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