Geometric structural optimization of the diffusion section in the angular Helmholtz cavitation jet nozzle via Kriging-differential evolution model

Cavitation jet demonstrates remarkable erosion capabilities, exhibiting substantial application potential across various fields. The nozzle configuration formed by incorporating a diffusion section at the outlet of a Helmholtz cavitation jet nozzle is termed an angular Helmholtz cavitation jet nozzle (AHCJN). Optimizing the diffusion section design can significantly enhance both the erosion efficiency and cavitation intensity of AHCJN. This study innovatively proposes a coupled computational fluid dynamics–machine learning methodology for the optimal design of the diffusion section in AHCJN. The computational fluid dynamics approach is employed to acquire fundamental datasets and conduct parametric sensitivity analysis, while machine learning techniques are utilized to approximate nonlinear response surfaces and achieve global optimization. The results indicate that when the diffusion angle is less than 15°, the pulse peak and amplitude increase linearly with the diffusion length. When the diffusion angle is between 20° and 25°, the pulse peak and amplitude first rise and then fall with increasing diffusion length. When the diffusion angle exceeds 30°, the pulse peak and amplitude decrease linearly with the diffusion length. The influence of diffusion angle on the pulse peak and amplitude follows a trend of first increasing and then decreasing. In contrast, the pulse frequency is relatively insensitive to changes in the diffusion sections' structural parameters, remaining stable in the range of 1.961–2.041 kHz. The Kriging-differential evolution model demonstrates outstanding predictive performance under small-sample conditions, with mean absolute error and root mean squared error values below 0.25 and coefficients of determination (R2) exceeding 0.98. Using this model, a nonlinear response surface of self-excited pulsation characteristics within the diffusion angle-length parameter space was established, yielding optimal structural parameters of 4.92 mm diffusion length and 17.26° diffusion angle. Under this configuration, the predicted values for self-excited pulsation characteristics are 20.42 MPa pulse peak, 8.90 MPa pulse amplitude, and 2.02 kHz pulse frequency, with corresponding prediction errors of 1.808%, 1.377%, and 1.020%. In the optimized structure, the pulse peak is enhanced by 18.6%, the pulse amplitude is increased by 42.2%, and the pulse frequency is maintained at constant. This research provides a novel methodology for the structural optimization design of cavitation jet nozzles.