Experimental study and scaling analysis on hydraulic jump formed by a circular liquid jet impacting a wall

The liquid film cooling formed by jet-wall impingement plays a crucial role in thermal protection of thrust chamber walls in rocket engines. Accurate prediction of hydraulic jump formation is essential for enhancing cooling reliability. This study systematically investigates the effects of fluid properties, wall wettability, and downstream obstacle parameters on jump patterns and sizes. Visualization results reveal that jump patterns are predominantly governed by flow conditions. Reduced volume flow rate or increased obstacle height induces instability in low-viscosity fluid jump structures. Quantitative analysis demonstrates a strong linear correlation between jump radius and volume flow rate, with the slope and intercept governed by different combinations of key parameters including dynamic viscosity, gravitational acceleration, surface tension coefficient, downstream obstacle parameters, and other factors. A novel empirical correlation is established through scaling analysis and coefficient of variation optimization, utilizing two characteristic lengths and two constants to precisely predict jump radius. The proposed empirical correlation demonstrates improved predictive accuracy compared to existing models, with 95.90% of predictions for 244 experimental cases falling within engineering-acceptable error margins.