Influence of droplet drag reduction on the numerical modelling of the interaction between water sprays and hot air jets

Recent investigations have highlighted the potential underprediction of droplet drag reduction in Computational Fluid Dynamics (CFD) simulations of dense water sprays [1]. In the Fire Dynamics Simulator (FDS, the current drag reduction model is based on the Ramirez correlation [2] that is developed for an idealized case of two droplets placed in tandem. This correlation mimics the wake effect on the trailing particle induced by a perfectly aligned leading particle. However, other interactions occurring in a full spray (such as lateral interactions) are not accounted for, which might explain (partially) the underestimation of drag reduction.Based on these observations, a novel expression for the drag reduction has been developed. The latter is based on a functional form with a predefined asymptomatic behaviour for very dilute and very dense spray, and a smooth transition in between. The proposed expression reads:F_D⁄F_D0 =(1-B) exp⁡[-(α+1-A)^n ]+Bwhere F_D/F_D0 is the drag force reduction, α is the local droplet volume fraction and A,B and n are three parameters that have been determined using available experimental data for several sprays (A=5×〖10〗^(-5),B=0.11,n=〖10〗^6).The development and the analysis of this novel expression against multiple water sprays (in the absence of fire-driven flows), with variable level of density has been described in a paper that is currently under revision. That previous study has shown that – for a very dense spray – by substantially reducing the drag force in dense regions of the spray, the spray expands more and leads to simulations results that are much closer to the experimental data.The present work aims at further consolidating the previous analysis by considering an additional test case examined experimentally in [3] and where a dense water spray is interacting with a hot air jet. Two simulations are carried out with FDS 6.7.6. In the first simulation, the default drag reduction model is used. In the second simulation, a modified version of the code is used and in which the novel drag reduction has been implemented. The preliminary simulation results show that by using the novel correction function, the interaction height between the water spray and the hot air jet is better predicted.[1] Liu Y., Beji T., Thielens M., Tang Z., Fang Z. and Merci B (2022) Numerical analysis of a water mist spray: The importance of various numerical and physical parameters, including the drag force, Fire Safety Journal, 127:103515, https://doi.org/10.1016/j.firesaf.2021.103515[2] Ramírez-Muñoz J., Soria A. and Sadinas-Rodríguez E. (2007) Hydrodynamic force on interactive spherical particles due to the wake effect, Int. J. of Multiphase Flow, 33:802-807 https://doi.org/10.1016/ j.ijmultiphaseflow.2006.12.009[3] Zhou X. (2015) Characterization of interactions between hot air plumes and water sprays for sprinkler protection, 35 – 3:2723-2729, https://doi.org/10.1016/j.proci.2014.05.078Recent investigations have highlighted the potential underprediction of droplet drag reduction in Computational Fluid Dynamics (CFD) simulations of dense water sprays [1]. In the Fire Dynamics Simulator (FDS, the current drag reduction model is based on the Ramirez correlation [2] that is developed for an idealized case of two droplets placed in tandem. This correlation mimics the wake effect on the trailing particle induced by a perfectly aligned leading particle. However, other interactions occurring in a full spray (such as lateral interactions) are not accounted for, which might explain (partially) the underestimation of drag reduction.Based on these observations, a novel expression for the drag reduction has been developed. The latter is based on a functional form with a predefined asymptomatic behaviour for very dilute and very dense spray, and a smooth transition in between. The proposed expression reads:F_D⁄F_D0 =(1-B) exp⁡[-(α+1-A)^n ]+Bwhere F_D/F_D0 is the drag force reduction, α is the local droplet volume fraction and A,B and n are three parameters that have been determined using available experimental data for several sprays (A=5×〖10〗^(-5),B=0.11,n=〖10〗^6).The development and the analysis of this novel expression against multiple water sprays (in the absence of fire-driven flows), with variable level of density has been described in a paper that is currently under revision. That previous study has shown that – for a very dense spray – by substantially reducing the drag force in dense regions of the spray, the spray expands more and leads to simulations results that are much closer to the experimental data.The present work aims at further consolidating the previous analysis by considering an additional test case examined experimentally in [3] and where a dense water spray is interacting with a hot air jet. Two simulations are carried out with FDS 6.7.6. In the first simulation, the default drag reduction model is used. In the second simulation, a modified version of the code is used and in which the novel drag reduction has been implemented. The preliminary simulation results show that by using the novel correction function, the interaction height between the water spray and the hot air jet is better predicted.[1] Liu Y., Beji T., Thielens M., Tang Z., Fang Z. and Merci B (2022) Numerical analysis of a water mist spray: The importance of various numerical and physical parameters, including the drag force, Fire Safety Journal, 127:103515, https://doi.org/10.1016/j.firesaf.2021.103515[2] Ramírez-Muñoz J., Soria A. and Sadinas-Rodríguez E. (2007) Hydrodynamic force on interactive spherical particles due to the wake effect, Int. J. of Multiphase Flow, 33:802-807 https://doi.org/10.1016/ j.ijmultiphaseflow.2006.12.009[3] Zhou X. (2015) Characterization of interactions between hot air plumes and water sprays for sprinkler protection, 35 – 3:2723-2729, https://doi.org/10.1016/j.proci.2014.05.078C