Numerical modeling and experimental measurements of water spray impact and transport over a cylinder

https://doi.org/10.1016/j.ijmultiphaseflow.2005.05.007Get rights and content

Abstract

This study compares experimental measurements and numerical simulations of liquid droplets over heated (to a near surface temperature of 423 K) and unheated cylinders. The numerical model is based on an unsteady Reynolds-averaged Navier–Stokes (RANS) formulation using a stochastic separated flow (SSF) approach for the droplets that includes submodels for droplet dispersion, heat and mass transfer, and impact on a solid surface. The details of the droplet impact model are presented and the model is used to simulate water spray impingement on a cylinder. Computational results are compared with experimental measurements using phase Doppler interferometry (PDI). Overall, good agreement is observed between predictions and experimental measurements of droplet mean size and velocity downstream of the cylinder.

Introduction

The fate of liquid droplets impacting surfaces is of significance to many applications including spray coating, painting, fuel injection in internal combustion engines, spray cooling, and fire-suppression with liquid agents. Over the past decades, a number of studies focusing on single-droplet impact have been conducted (Worthington, 1908, Foote, 1975, Chandra and Avedisian, 1991, Mundo et al., 1995, Pasandideh-Fard et al., 1996, Healy et al., 1996, Mao et al., 1997, Fukumoto et al., 2002, Aziz and Chandra, 2000, Roisman et al., 2002, Kim et al., 2000, Kim et al., 2003, Mehdizadeh et al., 2004, Manzello and Yang, 2004, Gentner et al., 2004), as well as studies focusing on the interaction of entire sprays with surfaces (Mundo et al., 1998, Schmehl et al., 1999). The present work takes advantage of work on single-droplet impact to provide predictive relations for the fate of droplets in a spray impinging on a cylinder with an emphasis on the degree to which the cylinder interferes with the downstream transport of the condensed-phase species. This topic is of particular interest in light of the need to suppress fires in cluttered compartments or rooms. The interaction between the condensed suppressant and various obstructions within a compartment can interfere with the suppressant’s distribution. With the phase-out of Halons, fire suppressants with higher boiling points are being employed in total flooding applications, and the issue of spray–clutter interaction takes on greater importance.

When individual droplets impact a surface, several post-impact states can occur. The droplet may elastically rebound, it may stick to the surface, or it may shatter (see Fig. 1). The energetically preferred state depends on the relative surface and kinetic energies along with the viscous dissipation of energy during the impact process. At low droplet kinetic energies, either “sticking” or elastic “rebounding” occurs, depending on the surface energy relative to the dissipated energy. At high droplet kinetic energies, splashing (or shattering) occurs when the kinetic energy is distributed among smaller droplets with a higher overall surface energy (relative to the original droplet). These results have been derived from a large number of experimental and computational studies of isolated droplets. The earliest work in this area dates back to Worthington (1908). Early numerical simulations of droplet impact, where only inertial and viscous forces were considered, include Harlow and Shannon (1967) and following works. The importance of surface tension was noted early in numerical studies like those of Foote (1975), where the inclusion of surface tension allows droplet rebound, as experimentally observed by Wachters and Westerling (1966). A simple energy balance was introduced by Ford and Furmidge (1967) and more recently by Chandra and Avedisian (1991) to relate the total energy of the pre-impact condition to the maximum spread of a single droplet following impact; this simple model was shown to be in reasonable agreement with experimental results in this work, and a number of similar works have offered refinements on this basic energy balance model. Implicit in this model is an estimate of the viscous dissipation occurring while the droplet spreads. Chandra and Avedisian (1991) assumed a linear velocity profile across the entire droplet height while Pasandideh-Fard et al. (1996), based on analysis of their numerical simulations, put forth a model for viscous dissipation that was based on stagnation flow. Mao et al. (1997) points out that the choice of model depends on the boundary layer thickness and it appears that both models are relevant at different times. Mao et al. (1997) also continued the energy balance to a third state where the excess surface energy at the point of maximum spread could cause the droplet to rebound off the surface; this last state appears to be most likely when the droplet contact angle is large, as for example when the Leiden frost temperature is exceeded, and droplet rebound was observed under these conditions by Chandra and Avedisian (1991). Mundo et al. (1995) investigated the critical characteristic impingement parameter (Kcrit), which distinguished the “shattering” regime from the sticking and rebounding regimes. Fukumoto et al. (2002) suggested an improved model for the characteristic impingement parameter relative to that of Mundo et al. (1995). The experimental and analytical investigations of Aziz and Chandra, 2000, Kim et al., 2000, Kim et al., 2003, Mehdizadeh et al., 2004 indicated that the droplet impact is governed essentially by the surface tension instability and, therefore, the effect of viscosity is of little importance.

Several groups have studied the impingement of a spray on flat surfaces. Schmehl et al., 1999, Park and Watkins, 1996, Bai et al., 2002 developed numerical formulations that were based on the experimental work of Wachters and Westerling (1966). Mundo et al. (1998) carried out both experimental measurements and developed a numerical formulation that was based on the model of Wang and Watkins (1993), but included shattering criteria (see Mundo et al., 1995) for their spray simulation. Inclusion of the shattering criteria resulted in a smaller overall droplet size for their numerical prediction than predicted by Wang and Watkins (1993), and better agreement with the experimental data.

The current work examines the transport of water droplets around a circular cylinder. This problem is a simplification of the more challenging problem of modeling water spray fire suppression in cluttered environments (Presser et al., 2001, Presser et al., 2002). The objective of this study is to develop a simplified phenomenological droplet impact model for use in fire suppression applications that is suitable for numerical simulation of sprays involving a multitude of droplets of varying size and velocity, and to validate this model using experimental measurements of droplet size and velocity.

Section snippets

Experimental facility

A schematic of the experimental facility is shown in Fig. 2. The salient features of the experimental apparatus and operating conditions are presented for brevity. The facility is oriented so that the flow issues horizontally to allow for the collection of liquid agent that drips off the cylinder, and prevent liquid droplets downstream of the obstacle from falling back upstream into the oncoming flow. The agent used in the present study was water, supplied through a 60° solid-cone, pressure-jet

Modeling background

Numerical simulations are conducted using Sandia’s fire field modeling code VULCAN, which has been extended to handle the dilute multiphase flow physics found in evaporating and reacting sprays (DesJardin and Gritzo, 2002, Yoon et al., 2004). The spray model is coupled with the Navier–Stokes solver, based on a Reynolds-averaged Navier–Stokes (RANS) formulation employing a standard kε turbulence closure model (Jones and Launder, 1972). The gas-phase flow is calculated on a Eulerian staggered

Nonheated cylinder

Fig. 11 presents the variation of D32 and U with axial (streamwise) position for different radial (cross-stream) locations of z = 0, 10 mm, and 20 mm. The variable U is the droplet mean axial (streamwise) component of velocity. The computational and experimental results are compared, using the initial condition for the simulations of q = 3 and D10 = 25 μm at the nozzle exit. The experimental Type A evaluation of the standard uncertainty for D32 is 1.9 μm (7.4% of the mean value), and for U is 0.18 m/s

Conclusions

Transport of a water spray over a circular cylinder in a turbulent flow field for the fire-suppression applications is simulated using a stochastic separated flow technique that includes sub-models for droplet dynamics, heat and mass transfer due to evaporation, and a newly developed wall-impact model. Results using this model show good agreement to experimental measurements of droplet mean size and velocity around the cylinder. Discrepancies in the prediction of droplet size and velocity

Acknowledgements

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. The first author acknowledges that this research was conducted during his presence at Sandia National Laboratories. The second author acknowledges the support of National Science Foundation under Grant No. CTS-0348110. The third author wishes to acknowledge the partial support of this

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