Prediction Of Critical Heat Flux Research Articles

Derivation of Uncertainty Distributions for Channel Flow Rate and Fuel Critical Heat Flux Predictions for Best-Estimate Plus Uncertainty Analysis of Slow Loss-of–Reactor Power Regulation Accidents in CANDU Stations

Derivation of Uncertainty Distributions for Channel Flow Rate and Fuel Critical Heat Flux Predictions for Best-Estimate Plus Uncertainty Analysis of Slow Loss-of–Reactor Power Regulation Accidents in CANDU Stations

Saturated/subcooled flow boiling heat transfer characteristics for R134a, HFE-7100 and Deionized water inside micro/mini-channels: Part Ⅱ – New CHF prediction model establishment

A new flow pattern map has been developed and presented in Part Ⅰ of this paper for R134a, HFE-7100 and Deionized water inside micro/mini-channels. To further explain the phenomenon and understand the mechanism of triggering critical heat flux (CHF), the theoretical model to predict the CHF of saturated/subcooled flow boiling inside the micro/mini-channels is proposed based on the liquid layer dry-out and Helmholtz instability (intermittent and continuous vapor blanket) theories. Both the effect of the dry-out flows and the liquid sublayer under the vapor blanket were taken into consideration. For saturated and subcooled boiling, the two mechanisms of triggering the CHF were revealed based on different flow patterns and experimental phenomena, respectively. The boiling heat transfer performance has been experimentally investigated under different liquid subcoolings, mass fluxes and geometry parameters. By analyzing the previous models and establishing a database, the comparison of new model predictions with present experimental data shows good agreement within a standard deviation of ± 10 %. Besides, prior CHF data were used to verify this new model, which also presents varying degrees of success in predicting the CHF.

Investigation of Machine Learning Regression Techniques to Predict Critical Heat Flux Over a Large Parameter Space

A unifying and accurate model to predict critical heat flux (CHF) over a wide range of conditions has been elusive since wall boiling research emerged. With the release of the experimental data utilized in the development of the 2006 Groeneveld CHF lookup table (LUT), by far the most extensive public CHF database available to date (nearly 25 000 data points), the development of data-driven prediction models over a large parameter space in simple geometry (vertical, uniformly heated round tubes) can be achieved. Furthermore, the popularization of machine learning techniques to solve regression problems has led to more advanced tools for analyzing large and complex databases. This work compares three machine learning algorithms to predict the CHF database. For each selected regression algorithm (ν-Support vector, Gaussian process, and neural network), a set of optimized hyperparameters is applied. Among the investigated algorithms, the neural network emerges as the most effective, achieving a CHF predicted/measured factor standard deviation of 12.3%, three times less than that of the LUT. In comparison, the Gaussian process regression and the ν-support vector regression achieve a standard deviation of 17.7%, about two times lower than the LUT. Hence, all considered algorithms significantly outperform the LUT prediction performance. The neural network model and training methodology are designed to prevent overfitting, which is confirmed by data analyses of the CHF predictions. Finally, future development directions (including data coverage, transfer learning, and uncertainty quantification) are discussed.

Development and application of data-driven CHF model in system analysis code

In nuclear reactor systems, when the fuel rods reach the critical heat flux (CHF), a sharp increase in fuel temperature occurs due to a drastic reduction in heat transfer capacity, thus posing a considerable risk to the reactor’s safety. Consequently, accurate CHF prediction holds paramount importance in accurately simulating accident scenarios and enhancing the overall safety of reactor systems. To tackle the challenge of limited prediction accuracy in existing CHF models, this study initially established a comprehensive database by utilizing available experimental data and lookup tables. Subsequently, various methodologies, including the Back Propagation Neural Network (BPNN), Random Forest (RF), and Physics-Informed Machine Learning (PIML), were employed to develop multiple CHF prediction models, and their performance was thoroughly evaluated. Furthermore, the optimal CHF model was integrated into the self-developed analysis code ARSAC, which was then validated using the ORNL-THTF experiment. The results indicated that the BPNN-based model not only demonstrated exceptional prediction accuracy but also exhibited rapid calculation speeds. Notably, the average relative error between the experimental data points and the calculation results of the modified code is 3.64%, while for the original code, it is 22.84%. This study effectively leverages the strengths of data-driven approaches, providing a robust technical solution for high-precision, efficient, and adaptive numerical prediction and analysis of reactor accidents.

Two-Phase Particle Image Velocimetry Visualization of Rewetting Flow on the Micropillar Interfacial Surface.

Boiling heat transfer has a high thermal efficiency by latent heat absorption, which makes it an attractive process for cooling electronic device chips. Critical heat flux (CHF), the maximum heat flux, is a crucial factor determining the operating range of the boiling applications. The CHF can be enhanced by improving the fluid supply to the boiling surface. Herein, micropillar interfacial surfaces have been proposed to increase the CHF by increasing the rewetting flow, which determines the fluid-supply capacity near the bubble contact line. A state-of-art two-phase particle image velocimetry (two-phase PIV) technique is introduced for rewetting flow measurement on micropillar structures (MPSs) to analyze the CHF-enhancement mechanism. The two-phase PIV visualization setup offers high spatial (∼120 μm) and temporal (∼2000 Hz) resolutions for measuring rewetting flow during bubble growth. The MPS samples exhibit enhanced CHF and rewetting flows compared to those on a plain surface. The roughest case, D04G10 sample, had a CHF of 164 W/cm2, 1.84 times higher than that of the plain surface. The D04G10 sample also recorded the highest rewetting velocity of 0.311 m/s, 4.7 times higher than that of the plain surface. The comparison between the rewetting flow and wicking performance shows that wicking-induced flow accounted for a substantial part (∼17%) of the rewetting flow and contributed significantly to the CHF enhancement owing to large rewetting flow by delaying vapor-film formation. Based on these findings, a new CHF model suggested by introducing the rewetting parameter shows a high CHF prediction accuracy of 94%.

Machine learning-based model for the intelligent estimation of critical heat flux in nanofluids

The rising demand for advanced energy systems requires enhanced thermal management strategies to maximize resource utilization and productivity. This is quite an important industrial and academic trend as the efficiency of energy systems depends on the cooling systems. This study intends to address the critical need for efficient heat transfer mechanisms in industrial energy systems, particularly those relying on pool boiling conditions, by mainly focusing on Critical Heat Flux (CHF). In fact, CHF keeps a limit in thermal system design, beyond which the efficiency of the system drops. Recent research materials have highlighted nanofluids’ superior heat transfer properties over conventional pure fluids, like water, which makes them a considerable substitution for improving CHF in cooling systems. However, the broad variability in experimental outcomes challenges the development of a unified predictive model. Besides, Machine Learning (ML) based prediction has shown great accuracy for modeling of the designing parameters, including CHF. Utilizing ML algorithms—Cascade Forward Neural Network (CFNN), Extreme Gradient Boosting (XGBoost), Extra Tree, and Light Gradient Boosting Method (LightGBM)— four predictive models have been developed and the benchmark shows CFNN’s superior accuracy with an average goodness of fit of 89.32%, significantly higher than any available model in the literature. Also, the iterative stability analysis demonstrated that this model with a 0.0348 standard deviation and 0.0268 mean absolute deviation is the most stable and robust method that its performance minorly changes with input data. The novelty of the work mainly lies in the prediction of CHF with these advanced algorithm models to enhance the reliability and accuracy of CHF prediction for designing purposes, which are capable of considering many effective parameters into account with much higher accuracy than mathematical fittings. This study not only explains the complex interplay of nanofluid parameters affecting CHF but also offers practical implications for the design of more efficient thermal management systems, thereby contributing to the broader field of energy system enhancement through innovative cooling solutions.

Critical heat flux of liquid hydrogen, liquid methane, and liquid oxygen: a review of available data and predictive tools

Available experimental data dealing with critical heat flux (CHF) of liquid hydrogen (LH2), liquid methane (LCH4), and liquid oxygen (LO2) in pool and flow boiling are compiled. The compiled data are compared with widely used correlations. Experimental pool boiling CHF data for the aforementioned cryogens are scarce. Based on only 25 data points found in five independent sources, the correlation of Sun and Lienhard (1970) is recommended for predicting the pool CHF of LH2. Only two experiments with useful CHF data for the pool boiling of LCH4 could be found. Four different correlations including the correlation of Lurie and Noyes (1964) can predict the pool boiling CHF of LCH4 within a factor of two for more than 70% of the data. Furthermore, based on the 19 data points taken from only two available sources, the correlation of Sun and Lienhard (1970) is recommended for the prediction of pool CHF of LO2. Flow boiling CHF data for LH2 could be found in seven experimental studies, five of them from the same source. Based on the 91 data points, it is suggested that the correlation of Katto and Ohno (1984) be used to predict the flow CHF of LH2. No useful data could be found for flow boiling CHF of LCH4 or LO2. The available databases for flow boiling of LCH4 and LO2 are generally deficient in all boiling regimes. This deficiency is particularly serious with respect to flow boiling.

Prediction of Critical Heat Flux in Tube Bundles With Crossflow

Abstract Evaporators and boilers with flow across horizontal tube bundles are widely used in industries including refrigeration and chemical processing. As yet there is a lack of a well-verified correlation for predicting local or average CHF (critical heat flux) in such bundles. The available data and correlations are reviewed. The available methods for predicting bundle mean CHF were found to be too conservative. More realistic values of bundle average CHF are proposed based on published test data. The author's well-verified correlations for CHF on a single tube with the subcooled and saturated flow at zero quality across it are compared with test data for tubes in tube bundles together with other correlations. The author's correlations agree well with all data while the others fail for data other than their own. The results of the comparison are presented and discussed. The needs for further research are identified.

Data-driven dimensional analysis of critical heat flux in subcooled vertical flow: A two-stage machine learning approach

This study presents a novel two-stage machine learning algorithm that identifies dominant dimensionless numbers for critical heat flux (CHF) prediction, circumventing the limitations of traditional dimensional analysis by integrating the Buckingham Pi theorem with advanced computational methods, including the active subspace method and machine learning. When applied to extensive datasets, including 1438 data points from subcooled departure from nucleate boiling (DNB) conditions and validated against a non-overlapping 24,284-point lookup table dataset, our algorithm effectively discerns and validates the dimensionless numbers critical to the CHF phenomena. Notably, it identifies a significant negative correlation between a newly discovered dominant dimensionless number and the boiling number Bochf = q″w,chf / (G hfg), and introduces a new simplified scaling law for water under earth's gravitational conditions, outperforming existing models with substantial predictive accuracy. This scaling law and the identified dimensionless numbers, derived from an initial dataset of 1438 data points, exhibit exceptional generalization capabilities when validated against a significantly larger dataset of 24,284 points. These findings also emphasize the nonlinear effects of inlet quality on the boiling number Bochf. The contribution of this research lies in its potential to deepen the understanding of CHF based on data-driven fashion, with the potential to enhance thermal management and design optimization across various applications.

Investigation of droplet boiling on superhydrophilic CuO multiscale hierarchical structured surfaces

This work presents the experimental investigation of droplet boiling characteristics on superhydrophilic surfaces. These surfaces are prepared on a copper substrate, and the boiling characteristics are studied and compared with the bare copper surface. Two types of superhydrophilic surfaces exhibiting needle-like (CuO-1) and sheet-like (CuO-2) nanostructures are prepared by the chemical etching oxidation technique. The hierarchical surface structures are characterized by carrying out SEM and XRD analysis. We employ high-speed imaging along with temperature measurement to characterize the heat transfer phenomenon. The surface temperature varies from 100 °C to 190 °C, and the Weber number is maintained constant at 2.78, corresponding to the gentle droplet impact regime. The effectiveness in the heat transfer performance of the different surfaces is characterized by measuring the critical heat flux (CHF) and the Leidenfrost point (LFP), and it is correlated with the surface properties viz. roughness, wettability, and porosity. The superhydrophilic surface alteration reduces the contact angle by about 99.7% compared to the bare surface. This reduction in contact angle corresponds to an increase in Critical Heat Flux (CHF) by 69.95% for CuO-1 and 47.17% for CuO-2, respectively, compared to bare copper. It is also seen that the LFP is delayed on the superhydrophilic surfaces, with an increase in the LFP temperature by 16.67% and 14.28% for CuO-1 and CuO-2 coatings, respectively. The effect of structures on the atomization and formation of secondary droplets is also presented. We report the contact coefficient (kw) for superhydrophilic surfaces for the first time, which is helpful in the theoretical prediction of CHF. These results show that significant improvement in heat transfer can be obtained in spray cooling and hot spot cooling applications without resorting to sophisticated microfabrication techniques.

A knowledge gap analysis for transient CHF prediction within RELAP5-3D

We compare several experimental pool and flow boiling critical heat flux experiments with corresponding computational models developed with RELAP5-3D. Encompassed within this paper are several sensitivity analyses for the boiling heat transfer correlations, critical heat flux (CHF) prediction within RELAP5-3D and the thermal properties of the cladding for experiments in the Transient Reactor Test Loop (TRTL) and Transient Reactor Test (TREAT) facilities. The sensitivity analyses were consistent in determining that there is a large contribution from the critical heat flux multiplier which in this application, accounts for the effects of power transient critical heat flux. Comparison to experimental results of both the TREAT CHF-SERTTA experimental campaign and a University of New Mexico (UNM) pool boiling experimental campaign demonstrate both the under-prediction of transient CHF and nucleate boiling heat transfer. To address the gaps in knowledge regarding the transient heating effect for both boiling heat transfer and CHF prediction, we present an experimental test matrix for the TRTL facility that will isolate the power transient effect under PWR relevant operational conditions. The test matrix will incorporate 6 power pulses with a constant energy deposition and a timescale that spans over several orders of magnitude, including a steady state test with an exponential period of 10 s.

Prediction of Critical Heat Flux during Downflow in Fully Heated Vertical Channels

Boiling with downflow in vertical channels is involved in many applications such as boilers, nuclear reactors, chemical processing, etc. Accurate prediction of CHF (Critical Heat Flux) is important to ensure their safe design. While numerous experimental studies have been done on CHF during upflow and reliable methods for predicting it have been developed, there have been only a few experimental studies on CHF during downflow. Some researchers have reported no difference in CHF between up- and downflow, while some have reported that CHF in downflow is lower or higher than that in upflow. Only a few correlations have been published that are stated to be applicable to CHF during downflow. No comprehensive comparison of correlations with test data has been published. In the present research, literature on CHF during downflow in fully heated channels was reviewed. A database for CHF in downflow was compiled. The data included round tubes and rectangular channels, hydraulic diameters 2.4 mm to 15.9 mm, reduced pressure 0.0045 to 0.6251, flow rates from 15 to 21,761 kg/m2s, and several fluids with diverse properties (water, nitrogen, refrigerants). This database was compared to a number of correlations for upflow and downflow CHF. The results of this comparison are presented and discussed. Design recommendations are provided.

Dependence of critical heat flux in vertical flow systems on dimensional and dimensionless parameters using machine learning

The critical heat flux (CHF) associated with the departure from nucleate boiling (DNB) determines the design and safety aspects of two-phase flow boiling systems. Despite the availability of several predictive tools, within the thermal engineering community, the pursuit of an accurate and robust CHF model remains a significant challenge. In this unique study, we extracted a substantial database from literature to develop machine-learning (ML) models to predict CHF for vertical flows commonly employed in the process industry. The extensive database encompasses 15,006 experimental data points gathered from diverse sources covering wide range of geometric and operational ranges of D, L, P, G, h, and x. This database is then employed to develop five ML – based models, namely Artificial Neural Networks (ANN), K-Nearest Neighbors (KNN), Adaptive Boosting (AdaBoost), Extreme Gradient Boosting (XGBoost), and Random Forests (RF). The selection of optimal input features is conducted by exploring various combinations of both dimensional and dimensionless parameters to identify the most influencing inputs for CHF prediction. The models incorporating features D, L, P, G, h, x, L/D, ρr, We, and BO achieve CHF predictions with Mean Absolute Errors (MAEs) of 8.85 % for the ANN model and 10.39 % for the XGBoost model. The optimized ML models outperformed even the highly reliable CHF correlations and lookup tables. The feature importance analysis of input parameters highlights strong dependence of CHF on dimensionless numbers such as Weber number and Boiling number.

Numerical simulation prediction of critical heat flux for 5 × 5 rod bundle with multiple grid spacers and different cladding materials

The critical heat flux (CHF) is one of the safety standards for core thermal design and is crucial for the normal operation of the reactor. The CHF problem of rod bundles with grid spacers is a hot topic in related research. The successful design of grid spacers can improve channel CHF by affecting the flow of downstream coolant, and this detection analysis can be achieved through numerical simulation methods. In addition, most simulation studies have not considered the solid region of the cladding, so there is little research on the effect of cladding materials on CHF. The role of grid spacers in rod bundle CHF is the focus of this paper, and the influence of cladding materials is another discussion direction. In this paper, following meticulous mesh generation and computational model validation, a study on the CHF of the 5 × 5 rod bundle with multiple grid spacers and different cladding materials is carried out by using CFD software. The verification results indicated that the physical model established in this study can reasonably predict the generation location and critical power value in the 5 × 5 rod bundle with grid spacers. Furthermore, the study identified that the grid spacer exerts a significant influence on coolant flow within the channel, while the weakening of the mixing effect of the grid spacer on the coolant flow is the main factor to lead the boiling crisis upstream of the grid spacer. By comparing the effects of thermal properties of different materials on CHF, it was found that when the thermal conductivity ratio of the two materials is 1.08, CHF is almost identical under the condition of a reference heat flux of 0.1 MW/m2 as a step size. In addition to thermal properties, further attention may be paid to the influence of surface characteristics of materials on CHF in future work.

Prediction of critical heat flux in rod bowing geometries by coupled subchannel analysis and mechanistic model

The penalty of fuel rod bowing on the departure from the nucleate boiling ratio limits must be considered in the thermal–hydraulic design. Different from the traditional penalty factor method, in this study, a relatively strong versatile method is proposed to predict the critical heat flux in rod bowing geometries by coupled subchannel analysis and mechanistic model. A subdivisional subchannel method is used to obtain more detailed local flow parameter and a distributed resistance model for rod bowing is developed to quantify the effect of rod bowing on local flow field. The bubble crowding model is coupled to the subchannel code to predict the CHF of the rod bowing bundles. The results showed that the present method can predict the CHF in rod bowing bundle well, even in the bowed-to-contact geometries. The effect mechanism of rod bowing on CHF is the variation of local parameter and the decrease of hydraulic-diameter.

Prediction of CHF location through applied machine learning

The prediction of critical heat flux (CHF) location is a challenging issue in power generation industries. Several factors viz. geometric parameters and operating conditions influence the occurrence of CHF, and many mechanisms have been proposed to better explain the physics behind the occurrence of CHF. As CHF is a complex phenomenon, its dependency on these factors exhibit non-linear relationship. Further, it is challenging to account for all the factors simultaneously in a single model. Moreover, the benchmark experimental data has to be available to validate the constructed model with all the factors viz., operating pressure and power, inlet mass flux and subcooling etc. Due to these reasons, the influence of these factors remain unresolved. Considering the above issues, the present study employs different machine learning models to predict CHF location and identify the accurate model based on the comparisons against the chosen benchmark experimental data. Becker et al. (1983) data bank was selected for machine learning model training as well as the testing due to the wide range of operating conditions covered. Hyperparameter tuning is applied to optimize the performance of the models. Among all the implemented models, the artificial neural network (ANN) model is found to perform well with the training and the test datasets. The mean absolute percentage error (MAPE) of the training and testing data points are 4.01% and 6.04%, respectively. The accuracy score of the ANN model is approximately 96% for the training and 94% for the testing datasets. The proposed model is helpful for design engineers and analysts of power plants for design optimization and to reduce the computational time.

Prediction of critical heat flux in non-uniform heated rod bundle based on modified CHF empirical correlations

The accurate estimation of critical heat flux (CHF) continues to be a significant challenge in the study of radial and axial non-uniform heated rod bundles under NHR-200Ⅱ operating conditions. The present work develops the subchannel analysis code CTF algorithm that incorporates modified CHF empirical correlations to forecast CHF of non-uniform heated rod bundles preliminarily. The article selected experimental data from HTRF, which includes both uniform heated and non-uniform heated rod bundle CHF experiments, for preliminary validation and analysis of this method. The results demonstrated that the predicted results of modified Barnett correlation have the good agreement with the experimental values. Additionally, the modified Barnett correlation is used to predict the CHF of rod bundles under various power distribution. In different radial power distribution, the critical power of rod bundles decreases with the increase of radial power factor ratio. In different axial power distribution, the critical power in inlet and outlet peak distribution is lower than uniform heated rod bundle. Regarding the case of radial uniform heating and axial inlet peak distribution, CHF locations often occur near the central section of the heated rod height. In the axial intermediate peak distribution, CHF positions often emerge in the intermediate and downstream sections of the heated rod to the outlet. In a typical operating scenario of the NHR-200II, the CHF will occur towards the exit of the hot central subchannel, particularly near the radial heated rod exhibiting the maximum thermal power. The occurrence of CHF can be attributed to factors such as lower mass flux, higher local equilibrium quality, and heat flux.

Prediction of critical heat flux and position in narrow rectangular channels using deep feed-forward neural networks coupling with empirical correlations

The critical heat flux (CHF) is a crucial thermo-hydraulic parameter or phenomenon in boiling heat transfer in many industry applications. For a long narrow rectangular channel, a fundamental heat transfer unit in the nuclear industry, the CHF is hard to measure and predict owing to the large aspect ratio (>1000) in geometry. Current technologies can only predict the value of CHF. Still, they cannot predict where the CHF occurs (the positions occurring dry out in narrow rectangular channels) in the large aspect ratio narrow rectangular channel. In this study, we establish a nonlinear relationship between CHF values and their specific occurrence locations under various operating conditions (various inlet mass flow rate, inlet temperature, wall heat flux density) using deep feed-forward neural networks (DFNN) coupled with CHF empirical correlations. Compared with the traditional empirical correlation method and the neural networks (NN) method, the new proposed method can predict both the value of CHF and the specific location where the CHF occurs. By inducing the empirical correlations into the neural networks, the prediction error decreases from 10% to 5% compared to the traditional NN methods. This work aims to provide a predictable and controllable strategy for CHF in narrow rectangular channels.

Heat transfer incipience of capillary-driven liquid film boiling

High-power electronic devices bring both unprecedented challenges and great opportunities to two-phase cooling technologies for efficient thermal management. Capillary-driven liquid film boiling with wicking structures combines the advantages of capillary evaporation and nucleate boiling, and thus could be one of the most promising cooling methods. However, a comprehensive understanding of liquid film boiling mechanism is lacking. For example, the current prediction of liquid film boiling incipience is based on the bubble nucleation model utilized in pool boiling, which assumes that bubbles nucleate inside the thermal boundary layer with linear temperature distribution due to heat conduction. In liquid film boiling, heat transfer processes are quite different, including both heat conduction inside the liquid film and evaporation at the liquid-vapor interface. In this work, based on the thermal resistance network considering evaporation at thin-film region near the tri-phase line, we develop a model to predict liquid film boiling incipience. Both visualization and heat transfer experiments are conducted using copper micromesh to validate this model. The model predictions of critical liquid film thickness, surface superheat, and heat flux at the onset of nucleate boiling (ONB) are compared with the experimental data on various wicking structures in the literature, including silicon micropillar, copper micropowder, and copper micromesh. The results show that the heat flux and superheat reduce as the wick thermal conductivity decreases, the wick thickness increases, and the wick porosity increases.

Enhanced liquid replenishment for pool boiling heat transfer and its CHF mechanism on patterned freeze-casted surfaces

In the current investigation, the pool boiling heat transfer process of patterned porous surfaces, as well as a smooth surface, in ethanol was examined from an academic perspective. The freeze casting (also known as ice-templating) processes was used to fabricate the structured surfaces. It was discovered that freeze-casted coatings significantly improved the performance of boiling heat transfer in comparison to the smooth surface (SMS). The most remarkable increase in Critical Heat Flux (CHF) was achieved by checkerboard porous surface(CHECKERBOARD), with an improvement of 81.6% relative to that of SMS. The maximum Heat Transfer Coefficient (HTC) enhancement was obtained by full porous surface (FULLY-COVERED), with an HTC value 215.8% higher than that of the SMS. For the semicircular porous surface (SEMICIRCULAR), striped porous surface (STRIPED), annular porous surface (ANNULAR) and checkerboard porous surface(CHECKERBOARD) with 50% coating coverage, CHECKERBOARD demonstrated the best heat transfer performance, with CHF and HTC increased by 32.3% and 48.9%, respectively, compared to the SEMICIRCULAR surface. The mechanism of liquid supply at the CHF of the patterned porous surfaces was investigated through phenomenological observations of the boiling phenomena. A modified model, accounting for the coalesced bubble departure frequency and capillary wicking effects, was proposed for CHF prediction. It is noteworthy that the fluid replenishment considers both vertical and lateral replenishment of porous coatings. The CHF data from this study, along with existing literature, were utilized to validate the model, and the predicted results exhibited good agreement with the experimental data, with errors within ±8%.