The main objective of this paper is to evaluate the validity of the existing methods for analytically solving the governing equation of smoke filling in enclosures with floor leaks and growing fires. Since the complete form of the governing equation is inseparable, it can hardly be exactly solved analytically. Up to now, there are mainly five analytical solutions available in the literature. The first is derived by Mowrer (Fire Saf J 33: 93–114, 1999), the second is derived by Yamana and Tanaka (Fire Sci Technol 5: 31–40, 1985; Fire Sci Technol 5: 41–45, 1985), and the other three are derived by Delichatsios (Fire Saf J 38: 97–101, 2003; Fire Saf 39: 643–662, 2004). Among these solutions, the first has been incorporated into the SFPE handbook (SFPE handbook of fire protection engineering, 5th edn. Springer, New York, 2016), and one of the Delichatsios' solutions has been incorporated into the ISO standard (Fire safety engineering—Requirements governing algebraic equations—Smoke layers, 2006). These analytical solutions provide convenient ways for estimating the smoke-interface height. However, it should be noted that all of these solutions are approximate for the case of "floor leak & growing fire", so they must be used with caution. By comparing with the "exact" numerical solutions of the governing equation, errors of the five analytical solutions are calculated systematically. An absolute error contour plot and a relative error contour plot are made for each solution, which can be directly used to judge the validity of the solution. It is found that all the five analytical solutions sometimes produce considerable errors, and the error distribution characteristics are quite different from one solution to another. The error sources are analyzed. The analyses provide not only explanation for the error distribution characteristics but also deep insights into the analytical solutions. Based on the error contour plots made for each solution, the prediction of the corresponding solution can be corrected to a more accurate value. An example is presented to illustrate how to do this.

本文的主要目的是评估现有解决方法的有效性，该方法可用于解析地漏和火势越来越大的机柜中的烟雾填充控制方程。由于控制方程的完整形式是不可分割的，因此很难通过解析来精确求解。到目前为止，文献中主要有五种分析解决方案。第一个由Mowrer推导（Fire Saf J 33：93–114，1999），第二个由Yamana和Tanaka推导（Fire Sci Technol 5：31–40，1985; Fire Sci Technol 5：41–45，1985） ，另外三个则由Delichatsios派生（Fire Saf J 38：97-101，2003； Fire Saf 39：643-662，2004）。在这些解决方案中，第一个已纳入SFPE手册（SFPE消防工程手册，第五版，Springer，纽约，2016年），并且Delichatsios的一种解决方案已被纳入ISO标准（消防安全工程-代数方程式的要求-烟层，2006年）。这些分析解决方案提供了估算烟气界面高度的便捷方法。但是，应注意，所有这些解决方案都是针对“地板泄漏和着火情况”的近似值，因此必须谨慎使用。通过与控制方程的“精确”数值解进行比较，系统地计算了五个解析解的误差。为每个解决方案制作一个绝对误差轮廓图和一个相对误差轮廓图，它们可以直接用于判断解决方案的有效性。发现所有五个分析解决方案有时都会产生相当大的误差，而且错误分配的特性从一种解决方案到另一种解决方案是完全不同的。分析错误源。这些分析不仅提供了错误分布特征的解释，而且还提供了对分析解决方案的深入了解。基于为每个解决方案制作的误差轮廓图，可以将相应解决方案的预测校正为更准确的值。提供了一个示例来说明如何执行此操作。