Heat Flux Correlation Research Articles

Heat Flux Correlations for Condensation From Steam and Air Mixtures on Vertical Flat Plates

Abstract In this study, heat fluxes qc for condensation from steam and air mixtures on vertical flat plates were evaluated by using existing experimental data and qc correlations, in order to provide one of boundary conditions for computational fluid dynamics (CFD) analysis in a primary containment vessel (PCV) of nuclear power plants during accident conditions. Existing qc,fc correlations for forced convection condensation overestimated or underestimated experimental data qc,exp measured with the CONAN facility, and a combination of the selected existing qc,fc correlation and the suction correction factor θC was proposed to obtain good agreement between the qc,cal values computed with the combination and the qc,exp values. For natural convection condensation, it was found that the qc,nc values were largely different between those measured in closed vessels with evaporation and condensation and in flow channels with decreasing the mixture velocity, and hence, the present evaluation focused on qc,nc obtained in the flow channels. It was also found that uncertainty became large when the qc,nc values were computed by changing the Sherwood number Shfc in the qc,fc correlation to Shnc for natural convection. The qc,exp values measured with the COPAIN facility were well expressed by the qc,nc correlation proposed by Corradini (1984, “Turbulent Condensation on a Cold Wall in the Presence of a Noncondensable Gas,” Nucl. Technol., 64(2), pp. 186–195), but the published data were few. Therefore, collection of experimental or numerical qc,nc values is necessary in the future.

Heat flux partition based on onset of significant void

The thermal log-law Θ+(y+)=β+2.12log(y+) is valid in flow boiling with a value of β that evolves as the flow develops. Using a multiphase flow cross-literature database, this constant is shown to be βOSV=−7 at the point of onset of significant void (OSV). This means that at the OSV the liquid is at saturation temperature up to y+≃30. The OSV predictions using this model have a similar mean average error as the Saha and Zuber 1974 correlation for one less fitted constant for channel, pipe and annular flows for pressure from 1 to 147 bar and Peclet numbers from 3.5⋅103 to 4⋅105. This model is used to build a heat flux partitioning (HFP) inspired from system-scale codes (Lahey 1978). It predicts the distribution of the heat flux between the liquid phase and the evaporation term when the total heat flux is known. It does not give information on the total heat flux as a function of wall temperature and cannot be used to draw a boiling curve. In imposed flux conditions, this partition provides more coherent flux distribution between the evaporation and liquid terms than Kurul and Podowski (1990) based approaches and improves void fraction predictions in high-subcooling regions on the DEBORA database (Garnier et al. 2001) and on experiments by Bartolomei and Chanturiya (1967) and Bartolomei et al. (1982). When the wall temperature is imposed, it must be coupled with an empirical boiling total heat flux correlation to replace a traditional HFP. The prediction of the total heat flux is then as good as that of the correlation.

Investigation of Surface-Catalycity Effects on Hypersonic Glide Vehicle Trajectory Optimization

The optimization of a hypersonic glide vehicle’s reachable domain is studied using different models to constrain the stagnation-point heat transfer. The vehicle is modeled as a high-lift common aero vehicle that uses bank-angle modulation for crossrange maneuvering with a leading-edge thermal protection system made of an ultra-high-temperature ceramic. A constrained nonlinear optimization problem is formulated to determine the range of feasible trajectories that satisfy aerodynamic heating and loading constraints. The optimal control profile is determined using a modified particle swarm optimization routine that employs a penalty function approach to handle path and terminal constraints. Baseline trajectories are determined using an existing convective heat-flux correlation, and the effect of surface catalycity on the optimized trajectories is investigated by applying a correction factor, derived from high-fidelity computational fluid dynamics simulations, to the heat-flux correlation. Results demonstrate a high sensitivity of the optimized trajectories to the underlying aerothermodynamics model such that accounting for surface catalycity expands the reachability by an order of magnitude.

Self-Assembly and the Properties of Micro-Mesoporous Carbon.

This study introduces a new approach for constructing atomistic models of nanoporous carbon by randomly distributing carbon atoms and pore volumes in a periodic box and then using empirical and ab initio molecular simulation tools to find the suitable energy-minimum structures. The models, consisting of 5000, 8000, 12000, and 64000 atoms, each at mass densities of 0.5, 0.75, and 1 g/cm3, were analyzed to determine their structural characteristics and relaxed pore size distribution. Surface analysis of the pore region revealed that sp atoms exist predominantly on surfaces and act as active sites for oxygen adsorption. We also investigated the electronic and vibrational properties of the models, and localized states near the Fermi level were found to be primarily situated at sp carbon atoms through which electrical conduction may occur. Additionally, the thermal conductivity was calculated using heat flux correlations and the Green-Kubo formula, and its dependence on pore geometry and connectivity was analyzed. The behavior of the mechanical elasticity moduli (Shear, Bulk, and Young's moduli) of nanoporous carbons at the densities of interest was discussed.

Development of a critical heat flux correlation based on an annular film dryout mechanistic model under the annular flow conditions

ABSTRACT This study proposes a mechanistic model-based correlation for the critical heat flux to meet the practical requirements for the design and safety analysis of light water reactors. The correlation is based on an annular film dryout mechanistic model for a single tube, which needs numerical integration from the onset of annular flow to the dryout point, expressed as an explicit non-dimensional equation to ensure a wide applicable range of coolant conditions. The correlation predicts a critical heat flux for the annular flow region in the pressure range of 1–16 MPa, the mass velocity range of 500–3000 kg/m2s, and the thermal equilibrium quality range of 0.05–0.7. The prediction by the developed correlation agrees well with that of the existing mechanistic model without any numerical integration of the annular flow conditions.

Optimization of jet impingement heat transfer: A review on advanced techniques and parameters

The jet impingement heat transfer process promises exceptional heat transfer performances, attracting worldwide attention for cooling potential industrial applications. This cooling or heat transfer process has been determined by various factors and parameters. The several affecting factors include Reynolds number, flow velocity, and impact ratio, are responsible for achieving this goal and are critically reviewed in the present article. Jet impingement heat transfer parameters such as heat transfer coefficient, heat flux, Nusselt number, and cooling rate are also discussed in detail. There are many conflicting results of affecting factors on the heat transfer characteristics found in the literature, but the behavior in the resultant trend of the parameters is the same. In the present review, all the factors and parameters are analyzed for various coolant conditions and surface conditions. Various Nusselt number and heat flux correlations for all conditions corresponding to single and two-phase heat transfer published in the literature are also mentioned in the present review.

Modelling and experimental validation of heat transfer behavior during trans-critical transients

Though designed to be operated in supercritical conditions, supercritical power systems could experience trans-critical transients in which the pressure transfers between supercritical and subcritical condition during startup, shutdown, or accident condition. In the present work the thermal–hydraulic code ATHLET-SC was upgraded to predict the heat transfer behavior during trans-critical procedures. Prediction model of dispersed droplet flow film boiling (DFFB) heat transfer correlation, critical heat flux (CHF) correlation, and the correlation of minimum film boiling temperature TMFB has been upgraded. It is demonstrated by the validation work that the prediction error is large in the inverted annular film boiling (IAFB) regime. However, steady-state IAFB heat transfer experiment at high-pressure condition is unavailable. Hence, a calibration approach to IAFB heat transfer correlation is developed based on trans-critical transient experiment. As validated, the change of the wall temperature during the trans-critical transient gets well predicted by the corrected Bromley correlation.

Critical Heat Flux Condition and Post-Critical Heat Flux Heat Transfer of Carbon Dioxide at High Reduced Pressures in a Microchannel

Abstract Flow boiling heat transfer around the critical heat flux (CHF) condition at high reduced pressures of carbon dioxide in a 296-μm hydraulic diameter microchannel was experimentally studied. The CHF conditions for developing flow and fully developed flow were measured and compared to established correlations. The post-CHF heat transfer coefficient was obtained for l/d of 3.2, 7.4, and 11.6 for inlet Reynolds numbers, based on the homogeneous two-phase flow model, ranging from 6622 to 32,248. The critical heat flux conditions seemed to peak around a reduced pressure of about 0.5 and gradually decreased with reduced pressure. However, the typical rapid increase in the surface temperature following the CHF condition decreased with increasing pressure, and the post-CHF heat transfer coefficient was appreciably high (up to about 50 kW/m2K) at high reduced pressures. The enhancement in the heat transfer coefficient and CHF condition near the inlet were quantified. The experimental results were compared to established CHF correlations and heat transfer coefficient correlations with some limited success. Thus, the Katto CHF correlation (Katto and Ohno, 1984, “An Improved Version of the Generalized Correlation of Critical Heat Flux for the Forced Convective Boiling in Uniformly Heated Vertical Tubes,” Int. J. Heat Mass Transfer, 27(9), pp. 1641–1648) and the Bishop correlation (Bishop et al., 1964, “Forced-Convection Heat Transfer to Water at Near-Critical Temperatures and Supercritical Pressures,” Westinghouse Electric Corp, Atomic Power Division, Pittsburgh, PA.) for the post-CHF heat transfer coefficient were adjusted to better predict the experimental results. Additionally, an enhancement factor was derived to predict the increase in the heat transfer coefficient in the developing region.

Critical heat flux correlations for tube and annulus geometries under inclination and rolling conditions

In floating nuclear reactors, critical heat flux (CHF) prediction is crucial because the CHF can be influenced under heaving, rolling, and inclination conditions, unlike in land-based reactors. Hence, the existing land-based empirical correlations of the CHF can be invalid under some conditions in marine reactors. Therefore, empirical correlations of the flow boiling CHF were developed in this study to predict the CHF under inclination and rolling motions in tubes and annuli. Available experimental CHF data (616 points) were collected including our previous experimental data (405 points) and their trends under marine conditions were analyzed. The CHF variation was expressed using two types of modified Froude numbers depending on the CHF regime—departure from nucleate boiling and dryout. These parameters were used in correlations for the CHF under inclination. CHF correlations under rolling conditions were developed. Rolling was found to attenuate the CHF variation through the inclination. This observation was reflected in the newly developed rolling CHF correlation. The proposed correlations adequately described the existing CHF experimental data under inclination and rolling within an uncertainty of 9.5%. The developed CHF correlations can be used for the safety analysis and reactor core thermal–hydraulic design of marine reactors.

General correlation for critical heat flux during saturated flow across a cylinder

A correlation is presented for prediction of CHF (critical heat flux) during upward flow of saturated liquids across single cylinders. The correlation was verified against all available published test data. It includes six fluids (water, R-12, R-113, methanol, isopropanol, acetone), tube diameter 0.26 - 19.1 mm, reduced pressure 0.0046 - 0.3554, liquid velocities 0.01 - 10.7 m/s, and CHF 0.14 – 10.7 MW/m2. The new correlation predicts 558 data points from 62 data sets from 15 sources with mean absolute deviation of 18.0%. The same data were also compared to seven other published correlations; their MAD ranged from 24.1% to 287.0%.

Assessment and development of flow boiling critical heat flux correlations for partially heated rectangular channels in different gravitational environments

This study investigates critical heat flux (CHF) of n-Perfluorohexane flowing in a partially heated rectangular channel of 2.5-mm × 5.0-mm cross-section, within NASA's Flow Boiling and Condensation Experiment's (FBCE) Flow Boiling Module (FBM). A consolidated FBCE-CHF database is formed by compiling datasets from prior years of testing the FBM both at different orientations in Earth gravity (horizontal flow, vertical upflow, and vertical downflow) and on parabolic flights until it was launched to the International Space Station (ISS) in August 2021. This database encompasses a wide range of operating conditions (both subcooled liquid inlet of different inlet subcoolings and saturated two-phase inlet of different inlet qualities at different mass velocities and system pressures), heating configurations (single- and double-sided inlet), and different gravitational environments. The database is further categorized into three based on the type of CHF: subcooled CHF, saturated CHF with single-phase inlet, and saturated CHF with two-phase inlet. An exhaustive literature search is conducted to identify almost all flow boiling CHF correlations, which are then utilized to make predictions of the database and their accuracies assessed for each small subset of the database. Some correlations are capable of providing adequate CHF predictions for large portions of the database, while some provide very good predictions for very small subsets of operating conditions, typically those for which they were developed for. No single existing correlation is capable of predicting the entire database with good accuracy. Many correlations do not consider the effects of gravity on CHF, which is important for the different orientations tested, and even the few that do, are unsuccessful in predicting the microgravity data. A new simple CHF correlation is developed to address the drawbacks of the existing ones and is easy to use. This new correlation predicts the entire consolidated database with a mean absolute error of 17.44% with good accuracies for each subset of the database.

Development of a Critical Heat Flux Correlation based on a Mechanistic Model under Subcooled Flow Boiling Conditions

In this study, a mechanistic model-based correlation for the critical heat flux is proposed to meet the practical requirements for the design and safety analysis of pressurized water reactors. The correlation is based on a liquid sublayer dryout model for a single tube, which includes physical parameters, such as sublayer thickness and vapor blanket velocity, expressed as an explicit nondimensional equation and modified using a look-up table for critical heat flux to ensure a wide applicable range in coolant conditions. The correlation predicts critical heat flux for the subcooled region under the pressure range of 0.1–18 MPa, mass velocity range of 500–8000 kg/m2s, and thermal equilibrium quality ranging from −0.5 to −0.05 with high accuracy of the departure from nucleate boiling ratio limit based on a 95% probability and a 95% confidence of 1.20.

Improvement of the critical heat flux correlation in a thermal-hydraulic system code for a downward-flow narrow rectangular channel

Several critical heat flux (CHF) correlations including the look-up table in the MARS code have been assessed for the prediction of CHF in a downward-flow narrow rectangular channel. For the assessment, we built an experiment database that covers pressures between 1.01 and 39.0 bar, gap sizes between 1.09 and 6.53 mm, mass fluxes up to 25,772 kg/m2s, and under one-sided and two-sided heating conditions. The results of the assessment showed that the Kaminaga correlation has the best overall prediction compared to others. However, because the correlation uses global variables, such as inlet and outlet subcooling and total heat transfer area, it is difficult to use in a system code. A new CHF correlation is then proposed by replacing the global variables in the Kaminaga correlation with local ones and adding correction factors to consider the effect of gap size, mass flux, and the number of heating walls. Additional correction factor is added to consider the effect of inlet subcooling. It is shown that the new one is better than the Kaminaga correlation and it is easy to implement to any system code.

Visualization experiments and a new correlation of critical heat flux in a narrow rectangular channel

Critical heat flux (CHF) is a crucial factor in ensuring safe operation and improving the economy of the plant. This study carried out a visualization experiment to identify the dominated parameters affecting the CHF in a narrow rectangular channel at different gap sizes (1–5 mm). The experiments were performed at pressures ranging from 1 to 4 MPa, with inlet subcooling ranging from 65 to 120 K and mass flux ranging from 350 to 2000 kg/(m2·s). A large amount of CHF correlations were compared with experimental values, and the results proved that among them Sudo correlation has the smallest prediction error. The Look-up Table method is suitable for predicting CHF in narrow rectangular channels, considering the limitation of the gap size by employing a correction factor. The increase of gap size, system pressure, inlet subcooling, and mass flux contributes to enhancing the CHF values. A new CHF correlation was proposed based on these parameters through step regression method. The comparison between prediction and experimental data demonstrates that the new correlation can accurately predict the CHF in a narrow rectangular channel with a maximum discrepancy of 20%.

Critical Heat Flux Correlations for Tube and Annulus Geometries Under Inclination and Rolling Conditions

Critical Heat Flux Correlations for Tube and Annulus Geometries Under Inclination and Rolling Conditions

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%.

Safety Analysis of 250-kW Philippine Research Reactor-1 Thermal-hydraulics under Steady-state Operations Using MARS-KS Code

Julius Federico M. Jecong1,3,4*, Alvie A. Astronomo2, Frederick C. Hila1, Neil Raymund D. Guillermo1, and Sweng Woong Woo4 1Applied Physics Research Section; 2Nuclear Reactor Operations Section Department of Science and Technology–Philippine Nuclear Research Institute Quezon City, Metro Manila 1101 Philippines 3Nuclear and Quantum Engineering Department Korea Advanced Institute of Science and Technology 291 Daehak-ro, Yuseong-gu, Daejeon 34141 Republic of Korea 4Reactor and Safety Evaluation Department Korea Institute of Nuclear Safety 62 Gwahak-ro, Yuseong-gu, Daejeon 34142, Republic of Korea Safety Analysis of 250-kW Philippine Research Reactor-1 Thermal-hydraulics under Steady-state Operations Using MARS-KS Code Keywords: 250-kW TRIGA reactor, MARS-KS, safety analysis, steady-state, thermal-hydraulics The Philippine Nuclear Research Institute (PNRI) of the Department of Science and Technology (DOST) is implementing a project to use the Philippine Research Reactor-1 (PRR-1) TRIGA nuclear fuel in a subcritical reactor (SCR) for training, education, and research in nuclear science and technology. However, although an SCR is a valuable training and research facility, it offers limited industrial applications. To potentially reap more benefits, DOST-PNRI is also investigating the feasibility of converting the zero-power SCR to a low power critical reactor in the future. In this work, the thermal-hydraulic behavior of a hypothetical 250-kW low power configuration of the PRR-1 TRIGA reactor is investigated using the MARS-KS code. At this power level, the fuel centerline or the hottest region of the fuel was determined to have 236.85- °C temperature during steady-state conditions. This temperature is well below the 749.85-°C temperature limit of TRIGA fuel that will result in excessive swelling. The peak heat flux occurs at the axial center of the fuel rod while the calculated departure from nucleate boiling ratio (DNBR) of 6.18 is minimum at this location. Moreover, the maximum fuel temperature is found to be insensitive to variations in coolant velocity, which ranges from 0.20–0.26 m/s within the natural circulation conditions of this facility. Based on the Bernath critical heat flux (CHF) correlation, coolant velocities below 0.2 m/s will still yield a DNBR above 5.0. These results demonstrate that a 250-kW PRR-1 TRIGA reactor operating under steady-state conditions is capable of safely removing the heat generated in the fuel

Analysis and Solution to Abnormity of DNBR Indicated by ICIS of a WWER Unit

To analyze the reason of difference between the departure from nucleate boling ratio (DNBR) indicated by the upper-level software and lower-level software of the in-core instrumentation system (ICIS) at a certain water-cooled water-moderated power reactor (WWER) unit under its first thermal test during raising power, an investigation was made on the critical heat flux (CHF) correlations adopted in the reactor thermal and hydraulic design and accident analysis of WWER unit. On the above basis, the reason behind the difference was found to be the use of different CHF correlations by the upper-level software and the lower-level software of ICIS through the simulation of thermal tests under 50%, 75% and 90% power level using WWER accident analysis code DINAMIKA-97, calculation of DNBRs and comparison with the ones measured in thermal-hydraulic tests. DNBR under 100% power level was predicted, which coincided with the measured DNBR very well and proved the correctness of the guess further. It is suggested that the CHF correlations adopted by the upper-level software and the lower-level software shall be modified to the same conservative CHF correlation to get a conservative DNBR.

On water-ingression during top-flooding of corium melts

In the course of severe accident in a nuclear power plant, the corium mixture may flow down in the reactor pit and start a thermal attack of the basemat concrete. A simple way to terminate the melt progression may be to add water on top of it. Among the various physical processes that may participate in the quenching, water may penetrate into the solidified corium through cracks generated by the thermal stress during the solidification.The present paper aims at providing a clarification of the process though an analysis of the few dedicated experimental data available using proto-typical corium, namely the SSWICS 1-7 experiments. At first, a general reminder and analysis of the data is given. Then, the thermal-hydraulic aspects are investigated through the construction of a dedicated heat flux correlation and its use via the experimentally measured post-test permeabilities. The analysis is supported by 1D and 2D evaluations with the multiphase flow code MC3D-PREMIX, slightly modified for the purpose. It is concluded that the heat flux drastically decreases with the amount of added concrete material. Furthermore, 2D border effects are investigated and their importance highlighted in view of the experimental results analysed. These effects should explain the absence of observation of water ingression heat flux in the cases with large concrete amounts. Following, the paper proposes a model for the created permeability. Due to the complexity of the process and to the large uncertainties of the needed material properties in the considered situation with very high temperatures, a semi-empirical model is derived.Lastly, the model is adapted to the situation with internal decay heat, although no open experimental data is available to precisely support any model. A complete modeling is out of the scope of the paper, hence the focus is to provide hints for a first analysis of the impact of decay heat on its coolability.

A study on heat flux predictions for re-entry flight analysis

The analysis of the risk from re-entry objects has become an important topic. Concerning the uncertainties and different flow regimes, the object-oriented tools have been developed and used for various re-entry mission scenarios because of the simplified computation process and low calculation burden, which allow a probabilistic analysis. In this study, the heat flux correlations that are used in the object-oriented tools are investigated and compared to better understand the heat flux predictions with respect to re-entry survivability. Often these tools calculate the continuum stagnation-point heat flux using the correlation formulae of Lees and Fay–Riddell, which usually assume local thermo-chemical equilibrium with a fully-catalytic wall condition in the shock layer. Based on this observation, heat flux measurements were conducted in a hypersonic wind tunnel, and validated with the theory of Fay–Riddell considering the equivalent velocity gradient. For the comparison, in total, 11 different heat flux correlations were examined. It is shown that, based on the formula of Fay–Riddell, the differences in the final integrated heat flux were less than 16% which led to a large discrepancy in the survivability estimations for the cases of small spheres made of aluminum. This shows the importance of considering the heat flux correlation as well as the velocity gradient effect for such re-entry analysis.