Effects of velocity and spacing on successive droplet cooling of a hot steel pipe

Successive droplet impingement provides a controllable route for rapid and spatially uniform cooling of hot-rolled seamless steel pipes, but the coupled effects of impact velocity and droplet spacing remain unclear. To clarify these effects, this study aims to elucidate how the impact velocity and droplet spacing influence the interaction regimes, transient heat transfer, wall-temperature evolution, and cooling uniformity during successive droplet impingement. A three-dimensional VOF-based numerical model was developed for three successive water droplets impacting a steel pipe initially heated to 900 °C. Impact velocity was varied from 0.5 to 4 m/s, and the spacing-to-diameter ratio (s/d) was varied from 1 to 4. The simulations quantify droplet dynamics, transient heat transfer coefficient (HTC), wall-temperature evolution, and cooling uniformity. Increasing impact velocity strengthens spreading and liquid-film disturbance, enlarging the high-HTC coverage by more than 30% and accelerating local cooling. However, excessive inertia promotes fragmentation and shortens effective liquid-solid contact. Droplet spacing governs the persistence and uniformity of the cooling process. Small spacing enhances droplet coalescence and sustained film cooling, whereas s/d = 4 weakens interaction and produces localized heat removal. A regime map is proposed, distinguishing Independent Cooling, Synergistic Film Cooling, and Fragmentation-Enhanced Cooling. The results show that peak HTC alone is insufficient for evaluating spray cooling performance; a moderate Weber number and droplet spacing provide a better balance between rapid heat removal and cooling uniformity.