Critical Heat Flux Model Research Articles

Numerical investigation on the CHF model and prediction for the external cooling channel of lower head

External cooling of the lower head can reduce the possibility of the damage to the pressure vessel in serious accidents. However, when the core melt heats the lower head with a high heat flux subcooled boiling under natural circulation may cause bubble accumulation, which results in the deterioration of heat transfer or even radioactive leakage. This phenomenon is essentially the critical heat flux (CHF) on a curved surface with a downward heating boundary. The estimation of this phenomenon is indispensable for reactor safety design.In this paper, improvement in the nucleation density model exhibits higher resulting calculation performance for CHF with new geometries or working conditions. The CHF values and CHF distribution along the ellipsoidal and spherical structures are obtained, and detailed comparison between these two structures is made. The characteristics of elliptical cooling channel prove completely different from those of spherical structure, which requires more experimental studies.

Critical heat flux on heterogeneous fractal surfaces with micro-pin-fins in pool boiling – Part II: Model establishment and analysis

The heterogeneous fractal surfaces can achieve higher critical heat flux (CHF) than that with the uniformly distributed surfaces, which is reported in Part Ⅰ. In order to explain the phenomenon and understand the trigger mechanism of CHF, a theoretical model of CHF for the heterogeneous structure surfaces is proposed based on the bubble coalescence caused by the hydrodynamic instability and the wall dryout induced by the liquid supply impediment. The continuous expansion and coalescence of the dry spots lead to the formation of the vapor blanket covering the whole surface, which triggers the occurrence of critical phenomenon. The CHF is obtained according to the arrangement of the vapor columns on the heating surface. Both the distribution of the heterogeneous structure and the subcooling of liquid affect the bubble behaviors and liquid supply, which result in an optimal structure distribution to reach the highest CHF under different subcoolings. Compared with the uniform distribution, the width of smooth region surrounding the bubble increases with the increase of heat flux and bubble diameter on the fractal structure, which can effectively provide liquid replenishment at high heat fluxes and achieve higher CHF. The CHFs calculated from this model agree well with the experimental results, and the vapor column arrangement is consistent with the bubble distribution observed from the experimental phenomenon. Moreover, the model can also be used to calculate the CHF of the uniformly distributed heterogeneous surfaces and the homogeneous microstructure surfaces with good precision, which verifies the correctness and extensive applicability of the model.

Theoretical CHF predicted model for subcooled flow boiling

To predict the critical heat flux (CHF) of flow boiling under subcooled conditions, this study comes up with a new model based on the Interfacial Lift-off CHF model. The new model makes up the shortcomings of the previous one used only under saturated conditions, and it also considers the effect of condensation on the interface between liquid and vapor phases. An all-new subcooled correctional coefficient is risen up based on the CHF value for the corresponding flow velocity under near-saturated conditions. By comparison between the predicted results of this model and the experimental ones at 6 subcoolings from 3 to 30 °C, and 18 flow velocities from 0.75 to 8 m/s, with the mean absolute error of 9.4%, the predicted trends are both intuitively reasonable and numerically accurate. It reflects the rule under which CHF changes with the outlet subcooling and flow velocity under both saturated and subcooled conditions, and the vapor amount within a vapor bulk decreases with the increase of subcooling. But as the flow velocity increases, it decreases first, and then tends to be a fixed value gradually.

CFD modeling of critical heat flux in flow boiling: Validation and assessment of closure models

The present study describes the Computational Fluid Dynamics (CFD) modeling of two phase flow boiling for the prediction of Critical Heat Flux (CHF) and its location in a tube, an annulus and a 4×4 rod bundle geometry. A number of different closure models employed for the calculation of the interface momentum exchange are assessed based on a comparison of wall temperature predictions against available experimental data. From detailed and systematic validations, a mean relative error of 15% and 7% for tube and annulus cases respectively was noticed. These simulations identify the CHF location in an annulus and in a rod bundle. The wall temperature variations are predicted for the concentric and eccentric annulus as well as a 4×4 rod bundle geometry. Eccentricity was found to promote early occurrence of CHF in the narrow gap and delay in the wide gap regions. For the 4×4 rod bundle considered, the corner rod facing the pressure tube was found to have an early shoot up in the wall temperature.

Bubble Dynamics and Enhanced Heat Transfer During High-Pressure Pool Boiling on Rough Surface

In the present study, the influence of surface roughness () on critical heat flux (CHF) of water at pressure of 1, 5, and 10 bar is investigated. The desired value of is achieved by making unidirectional scratches on the flat copper surface. Surface roughness varies from 0.106 to . The high-speed camera of 1000 fps is used for the boiling visualization study. The effect of surface roughness on bubble departure diameter and bubble frequency at different pressure is reported. Kim’s CHF model is modified to include the contact angle as a function of surface roughness and temperature, which predicts the experimental CHF with mean absolute error (MAE) of 10.50% at pressure up to 10 bar. The correlation developed for bubble departure diameter predicts the experimental values with MAE of 17.09%. The relation between bubble departure diameter and bubble frequency is also developed, which predicts the corresponding experimental values with MAE of 25.26%.

Investigation on the critical heat flux in a 2 by 2 fuel assembly under low flow rate and high pressure with a CFD methodology

A high pressure critical heat flux (CHF) facility was built at the University of Wisconsin-Madison to investigate the CHF phenomena in rod bundles under lower mass flux and high pressure prototypical to small modular reactor fuel assemblies. With this facility, CHF values and locations can be obtained in a 2 by 2 fuel assembly with 2 m heated length. CFD models were used to predict the experiment data for the purpose of phenomena investigation and model validation. The CFD models can predict the dry spot at the heated surface and the temperature increase. Besides, the predicted CHF values and locations were compared with the experimental data. Good agreement can be observed for the cases with relative high mass flux. Nevertheless, the predicted CHF values were all less than experiment data and the deviations increased with decreasing the mass flux to a relative error larger than 20% for the case with mass flux around 550 kg/m2/s. The accuracies of current model for the prediction of CHF under the conditions of bubbly flow and slug flow were higher than to predict CHF under churn flow condition. The deficiency of the CHF models might be caused by the flow regime transition from bubbly flow to the churn flow with reducing the mass flux. This paper demonstrates an application of two-phase CFD models in the prediction of CHF phenomena in fuel assembly with spacers.

CHF correlation development under ERVC conditions by using the local liquid velocity from PIV measurements

In-vessel retention through external reactor vessel cooling (IVR-ERVC) is a severe accident management strategy that removes the decay heat from the molten corium in the reactor vessel by flooding the reactor cavity. In ERVC conditions, the critical heat flux (CHF) on the outer wall of the vessel is a crucial factor that indicates a thermal margin of the system. Previous studies used averaged mass flux to predict CHF (Haramura and Katto, 1983; Lee and Mudawwar, 1988, Katto, 1990; Jeong et al., 2005; Park et al., 2013). The averaged value cannot indicate the degree of liquid supply which is the most critical factor in the CHF model. Local liquid velocity near the heated surface is one of the most crucial factors that should be quantified to develop a CHF model. In this study, the local liquid velocity near the surface has been measured. A curved rectangular flow channel was devised to simulate the gap between the external reactor vessel wall and the insulation. The boiling heat transfer and CHF were simulated with air injection at the inner wall of the test section. In the experiment, the flow field under the simulated ERVC conditions was measured using the particle image velocimetry (PIV) technique. The PIV measurement was validated by comparing the measured velocity data and the analytic solution under circular pipe flow. The liquid velocity profile at the middle plane of the curved rectangular test section was obtained in the multiple mass flux and inclination angle conditions. Based on the velocity data, a local velocity correlation was developed. The local velocity correlation was applied to improve the CHF prediction model.

Investigation of subcooled flow boiling and CHF using high-resolution diagnostics

We present an experimental methodology that enables accurate measurement of fundamental subcooled flow boiling quantities, such as nucleation site density, bubble growth and wait time, and bubble departure diameter, up to the Critical Heat Flux (CHF) limit. The methodology is based on high-speed video and high-speed InfraRed (IR) diagnostics, combined with advanced post-processing techniques developed in-house. It also provides hitherto unavailable direct estimates of the individual terms of wall heat flux partitioning in subcooled flow boiling; such information is crucially relevant to the validation of the latest mechanistic flow boiling heat transfer and CHF models. Experiments were performed using deionized (DI) water, on a rectangular cross-section channel (3 × 1 cm2), at atmospheric pressure and 10 °C of subcooling, for three mass fluxes (500 kg/m2/s, 750 kg/m2/s, and 1000 kg/m2/s). For each set of operating conditions, the average heat flux was escalated from single-phase forced convection up to the occurrence of CHF, and all boiling parameters were recorded at each heat flux. The trends of measured wait time, growth time and bubble departure diameter were successfully captured by mechanistic models developed or co-developed by the authors. Measurements of the wall heat flux partitioning have revealed that the contribution of microlayer evaporation increases monotonically with the increase of the average heat flux, due to the increase of nucleation site density and bubble departure frequency. However, for our specific heater and operating conditions, the contribution of the microlayer evaporation barely exceeds 50% of the total heat flux, right before CHF.

Study on safety boundary of flow instability and CHF for parallel channels in motion

The safety boundary of flow instability and critical heat flux(CHF) for parallel channels was theoretically investigated in static and motion. For flow instability, a parallel-channel instability mechanistic model was adopted. For CHF, the liquid sublayer dryout mechanism model was used. Also, a unified form of additional forces caused by motion was derived for both flow instability and CHF model. An in-house code was developed combining the flow instability model and the CHF model in motion. The safety boundary of twin rectangular parallel channels with length of 40 mm, width of 2 mm and height of 1 m was calculated in static, inclination, heaving, pitching and rolling motions. The results show that the safety boundary consists of CHF lines and instability boundary. The heating power of the parallel channels is limited by flow instability or CHF depending on the mass flux. All the motions have little influence on the instability boundary. The effects of longitudinal inclination, heaving and pitching motions on the safety boundary are no more than 1%. However, the CHF is obviously reduced in transverse inclination due to flow maldistribution and in rolling motion due to pulsating flow.

Pool boiling heat transfer of FC-72 on pin-fin silicon surfaces with nanoparticle deposition

In the present study, two types of micro-pin–fin configurations were fabricated on silicon surfaces by a dry etching method, i.e., staggered pin fins (#1) and aligned pin fins with empty areas (#2). The micro-pin–fin surfaces were then further modified by depositing FeMn oxide nanoparticles (∼35 nm) electrostatically for 8 h and 16 h, respectively, namely #1-8h, #1-16h, #2-8h and #2-16h. Subcooled pool boiling heat transfer was experimentally studied on these surfaces at atmospheric pressure, using FC-72 as the working fluid. The results showed that in comparison to the smooth surface, pool boiling heat transfer was significantly enhanced by the micro-pin-fin surfaces and the maximum superheat was considerably decreased. Additionally, critical heat fluxes were also greatly improved, e.g., the critical heat flux on #1 was almost twice of that on the smooth surface. Generally, the nanoparticle deposition could further enhance pool boiling heat transfer, including the heat transfer coefficient and critical heat flux (CHF). High speed visualizations were taken to explore the mechanisms behind the heat transfer performance. The bubble behavior on the micro-pin–fin surfaces with and without nanoparticles was compared at low, moderate and high heat fluxes, respectively. The wickability of FC-72 on the test surfaces was measured, based on which, a modified CHF model was proposed to predict the experimental CHFs. Accordingly, a possible mechanism of CHF enhancement was described.

Corrections for the Hydrodynamic Instability-Based Critical Heat Flux Models in Pool Boiling—Effects of Viscosity and Heating Surface Size

This paper presents corrections for existing hydrodynamic instability-based critical heat flux (CHF) models in pool boiling by taking into account the effect of the viscosity, geometry and size of the liquid–vapor interface. Based on the existing literature, the Kelvin–Helmholtz (KH) theory, used by the most commonly adopted CHF models, can lead to noticeable errors when predicting the instability conditions. The errors are mainly due to the inaccuracy of the inviscid flow assumptions and the oversimplification of the interface geometry. In addition, the literature suggests the most unstable condition predicted by the viscous correction for viscous potential flow (VCVPF) theory for the cylindrical interfaces best match the observed air column breakup conditions in water. In this paper, the most unstable instability conditions predicted by the VCVPF theory are used to correct the existing CHF models. The comparison between the existing and corrected CHF models suggests that the corrected models always predict a higher CHF value. In addition, the corrected Zuber model predicts similar CHF value to the Lienhard and Dhir model. The comparison with experimental data suggests that the correction to the Zuber model can increase its prediction accuracy in most cases, but not necessary for the Lienhard and Dhir model. When compared to experimental CHF data for boiling cryogens at different pressures, the corrected CHF models are consistently more accurate than the original CHF models.

Transient CHF enhancement in high pressure pool boiling on rough surface

Experimental investigation of transient pool boiling heat transfer (PBHT) to saturated water from thick, non-lumped 20 mm diameter copper sample is carried at 1 bar, 5 bar and 10 bar pressure. The time constant (γ) of exponential heat supply is varied from 1 to 6. The unidirectional scratches are made on the surface to obtain wide range of surface roughness varying from Ra = 0.106 μm to Ra = 4.03 μm. The effect of surface roughness, pressure and time constant on transient critical heat flux (CHF) is extensively studied. Transient CHF enhancement for Ra = 4.03 μm when γ = 1 is found to be 98.88%, 76.55% and 53.21% at pressures P = 1 bar, P = 5 bar and P = 10 bar, respectively, however it is found to be lower by 9.38%, 21.40% and 9.73%, compared to steady state CHF enhancement for Ra = 4.03 μm, at respective pressures. The Gorenflo correlation is modified by including the additional parameter γ and it predicts the present transient HTC values with mean absolute error (MAE) of 14.91%. The CHF model is developed by considering the effect of capillary wicking in the narrow unidirectional scratches and the bubble angle. This model predicts the present transient CHF values with MAE of 11.89%.

Critical heat flux model on a downward facing surface for application to the IVR conditions

A mechanistic model, which is widely applicable to the flow boiling regime, is developed to predict the critical heat flux (CHF) in the In-Vessel Retention (IVR) configuration. The model is based on five general equations describing the CHF mechanism and four primary CHF variables: vapor velocity, liquid velocity, microlayer thickness and the slug length. The CHF mechanism of liquid film dryout underneath the slug is considered. Velocities of vapor and liquid are determined by the Karman velocity distribution and the force balance between buoyancy and drag force. The microlayer thickness is defined by Cheung and Haddad (Cheung and Haddad, 1997) model, based on the Helmholtz instability for the vapor stem located in the microlayer. The slug length is postulated to be the critical Helmholtz wavelength. The solution is numerically obtained starting from seven scattered input parameters: mass flux, local quality, pressure, inclination angle, gap size, working fluid and heater material. In the model, four unknown constants are used for the premature CHF due to heater deformation, the minimum length of slug and the approximation of microlayer thickness and liquid velocity. To find the best-fitted values of the unknown constants, the URANIE code, developed by Commissariat à l'Energie Atomique (CEA), is used. The CHF predicted by the new model is compared with the integrated IVR-CHF database, including experimental data from KAIST, CEA (SULTAN experiments), UCSB (ULPU experiments) and MIT. Starting from 278 experimental data points, the CHF model is affected by a root-mean-square (RMS) error of 14.8%. The CHF predicted by the model is in good agreement with the experimental IVR-CHF database, except for the condition of high mass flux conditions (>500 kg/m2 s) and low inclination angle (<16°). Further improvement of the model is suggested to cover this range and reduce the RMS error based on future worldwide experimental series.

A critical heat flux model for saturated flow boiling on the downward curved heated surface

The critical heat flux (CHF) distribution on the outer surface of the lower head is a crucial parameter to assess the coolability limits of the in-vessel retention strategy through external reactor vessel cooling. Several CHF correlations concerning the orientation angle of heated wall have been proposed while the theoretical analysis is relatively insufficient. Based on the liquid microlayer dryout mechanism, a theoretical CHF model for the saturated flow boiling on the downward curved heated surface has been proposed in this work. With a thorough analysis of the vapor blanket behavior in the near-wall region, the effects of the mass velocity and orientation angle of the heated wall on the CHF are considered in present model. The well agreement between the predicted CHF and the experimental data suggests the validity and applicability of present CHF model to assess the CHF limits on the outer surface of the lower head under in-vessel retention.

Effect of Thermophysical Properties of the Heater Substrate on Critical Heat Flux in Pool Boiling

While the role of the liquid properties, surface morphology, and operating conditions on critical heat flux (CHF) in pool boiling is well investigated, the effect of the properties of the heater material is not well understood. Previous studies indicate that the heater thickness plays an important role on the CHF phenomenon. However, beyond a certain thickness, called the asymptotic thickness, the local temperature fluctuations on the heater surface caused by the periodic bubble ebullition cycle are evened out, and the CHF is not influenced by further increasing the thickness. In the present work, data from literature and pool boiling experiments conducted in this study with seven substrates—aluminum, brass, copper, carbon steel, Monel 400, silver, and silicon—are used to determine the effect of the thermophysical property of the material on CHF for thick heaters that are used in industrial pool boiling applications. The results indicate that the product of density (ρ) and specific heat (cp) represents an important substrate property group that affects the CHF, and that the thermal conductivity is not an important parameter. A well-established force-balance-based CHF model (Kandlikar model) is modified to account for the thermal properties of the substrate. The predicted CHF values are within 15% of the experimental results.

Pool boiling with four non-ozone depleting refrigerants and comparison with previously established correlations

Four high performance fluorocarbon liquids have been investigated for their application in pool boiling. Boiling offers the ability to dissipate large amounts of heat through relatively small areas due to significant heat removal acting through the latent heat of vaporization. Perfluoro-2-methylpentane (PP1), perfluoromethylcyclopentane (PP1C), perfluoro-1,3-dimethycyclohexane (PP3), and perfluoro-2-methyl-3-ethylpentane (PP80) have been employed in a closed loop pool boiling system to determine their performance under atmospheric conditions. The critical heat flux (CHF) and maximum heat transfer coefficient (HTC) found for each was 15.6W/cm2, 16.0W/cm2, 13.4W/cm2, and 14.2W/cm2 and 5.8kW/m2°C, 4.8kW/m2°C, 4.4kW/m2°C, and 4.3kW/m2°C respectively. Each fluid has been tested five times to ensure repeatability. The pool boiling results have been compared with well-established pool boiling correlations from Rohsenow and Stephan and Abdelsalam, and CHF values have been compared with Kandlikar and Zuber’s CHF correlations. All pool boiling models have shown to be reasonably accurate in their predictions. CHF models vary in accuracy depending upon fluid.

垂直下降流の限界熱流束予測モデル

Critical heat flux is one of the most important keys for various systems involving two-phase flow and heat transfer, such as nuclear reactors and boilers. But under downward flow condition, it is very difficult to predict critical heat flux because of complex flow caused by buoyancy. In series studies, obtained critical heat flux for downward flow were classified into four modes, however there are still not enough information about critical heat flux on stagnant region. In this investigation, critical heat flux experiment was carried out on a forced convective boiling system with a stainless steel tube of 15 mm in inner diameter and 200 mm in heating length. As the results, in the stagnant region, critical heat flux occurred in intermittent flow region, and the critical heat flux value was evaluated by a critical heat flux model taking into account of Kelvin-Helmholtz instability. In the high mass flux region, critical heat flux was observed in subcooled region. The obtained critical heat flux could be estimated by a departure from nucleate boiling model with modified departing bubble diameter correlation.

Control of pool boiling heat transfer through photo-induced wettability change of titania nanotube arrayed surface

In the present experimental study, the pool boiling heat transfer performance was controlled and enhanced through the photo-induced wettability change of titania (TiO2) nanotube arrayed surface (TNAS). The TNAS was analyzed using various spectroscopic techniques such as the scanning electron microscopy (SEM), energy dispersive spectrum (EDS), transmission electron microscopy (TEM), and water contact angle (WCA) measurements. The WCA of TNAS was tuned by the ultraviolet (UV) light irradiation time. The increase in UV light irradiation time to TNAS decreased the WCA. Enhanced wetting of TNAS had strong impact on the boiling heat transfer performance. As the WCA of TNAS decreased, the boiling curve was shifted to the right (i.e., higher wall superheat condition) accompanying critical heat flux (CHF) improvement. Measured CHF results of TNAS in the present study were different from those of plain TiO2 surface without the special structures tested in some previous reports. This discrepancy could be caused by the nanotube arrayed structures of the present TiO2 surface. The surface wettability was an important factor to determine the boiling heat transfer of TNAS. The present CHF measurement data were in good agreement with Liaw and Dhir (1989) correlation in the earlier CHF models tested in this work. Based on this study, it was found that the boiling heat transfer can be controlled and enhanced successfully by the photo-induced wettability change of TNAS through the UV light irradiation.

A Discussion of Uncertainty Quantification for CHF as Performed in COBRA-IE

An assessment of the predictive capability of Coolant Boiling in Rod Arrays—Integrated Environment (COBRA-IE) for critical heat flux (CHF) using the 2005 Groeneveld CHF lookup table is presented. The assessment was performed against 13 different open literature CHF experiments that were conducted over a wide range of conditions in various internal flow geometries. Overall, approximately 1300 data points were evaluated.Different methodologies to quantify the uncertainty inherent in the CHF models are discussed in this paper. The simulation techniques, uncertainty methods, and results of two of the methods are provided. A discussion of the appropriate use of the CHF uncertainty methods is included. The results indicate that for the method associated with the largest uncertainty, the average measured/predicted value in CHF is 1.19, and the standard deviation is 0.62. For the second method, similar to the critical power ratio used for boiling water reactors, the average ratio is 0.98, and the standard deviation is 0.13. Finally, a method to translate between the methods is proposed and shown to be accurate. The use of this transformation could permit significant time and cost savings by allowing a single uncertainty assessment to serve two very different analytical needs.

Enhanced pool boiling critical heat flux with a FeCrAl layer fabricated by DC sputtering

During the recent development of Accident Tolerant Fuels (ATFs), FeCrAl has received attention for its excellent high temperature performance and slower reaction kinetics with steam. In this study, we fabricated a FeCrAl layer on top of the metal substrate by DC sputtering. We found that the substrate temperature and sputtering time affected the surface characteristics of the FeCrAl-layered heaters. A substantial increase in surface roughness was realized in the substrate temperature range from 150 to 600°C during DC sputtering. Extensive pool boiling critical heat flux (CHF) experiments were conducted to confirm the effect of the FeCrAl layer on the thermal safety margin of the heaters. Substantial CHF enhancement was achieved for the first time with all types of FeCrAl-layered heaters. The highest CHF enhancement (60%) was observed for the layer sputter deposited for 1h at a substrate temperature of 150°C. State-of-the-art CHF models incorporating the textured surfaces were employed to elucidate the physical mechanism for the improved CHF. The enhanced CHF was attributed to an increase in the roughness factor at the micrometer scale. This, in turn, could have a desirable effect on shortening the rewetting interval with the FeCrAl-layered heaters. Systematic experiments related to the surface characteristics and high-speed bubble departure images were also obtained. This first-of-a-kind CHF enhancement with FeCrAl-layered heaters is expected to find use for an advanced fuel system.