Critical Heat Flux Data Research Articles

Development of a dimensionless rod-bundle CHF correlation based on stepwise regression method, Part II: determination of correction factors accounting for the effect of unheated guide tube and non-uniform axial heat flux profile

Correlation for rod-bundle critical heat flux (CHF) is of vital importance for design and assessment of a Pressurized Water Reactor (PWR). In our previous study, the basic form of a dimensionless rod-bundle CHF correlation has been developed based on stepwise regression with CHF data obtained in test bundles of uniform axial heat flux. It proves that stepwise regression is an effective method to develop simple, but reliable CHF correlation consisting of only dimensionless parameters with rigorous physical meanings. As a continuation of the previous investigation, revision of the basic form was conducted. Dimensionless correction factors accounting for the cold-wall effect due to unheated guide tube and the effect of non-uniform axial heat flux were developed. For the data set of 486 rod-bundle CHF points obtained in 7 test bundles, the average ratio of the measured to predicted CHF is 1.002 with a standard deviation from the mean of 5.51%.

Fluid-to-Fluid modelling of CHF at High-Pressure subcooled water conditions

An experiment was carried out to obtain data on critical heat flux (CHF) in an 8-mm vertical heated tube cooled with Refrigerant (R-134a) at high-pressure subcooled and low-quality conditions. Parametric trends of the CHF data were examined and have been shown consistent with those obtained in experiments with water flow. Variations of CHF depends mainly on local flow conditions and the length effect appears to be diminished at length-to-diameter (L/D) ratios from 30 to 200. The Katto scaling law has been shown applicable for transforming R-134a CHF values into water CHF values at subcooled and low-quality conditions. The R-134a CHF data have been transformed using the Katto fluid-to-fluid scaling law and assessed against the water CHF values obtained from the 2006 CHF look-up table (LUT-2006). The results showed that the LUT-2006 is conservative and need further development.

Experimental investigation on the flow CCD by analogically utilizing the CHF correlation

We simulated the critical heat flux (CHF) of flow boiling using the hydrogen evolution at a water electrolysis. Hydrogen bubbles were evolved at the cavities of the cathode surface just like the vapor bubbles in boiling. Critical current density (CCD) was reported similarly where the hydrogen film is formed on the cathode surface. The influences of mass flux and inclination on the CCD on a downward-facing surface were investigated, for which CHF data have not been sufficiently accumulated. The measured CCD increased as the mass flux increased and decreased as the inclination became more horizontal. The photographic analysis showed similar trends of the CCD and CHF conditions with respect to the test parameters. However, the superficial gas velocity at the CCD condition was lower than that at the CHF condition, and sensitivity of the mass flux on the CCD was also less than that of the CHF. A set of correlations were developed as the function of mass flux and inclination. The present work reveals the possibility of experimental simulation of the CHF condition using the CCD condition.

Evaluation of nanofluids for enhancing critical heat flux for in-vessel retention during sever reactor accidents

ABSTRACT In-vessel retention (IVR) of a molten core through external cooling of the reactor vessel is a severe accident management strategy at nuclear power plants. The enhancement of critical heat flux (CHF) is one of the measures to improve the success probability of IVR. A nanofluid, in which nanoparticles are dispersed in a liquid, is known to reliably enhance CHF, mainly under pool boiling conditions. However, to apply nanofluids to IVR, it is necessary to clarify the effect of CHF enhancement under convection boiling similar to that in an actual IVR event. Therefore, CHF tests were conducted using a rectangular test section 50 mm wide × 50 mm deep × 600 mm long under conditions simulating severe accidents. From the CHF data obtained for various nanofluid parameters under typical severe accident conditions, each parameter’s effect on CHF enhancement was clarified. It was found that CHF was improved by 50% or more by a nanofluid as compared with deionized water. Furthermore, the CHF of nanofluid obtained in the tests simulating the actual severe accident conditions increased from 30% to 50% compared with that of deionized water, suggesting that CHF can be enhanced by nanofluids even in an actual plant.

Mechanistic critical heat flux prediction for in-vessel retention conditions

In-vessel retention (IVR) is considered a feasible technique to keep reactor pressure vessel (RPV) integrity in a severe reactor accident. For light water reactor (LWR), the effectiveness of this strategy relies soundly on the critical heat flux (CHF) distribution over the external surface of the lower plenum of RPV, whose orientation varies gradually from downward-facing horizontal to vertical. The CHF prediction capability of the liquid sublayer dryout model is efficient for high mass flux in vertical flow boiling conditions. This paper focuses on how to adapt the model to the changed orientation of the heating surface. Bubble departure diameter (dB) and net vapor generation point (NVG), the starting point for the void fraction developing in a heating channel, is one of the important key points in the CHF prediction. Therefore, to assess the predictive potential of CHF under IVR, experimental research was performed to measure bubble departure diameter and NVG for a changing heating surface orientation from downward-facing horizontal to vertical with a mechanistic model basing on the force balance. A modified liquid sublayer dryout model was then proposed where the channel orientation effect is considered to measure the bubble departure diameter (vapor blanket diameter) using the improved force balance model. The NVG is modified according to the departure diameter. The predicted departure diameter and subcooling at NVG show good consistency with the experimental data, and the modified liquid sublayer dryout model can predict the CHF data with an average relative error of 18.36% in IVR.

Developing a robust and flexible smart tool to predict a full range Critical Heat Flux (CHF) in different LWRs by using deep learning Artificial Neural Networks (ANN) via parallel multi-processing

In this paper, a practical smart tool has been developed to predict CHF in LWRs. The tool is based on the strengthen cascade feed forward ANNs in addition of some of the deep learning features. The most complete experimental CHF data available for LWRs are chosen as the training and test data sets. Input layer can get different thermodynamic qualities, mass flow rates, and pressures to predict the CHF. Then it gains a full range CHF simulator for LWRs fortunately covering both anticipated and unknown transients. Although training such a huge ANN structure and the huge training data set is time consuming, but after the training it acts fast especially via a multi-processing platform. Results are quite satisfactory due to the very good network performance and regressions. Briefly, this is a fast, flexible, and robust tool to predict the CHF deep inside the physics of the most broadening CHF data set ever published for the LWRs.

Experimental Study of Critical Heat Flux During Pool Boiling on Mini Tubes: Effect of Subcooling, Orientation, and Dimensions

Pool boiling is cost-effective, simple and prevalent amongst all available cooling schemes. The lack of quantitative data, qualitative theories and explanations in the area of critical heat flux (CHF) in mini tubes makes it an interesting domain of research. This paper discusses the effect of heater length, diameter, orientation and subcooling on CHF. There is the scarcity of literature that considers all the effects altogether. This paper analyses the effect of all the parameters together in a single study. SS304 mini tubes of 2.5- and 1.2-mm diameters with various lengths are used as a heater in horizontal and vertical orientations. The water pool is kept at 30, 50, 75 °C and saturation temperature. The study is performed at atmospheric pressure. It has been observed that with the increase in pool temperature, the magnitude of CHF decreases. The shortest length has a higher magnitude of CHF corresponding to a given pool temperature. The values of CHF decrease with an increase in tube diameter. The CHF value is higher for horizontal as compared to vertical orientation. An empirical correlation, including the effect of subcooling, orientation and tube dimensions is derived from the CHF data. The experimental data is presented in a tabulated form to contribute to pool boiling CHF databank.

Investigation of the critical heat flux in small-diameter channels

The paper describes experimental studies into the hydrodynamics and heat exchange in a forced water flow in small-diameter channels at low pressures. The timeliness of the studies has been defined by the growing interest in small-size heat exchangers. Small-diameter channels are actively used in components of compact heat exchangers for present-day engineering development applications. The major difficulty involved in investigation of heat-transfer processes in small-diameter channels consists in the absence of common methodologies to calculate coefficients of hydraulic resistance and heat transfer in a two-phase flow. The channel size influences the heat exchange and hydrodynamics of a two-phase flow as one of the determining parameters since the existing internal scales (vapor bubble size, liquid droplet diameter, film thickness) may become commensurable with the channel diameter, this leading potentially to different flow conditions. It is evident that one cannot justifiably expect a change in the momentum and energy transfer regularities in single-phase flows as the channel size is reduced for as long as the continuum approximation remains valid. The authors have analyzed the experiments undertaken by Russian scientists to investigate the distribution of thermal-hydraulic parameters in channels with a small cross-section in the entire variation range of the flow parameters in the channel up to the critical heat flux conditions when the wall temperature increases sharply as the thermal load grows slowly. The experimental critical heat flux data obtained by Russian and foreign authors has been compared.

Numerical investigation of the CHF in a vertical round tube and a single rod channel based on the eulerian two-fluid model

The critical heat flux (CHF) is essential to the operational safety of nuclear power plants (NPP), and it plays a vital role in the thermal-hydraulic and structural design of a fuel assembly. In this study, the commercial computational fluid dynamics package STAR-CCM+ was used to predict the departure from the nucleate boiling (DNB) phenomenon. Based on the Eulerian two-fluid model and the extended Rensselaer Polytechnic Institute (RPI) wall boiling model combined with the Weisman-Pei bubble crowding model, the DNB phenomenon was investigated for two coolants (water and R134a) with different geometric structures and working conditions. The results demonstrated that one set of Eulerian two-fluid models could accurately predict the CHF within a certain range of working conditions. The CHF value calculated in this study show good agreement with the experimental measured CHF data, which indicated that the Eulerian two-fluid model had a good application prospect for CHF prediction. The observed mean error was less than 10%. The results of this study may contribute to an advanced boiling model development for CHF prediction in complex geometric structures such as fuel assembly. In addition, these results demonstrated that it was feasible to use the refrigerant R134a, which had a low critical pressure and low latent heat of vaporization, as the modeling fluid to replace water, which had a high latent heat of vaporization and a high critical pressure in the experimental study.

Upstream Critical Heat Flux and Its Design Implications

While most critical heat flux (CHF) studies focus on relatively straightforward geometries, actual equipment applications are complex. This paper summarizes literature which provides insights into the effects of selected inlet conditions on CHF and the occurrence of upstream CHF. Vertical smooth bore tube CHF tests found that the concept of “local conditions hypothesis”, though not universally defensible, provides an adequate basis for applying CHF data to design. Upstream CHF indications have been found to be associated with a minimum in the CHF versus quality curve which has been attributed to the transition from intermediate flow regimes to annular flow regimes. Design implications are discussed including: 1) for vertical smooth bore tubes, upstream CHF is generally not observed except at very high masses where specific data are required - at lower mass fluxes, special design procedures are needed where nonuiform circumferential heating is present, 2) for inclined smooth bore tubes, design specific data are needed as upstream CHF observations are more prevalent, 3) for vertical and inclined multi-lead ribbed bore tubes (common in the power industry), minimum mass fluxes are specified to avoid upstream CHF, and 4) coiled and serpentine tubes are discussed.

Critical Heat Flux (CHF) Correlations for Subcooled Water Flow Boiling at High Pressure and High Heat Flux

The subcooled water flow boiling is beneficial for removing the high heat flux from the divertor in the fusion reactor, for which an accurate critical heat flux (CHF) correlation is necessary. Up to now, there are many CHF correlations mentioned for subcooled water flow boiling in the open literatures. However, the CHF correlations’ accuracies for the prediction of subcooled water flow boiling are not satisfactory at high heat flux and high pressure for reactor divertor. The present paper compiled 1356 CHF experimental data points from 15 independent open literatures and evaluated 10 existing CHF correlations in subcooled water flow boiling. From the evaluation, the W-2 CHF correlation performs best for the experimental CHF data in all existing critical heat flux correlations. However, the predicted mean absolute error (MAE) of the W-2 correlation is not very ideal for all database and the MAE of the W-2 correlation is from 30% to 50% for some database. In order to enhance the CHF prediction accuracy in subcooled water flow boiling at high heat flux and high pressure, the present paper developed a new CHF correlation. Compared with other existing CHF correlations, the new CHF correlation greatly enhances the prediction accuracy over a broad range of pressures and heat fluxes which are desired in the cooling of high heat flux devices, such as those in the fusion reactor divertor. The validation results show that the new correlation has a MAE of 10.05% and a root mean squared error (RMSE) of 16.61%, predicting 68.1% of the entire database within ±10% and 81.5% within ±15%. The MAE of the new CHF correlation is 7.4% less than that of the best existing one (W-2 correlation), further confirming its superior prediction accuracy and reliability. Besides, the new CHF correlation works well not only for a uniform power profile but also for a non-uniform power profile in subcooled water flow boiling at high pressure and high heat flux.

Recommendation for prediction of pool boiling heat transfer of various liquids on microstructured surfaces

Recommendations for prediction heat transfer coefficients and critical heat flux according to available in the literature experimental data of heat transfer and critical heat flux for boiling different liquids on microstructured surfaces made by deformed cutting method are obtained. In the work, on available in the literature sources of experimental data on heat transfer and critical heat flux at boiling of various liquids on the microstructured surfaces made by the deforming cutting method, recommendations for prediction of heat transfer coefficients and critical heat fluxes are received. Microstructured surfaces allow to intensify the heat transfer is 1.1 to 6 times. Due to the variable wettability of microstructured surfaces elements, critical heat flux increase before 4 times. The proposed criteria equations allow predicting heat transfer coefficients with an error of 30%, and critical heat fluxes with an error of 30-35%. In order to improve the accuracy of forecasting, the possibility of using an artificial neural network model for generalizing heat transfer coefficients is shown. Forecasting using an artificial neural network model allows us to determine the heat transfer coefficients with an error of ±20%.The equations are of interest for designing cooling systems for microelectronic devices, heat and mass transfer devices, boiling zones of heat pipes and thermosyphons, etc.

Universal Critical Heat Flux (CHF) Correlations for Cryogenic Flow Boiling in Uniformly Heated Tubes

Experiments to determine critical heat flux (CHF) for cryogen flow in uniformly heated, round tubes have been performed throughout the globe during the past sixty years. However, experimental CHF data for cryogens are rarely published, remaining in the archives of authors, or in obscure technical reports of an organization or other inaccessible sources. In the present study, the Purdue University-Boiling and Two-Phase Flow Laboratory (PU-BTPFL) Cryogen Flow Boiling CHF Database is consolidated from world literature dating back to 1959. With 2312 data points for LH2, LHe, LN2 and LCH4, it represents the largest cryogen CHF database assembled to date. The database encompasses diameters from 0.5 to 14.1 mm, critical length-to-diameter ratios from 2.5 to 230.8 (term ‘critical’ refers to axial location where CHF is detected), system pressures from 0.01 to 4.07 MPa, reduced pressures from 0.1 to 0.93, mass velocities from 2.2 to 8203.9 kg m−2 s−1, inlet subcoolings from 0 to 78.9 K, inlet qualities from -2.06 to 0.95, critical subcoolings from 0 to 48.5 K, critical qualities from -1.23 to 1.00, critical void fractions from 0 to 1, and CHF values from 0.05 to 8203.9 kW m−2. The consolidated database represents an invaluable tool for development of CHF correlations – a primary goal for the present study – as well as future analytic and computational models. Using this database, new universal CHF correlations are constructed for two distinct CHF mechanisms, Departure from Nucleate Boiling (DNB) and Dryout, after careful physics-based segregation of the data. With mean absolute errors below 30%, the new CHF correlations are shown to provide good predictive agreement with the database.

Pool boiling critical heat flux studies of accident tolerant fuel cladding materials

Pool boiling experiments have been performed at atmospheric pressure on potential accident tolerant fuel (ATF) cladding materials (Zirlo®, Cr coated Zirlo®, FeCrAl coated Zirlo®, and monolithic SiC) to evaluate the Critical Heat Flux (CHF) points. Corrosion resistant coatings of Cr and FeCrAl alloy were deposited on flat Zirlo® samples using cold spray technology. The as-prepared samples after uniform surface polishing were subjected to autoclave tests at 360 °C water and 18.6 MPa for 360 h to simulate prototypic corrosion of the ATF cladding materials in LWR normal operation. Surface characteristics potentially influencing CHF such as surface morphology, roughness, static contact angle, and surface chemistry were characterized using a suite of characterization methods including scanning electron microscopy, 3D optical profilometry, optical contact angle measurements, and x-ray photoelectron spectroscopy (XPS). Thermo-physical properties of the samples such as density, thermal conductivity, and heat capacity were measured by differential scanning calorimetry and laser flash thermal diffusivity measurement. FeCrAl coatings showed CHF values comparable to bare Zirlo® samples, while slightly lower CHF values were observed for Cr coated samples and bulk SiC flats (produced by chemical vapor deposition, CVD). As-deposited Cr coatings showed 67% higher CHF than the as-polished Cr coatings due to its higher surface roughness level. The autoclave testing for the prepared samples generally increased the CHF except for the surface polished Cr coatings. Similar CHF values of bare Zirlo®, FeCrAl coating, and CVD SiC samples were observed after autoclave test but there were negligible change CHF of Cr coatings. XPS studies indicated that the formation or deposition of a few monolayers of hydrophobic carbonaceous species on surface can affect CHF values. The trends in CHF data are discussed in terms of evolution of the surface characteristics of the ATF materials.

Investigation of flow distribution and effect of aspect ratio on critical heat flux in multiple parallel microchannel flow boiling

In this paper, an experimental study on the effect of the low aspect ratio of microchannel on the critical heat flux (CHF) during saturated flow boiling of water is presented. Multiple parallel silicon microchannels with different aspect ratios, hydraulic diameter, and number of channels in the range of 0.2–0.5, 154.0–184.8 μm, and 3–9 respectively are fabricated, and the experiments are performed in the range of mass fluxes 24.1–806.5 kg m−2 s−1. It is found that the CHF is caused by the wall dryout near the microchannel exit. The effect of microchannel aspect ratio with the same hydraulic diameter on the CHF is found to be insignificant. Twenty-five CHF data points are obtained for microchannel flow boiling of water and are compared with the CHF predictive methods reported in the literature. A new CHF correlation is proposed, which predicts the measured CHF with the mean absolute deviation of 12.1%, which is substantially better than available CHF predictive methods. The findings from this study provide guidelines for designing multiple parallel microchannel heat sinks in two-phase flow for the thermal management of electronic equipment, spacecraft, satellites, energy conversion devices, and biomedical engineering.

Experimental correlation for critical heat flux in helical coils

The present work experimentally investigated the Critical Heat Flux (CHF) phenomena in helical coils. Literature on the CHF in helical coils is scarce. The centrifugal force and hence secondary flows of fluid is generated inside the coil due to its curvature. The Secondary flows of fluids may affect the heat transfer mechanism and hence, CHF inside helical coils. In present work, the experimental CHF data is compared with correlation available in literature. Fifteen empirical CHF correlations, that include correlation developed for straight horizontal tubes and helical coils, are compared with the experimental CHF databank. The CHF databank contains 413 CHF data of different helical coils. The data includes two fluids namely refrigerant R123 and water. Data covers the parameter range of tube diameter 5.5–10 mm, coil to tube diameter ratio 14–58, mass flux 92–2062 kg/m2s, heat flux 37–2984 kW/m2, density ratio 31–1352 and exit quality −0.1 to 1.2. The data mainly covers CHF in redeposition zone. The helical coil correlations are working reasonably well for long length helical coils but not working for short length helical coils. The straight tubes correlations are working reasonably well for all helical coils data. A generalised correlation is suggested for CHF in helical coils. The experimental data of CHF is published to contribute to the databank for helical coils.

Experimental study for critical heat flux in 2x2 rod bundles at high pressure conditions

Critical heat flux (CHF) phenomena has been a topic of study for over fifty years yet remains a serious concern across industries and especially in water-cooled nuclear reactor design. CHF data in the high-pressure range is limited, and the effects of bundle geometry and non-uniform heat flux profile are challenging to quantify. In this study, CHF experiments were performed in upward flowing water in a 2 × 2 rod bundle with a cosine profile heat flux. Data were collected between 16.5 and 18 MPa at two mass flux conditions with three inlet subcooling conditions. Under these conditions, average CHF was shown to decrease with increasing pressure. However, pressure had less of an effect than decreasing the inlet subcooling or the mass flux, both of which reduce the CHF value considerably. Interestingly, correlations that have been developed for lower pressure continued to predict CHF occurrences with moderate accuracy outside their ranges of validity. Nearly all predicted values were within 20% of experimental values.

Development of critical heat flux correlation for In-vessel retention

ABSTRACT In-vessel retention (IVR) is a strategy for severe accident management in which the lower head of the reactor vessel is submerged in a water-flooded reactor cavity. Critical heat flux (CHF) data for IVR are important for estimating cooling capacity of the reactor vessel. The existing CHF data for IVR which were obtained for the specific geometries and thermal-hydraulic conditions of actual plants are difficult to be applied to plants with other specifications. Hence, the purpose of this study is to develop CHF correlations applicable to various pressurized water reactor plants in a wide range of thermal outputs based on newly obtained CHF data. A rectangular test section with a cross-section of 150 mm × 150 mm and length of 600 mm was used for simulating a cooling channel. The thermal-hydraulic conditions expected in actual plants were studied, and the results were used in the experiment. The effects of parameters such as pressure, mass flux, thermodynamic quality, and angle on CHF were investigated . Based on these results, we developed a CHF correlation formula that can be applied to a wider range than previously, up to a maximum heat flux of 3000 kW/m2, and that predicts CHF with an error of ± 10%.

Development of a dimensionless rod-bundle CHF correlation based on stepwise regression method, Part I: determination of the basic form with CHF data obtained with uniform axial heat flux profile

Accurate prediction of rod-bundle critical heat flux (CHF) is a main challenge in thermal-hydraulic design and safety assessment of Pressurized Water Reactor (PWR). The most widely applied approach is empirical correlation developed based on rod-bundle experiments carefully tested with geometry and power distribution representative to PWR working conditions. The standard procedure is to correlate the experimentally obtained CHF values as empirical functions of local thermal-hydraulic conditions obtained with subchannel analysis. However, up-to-date empirical correlations developed according to this manner are in general quite complicated with a number of dimensional coefficients and correction factors with less or non-physical meanings. In this study, stepwise regression method was used to develop a novel, dimensionless rod-bundle CHF correlation covering typical PWR working conditions. First, various dimensionless parameters affecting CHF were selected as candidate independent variables. With stepwise regression, the form and coefficients of the proposed CHF correlation were dynamically optimized and determined.

Critical Heat Flux Model for Vertical Annular Mist Flow Conditions in a Rod Bundle

As part of its design certification effort, NuScale Power has completed a series of low mass flux [<1000 kg/(m2‧s)] critical heat flux (CHF) tests for a wide range of pressures at Stern Laboratories in Canada. Earlier studies have demonstrated that under annular flow conditions, disturbance waves with circulating vortices traverse the rod surface. The disturbance wave slides over and significantly influences energy transport in the co-current vapor-liquid sublayer at the heater interface. This paper describes the mechanisms leading to the onset of CHF in a vertical rod bundle experiencing annular mist flow conditions. The paper presents a new CHF model that implements a local disturbance wave velocity. A comparison of the model to the U1 CHF data set from Stern Laboratories shows excellent agreement over the full range of annular mist flows, pressures, and subcooled conditions for the specific spacer grids implemented in the study.