Modeling subcooled flow boiling in vertical channels at low pressures – Part 2: Evaluation of mechanistic approach
Introduction
Detailed modelling of local phenomena of subcooled flow boiling in heated channels generally involves the combination of a multi-dimensional model of two-phase flow and heat transfer inside the channel with a model of coupled single-phase and boiling heat transfer phenomena in the near-wall region. The accuracy of such simulations is highly dependent on the availability of mechanistic closure laws of local boiling mechanisms especially inside the boundary layer near the heated wall. An approach based on partitioning the total wall heat flux into three components has been frequently adopted to model the local near-wall heat transfer such as developed by Podowski [1]. These heat flux components, which comprise the single-phase heat transfer component corresponding to the non-boiling sections of the heated wall, the quenching component associated with heating the liquid which approaches the wall after bubble lifting off the heated surface and the rate of heat transfer due to evaporation which is directly used to convert liquid into vapour at the heated wall, requires the determination of important parameters associated with the active nucleation site density, bubble departure diameter and frequency. The original heat flux partitioning model developed by Kurul and Podowski [2] is one model that has been widely adopted by various researchers [3], [4], [5]. Nevertheless, the model suffers from a number of major drawbacks.
Inherently, the original heat flux partitioning model assumes that bubbles are immediately released into the bulk subcooled liquid during the flow boiling process. This assumption may be possibly valid for restricted cases of horizontally oriented pool flow boiling. Experimental observations by Klausner et al. [6] and recently by Ahmadi et al. [7] clearly revealed the presence of sliding bubbles affects not only the associated thermodynamic non-equilibrium that occurs between the vapour bubbles and bulk subcooled liquid but also plays an important role in causing Net Vapour Generation (NVG) downstream of the flow boiling after the point of Onset Nucleate Boiling (ONB). As indicated in Basu et al. [8], [9] and Sateesh et al. [10], the transient conduction due to sliding bubbles becomes the dominant mode of heat transfer. For vertical subcooled flow boiling, it is paramount that the heat flux partitioning model incorporates the area of influence and transient conduction component due to these sliding bubbles. In Yeoh et al. [11], improvements have been made to the heat flux partitioning model by further developing the model to incorporate the sliding period.
As summarized in the Part 1, numerous empirical correlations have been proposed to evaluate the active nucleation site density, bubble size and bubble frequency, with each applicable to a restricted range of experimental conditions. It should be noted that majority of these correlations have been developed for subcooled flow boiling at high pressures. It is not surprising that the application of these correlations to flow conditions and imposed wall heat fluxes at low pressures has been found to be less successful with model predictions deviating significantly from measurements. This has certainly prompted the revisiting the fundamental physics governing the boiling process in order to circumvent the problem associated with the use of empirical correlations for subcooled flow boiling at low pressures. To ensure that the heat flux partitioning model is applicable for subcooled flow boiling not only at low pressures but also at high pressures, a more mechanistic approach to evaluate the active nucleation site density, bubble size and bubble frequency is required. In Yeoh et al. [11], improvements have also been made by mechanistically determined the bubble frequency as well as the bubble diameters at sliding and lift-off determined via the force balance model developed in Yeoh and Tu [12]. However, the heat flux partitioning model remains lacking to adequately predict important phasic parameters for particular subcooled flow conditions and imposed wall heat fluxes especially through the use of empirical correlations for the active nucleation site density.
A preliminary scoping study on the use of the fractal model proposed by Xiao and Yu [13] for a specific vertical subcooled flow boiling configuration has been carried out in Yeoh et al. [14]. In essence, the fractal distribution of sizes of active cavities on the heated surface is considered of which it is strongly dependent on not only the wall superheat as has been typified in most correlations for active nucleation site density but also on other flow parameters including the liquid subcooling, fractal dimension, minimum and maximum active cavity sizes contact and bulk velocity and physical properties of the adjacent fluid. From a mechanistic consideration, the model has demonstrated enormous potential in appropriately determining the active nucleation site density distribution especially on the heated wall for subcooled flow boiling at low pressures.
In this current study, the modelling framework entails the consideration of the different mechanistic models in determining the active nucleation site density, bubble size and bubble frequency for the improved heat flux partitioning model. In combination with the two-fluid and population balance models which have been presented in Part 1, the numerical predictions are evaluated against the experimental data for vertical subcooled flow boiling at low pressures described in Part 1. The main focus of this paper is to try to extend the numerical model to hopefully leading towards a more systematic way to resolve the underlying physics. Therefore, in this paper, the performance of the proposed mechanistic model is assessed to see whether it could cover a wider range of flow conditions which has always been a problem for existing empirical heat partition models (also demonstrated in the results presented in Part 1). We must also admit that there is still room for improvement and the predictions are less than perfect at the moment. However, the predicted results have proved that the proposed mechanistic approach could be a viable solution for a wider range condition and it is a possible direction for future work.
Section snippets
Active nucleation site density – fractal model
The active nucleation site density for subcooled flow boiling in vertical channels at low pressures could be determined based on the fractal distribution of the nucleation sites on heated surfaces. According to Xiao and Yu [13] the generated active cavities on the heated surface can be taken to be similar to the existence of pores in porous media. Thus, the cumulative number of active cavities with diameters equal to and greater than a particular active cavity diameter, Dc, can be described by
Results and discussion
For the MUSIG boiling model, a total number of 15 bubble classes have been adopted to accommodate coalescence, break-up and condensation of bubbles. This represented a set of 15 transport equations to be solved in addition to the flow equations governing the conservation of mass, momentum and energy. For all cases considered, uniform heat flux is applied on the inner wall of the annulus; only one quarter of the annulus is thus modelled as the computational domain. Grid independence is examined;
Conclusions
The coupling of the improved heat flux partitioning model with the two-fluid and MUSIG models have been assessed against axial and local radial measurements covering a wide range of different mass and wall heat fluxes for subcooled flow boiling at low pressures. Predictions made from the fractal approach in determining the active nucleation site density show a clear dependence of the subcooling effect from the bulk liquid in affecting the activation of nucleation sites at the heated wall.
Acknowledgement
The financial support provided by the Australian Research Council, Australia (ARC project ID DP130100819) is gratefully acknowledged.
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