Elsevier

Fire Safety Journal

Volume 106, June 2019, Pages 124-135
Fire Safety Journal

Assessment of heating and evaporation modelling based on single suspended water droplet experiments

https://doi.org/10.1016/j.firesaf.2019.04.012Get rights and content

Abstract

The work described in this paper is undertaken with the purpose of providing a detailed assessment of the current modelling capabilities of the effects of fire suppression systems (e.g., sprinklers) in fire-driven flows. Such assessment will allow identifying key modelling issues and, ultimately, improving the reliability of the numerical tools in fire safety design studies. More specifically, we studied herein the heating and evaporation of a single water droplet. This rather ‘simple’ configuration represents the first step in a tedious and rigorous verification and validation process, as advocated in the MaCFP (Measurement and Computation of Fire Phenomena) working group (see https://iafss.org/macfp/). Such a process starts ideally with single-physics ‘unit tests’ and then more elaborate benchmark cases and sub-systems, before addressing ‘real-life’ application tests. In this paper, we are considering the recently published comprehensive and well-documented experimental data of Volkov and Strizhak (Applied Thermal Engineering, 2017) where a single suspended water droplet of initial diameter between 2.6 and 3.4 mm is heated up by a convective hot air flow with a velocity between 3 and 4.5 m/s and a temperature between 100 and 800 °C. In the present numerical study, 36 experimental tests have been simulated with the Fire Dynamics Simulator (FDS 6.7.0) as well as with an in-house code. The results show that the droplet lifetime is overpredicted with an overall deviation between 26 and 31%. The deviation in the range 300–800 °C is even better, i.e., 5–8%, whilst the cases of 200 and, more so 100 °C, showed much stronger deviations. The measured droplet saturation temperatures did not exceed 70 °C, even for high air temperatures of around 800 °C, whereas the predicted values approached 100 °C. A detailed analysis shows that the standard Ranz & Marshall modelling of the non-dimensional Nusselt and Sherwood numbers may not be appropriate in order to obtain a simultaneous good agreement for both the droplet lifetime and temperature. More specifically, the heat-mass transfer analogy (i.e., Nu = Sh) appears to be not always valid.

Introduction

An accurate water heating and evaporation model is essential for the assessment of the effectiveness of active fire protection measures that are based on, for example, Early Fire Suppression Response (EFSR) sprinklers or water mist. In most of the Computational Fluid Dynamics (CFD) codes, droplet evaporation modelling is based on the so-called ‘film theory’ [1]. The film is a very thin layer at the interface between the liquid and the surrounding environment where heat and mass exchange as well as phase transformation occur. The thickness of the film is generally significantly (sometimes orders of magnitude) smaller than typical cell sizes used in fire dynamics (or combustion) simulations, except if Direct Numerical Simulations (DNS) are carried out, which could not be afforded for practical fire scenarios. Consequently, several correlations have been developed in the literature to estimate the convective heat and mass transfer film coefficients around droplets. These correlations are based on single suspended water droplet experiments where the droplet is subjected to a convective air flow (natural or forced) with a fixed velocity and temperature. The most widely used correlations date back to the early work of Ranz and Marshall for a forced convection flow [2] where the evaporation of water droplets in air is examined for a room temperature up to 220 °C, a droplet diameter between 0.6 and 1.1 mm and a droplet Reynolds number, Red, between 2 and 200. Thanks to the significant advances in measuring technologies that could be used to characterize in detail the heating and evaporation process of a water droplet, more accurate data is available for model validation. For example, very recently, Volkov and Strizhak [3] published a very interesting set of data for the heating and evaporation of a water droplet with an initial diameter between 2.6 and 3.4 mm in a hot environment with free stream temperatures between 100 and 800 °C and velocities between 3 and 4.5 m/s. The first objective of this paper is to rely on this dataset to assess the capabilities of a CFD code widely used in the fire safety community, namely the Fire Dynamics Simulator (FDS 6.7.0), in the modelling of the heat up and evaporation process of single suspended water droplets [[5], [6], [7]]. The second objective of the paper is to develop an in-house code that allows to focus on the heat and mass transfer aspects of the problem (the momentum equation is not solved) and more particularly, study the influence of the correlations used for the Sherwood (Sh) and the Nusselt (Nu) numbers.

Section snippets

The fire dynamics simulator

A detailed description of the mathematical modelling for droplet evaporation in FDS 6.7.0 is provided in Refs. [[4], [5], [6]]. Only the main equations for the case at hand are recalled herein for the sake of clarity.

Experimental setup and measurements

The experimental dataset relied upon herein for validation purposes has been obtained by Volkov and Strizhak [3]. The experimental configuration consists of a single water droplet (with an initial diameter, dd,0, between 2.67 and 3.37 mm) suspended in the middle of a hollow and transparent silica-glass cylinder of 0.1 m inner diameter. A hot air blower positioned below the cylinder blows hot air upwards with temperatures, Ta, between 100 and 800 °C and velocities, Ua, between 3 and 4.5 m/s. The

Preliminary FDS simulations

Generally speaking, a mesh sensitivity analysis in gas phase simulations leads to convergence of the results when the cell size is sufficiently fine. However, the results displayed in Fig. 4c show that the more refined the grid is, the longer the droplet lifetime. This rather ‘counter-intuitive’ behaviour, which is also encountered in the simulation of sprays using Lagrangian particles, is well explained in Refs. [16,17]. In Ref. [16], three sources of error have been identified: (1) the

Conclusions

In this paper we assessed the capabilities of the Fire Dynamics Simulator (FDS 6.7.0) in the modelling of the heat up and evaporation of a water droplets based on the experiments carried out by Volkov and Strizhak (Applied Thermal Engineering, 2017). In these experiments, a single suspended water droplet of a diameter between 2.6 and 3.4 mm is heated up by a convective hot air flow with a velocity between 3 and 4.5 m/s and a temperature between 100 and 800 °C. The results, based on the

Acknowledgments

Martin Thielens is a PhD student who holds a grant for fundamental research from the Fund of Scientific Research – Flanders (FWO - Vlaanderen). The FWO file number of his mandate is 1182919N.

References (20)

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