Two phase critical flow in capillary tubes and short channels is governed by coupled effects of flashing, acceleration, friction, inlet state, and fluid properties, making compact mass flux scaling difficult. This study develops a momentum equation inspired dimensionless learning framework for circular capillary tube and short channel flows. A traceable multi source database is constructed from published measurements and reduced using consistent geometry, inlet state, thermophysical property, and target variable definitions. Literature correlations are first evaluated with a unified validation procedure to distinguish physical applicability from algebraic evaluability. Dimensionally homogeneous candidate forms are then screened using mutual information. In addition to a conventional power product family, a two group form is introduced to separate an effective driving coordinate from an effective resistance coordinate. The selected simplified correlation gives a mass flow rate MAPE of 6.029% for 7884 equal area circular records. When the channel category is known, the long capillary and short channel correlations give MAPE values of 5.061% and 8.278%, respectively. Compared with the power product baseline, the selected simplified two group form reduces MAPE by 39.28% for all equal area circular channels and 24.39% for short channels. Perturbation tests show robust behavior near the fitted domains, with stronger perturbations mainly broadening prediction ratios rather than causing widespread nonphysical behavior. This work provides an interpretable route for correlation selection and reliable critical mass flux prediction in circular capillary tubes and short channels.

To improve the stable output of solar thermal power generation under fluctuating irradiation, this study proposes a power generation system coupling sand thermal storage with a supercritical carbon dioxide (sCO2) recompression Brayton cycle. A closed-loop compressed-air circuit extracts heat from the packed-bed sand tank and supplies stable heat to the sCO2 cycle through a primary heater. A steady-state thermo-economic model is developed for the coupled sand heat-release and sCO2 power-generation system, while a one-dimensional segmented model is used to evaluate the heat transfer, pressure drop, and metal volume of printed circuit heat exchangers (PCHEs). Multi-objective optimization is conducted using NSGA-II to maximize system net efficiency and minimize total exergy destruction rate and total construction cost. The results show clear trade-offs among efficiency, irreversibility, and cost. The equal-weight TOPSIS compromise solution achieves a system net efficiency of 31.99%, a total exergy destruction rate of 6.88 MW, and a total cost of 30.26 MUSD, indicating a balanced design among thermodynamic performance, exergy utilization, and system economics. Key-variable analysis shows that recompression split ratio, minimum discharge sand temperature, and low-side pressure strongly affect the Pareto front. In contrast, turbine inlet temperature is not monotonically beneficial because its effect is constrained by the sand temperature level and primary-heater matching. Sensitivity analysis further indicates that air-side PCHE Reynolds number and closed-loop air pressure strongly influence pressure drop, auxiliary power consumption, and system economics. These results provide guidance for the coupled design of sand thermal storage systems and sCO2 power cycles.

Two-phase heat transfer loops are a promising technology for spacecraft thermal management due to their efficient heat dissipation, long-distance heat transport capability, and precise temperature control. A critical parameter in designing these systems is the critical heat flux (CHF), which is sensitive to gravitational conditions. Validating CHF under varying gravity levels, however, is experimentally challenging and costly. Similarity criteria offer practical alternatives, enabling ground-based scaled experiments to simulate microgravity phenomena, though existing criteria lack universality and quantitative rigor. This study applies a data-driven dimensional analysis method, integrating the Buckingham Pi theorem with the active subspace approach, to systematically investigate CHF under microgravity conditions. Based on a comprehensive dataset of 2298 points, two dominant dimensionless numbers were identified, with the most influential number exhibiting a clear power-law correlation with the boiling number (BoCHF) and a subtle gravitational dependency (proportional to g0.06). The derived gravity-dependent similarity criterion enables effective laboratory-scale modeling of CHF behavior under microgravity, potentially reducing reliance on costly space-based experiments. The findings offer a practical foundation for enhancing thermal management system design in future space missions.

Channel blockage alters hydraulic and thermal performance in printed circuit heat exchangers (PCHEs), yet its engineering-scale response remains unclear. A high-temperature recuperator in a 50 kW supercritical carbon dioxide recompression Brayton cycle is investigated using a multiscale framework coupling three-dimensional header flow with a full-scale one-dimensional conjugate model. The model resolves 840 channel locations per side, assigns each 1.0 m channel a hydraulic resistance iteratively updated by a 40-segment variable-property calculation, and retains transverse metal conduction. Blockage distribution, affected-channel fraction (2.5-30%), and single-channel resistance multiplier were varied at fixed boundary conditions. Clean-flow maldistribution changed the heat-transfer rate by less than 0.01% relative to uniform flow. Both pressure sides exhibited similar redistribution patterns, with larger spatial variations on the high-pressure side. For affected channels at a resistance multiplier of 100, dispersed and clustered blockage produced overlapping pressure-drop-increase ranges of 23.4–23.8% on the low-pressure side, whereas the heat-transfer-rate losses were 0.21% for dispersed blockage and 2.19–2.99% for clustered blockage. At 30% affected channels, dispersed and clustered blockage increased pressure drop by 100.3% and 100.9%, but their effectiveness losses were 0.70 and 8.75 percentage points, respectively. Clustering generated continuous, directional pressure and flow anomalies; downstream disturbances underwent sign reversal and reintensification, indicating potential for blockage localization. Overall, affected-channel fraction and resistance governed the hydraulic penalty, whereas spatial clustering controlled local redistribution and thermal degradation.

This paper proposes a novel poly-generation system that integrates a high-temperature proton exchange membrane fuel cell (HT-PEMFC), spray flash desalination (SFD), heat pump (HP), externally fired gas turbine (EFGT), and organic Rankine cycle (ORC), capable of simultaneously generating power, heating, and fresh water. A comprehensive energy, exergy, economic, and environmental (4E) analysis is conducted to assess the influence of crucial operating parameters, such as current density, H2 utilization ratio, and evaporation temperature, on system performance. Local sensitivity analysis, life cycle assessment and multi-objective optimization are conducted. The results indicate that a current density of 12,000 A/m2 is optimal for maximizing the system's net electrical power. Rice husk is typically the most suitable choice for achieving optimal economic and environmental performance. Local sensitivity analysis reveals that the most sensitive parameter affecting the performance of the proposed system is the evaporation temperature in SFD. The optimal values for environmental benefit, specific fuel consumption, and net present value are 127.63 x 103 $/y, 0.28 kg/kWh, and $6,114,416, respectively. Life cycle analysis identifies the operational phase as the dominant contributor to emissions.

Printed circuit heat exchangers (PCHEs) used in supercritical carbon dioxide (sCO2) Brayton cycles may experience channel-wise flow maldistribution owing to local blockage. However, most existing reduced-order models assume uniform flow distribution and neglect lateral heat-flux redistribution through the solid wall. In this study, multi-channel conjugate numerical simulations are first performed to elucidate the thermal response of PCHEs to local blockage. Based on the revealed mechanism, a reduced-order multi-channel model with discretized fluid and solid elements is then developed to account for transverse heat conduction within the wall and applied to evaluate overall heat-transfer degradation under multi-channel blockage conditions. The results show that, when the mass flux in a blocked channel decreases, the solid wall strongly redistributes the excess heat flux to neighboring channels while keeping local wall-temperature variations relatively small. For a given blockage number and single-channel blockage severity, the overall heat transfer degradation is nearly independent of the random blockage locations, whereas concentrated blockage markedly weakens the wall-buffering effect and causes pronounced local temperature rise. As the number of blocked channels increases, the overall heat transfer rate decreases approximately linearly. In contrast, increasing the blockage severity of a single channel leads to accelerated nonlinear deterioration. For the same overall blockage ratio, a few severely blocked channels are more detrimental than many mildly blocked channels. These results demonstrate that the solid wall plays a decisive role in buffering local blockage and that blockage distribution must be explicitly considered in the performance assessment of PCHEs operating under flow-maldistribution conditions.

​​Supercritical heat exchangers are often subjected to non-uniform boundary conditions during operation, and rational heat flux regulation is beneficial for improving overall heat transfer performance. In this study, the flow and heat transfer characteristics of supercritical water in a horizontal tube are experimentally investigated under four axial heat flux styles (uniform, semi-sinusoidal, increased and decreased), over the ranges of P=23.5-26.5 Mpa, G=200-400 kg·m-2·s-1, qave=50-200 kW·m-2. Variations in heat flux distribution are found to significantly alter the streamwise distributions of bulk enthalpy and cross-sectionally averaged heat transfer coefficient. Before the bulk enthalpy reaches the pseudocritical point, the increased heat flux style yields a higher overall heat transfer coefficient, but tends to produce a higher wall temperature or a larger wall temperature difference near the outlet. Under the decreased heat flux style, the maximum wall temperature lags behind the location of maximum heat flux because of the thermal entrance effect, whereas the overall heat transfer coefficient remains relatively low. The results indicate that heat transfer under non-uniform heat flux conditions is governed by the combined effects of thermal entrance effect, variations in fluid thermophysical properties, and heat flux distribution, which further refines the spatiotemporal matching theory of supercritical substance flow and energy flow. Based on the experimental data, an explicit heat transfer correlation for supercritical water under axially non-uniform heat flux conditions is developed by combining the Buckingham Pi theorem with the active subspace method, and its predictive performance is significantly better than that of existing correlations. On this basis, a method is further proposed for constructing matched heat flux distribution schemes under given constraints, thereby improving overall heat transfer performance while avoiding the risk of locally excessive wall temperature. This study provides theoretical support for the heating design and operational optimization of supercritical heat exchangers.

As a renewable energy source, fuel ethanol was employed either as a gasoline additive or as a direct combustion fuel, thereby contributing to the growing demand for alternative fuels. However, the production of ethanol was considered too energy-consuming. Spray flash evaporation was regarded as a potential technology in ethanol production. An experimental platform was constructed to investigate the spray and mass transfer characteristics under different experimental conditions. Response surface methodology (RSM) was used to perform analysis of variance (ANOVA), statistical analysis, and optimization within the experimental parameter range. The results indicated that the degree of influence of the input parameters on the distillation flow rate (DFR), in descending order, was initial temperature, initial concentration, vacuum chamber pressure, and nozzle diameter. Initial temperature was identified as the factor with the greatest effect on flash evaporation ratio (FER). An increase in the vacuum chamber pressure within the experimental range led to a decrease in FER. When the nozzle diameter interacted separately with initial concentration, initial temperature, and vacuum chamber pressure, the interaction between vacuum chamber pressure and nozzle aperture was identified as the most significant. The FER of both ethanol and water in the distillate increased concurrently with the superheat degree. However, the rate of increase in the FER of ethanol significantly exceeded that of water. The optimal system parameters were identified as an initial concentration of 40%, an initial temperature of 74 degrees C, a vacuum chamber pressure of 14 kPa, and a nozzle diameter of 1.8 mm. This study was designed to provide guidance for aspects of ethanol production.

Heat transfer deterioration (HTD) in supercritical carbon dioxide (sCO2) significantly compromises the thermal efficiency and operational stability of Brayton cycle systems. Although previous studies have demonstrated that inlet parameters play a critical role in HTD occurrence, most existing HTD onset criteria for supercritical carbon dioxide flows neglect their influence, limiting predictive accuracy and general applicability. To address this limitation, this study integrates the Buckingham Pi theorem with the Active Subspace Method to establish a datadriven, dimensionless analysis framework that explicitly incorporates inlet parameters and automatically identifies the dominant dimensionless groups governing HTD in upward supercritical carbon dioxide flow. Based on a comprehensive database comprising 37100 data points collected from 25 published studies, a new HTD onset criterion that accounts for inlet conditions is developed. Quantitative comparisons with established supercritical carbon dioxide HTD criteria demonstrate that the proposed criterion substantially outperforms existing methods, achieving an accuracy of 91.4%, a precision of 87.8%, and an F1 score of 91.0%. By explicitly incorporating inlet parameters, the new criterion improves both predictive accuracy and generalizability, providing a robust and practical tool for safety margin design and performance optimization of supercritical carbon dioxide heat exchangers.

Printed circuit heat exchangers (PCHEs) for supercritical carbon dioxide (sCO2) cycles are vulnerable to partial channel blockages from corrosion products and particle deposition. Such blockages increase pressure drop and further reduce system efficiency. This study numerically investigates sCO2 flow and heat transfer in a single circular channel with a localized blockage. The blockage is parametrised by the dimensionless blockage length, blockage ratio, eccentricity and edge taper, and channel performance is assessed using the mean Nusselt number and friction factor, together with a performance evaluation criterion. The results show that performance degradation is dominated by pressure drop rather than heat transfer enhancement. The mean Nusselt number increases by less than 8%, while the mean friction factor rises by up to a factor of 3.4. The influence of different blockage characteristics on velocity distribution within the Blockage Influence Zone is the key factor determining the magnitude of local resistance loss. Among all blockage characteristics, the blockage ratio is the decisive parameter, causing a strongly nonlinear response of the performance criterion once the blockage ratio exceeds approximately 0.45. The total pressure loss can be decomposed into a distributed component, which is essentially unaffected by blockage geometry, and a local component controlled by the velocity field in the blockage region. A correlation for the blockage-induced local loss coefficient is proposed, which keeps the error in total pressure loss below 4.5% over the investigated parameter range and provides a physics based closure for PCHE performance analysis with blocked channels.

Printed Circuit Heat Exchangers have garnered widespread application in supercritical carbon dioxide power cycles owing to their superior thermal efficiency and compact configuration. Nevertheless, localized blockages arising from fouling, corrosion, or mechanical deformation can markedly disrupt flow and heat transfer behavior, thereby posing significant challenges to exchanger performance and system reliability. To date, no studies have systematically examined the operational behavior of Printed Circuit Heat Exchangers under blockage conditions. A comprehensive understanding of flow and thermal responses in a blocked single channel is fundamental to the identification and mitigation of such blockages. A numerical investigation is conducted to examine the flow and heat transfer characteristics in circular microchannels subjected to localized obstruction. Emphasis is placed on delineating the blockage influence zone and assessing the severity of blockage under varying heat flux and mass flux conditions. Results indicate that the impact on flow resistance is substantially more pronounced than that on heat transfer. Two distinct subdomains-the Heat Transfer Influence Zone and the Pressure Drop Influence Zone-are defined based on the spatial persistence of blockage-induced deviations. The Heat Transfer Influence Zone consistently exceeds the Pressure Drop Influence Zone in length, primarily due to the contribution of buoyancy-driven radial flow. Sensitivity analyses demonstrate that heat and mass fluxes significantly affect the recovery of thermal fields, which can be used to locate blockages. To quantify blockage severity, a pressure-based indicator is proposed, defined as the ratio of local pressure loss to total channel pressure drop. This approach circumvents the limitations of existing blockage definitions based on geometric alteration or flow rate reduction, offering a more practical and diagnostic tool for Printed Circuit Heat Exchanger applications. The findings provide valuable guidance for blockage detection, localization, and structural optimization of compact heat exchangers operating under supercritical conditions.

To improve the numerical prediction accuracy of supercritical carbon dioxide (sCO2) flow and heat transfer in horizontal tubes, this study systematically evaluates the performance of typical existing turbulent Prandtl number (Prt) models using the SST turbulence model, validated against publicly available experimental wall temperature data. Results demonstrate that the constant Prt=0.85 model exhibits significant operating condition-dependent systematic biases, while variable Prt models developed for vertical tubes fail to account for the circumferential buoyancy-turbulence coupling in horizontal tubes, leading to poor prediction accuracy near the pseudocritical temperature, particularly in the top wall region. Combined with three-zone boundary layer theory and the buoyancy mechanism in horizontal tubes, a modified variable Prt model is developed, adopting the turbulent-to-molecular viscosity ratio for boundary layer zoning, and introducing turbulent Peclet number, buoyancy correction factor and gas-like/liquid-like differential correction terms to enable adaptive Prt calculation. The proposed model effectively reproduces buoyancy-induced heat transfer deterioration and circumferentially non-uniform heat transfer characteristics, significantly reduces wall temperature prediction errors across the full operating range. This work finally reveals the four-stage evolution law of cross-sectional Prt distribution, providing reliable theoretical support for the design of horizontal heat exchange equipment in sCO2 power systems.

Supercritical heat exchangers often operate under non-uniform boundary conditions, and rational heat flux regulation is beneficial for improving overall heat transfer performance. In this study, the heat transfer characteristics of supercritical water in horizontal tubes are experimentally investigated under four axial heat flux profiles (uniform, semi-sinusoidal, increased and decreased). Results show that heat flux distribution significantly affects the streamwise distributions of bulk enthalpy and heat transfer coefficient. Compared with uniform heat flux, the increased heat flux profile enhances overall heat transfer coefficient by up to 8.73% before the pseudocritical point, but tends to produce a larger wall temperature difference near the outlet. In contrast, the decreased profile causes a delayed wall temperature peak due to the thermal entrance effect and yields relatively weak overall heat transfer coefficient (is reduced by 12.63%). The heat transfer process under non-uniform heat flux is governed by the combined effects of thermal entrance effect, fluid property variation, and heat flux distribution, thereby revealing the matching characteristics between supercritical fluid flow and energy transport. An explicit heat transfer correlation is developed by combining the Buckingham Pi theorem with the active subspace method, and its predictive performance is significantly better than that of existing correlations. On this basis, a method is further proposed for constructing matched heat flux distribution schemes under given constraints, thereby improving overall heat transfer performance while avoiding the risk of locally excessive wall temperature. This study provides theoretical support for heat flux optimization in heat exchangers.

This study systematically evaluates and advances methods for identifying heat transfer deterioration (HTD) and its onset in vertical upward flow of supercritical carbon dioxide (sCO2). We compiled and rigorously curated the largest experimental dataset to date, comprising 47338 data points from 41 publications and covering pressure, inlet temperature, heat flux, mass flux, pipe diameter, material and lengths of heated and insulated sections; uniform screening, calibration and categorization produced 1095 directly comparable cases spanning the complete q-G and q/G-d operating space. A systematic assessment of existing identification techniques motivated the development of an improved temperature fluctuation approach, which achieves 89.2% accuracy. Comprehensive evaluation of buoyancy and thermal acceleration dimensionless groups demonstrated that no single effect parameter maintains a stable HTD threshold across all conditions, highlighting the need for multi effect coupled modeling. Finally, after reviewing nineteen classical onset criterion correlations, we introduce a data driven framework based on Buckingham Pi analysis and active subspace methods to select dominant dimensionless groups and formulate a novel onset criterion with adjustable probability thresholds that outperforms existing methods in accuracy. This work provides a high quality experimental database, refines HTD identification techniques and proposes an advanced onset criterion, thereby laying the groundwork for future standardization, online monitoring, mechanistic insight and practical engineering applications in sCO2heat transfer systems.

Local blockage disturbs the hydraulic-resistance balance of parallel microchannels in printed circuit heat exchangers (PCHEs), but its system-level influence on supercritical CO2 flow redistribution remains insufficiently understood. In this study, conjugate heat-transfer simulations were performed for a representative periodic PCHE unit with seven parallel rectangular channels on each side. Local blockage was treated as a position-dependent resistance perturbation in a coupled microchannel network. The effects of blockage ratio, blocked-channel number, blockage side, and lateral interconnections on flow maldistribution and thermo-hydraulic performance were examined. Results show that local blockage produces network-scale redistribution through upstream static-pressure accumulation, throat acceleration, downstream momentum deficit, and compensating flow in open channels. For 91% blockage in one hot-side channel, the blocked-channel mean Nusselt number decreases to about 46% of the clean value, whereas the open-channel mean Nusselt number increases by 11.8% because of compensating flow. Pressure drop and the performance evaluation criterion are more sensitive to blockage than the total heat-transfer rate, indicating that hydraulic penalty dominates early performance deterioration. Hot-side blockage causes stronger pressure-drop amplification than cold-side blockage because of the lower density and higher velocity of supercritical CO2 on the hot side. Lateral interconnections convert blockage-induced transverse pressure differences into passive compensating flow, reactivating blocked-channel downstream regions and reducing exit maldistribution. Under dual-side multi-channel blockage, lateral interconnections reduce the mean pressure drop by 22.8–34.4% and improve the performance evaluation criterion by 18.2–33.6%. These results identify lateral interconnections as a passive flow-redistribution strategy for blockage-tolerant PCHE design.

Flow boiling critical heat flux (CHF) is crucial for the safe operating limits of nuclear reactors, electronic cooling systems, and aerospace propellant management, yet the rational design of fluid-to-fluid scaling experiments remains hindered by the absence of a systematic framework for evaluating and optimizing similarity laws. Existing approaches either require matched experimental points rarely available in practice or inherit bias from fitted correlations. This study introduces an information-theoretic framework combining joint mutual information and coefficient sparsity to discover Pareto-optimal similarity laws directly from a consolidated database of 32,209 CHF points spanning 20 fluids. Two physically interpretable dimensionless groups emerge from the data: Cr, reflecting the combined effects of inlet subcooling, density ratio, flow condition, and surface-related nucleation ability, and Catp, representing the competition between interfacial viscous shear and surface tension stabilization. These data-driven groups not only outperform ten published similarity laws in the mutual-information-sparsity space, but also reveal a natural segmentation of Bo∗ = (xc − xi)/(1 − xi) into three distinct regimes within the Cr-Catp coordinate, offering new insight into the underlying CHF mechanisms. A correlation built on Cr and Catp achieves a mean absolute percentage error of 14.65%, competitive with and exceeding seven established correlations. In addition, an alkali metal dataset that does not overlap with the above database provides further evidence for the robustness of the proposed dimensionless groups. The present work demonstrates that an information-theoretic approach can discover compact, physically meaningful governing quantities directly from experimental data, providing a reproducible pathway for similarity law evaluation, scaling experiment design, and mechanistic CHF analysis.

To clarify blockage-induced deterioration and structural mitigation in supercritical carbon dioxide printed circuit heat exchangers (PCHEs), a periodic parallel multi-channel numerical framework was established. Effects of blockage ratio, blocked-channel number, blocked side, and interconnecting-channel configuration on flow redistribution, heat transfer, pressure loss, and overall performance were examined. The results show that blockage deterioration is governed mainly by hydraulic penalties caused by additional local resistance and flow maldistribution, rather than by reduced overall heat transfer. When three channels on both sides were blocked, increasing the blockage ratio from 51% to 91% reduced the 𝑃𝐸𝐶 from 0.955 to 0.713 on the hot side and from 0.974 to 0.730 on the cold side, indicating higher blockage sensitivity on the hot side. For 91% blockage in a single channel, the mass flow rate in the blocked channel dropped to about 15% of the baseline, while that in adjacent channels increased by about 12%, showing that flow redistribution links local blockage to system-level deterioration. Cross-coupled interconnecting channels alleviated this deterioration by redistributing local flow. Under blocked conditions, the coefficients of variation of flow distribution on the two sides were reduced by 8.8% and 9.8%, respectively, and the 𝑃𝐸𝐶 increased from 0.851 to 0.867 on the hot side and from 0.894 to 0.906 on the cold side, with almost no penalty under clean conditions. These results identify the dominant pathway from local blockage to system-level deterioration and demonstrate the passive mitigation potential of interconnecting structures for anti-blockage PCHE design.

Accurate prediction and modeling of subcooled flow boiling critical heat flux (CHF) are essential for the safe operation of two-phase heat transfer systems across a wide range of engineering applications. A fundamental challenge lies in the empirical and often inconsistent selection of dimensionless numbers, which affects correlation performance, mechanistic interpretation, and the design of similarity experiments. In this study, a data-driven dimensional analysis approach is employed to overcome the non-uniqueness of traditional dimensional analysis. A comprehensive subcooled flow boiling CHF dataset comprising 4238 data points across 11 fluids is compiled; to the best of the authors’ knowledge, this is the largest multi-fluid dataset currently available. Using this method, a new key dimensionless number, denoted as πCHF, is discovered, showing a strong negative correlation with the modified boiling number (Bo*). The core of πCHF is formed by a newly designed Evaporation number (Ev), representing the proportion of surface tension energy overcome during bubble growth relative to the total absorbed energy, and the gas phase Peclet number (Peg), characterizing the relative importance of convective versus diffusive heat transfer within the gas phase. Based on πCHF, a new predictive correlation is developed, achieving an overall mean absolute percentage error (MAPE) of 12.55

Accurate prediction of crack leakage in pressurized steam energy systems is important for transient safety analysis, operational reliability, and rapid simulation at the system scale in thermal and nuclear energy applications. For steam with low superheat, rapid depressurization inside a crack channel may induce condensation and critical flow involving two phases, which makes it difficult to develop leakage models that are simultaneously accurate, physically interpretable, and computationally efficient. In this work, a study combining experiments and data analysis is performed for critical leakage of superheated steam through fatigue cracks. A closed circulation facility under high temperature and high pressure is established to obtain critical leakage data, and a hydrostatic calibration test at room temperature is carried out to determine the crack opening as a function of pressure, which is then used to correct the effective flow area. On this basis, a framework based on integer mutual information is proposed to identify dominant dimensionless groups from experimental data under strict dimensional consistency. By combining joint mutual information, sparsity, and integer exponent constraints, the proposed method directly extracts compact integer scaling expressions with improved physical interpretability. Compared with the conventional formulation with continuous exponents, the integer mutual information framework yields a dominant dimensionless group with clearer explicit regularity, stronger variable screening capability, and better transferability across different crack and channel geometries. The resulting integer correlation gives a MAPE of 6.62%, an MAE of 5010.91, and an R2 of 0.989 for the target Reynolds number. Compared with the continuous-exponent correlation, it gives a slightly lower MAPE and a much higher coefficient of determination, while retaining a more compact and transferable scaling structure. After transformation to the inlet critical mass flux, the proposed integer correlation outperforms the homogeneous equilibrium model under the present operating conditions. When embedded into a transient leakage calculation framework, it also provides more accurate predictions of vessel pressure and fluid temperature than the homogeneous equilibrium model, while retaining a clear advantage in computational efficiency. The main significance of this work lies not only in the correlation developed for the present dataset, but more importantly in demonstrating that the proposed framework based on integer mutual information has strong potential for identifying transferable and physically meaningful scaling laws from richer experimental databases for rapid leakage prediction and engineering simulation with reduced model complexity.