A Hydrodynamic Model for Planar Jet Impingement at the Leidenfrost Condition

ABSTRACT

Stable film boiling occurs in the stagnation region of an impinging jet during cooling of very hot surfaces. During film boiling, the liquid is separated from the wall by a vapor layer. Due to the pressure gradient in the impingement region, both the vapor and the liquid flow outwards from the stagnation point. The minimum surface temperature required to support film boiling is referred as the Leidenfrost temperature. The present work is devoted to development of a theoretical model for determination of vapor layer thickness, wall superheat and wall heat flux at the Leidenfrost condition. The model is developed for jet impingement region with a strong transverse pressure gradient, i.e. within the stagnation and the acceleration regions. For convenience the whole of the stagnation and acceleration region is referred to as the stagnation region in this article. It is assumed that the Leidenfrost condition corresponds to zero shear stress at the vapor-liquid interface in the entire stagnation region. Our analytical model is developed for a planar jet, assuming that the entire stagnation region satisfies this Leidenfrost condition. It is based on a solution of the momentum balance equation in the vapor layer, and the energy equation in the liquid. The predicted vapor layer thickness is in good agreement with the experimental data of Bogdanić et al. [1]. A vapor film thickness of 8 ± 2μm for stable film boiling close to the Leidenfrost state has been measured, while the current model predicts a film thickness of 8.85μm at the stagnation point for the same conditions. The wall heat flux is underpredicted by about 30–50% compared to the experimental data available in the literature, while the wall superheat is under-predicted in the range of 40–70%. In the present analysis, the entire stagnation region has been considered to be at the Leidenfrost condition but this is unrealistic for experiments. In the published experiment, wall regions with temperatures higher than the Leidenfrost temperature may also exist. Hence, the wall superheat estimations in this study deviate more than the heat flux estimations. Accurate experimental data are required to validate the model over a wider range of parameters.

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