating droplet, are suggested. The first solution is the explicit analytical solution to this equation, while the second one reduces the solution of the differential transient heat conduction equation to the solution of the Volterrarnintegral equation of the second kind. Both solutions take into account the effect of the reduction of the droplet radius due to evaporation, assuming that this radius is a linear function of time. This approach can be considered as the generalisation of the approach currently used in all research and commercial CFD codes known to us (e.g. KIVA, FLUENT, PHOENICS), in which it is assumed that droplet radius is constant during the timestep. The new analytical solution has been incorporated into a zero-dimensional CFD code and applied to the analysis of Diesel fuel droplet heating and evaporation in typical engine conditions. The results have been compared with those which follow from the conventional (traditional) approach to modelling droplet heating and evaporation, based on the assumption that the droplet radius is constant over the timestep (but changes from one step to another). It has been pointed out that the new approach predicts lower droplet surface temperatures and slower evaporation rates compared with the traditional approach. The relative difference between evaporation times is shown to be practically independent of the values of the initial droplet radii and to increase with increasing gas temperatures. Larger timesteps can be used in the case of the new approach compared with the conventional one to achieve the same accuracy of calculation. It is recommended that the effect of a moving boundary on droplet heating is taken into account in modelling droplet heating and evaporation in CFD codes.
机译：提出了两个新的热传导方程解，它们描述了蒸发液滴的瞬态加热。第一个解决方案是该方程式的显式解析解，而第二个解决方案将差分瞬态热传导方程式的求解简化为第二类Volterrarnintegral方程式的求解。假设该半径是时间的线性函数，则两种解决方案都考虑了由于蒸发导致的液滴半径减小的影响。可以将这种方法视为目前在我们已知的所有研究和商业CFD代码（例如KIVA，FLUENT，PHOENICS）中使用的方法的一般化，其中假定液滴半径在时间步中是恒定的。新的分析解决方案已被纳入零维CFD代码中，并用于分析典型发动机工况下柴油燃料滴的加热和蒸发。在假设液滴半径在时间步长不变（但从一个步骤到另一个步骤变化）的前提下，将结果与传统（传统）方法对液滴加热和蒸发进行建模的结果进行了比较。已经指出，与传统方法相比，新方法可预测较低的液滴表面温度和较慢的蒸发速率。蒸发时间之间的相对差显示出实际上与初始液滴半径的值无关，并且随着气体温度的升高而增加。与传统方法相比，新方法可以使用更大的时间步长，以实现相同的计算精度。建议在CFD代码中模拟液滴加热和蒸发时，应考虑移动边界对液滴加热的影响。

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  • 来源
    《International Journal of Heat and Mass Transfer》 |2010年第14期|2826-2836|共11页
  • 作者

    S.S. Sazhin; P.A. Krutitskii; I.G. Gusev; M.R. Heikal;

  • 作者单位

    Sir Harry Ricardo Laboratories, Centre for Automotive Engineering, School of Environment and Technology, Faculty of Science and Engineering, University of Brighton, Brighton BN2 4GJ, UK;

    Keldysh Institute for Applied Mathematics, Department 4, Miusskaya Sq. 4, Moscow 125047, Russia;

    Sir Harry Ricardo Laboratories, Centre for Automotive Engineering, School of Environment and Technology, Faculty of Science and Engineering, University of Brighton, Brighton BN2 4GJ, UK;

    Sir Harry Ricardo Laboratories, Centre for Automotive Engineering, School of Environment and Technology, Faculty of Science and Engineering, University of Brighton, Brighton BN2 4GJ, UK;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    droplets; diesel fuel; heating; evaporation; moving boundary; analytical solution; stefan problem;

    机译：飞沫;柴油染料;加热;蒸发;移动边界分析溶液;斯蒂芬问题;

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