Numerical study on multi-scale unsteady cavitation flow within a scaling-up engine nozzle for methanol fuel

Cavitation inside fuel-injector nozzle governs injection accuracy, pressure oscillations, and subsequent atomization, yet its multi-scale dynamics remain difficult to predict—particularly for methanol. We develop an enhanced Euler–Lagrange multi-scale coupling framework that combines a volume-of-fluid (VOF) description of the continuous cavitating flow with a discrete bubble model (DBM) for Lagrangian microbubbles. The approach integrates a simplified Rayleigh–Plesset formulation for bubble dynamics and two-way momentum and mass coupling between phases. Applied to a scaled-up nozzle representative of engine injectors, the method is validated against experiments and a baseline VOF simulation. Across three injection pressures (0.40, 0.50, and 0.65 MPa), the flow exhibits quasi-periodic behavior: sheet cavitation growth, cloud-cavitation shedding, and subsequent collapse. With increasing injection pressure, cavitation intensity strengthens, the number of discrete bubbles rises markedly, and repeated collapses amplify mid-to-high-frequency pressure fluctuations, demonstrating the pivotal role of bubble dynamics in shaping the pressure spectrum. Relative to the standalone VOF model, the VOF–DBM framework improves volumetric-flow prediction, reducing errors by a factor of 2.3–3. Bubble statistics further show that the bubble number increases with increasing Pin and then approaches a constant level, while the Sauter mean diameter [SMD (D32)] remains nearly invariant at 19–23 μm, indicating weak sensitivity of bubble size to the operating condition. The present multi-scale methodology yields mechanistic insight into cavitation structure–bubble interactions and offers a robust, transferable numerical tool for optimizing nozzle design and methanol-based fuel-injection systems.