A universal model for surge frequency prediction based on the equivalent hydraulic spring: From theoretical derivation to experimental verification

This study proposes an innovative surge frequency prediction model based on an equivalent hydraulic spring analogy to address the critical limitation of conventional stability analysis methods (e.g., the B-parameter method) in predicting surge frequency, where they can only qualitatively assess stability but fail to accurately determine compressor surge frequency. The model establishes fundamental analogies between surge oscillations and mechanical mass-spring-damper systems by incorporating three key fluid dynamic characteristics: fluid inertia as equivalent mass, compressibility as equivalent stiffness, and viscous dissipation as equivalent damping. Through systematic axisymmetric simplification and linearization of the Navier-Stokes equations, we derive an analytical solution that reveals the nonlinear coupling between surge frequency and cavity geometric/fluid properties. Experimental validation was performed on a single-stage axial compressor test rig, where pressure fluctuations were measured under varying rear cavity volumes. Advanced signal processing techniques, including fast Fourier transform analysis and nonlinear regression, were employed for frequency extraction and model calibration. The results demonstrate exceptional prediction accuracy exceeding 95%, significantly outperforming traditional methods. The model's breakthrough lies in its first-time incorporation of post-surge airflow elasticity effects into the analytical framework, providing new insights into cavity-flow coupling mechanisms while offering practical design tools for turbomachinery stability optimization.