Superheated-steam critical flow through microcracks: experimental study and integer mutual-information-based scaling analysis

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.