Spray cooling simulation implementing time scale analysis and the Monte Carlo method

Abstract

Spray Cooling Simulation Implementing TimeScale Analysis and the Monte Carlo Method PAUL JOSEPH KREITZER Spray cooling research is advancing the field of heat transfer and heat rejection in high power electronics. Smaller and more capable electronics packages are producing higher amounts of waste heat, along with smaller external surface areas, and the use of active cooling is becoming a necessity. Spray cooling has shown extremely high levels of heat rejection, of up to 1000 W/cm 2 using water. Simulations of spray cooling are becoming more realistic, but this comes at a price. A previous researcher has used CFD to successfully model a single 3D droplet impact into a liquid film using the level set method. However, the complicated multiphysics occurring during spray impingement and surface interactions increases computation time to more than 30 days. Parallel processing on a 32 processor system has reduced this time tremendously, but still requires more than a day. The present work uses experimental and computational results in addition to numerical correlations representing the physics occurring on a heated impingement surface. The current model represents the spray behavior of a Spraying Systems FullJet 1/8-g spray nozzle. Typical spray characteristics are indicated as follows: flow rate of 1.05x10-5 m 3 /s, normal droplet velocity of 12 m/s, droplet Sauter mean diameter of 48 µm, and heat flux values ranging from approximately 50-100 W/cm 2. This produces non-dimensional numbers of: We 300-1350, Re 750-3500, Oh 0.01-0.025. Numerical and experimental correlations have been identified representing crater formation, splashing, film thickness, droplet size, and spatial flux distributions. A combination of these methods has resulted in a Monte Carlo spray impingement simulation model capable of simulating hundreds of thousands of droplet impingements or approximately one millisecond. A random sequence of droplet impingement locations and diameters is generated, with the proper radial spatial distribution and diameter distribution. Hence the impingement, lifetime and interactions of the droplet impact craters are tracked versus time within the limitations of the current model. A comparison of results from this code to experimental results shows similar trends in surface behavior and heat transfer values. Three methods have been used to directly compare the simulation results with published experimental data, including: contact line length estimates, empirical heat transfer equation calculations, and nondimensional Nusselt numbers. A Nusselt number of 55.5 was calculated for experimental values, while a Nu of 16.0 was calculated from the simulation.

Comparisons of Single Drop Impact Simulations with Experiments

“…It requires huge resources to successfully simulate the sprays even with modern meshing methods and numerical models. Kreitzer (2010) and Kuhlman et al (2011) state that the droplet impacts in a dense spray may reach fluxes exceeding 10 6 drops/(s-cm 2 ). These types of sprays pose difficulties in simulating.…”

“…These images were used in measuring the cavity formation and its lifetime. To develop a practical model of a spray a Monte-Carlo (MC) simulation model was developed to predict the spray characteristics similar to the experiments conducted by Kreitzer (Kreitzer, 2010).…”

“…Simulating sprays is time consuming and needs high computational power which is expensive. To reduce the cost and increase the efficiency, Monte-Carlo models have been developed by Kreitzer (2010) and by Hussain et al From these single droplet studies it is hoped that we will be able to predict the behavior of the full spray, and then the amount of heat transferred from the heated surface. All of these cases have been experimented and simulated at isothermal conditions.…”

Droplet Impact Sub-cavity Histories and PDPA Spray Experiments for Spray Cooling Modeling

“…__________________________________________________ 2 Figure 1.2: Single drop impingement into an unheated initial liquid surface and its components (Hillen et al 2013). 6 Figure 2.1: Simulated heater surface from the MC Spray Cooling model (Kreitzer, 2010). ___________________ 14 Figure 2.2: Droplet impact angle.…”

“…Thus, a more efficient and feasible solution such as a phenomenological model capable of capturing the basic, relevant physics would be very desirable. Kreitzer (2010) describes one approach to such a model in the form of a Monte-Carlo (MC) simulation spray cooling model. The initial MC model developed by Kreitzer (2010) is still in development with the ultimate goal to accurately predict the heat flux for given nozzle flow conditions, for smooth heater surface geometries, and heater surface temperatures below the Leidenfrost point in reasonable computation times.…”