Conclusions 67 

A semi-empirical model of the interaction of water droplets with hot air has been developed based on the principles of the conservation of mass, momentum and energy, and some empirical correlations. The contribution of radiation emanating from a flame is considered on the evaporation of a droplet. The effect of a high evaporation rate and the change of Re to the mass and heat transfer coefficient is also

Chapter 3: Development of a semi-empirical model for the evaporation of water droplets  

considered in the model. A forward finite difference technique is used to solve the resulting ordinary differential equations. A time step convergence analysis is conducted and an appropriate time step is selected leading to time step convergent results.

This proposed model has been validated and verified against experimental data and adiabatic saturation temperature. The validation indicates that the proposed model predicted the terminal velocity within 4% of the experimental data. The saturation temperature of droplets predicted by the proposed model agreed well with the calculated adiabatic saturation temperature. In the study, it is found that the proposed model is consilient with FDS and this has given us confidence in the use of this model. In comparison, Li and Chow [2008] and Barrow and Pope’s [2007] models should be treated with caution as they predict the longevity of the droplets, and the distance through which they penetrate through a smoke layer or hot air environment induced by a fire. This work provides a further tool with which to predict the behaviour of water droplets evaporating in a hot environment.

The characteristics of the evaporating droplets were evaluated using the proposed model and are presented in this chapter. The temperature profile, travel time history, velocity profile, evaporation rate and absorbed heat of a freely falling droplet are predicted. The findings of this study can be summarised as follows:

i) The saturation temperature of droplets is independent of the initial diameter and temperature of the droplets; it depends on the temperature and relative humidity of ambient air.

ii) The suspension time in air is longer for the smaller size of droplets, whereas the penetration capability is greater for the larger size of droplets through a hot air environment.

iii) The evaporation rate is higher for smaller droplets, whereas the quantity of heat absorbed is greater for the bigger size of droplets. However, the total amount of absorption of heat per unit mass of water is higher for the smaller size of droplets.

iv) The terminal velocity is larger for the bigger size of droplets. However, it is found that the speed of the smaller size of droplets has begun to reduce due to reduction of the diameter by evaporation.

v) The effect of the high mass transfer rate on evaporation of a droplet is insignificant within the range 0–100 of air temperature.

vi) In this study, a case study is conducted where the droplets are considered travelling through a hot smoke layer. The temperature of the smoke layer is 75 and relative humidity of air is 3%. In the analysis, the droplets with a size of less than 200 µm are found to be the most effective in evaporative cooling, as they have totally vaporised due to evaporation before reaching the floor. Moreover, the total absorbed heat per unit mass of water is highest for droplets sizes 100 and 200 µm. However, suspension time is highest for the droplet size 200 µm. The suspension time of this size is much higher than other sizes of droplets, which can lead this size to be the most effective where the suspension time is very important to block heat transfer from the source of fires.

This physical model has given us the confidence to analyse the behaviour of individual water droplets travelling through a hot environment induced by a room fire. This model can be used to evaluate the performance of different sizes of droplets in different actions of fire suppression mechanisms i.e. whether a particular size of droplet is suitable for the cooling of hot gas by heat extraction or the dilution of fuel vapours/air ratio by evaporation of water droplets, or whether it is suitable for the

Chapter 3: Development of a semi-empirical model for the evaporation of water droplets  

wetting and cooling of a fuel surface by reaching there before complete evaporation. The model can also be used for the validation of comprehensive CFD based models to obtain confidence in the use of that particular model. In this study, an example of the verification of a complex CFD model, FDS6, is presented.

In this part of the study we have elucidated the physics of the evaporation of water- mist droplets in hot air or a smoke layer and validated FDS in predicting the evaporation of individual droplets. However, as the performance of a spray in suppressing a fire is greatly influenced by its distribution pattern, any CFD based tool should be able to predict this phenomenon in its simulation. Hence this study is further proceeded to investigate the capability of FDS in predicting the distribution of flux densities on a horizontal surface.