Spatiotemporal nonlinear behavior of cavitation inside the hydraulic regulating valve

The highly nonlinear nature of cavitation within the regulating valve poses significant challenges for the quantitative assessment of flow-field instabilities, resulting in reduced flow performance, decreased control accuracy, and an increased risk of valve damage. In this study, high-speed visualization was employed to systematically investigate the evolution of cavitation under different inlet pressures. Time-series data of attached, free, and total cavitation areas were obtained using an image processing method. By combining chaos theory, phase-space reconstruction, and Lyapunov exponent analysis, the chaotic intensity associated with different cavitation forms was quantitatively analyzed. The results indicate that the fluctuation range and dispersion of phase points in phase space increase progressively with increasing inlet pressure. A confidence ellipsoid is employed to fit the phase-point trajectories, and geometric parameters k1 and k2 are introduced to characterize its shape. The centers of the confidence ellipsoids for all three cavitation forms shift toward the upper-right direction as the inlet pressure increases, and the ellipsoid of total cavitation is closer to a spherical geometry. In addition, the maximum Lyapunov exponent is calculated to quantify the chaotic intensity, and comparative analysis indicates that total cavitation exhibits the strongest chaotic behavior, with Lyapunov exponents ranging from 0.018 13 to 0.085 08. Moreover, the influence of cavitation-induced chaos on the valve's flow rate is discussed, showing that increasing inlet pressure leads to a higher degree of chaos and a significant deviation of the actual flow rate from the theoretical value. Understanding the nonlinear behavior of cavitation inside regulating valves provides a solid theoretical and experimental basis for improving valve performance and ensuring safe and stable operation under harsh operating conditions.