Analytical Model of the Stagnation Point in Oblique-Submerged Circular Impinging Jet

The stagnation point, defined as the location of maximum pressure, is a key characteristic of oblique submerged circular impinging jets. This study presents a theoretical analytical model to predict the stagnation point location based on mass and momentum conservation principles. An approximate linear solution is further derived from the model for practical application. Both the numerical and approximate linear solutions are validated against experimental and numerical simulation results available in the literature. Potential errors associated with model assumptions are evaluated, and the model’s applicability is defined for specific conditions: impingement angle β≥45° and impingement distance H≤50 times the nozzle diameter (d), or 45°≥β≥30° and H≤25d. Within these limits, the model achieves a root-mean-square error (RMSE) of 0.149 for the analytical solution and 0.160 for the linear solution, with a relative accuracy exceeding 80% even in extended scenarios. The analysis of model results reveals that the stagnation point location varies approximately linearly with impingement distance at fixed impingement angles and exhibits an approximate cotangent relationship with the impingement angle at fixed distances. This analytical model offers new insights into the dynamic behavior of oblique submerged circular impinging jets and serves as a practical tool for the design and optimization of hydraulic structures.