CFD simulation of upward subcooled boiling flow of refrigerant-113 using the two-fluid model

In this paper, a modified two-fluid model considering temperature dependent properties and saturation temperature variation was adapted to accurately simulate the process of subcooled boiling flow. The calculations were performed by a CFD code CFX-10 with an extended user defined FORTRAN. The refrigerant-113 boiling flow experiments in a vertical concentric annulus from reference were used to validate the modified two-fluid model of subcooled boiling flow. Compared with the previous published predicted results, the results in the present model show better and reasonable approximation with the experimental data, including the local distribution of void fraction, liquid temperature, axial liquid and vapor velocity. Results show that with increasing the wall heat flux, the bubble boundary layer will become thicker, the liquid temperature gradient at the near-wall region will be smoother and the profiles of axial liquid velocity will gradually depart from those of single-phase flow. Decreasing the inlet liquid subcooling or the mass flux will obtain the same results.     

Modeling of bubble-layer thickness for formulation of one-dimensional interfacial area transport equation in subcooled boiling two-phase flow

In relation to the formulation of one-dimensional interfacial area transport equation in a subcooled boiling flow, the bubble-layer thickness model was introduced to avoid many covariances in cross-sectional averaged interfacial area transport equation in the subcooled boiling flow. The one-dimensional interfacial area transport equation in the subcooled boiling flow was formulated by partitioning a flow region into two regions; boiling two-phase (bubble layer) region and liquid single-phase region. The bubble-layer thickness model assuming the square void peak in the bubble-layer region was developed to predict the bubble-layer thickness of the subcooled boiling flow. The obtained model was evaluated by void fraction profile measured in an internally heated annulus. It was shown that the bubble-layer thickness model could be applied to predict the bubble-layer thickness as well as the void fraction profile. In addition, the constitutive equation for the distribution parameter of the boiling flow in the internally heated annulus, which was used for formulating the bubble-layer thickness model, was developed based on the measured data. The model developed in this study will eventually be used for the development of reliable constitutive relations, which reflect the true transfer mechanisms in subcooled boiling flows.     

Subcooled flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the subcooled flow boiling heat transfer and associated bubble characteristics of refrigerant R-134a in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. From the measured boiling curves, the temperature undershoot at ONB is found to be relatively significant for the subcooled flow boiling of R-134a in the duct. The R-134a subcooled flow boiling heat transfer coefficient increases with a reduction in the gap size, but decreases with an increase in the inlet liquid subcooling. Besides, raising the imposed heat flux can cause a substantial increase in the subcooled boiling heat transfer coefficient. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are small in the narrow duct. Visualization of the subcooled flow boiling processes reveals that the bubbles are suppressed to become smaller and less dense by raising the refrigerant mass flux and inlet subcooling. Moreover, raising the imposed heat flux significantly increases the bubble population, coalescence and departure frequency. The increase in the bubble departure frequency by reducing the duct size is due to the rising wall shear stress of the liquid flow, and at a high imposed heat flux many bubbles generated from the cavities on the heating surface tend to merge together to form big bubbles. Correlation for the present subcooled flow boiling heat transfer data of R-134a in the narrow annular duct is proposed. Additionally, the present data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

Axial developments of interfacial area and void concentration profiles in subcooled boiling flow of water

Axial developments of the local void fraction, interfacial area concentration and bubble Sauter mean diameter were measured in subcooled boiling flow of water in a vertical internally heated annulus using the double-sensor conductivity probe technique. Measurements were performed under varying conditions of heat flux, inlet liquid velocity and inlet liquid temperature. A total of 10 data sets were acquired. Based on these measurements with the previous data obtained in the present test loop, the influence of flow condition on the profiles of local two-phase flow parameters was discussed. The measured average void fraction and interfacial area concentration were compared with the predictions by existing correlations for drift-flux parameters and interfacial area concentration. Also, the recently proposed bubble layer thickness model in subcooled boiling was evaluated for the measurement data.     

Subcooled flow boiling heat transfer of R-407C and associated bubble characteristics in a narrow annular duct

An experiment is conducted here to investigate how the channel size affects the subcooled flow boiling heat transfer and the associated bubble characteristics of refrigerant R-407C in a horizontal narrow annular duct with the gap of the duct fixed at 1.0 and 2.0 mm. The measured boiling curves indicate that the temperature overshoot at ONB is relatively significant for the subcooled flow boiling of R-407C in the duct. Besides, the subcooled flow boiling heat transfer coefficient increases with a reduction in the duct gap, but decreases with an increase in the inlet liquid subcooling. Moreover, raising the heat flux imposed on the duct can cause a significant increase in the boiling heat transfer coefficients. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are slighter. Visualization of the subcooled flow boiling processes in the duct reveals that the bubbles are suppressed to become smaller and less dense by raising the refrigerant mass flux and inlet subcooling. Raising the imposed heat flux, however, produces positive effects on the bubble population, coalescence and departure frequency. Meanwhile, the present heat transfer data for R-407C are compared with the R-134a data measured in the same duct and with some existing correlations. We also propose empirical correlations for the present data for the R-407C subcooled flow boiling heat transfer and some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density.     

Interfacial heat transfer of condensing bubble in subcooled boiling flow at low pressure

The interfacial heat transfer coefficient is an important parameter for the analysis of multi-phase flow. In subcooled boiling flow, bubbles condense through the interface of phases and the interfacial heat transfer determines the condensation rate which affects the two-phase parameters such as void fraction and local liquid temperature. Thus, the present experiments are conducted to correlate the interfacial heat transfer coefficient at low pressure in the subcooled boiling flow. The local liquid temperature is measured by microthermocouple and the bubble condensation rate is estimated by orthogonal, two-image processing. The condensate Nusselt number, which is a function of bubble Reynolds number, local liquid Prandtl number, and local Jacob number, is obtained from the experimental results. The bubble history is derived from the newly proposed correlation and the condensate Nusselt number is compared with the previous models.     

Modeling of the microconvective contribution to wall heat transfer in subcooled boiling flow

In the present work, the two-phase turbulent boundary layer in subcooled boiling flow is investigated. The bubbles in the near-wall region have a significant effect on the dynamics of the underlying liquid flow, as well as on the heat transfer. The present work develops a single-fluid model capable of accounting for the interactions between the bubbles and the liquid phase, such that the two-phase convective contribution to the total wall heat transfer can be described appropriately even in the framework of single-fluid modeling. To this end, subcooled boiling channel flow was experimentally investigated using a laser-Doppler anemometer to gain insight into the bubble-laden near-wall velocity field. It was generally observed that the streamwise velocity component was considerably reduced compared to the single-phase case, while the near-wall turbulence was increased due to the presence of the bubbles. Since the experimentally observed characteristics of the liquid velocity field turned out to be very similar to turbulent flows along rough surfaces, it is proposed to model the near-wall effect of the bubbles on the liquid flow analogously to the effect of a surface roughness. Incorporating the proposed approach as a dynamic boundary condition into a well-established mechanistic flow boiling model makes it possible to reflect adequately the contribution of the microconvection to the total wall heat transfer. A comparison against the experimental data shows good agreement for the predicted wall shear stress as well as for the wall heat flux for a wide range of wall temperatures and Reynolds numbers.     

低流速净蒸汽产生点模型预测过冷沸腾空泡率

空泡率是汽液两相流动的基本参数之一,而已有过冷沸腾空泡率计算方法研究以高质量流速为主,且大量文献报道现有空泡率模型难以适用于低流速过冷沸腾工况。本文基于低流速过冷沸腾净蒸汽产生点(NVG)理论模型,进一步建立了计算过冷沸腾空泡率的分布拟合模型。在较宽广的压力、质量流速、热流密度和流道尺寸范围内将模型计算结果与现有空泡率实验数据进行了比较,低流速工况下该模型与实验数据符合良好,表明该模型可适用于低流速过冷沸腾工况。     

Interfacial heat transfer during subcooled flow boiling

In order to develop a mechanistic model for the subcooled flow boiling process, the key issues which must be addressed are wall heat flux partitioning and interfacial (condensation) heat transfer. The sink term in the two-fluid models for void fraction prediction is provided by the condensation rate at the vapor-liquid interface. Low pressure subcooled flow boiling experiments, using water, were performed using a vertical flat plate heater to investigate the bubble collapse process. A high-speed CCD camera was used to record the bubble collapse in the bulk subcooled liquid. Based on the analyses of these digitized images, bubble collapse rates and the associated heat transfer rate were determined. The experimental data were in turn used to correlate the bubble collapse rate and the interfacial heat transfer rate. These correlations are functions of bubble Reynolds number, liquid Prandtl number, Jacob number, and Fourier number. The correlations account for both the effect of forced convection heat transfer and thickening of the thermal boundary layer as the vapor bubble condenses which in turn makes the condensation heat transfer time dependent. Comparison of the measured experimental data with those predicted from the correlations show that predictions are well within ±25% of the experimentally measured values. These correlations have also been compared with those available in the literature.     

Photographic study of high-flux subcooled flow boiling and critical heat flux

This study examines both high-flux flow boiling and critical heat flux (CHF) under highly subcooled conditions using FC-72 as working fluid. Experiments were performed in a horizontal flow channel that was heated along its bottom wall. High-speed video imaging and photomicrographic techniques were used to capture interfacial features and reveal the sequence of events leading to CHF. At about 80% of CHF, bubbles coalesced into oblong vapor patches while sliding along the heated wall. These patches grew in size with increasing heat flux, eventually evolving into a fairly continuous vapor layer that permitted liquid contact with the wall only in the wave troughs between vapor patches. CHF was triggered when this liquid contact was finally halted. These findings prove that the CHF mechanism for subcooled flow boiling is consistent with the interfacial lift-off mechanism proposed previously for saturated flow boiling.     

Oscillation of a liquid-vapor interface during flow film boiling

For both pool and flow film boiling, the liquid-vapor interface is rarely stationary, stable film boiling exhibits a continuously wavy interface with an amplitude of oscillation dependent on parameters such as liquid saturation temperature, amount of superheat, amount of subcooling, liquid velocity, and heater geometry. The present analysis treats from a theoretical point of view stagnation point flow film boiling on a sphere and on a cylinder immersed in a subcooled liquid. The effects of system parameters on the dynamic behavior as well as the response of a liquid-vapor interface to changes in the temperature and velocity fields are investigated.     

Flashing phenomena of depressurized liquid nitrogen in a pressure vessel. Part 2: Mist formation and behavior of the liquid surface in the early depressurization process

Flashing of liquid nitrogen in a pressure vessel (cryostat) was observed at depressurization rates from 0.01 to 4.0 MPa/s. The explosive boiling behavior was observed by using a video camera. Pressure and temperature changes in the pressure vessel were measured. In the case of high depressurization rates, mist formation was observed in the vapor phase near the vapor—liquid interface in the early stages of the depressurization process. The mist layer became more dense as the depressurization rate increased. Observations of mist formation and the estimated temperature drop of the vapor under an adiabatic expansion process show that mist formation depends on the vapor expansion and boiling near the liquid surface. Mist formation in flashing phenomena plays an important role in the relaxation of thermal nonequilibrium states between the subcooled vapor and the superheated liquid generated by depressurization. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(5): 327–335, 1998     

Non-linear dynamical analyses of transient surface temperature fluctuations during subcooled pool boiling on a horizontal disk

The class of dynamics in pool boiling on a large-size heater is assessed under subcooled pool boiling conditions. Transient surface temperature measurements are obtained using surface micro-machined K-type thin film thermocouples (TFT) in 10 °C subcooled pool boiling experiments on a 62.23 mm diameter silicon wafer using PF-5060 as the test liquid. Surface temperature data is obtained at each steady state condition to generate the boiling curve. The fraction of false-nearest neighbors, recurrence plots and space–time separation plots are obtained using the TISEAN package. The correlation dimension is then estimated from the re-constructed phase space data using a naïve algorithm. The correlation dimension varies from ～11.2 to 11.5 near onset of nucleate boiling (ONB), to ～7–10 in fully developed nucleate boiling (FDNB) ～7–9 near critical heat flux (CHF) condition, and from ～6.6 to 7.7 in film boiling. False-nearest neighbor estimates and recurrence plots show that nucleate boiling may be dominated by statistical processes near ONB and in partial nucleate boiling (PNB). In contrast, FDNB, CHF and film boiling seem chaotic and governed by deterministic processes.     

Temperature measurements near a heating surface at high heat fluxes in subcooled pool boiling

In previous papers (Int J Heat Mass Transfer, 2008;50:3481–3489, 2009;52: 814–821), the authors conducted measurements of liquid–vapor structures in the vicinity of a heating surface for subcooled pool boiling on an upward‐facing copper surface by using a conducting probe method. We reported that the macrolayer dryout model is the most appropriate model of the CHF and that the reason why the CHF increases with increasing subcooling is most likely that a thick macrolayer is able to form beneath large vapor masses and the lowest heat flux of the vapor mass region shifts towards the higher heat flux. To develop a mechanistic model of the CHF for subcooled boiling, therefore, it is necessary to elucidate the effects of local subcooling on boiling behaviors in the vicinity of a heating surface. This paper measured local temperatures close to a heating surface using a micro‐thermocouple at high heat fluxes for water boiling on an upward‐facing surface in the 0 to 40 K range of subcooling. A value for the effective subcooling, defined as the local subcooling during the period while vapor masses are being formed was estimated from the detected bottom peaks of the temperature fluctuations. It was established that the effective subcooling adjacent to the surface remains at considerably lower values than the bulk liquid subcooling. This suggests that, from nucleation to coalescence, the subcooling of a bulk liquid has a smaller effect on the behavior of primary bubbles than the extent of the subcooling would appear to suggest. An empirical correlation of the effective subcooling is proposed to provide a step towards quantitative modeling of the CHF for subcooled boiling. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20277     

Flow structure of subcooled boiling flow in an internally heated annulus

Local measurements of flow parameters were performed for vertical upward subcooled boiling flows in an internally heated annulus. The annulus channel consisted of an inner heater rod with a diameter of 19.1 mm and an outer round pipe with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. The double-sensor conductivity probe method was used for measuring local void fraction, interfacial area concentration, and interfacial velocity. A total of 11 data were acquired consisting of four inlet liquid velocities, 0.500, 0.664, 0.987 and 1.22 m/s and two inlet liquid temperatures, 95.0 and 98.0 °C. The constitutive equations for distribution parameter and drift velocity in the drift-flux model, and the semi-theoretical correlation for Sauter mean diameter, namely, interfacial area concentration, which were proposed previously, were validated by local flow parameters obtained in the experiment.     

Development of a Multi-Dimensional Fluid Dynamics Code and Its Benchmarking for the Subcooled Boiling Flow

In a two-phase flow analysis, the interfacial area concentration (IAC) is a dominant factor governing the interfacial transfer of the momentum or energy. For a dynamic analysis with the implementation of IAC transport equation, a multi-dimensional computational fluid dynamics code was developed. The code is based on the two-fluid model and the simplified marker and cell algorithm by using the finite volume method, where the conventional approach for a single-phase flow has been modified in order to consider the term for a phase change. As benchmark problems of a single-phase flow and two-phase flow, a natural convection in a rectangular cavity and a subcooled boiling in an annulus channel were selected, respectively. In the calculation for the single-phase flow, the developed code predicted a reasonable behavior for a buoyancy-driven flow depending on the Rayleigh number. In the analysis of the subcooled boiling, the calculation results showed the robustness of code for the analysis of the boiling phenomena and void propagation, where they represented limitations of the one-dimensional IAC model. To conduct a multi-dimensional analysis for the two-phase flow, it is confirmed that the implementation of an IAC transport equation into the code is essential.     

CHF model for subcooled flow boiling in Earth gravity and microgravity

This study is the first attempt at extending the Interfacial Lift-off CHF Model to subcooled flow boiling conditions. A new CHF database was generated for FC-72 from ground tests as well as from microgravity tests that were performed in parabolic flight trajectory. These tests also included high-speed video imaging and analysis of the liquid–vapor interface during the CHF transient. Both the CHF data and the video records played a vital role in constructing and validating the extended CHF model. The fundamental difference between the original Interfacial Lift-off Model, which was developed for saturated flow boiling, and the newly extended model is the partitioning of wall energy between sensible and latent heat for subcooled flow boiling. This partitioning is modeled with the aid of a new “heat utility ratio”. Using this ratio, the extended Interfacial Lift-off Model is shown to effectively predict both saturated and subcooled flow boiling CHF in Earth gravity and in microgravity.     

A BUBBLE MECHANISTIC MODEL FOR SUBCOOLED BOILING FLOW PREDICTIONS

Population balance equations combined with a three-dimensional two-fluid model are employed to predict subcooled boiling flow at low pressure in a vertical annular channel. The MUSIG (Multiple-Size-Group) model implemented in CFX4.4 is extended to account for the wall nucleation and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements is made for the void fraction, bubble Sauter diameter, interfacial area concentration, bubble population density, and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Good agreement is achieved with the local radial void fraction, bubble Sauter diameter, interfacial area concentration, bubble population density, and liquid velocity profiles against measurements. However, further improvement is needed for the accurate prediction of the vapor velocity using the present bubble mechanistic model. A proposal to include an algebraic slip model to account for bubble separation in the MUSIG boiling model is presented.