Wall Heat Flux Partitioning Model Research Articles

Modeling of transition boiling under an impinging water jet

Liquid jet impingement is known for its high capability of extracting heat from the surface it impinges on. Steady state subcooled boiling experiments were carried out in the stagnation region of a water planar jet of 0.6 and 0.75m/s jet velocity and 15°C of subcooling. The transition boiling regime is found to have a region of constant heat flux. After the critical heat flux (CHF) is reached, the heat flux decreases till a local minimum value is reached; called the first minimum. The heat flux then increases till it reaches a relatively constant value, even with the increase of the surface degree of superheat. The constant heat flux region is called the shoulder heat flux. With the aid of high speed imaging, Rayleigh–Taylor instability has been observed at the liquid–vapor interface which is accelerated by gravity and jet dynamic pressure. A modified expression for the interface acceleration is proposed. The vapor layer formed in the transition boiling is not stable; it follows periodic cycles of break up and formation. Two surface wetting mechanisms are proposed based on observations: (i) direct liquid touching the surface at moderate degrees of superheat and (ii) liquid columns intruding the vapor layer and touching the surface at discrete locations at high degrees of superheat. A new wall heat flux partitioning model is proposed. The proposed model divides the wall heat flux, based on the two observed wetting mechanisms, into two components: (i) quenching heat flux and (ii) intrusion heat flux. The current model estimates the wall heat flux during transition boiling covering the surface superheat range from the CHF till the Leidenfrost point with a normalized root mean square error (NRMSE) of 33%.

Computational fluid dynamics simulation of subcooled flow boiling in vertical rectangular 2-mm narrow channel

This work proposes and discusses a new wall boiling model for a 2-mm narrow rectangular channel with a copper heating surface at atmospheric pressure. The model includes a wall heat flux partitioning model and several sub-models that compute active nucleation site density, bubble departure diameter, and bubble departure frequency. This wall boiling model was developed based on our previous experimental work on narrow channel flow in order to account for the unique thermal-hydraulics that occur under these specific conditions. The model was implemented in CFX code to simulate the subcooled flow boiling in a narrow channel with a two-fluid model; we also considered the onset of nucleate boiling. The new model has been validated by the experimental data. Compared to the default model that had been developed in CFX code, the new model provides better predictions of the distribution of wall temperature in the 2-mm narrow channel.

Numerical Simulations of Gas-Liquid Boiling Flows Using OpenFOAM

The present work is aimed at development of an experimentally verified computational model based on OpenFOAM for the simu- lations of gas-liquid boiling flows. The open source CFD code OpenFOAM was developed further to include k-E turbulence model, different inter-phase coupling forces and energy transport accompanied with phase change. The most commonly used wall heat flux partitioning model, proposed by Kurul and Podowski 1, was implemented in the OpenFOAM to simulate two-phase boiling. The predicted axial and radial vapor volume fraction distribution, liquid temperature distribution and wall temperature profiles were compared with the DEBORA measurements 2. A good agreement between the predictions and measurements was observed. The experimentally verified model was used to understand the effects of various interfacial closures e.g. lift force, turbulent dispersion force and wall force, on the vapor volume fraction distribution. The effects of bubble induced turbulence and nucleation site density on the hydrodynamics of the gas-liquid boiling flows were studied. Such an experimentally verified open source CFD code will be useful to simulate boiling under different regimes and in complex geometries.

Assessment of subcooled boiling wall boundary correlations for two-fluid model CFD

Abstract An assessment of the heat and mass transfer wall boundary conditions used for subcooled boiling simulations with a CFD two-fluid model has been performed. This assessment was focused on the wall heat flux partitioning model using the state-of-the-art multidimensional Freon experimental data available in the literature. Various constitutive relations used to close the vapor generation rate at the heated wall were studied in order to obtain the best suited combination(s). The current study was restricted to vertical flows through pipe and annulus geometries. Two Freon data sets from the literature were considered: the first with R12 at about 2.6 MPa pressure and the second with R113 at 269 kPa pressure. In these data sets, the bubble diameter distribution measurements across the ducts were available. Bubble diameter estimation is the largest uncertainty in the boiling two-fluid model predictions and hence using the data with known bubble sizes allowed to focus on the assessment of other parameters to model vapor generation rate at the wall, in particular bubble nucleation site density and bubble departure frequency. From the parametric simulations with different combinations of the nucleation site density and frequency models, the discrepancy in obtaining a consistent frequency model for Freon became evident. The state-of-the-art frequency model under consideration is a function of the wall temperature which is estimated using a well-known empirical nucleate boiling heat transfer coefficient correlation. The frequency model provided inaccurate predictions in cases where the nucleate boiling heat transfer coefficient was inadequate to predict the wall superheat. The frequency model is now improved by using a more recent nucleate boiling heat transfer coefficient correlation with wider applicability, i.e., Freon. The simulations were carried out using the CFD code CFX (version 12). The Freon data used here corresponds to fluid-vapor density ratios ranging from 6 to 76. This assessment validated a consistent site density-departure frequency correlation combination for subcooled boiling simulations which has not been used so far for CFD simulations and an extension of the applicability of the correlation combination to high pressure steam–water conditions due to the favorable scaling of Freon physical properties.

Numerical Simulation of Subcooled Boiling Inside High-Heat-Flux Component with Swirl Tube in Neutral Beam Injection System

In order to realize steady-state operation of the neutral beam injection (NBI) system with high beam energy, an accurate thermal analysis and a prediction about working conditions of heat-removal structures inside high-heat-flux (HHF) components in the system are key issues. In this paper, taking the HHF ion dump with swirl tubes in NBI system as an example, an accurate thermal dynamic simulation method based on computational fluid dynamics (CFD) and the finite volume method is presented to predict performance of the HHF component. In this simulation method, the Eulerian multiphase method together with some empirical corrections about the inter-phase transfer model and the wall heat flux partitioning model are considered to describe the subcooled boiling. The reliability of the proposed method is validated by an experimental example with subcooled boiling inside swirl tube. The proposed method provides an important tool for the refined thermal and flow dynamic analysis of HHF components, and can be extended to study the thermal design of other complex HHF engineering structures in a straightforward way. The simulation results also verify that the swirl tube is a promising heat removing structure for the HHF components of the NBI system.

Prediction of dryout and post-dryout wall temperatures using film thickness model

In this paper, a model for calculating dryout and post-dryout wall temperature for two phase flow in a vertical tube using film thickness model is presented. The model is based on the mass and energy balance equations for vapor core, liquid film and corresponding closure laws for interface transfer processes. It is assumed that the dryout is reached when the local film thickness in the annular flow approaches zero. Thermal-hydraulic processes along the whole length of the boiling channel are simulated, from sub-cooled liquid flow at channel inlet, up to the liquid film dryout, gas entrained droplets, mist flow and post dryout region at tube exit. In the post dryout region, thermal non-equilibrium was assumed between vapor and entrained droplets and wall temperature was obtained iteratively by using a wall heat flux partitioning model. Also, the model is verified against several available experimental data and proved viable for prediction of the wall temperature and the dryout location.

Modeling Vertical Subcooled Boiling Flows at Low Pressures

Abstract An improved wall heat flux partitioning model at the heated surface was developed by Yeoh et al. This model, coupled with a three-dimensional two-fluid model and Multiple Size Group model, has led to satisfactory agreement being achieved between the model predictions and experimental measurements. Nevertheless, one shortcoming is the reliance on empirical correlations for the active nucleation site density in the wall heat flux partitioning model. This discrepancy brings about uncertainties, especially in appropriately evaluating the vapor generation rate, which greatly influences the model prediction on the axial and radial void fraction profiles within the bulk fluid flow. By considering the fractal model with the aforementioned subcooled boiling flow model in the absence of empirical correlations for the active nucleation site density, a comprehensive mechanistic model to predict vertically oriented subcooled boiling flows is developed. The proposed model is assessed against the experimental data of axial measurements of Zeitoun and Shoukri and the radial measurements of Yun et al. and Lee et al. for vertical subcooled boiling flows within annular channels. Improved model predictions are obtained when the model is compared against typically applied empirical correlations for active nucleation site density. Discussions on the agreement of other two-phase flow parameters are also presented.

English

Subcooled flow boiling in vertical channels have many industrial applications, including heat removal from core of nuclears. In the present work, subcooled flow boiling is simulated using open source simulation software OpenFOAM. A new solver is developed based on the OpenFOAM framework to predict subcooled flow boiling by incorporating various flow boiling models. Vapor generation in the heated wall is modeled with a wall heat flux partitioning model. Additional source terms are added to the governing equations to account for the phase change process. Energy equation is implemented for the liquid phase. The solver is validated against benchmark calculation of the DEBORA subcooled boiling data.

Improvement of the subcooled boiling model for low-pressure conditions in thermal-hydraulic codes

The functioning of the subcooled boiling model adopted in a thermal-hydraulic computer program has been investigated in detail, for low-pressure conditions, and necessary refinements have been incorporated into the code. The investigation has been carried out in two stages; in the first stage, the performance of the interfacial heat transfer/condensation is studied. Necessary refinements to the vertical flow map for the transition from bubbly to slug flow regimes and the interpolation with the ‘umbrella’ limitation that bounded the interfacial heat transfer values are carried out. Simulations of low-pressure subcooled boiling experiments were performed with the refined code version and a reasonable agreement with the experimental void fraction data was obtained. In addition, a high-pressure experiment was also simulated with the refined code version to check if these revisions do not affect the code performance at high pressures. No significant adverse effects were observed. In the second stage of the study, the performance of the wall heat flux partitioning model adapted in the code was investigated. In particular, the effectiveness of the ‘pumping factor’ formulation in the above model and its functioning at low-pressure conditions was investigated. Different ‘pumping factor’ formulations available in the literature were implemented into the code. Simulations of low-pressure subcooled boiling experiments were performed with the refined code version and the appropriate ‘pumping factors’ to be used for low-pressure conditions were determined.