Computational study of cryogenic jet impingement boiling on concave and singular needle surfaces

Abstract

Jet impingement boiling is a highly effective method of surface cooling and is particularly suited to high heat-flux applications such as microprocessor cooling and cryogenic probe cooling. In the present study, we computationally explore the effect that the geometric parameters of surface curvature, needle height and impingement height have on the boiling curve. The multiphase Eulerian model coupled with the {Rensselaer Polytechnic Institute (RPI) wall boiling model is employed in tandem with an axisymmetric steady-state assumption. {The RPI wall boiling model decomposes the wall heat flux into three components: quenching, convective and evaporative. Each of these components comprise of multiple closing models.} A focus is placed on selecting RPI closing models that are suitable for cryogenic fluids. Moreover, a new empirical correlation is proposed for the non-dimensional area of influence {(A_b) which determines the ratio of quenching to convective heat flux.} Based on results of a Monte Carlo experiment aimed at mimicking the distribution of nucleation sites and their overlapping area of influence, { this model is given as: A_b=1-e^{-1.5\beta^{1.2}}. The bubble waiting time coefficient (C_{wt}) can be described as the quenching heat flux pre-multiplicative coefficient and is responsible for adjusting the quenching heat flux independent of the evaporative and convective components. The range for which the bubble waiting time coefficient (C_{wt}) can vary is likewise computed using the results of the Monte Carlo method with the inclusion of the reduction of area of influence due to bubble growth (1 <C_{wt} <1.2). These findings are incorporated into a CFD model. Additionally, a computational fluid dynamics (CFD) }model based on RPI closing models developed for water and modified by increasing the bubble waiting time coefficient well beyond the applicable range (to a value of C_{wt}=3) is also developed for comparative purposes.

The CFD models are validated against experimental findings from literature concerning a jet of liquid nitrogen (2mm in diameter) impinging onto a heated surface (5mm in diameter) of various shapes (flat, hemispherical and singular needle) in a radially confined domain. The Reynolds numbers range from 3 700 to 12 200. The steady-state solver used was found to have a maximum deviation of 2.4% near the experimental critical heat flux when compared to a transient solution. The experimental parameters of subcooling, jet velocity and pressure had large ranges of uncertainty or were ill-defined. As such their impact on the CFD models was explored. It was revealed that increased subcooling increased the quenching and convective heat fluxes resulting in the nucleate boiling curve shifting to the left. Increased pressure displayed a similar shift of the boiling curve to the left for the cryogenic model due to the increase in nucleation site density (as a result of the change in the fluid saturation properties). However, as the nucleation site density was not dependent on fluid properties for the water based model, there was minimal impact of pressure on wall superheat. Increased jet velocity resulted in a marginal increase in boiling heat transfer coefficient (BHTC) for all models. The settings of the cryogenic CFD model selected for use in the subsequent parametric study were finalised based on the parameter combination (velocity, subcooling and nucleation site density) that resulted in the lowest root mean squared deviation across all three experimental surfaces.

A parametric study was then conducted to determine the influence of surface curvature (k=0-0.42) on confined cryogenic jet impingement boiling. It is revealed that increased curvature resulted in approximately quadratic growth of the BHTC. The main mechanism behind this was revealed to be the growth in surface area resulting from increased curvature. Additionally, the parametric study explored the impact of needle height (h_{needle}0-5 mm) on the BHTC when using both flat and curved surfaces. The BHTC was found to grow approximately linearly with increased needle height. This was again attributed largely to the increase in surface area with increased needle height. Lastly, the parametric study explored the effect of jet impingement height (a=0.5-5.5 mm) on both curved, needled and combined curved-needled surfaces. It was revealed that there exists an optimum impingement height of approximately a=1.5-2.5 mm for most of the tested surfaces (with slight variation depending on curvature and needle height). The optimum parameter combination was found to be [a=1.5 mm, k=0.42 and h_{needle}=4 mm] with a BHTC of 3.66 W/(cm^2 K).