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Transient heating of an evaporating droplet with presumed time evolution of its radius

机译：假定液滴半径随时间变化而瞬时加热蒸发液滴

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摘要

New solutions to the heat conduction equation, describing transient heating of an evaporating droplet, are suggested, assuming that the time evolution of droplet radius R_d(t) is known. The initial droplet temperature is assumed to be constant or allowed to change with the distance from the droplet centre. Since R_d(t) depends on the time evolution of the droplet temperature, an iterative process is required. Firstly, the time evolution of R_d(t) is obtained using the conventional approach, when it remains constant during the timestep, but changes from one timestep to another. Then these values of R_d(t) are used in the new solutions to obtain updated values of the time evolution of the distribution of temperatures inside the droplet and on its surface. These new values of droplet temperature are used to update the function R_d(r). This process continues until convergence is achieved, which typically takes place after about 15 iterations. The results of these calculations are compared with the results obtained using the previously suggested approach when the droplet radius was assumed to be a linear function of time during individual timesteps for typical Diesel engine-like conditions. For sufficiently small timesteps the time evolutions of droplet temperatures and radii predicted by both approaches coincided. This suggests that both approaches are correct and valid. Similarly to the case when droplet radius is assumed to be a linear function of time during the timestep, the new solutions predict lower droplet temperature and slower evaporation when the effects of the reduction of R_d are taken into account. It is shown that in the case of constant droplet initial temperature, models both taking and not taking into account the changes in the initial droplet temperature with the distance from the droplet centre predict the same results. This indicates that both models are correct.
机译：假设液滴半径R_d（t）的时间演化已知，建议对热传导方程式进行新的描述，描述蒸发液滴的瞬时加热。假定初始液滴温度是恒定的，或者允许其随着距液滴中心的距离而变化。由于R_d（t）取决于液滴温度的时间演变，因此需要迭代过程。首先，当R_d（t）在时间步长中保持恒定但从一个时间步长变为另一个时间步长时，使用常规方法获得R_d（t）的时间演化。然后，在新的解决方案中使用这些R_d（t）值来获取液滴内部及其表面温度分布随时间变化的更新值。液滴温度的这些新值用于更新函数R_d（r）。这个过程一直持续到实现收敛为止，收敛通常发生在大约15次迭代之后。将这些计算的结果与使用以前建议的方法获得的结果进行比较，在这种情况下，对于典型的类似于柴油机的条件，在各个时间步中假设液滴半径是时间的线性函数。对于足够小的时间步长，两种方法预测的液滴温度和半径的时间演变是一致的。这表明这两种方法都是正确和有效的。与假设液滴半径在时间步长内是时间的线性函数的情况类似，当考虑到R_d减小的影响时，新解决方案将预测较低的液滴温度和较慢的蒸发。结果表明，在恒定的液滴初始温度的情况下，考虑和不考虑初始液滴温度随液滴中心距离的变化的模型都可以得出相同的结果。这表明两个模型都是正确的。

著录项

  • 来源
    《International Journal of Heat and Mass Transfer》 |2011年第6期|p.1278-1288|共11页
  • 作者

    S.S. Sazhin; PA Krutitskii; I.G. Gusev; M.R. Heikal;

  • 作者单位

    Sir Harry Ricardo Laboratories, Centre for Automotive Engineering, School of Computing, Engineering and Mathematics, University of Brighton, Brighton BN2 4CJ, UK;

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

    Sir Harry Ricardo Laboratories, Centre for Automotive Engineering, School of Computing, Engineering and Mathematics, University of Brighton, Brighton BN2 4CJ, UK;

    Sir Harry Ricardo Laboratories, Centre for Automotive Engineering, School of Computing, Engineering and Mathematics, University of Brighton, Brighton BN2 4CJ, 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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