Abstract The paper presents a theoretical study on the ceiling jets induced by small fires in tunnels. The ceiling jet thickness, temperature rise and velocity are analyzed theoretically with Non-Boussinesq approximation. The study focuses on the radial and one-dimensional ceiling jets. Numerical solutions in the radial region and one-dimensional shooting region are obtained and new analytical solutions in the critical flow region are achieved. Analytical solutions indicate that the ceiling jet thickness increases with distance away from the fire source, which largely differs from the existing models implying that the ceiling jet thickness in the one-dimensional critical flow remains constant. Additionally, impacts of the air entrainment, friction and heat transfer on the ceiling jet are analyzed. It is found that in the radial and one-dimensional shooting flow regions, the air entrainment has a much more significant effect than the friction and heat transfer. However, in the one-dimensional critical flow region, the impact of air entrainment seems to be negligible and the flow is dominated by the friction and heat transfer. Further, validation of the present theory is made by comparing with previous theories, semi-empirical models, and experiments. The results show that the present theory provides a good prediction of the ceiling jet properties with natural ventilation for a small fire.

中文翻译：

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自然通风隧道火灾浮力驱动天花板射流的理论研究

摘要 本文对隧道小火引起的顶棚射流进行了理论研究。用非Boussinesq近似从理论上分析了天花板射流的厚度、温升和速度。该研究侧重于径向和一维天花板射流。获得了径向区域和一维射流区域的数值解，并获得了临界流动区域的新解析解。解析解表明，天花板射流厚度随着远离火源而增加，这与现有模型大不相同，这意味着一维临界流中的天花板射流厚度保持不变。此外，还分析了空气夹带、摩擦和热传递对天花板射流的影响。研究发现，在径向和一维射流区域，空气夹带比摩擦和传热的影响要显着得多。然而，在一维临界流动区域，空气夹带的影响似乎可以忽略不计，流动以摩擦和传热为主。此外，通过与以前的理论、半经验模型和实验进行比较，对当前理论进行了验证。结果表明，目前的理论为小火自然通风的天花板射流特性提供了良好的预测。空气夹带的影响似乎可以忽略不计，流动主要是摩擦和热传递。此外，通过与以前的理论、半经验模型和实验进行比较，对当前理论进行了验证。结果表明，目前的理论为小火自然通风的天花板射流特性提供了良好的预测。空气夹带的影响似乎可以忽略不计，流动主要是摩擦和热传递。此外，通过与以前的理论、半经验模型和实验进行比较，对当前理论进行了验证。结果表明，目前的理论为小火自然通风的天花板射流特性提供了良好的预测。