A report presents an evaluation of eight mathematical models of the evaporation of liquid droplets — models that are used in the numerical simulation of a variety of gas/liquid flows, including cooling sprays, burning liquid-fuel sprays, fire-suppression sprays, and air/fuel-premixing flows in combustors. Included in the study were two versions of a classical model that includes transient drop-heating effects, four versions of a heat-mass-transfer-analogy model, and two nonequilibrium models based on the Langmuir-Knudsen evaporation law. The models were used to predict evolutions of droplet diameters and temperatures, and the predictions were compared with experimental observations, for droplets of benzene, decane, heptane, hexane, and water vaporizing in convective airflows. All models performed nearly identically at low evaporation rates at gas temperatures significantly lower than the liquid-boiling temperatures. For gas temperatures at and above boiling temperatures, there were large deviations among the various model predictions. Nonequilibrium effects were found to become significant for initial droplet diameters <50 µm, and to increase with slip velocity. The models based on the Langmuir-Knudsen law agreed most closely with the experimental results, though not because they account for nonequilibrium effects; instead, the superiority of these models was attributed to the incorporation of a corrected heat-transfer equation.
This work was done by Josette Bellan, Kenneth Harstad, and Richard Miller of Caltech for NASA's Jet Propulsion Laboratory. To obtain a copy of the report, "Evaluation of Equilibrium and Non-Equilibrium Evaporation Model for Many-Droplet Gas-Liquid Flow Simulations," access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Physical Sciences category, or circle no. 140 on the TSP Order Card in this issue to receive a copy by mail ($5 charge).
NPO-20259
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Evaluation of Droplet-Evaporation Models for Gas/Liquid Flow
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Overview
The document presents an evaluation of eight mathematical models used to simulate the evaporation of liquid droplets in gas/liquid flows, which are relevant in various applications such as cooling sprays, combustion, fire suppression, and air/fuel premixing in combustors. The study was conducted by researchers Josette Bellan, Kenneth Harstad, and Richard Miller at Caltech for NASA's Jet Propulsion Laboratory.
The models evaluated include two classical versions that account for transient drop-heating effects, four heat-mass-transfer-analogy models, and two nonequilibrium models based on the Langmuir-Knudsen evaporation law. The primary objective was to predict the evolutions of droplet diameters and temperatures and to compare these predictions with experimental observations for droplets of different liquids, including benzene, decane, heptane, hexane, and water vaporizing in convective airflows.
The results indicate that all models performed similarly at low evaporation rates when gas temperatures were significantly lower than the liquid boiling points. However, as gas temperatures approached or exceeded boiling points, substantial deviations in model predictions were observed. Notably, nonequilibrium effects became significant for initial droplet diameters less than 50 μm and increased with slip velocity.
Among the models, those based on the Langmuir-Knudsen law provided the best agreement with experimental results. This success was attributed not to their handling of nonequilibrium effects but rather to their incorporation of a corrected heat-transfer equation, which improved their predictive accuracy.
The document emphasizes the complexity of modeling multi-phase gas-liquid flows, which involve intricate nonlinear couplings of momentum, energy, and mass exchange. Traditional modeling approaches typically focus on individual droplets, using governing equations that account for drag, convective heat transfer, and mass transfer, along with the effects of finite droplet Reynolds numbers.
Overall, the evaluation highlights the importance of selecting appropriate models for accurately predicting droplet behavior in various thermal environments, which is crucial for optimizing processes in engineering applications. The findings contribute to a better understanding of droplet evaporation dynamics and the development of more effective simulation tools for gas/liquid flow systems.
