Dynamic modeling of a hose-drogue aerial refueling system using variable-length absolute nodal coordinate formulation

Aerial refueling technology dramatically extends combat radius and flight endurance of fighter aircraft, serving as a crucial guarantee for success in modern warfare. The hose-drogue aerial refueling system has been widely adopted by most nations with aerial refueling capabilities. In aerial refueling operations using the hose-drogue system, the whipping phenomenon caused by excessive slack in the refueling hose is a critical factor that significantly affects both operational success and safety. Proper deployment and retraction of the hose can effectively prevent whipping. Accurate dynamic analysis of the hose during smooth towing and deployment/retraction is essential for ensuring safe and reliable aerial refueling.

The absolute nodal coordinate formulation (ANCF) is a flexible multibody dynamics modeling technique based on finite element theory and continuum mechanics principles. In ANCF, all nodal coordinates are defined in the global coordinate system, replacing the rotational coordinates typically used in conventional finite element methods with slope vectors. This approach not only yields higher accuracy in modeling flexible multibody systems but also performs well in scenarios with large deformations of flexible bodies. For modeling the fuel delivery hoses during steady towing and deployment/retraction, this study develops a dynamic model for variable-length three-dimensional beam elements using the principle of virtual work combined with ANCF. Equivalent stiffness terms and gyroscopic terms, both arising from variations in element length and potentially affecting system stability, are derived. When the element length is constant, the model can be simplified to the traditional ANCF with fixed-length elements. By applying a unified time-dependent function to set the lengths of all elements—where the undeformed lengths undergo simultaneous and identical changes—the method enables dynamic simulation of hoses at arbitrary non-zero lengths while reducing the overall degrees of freedom. Based on Green-Lagrangian strain theory, both axial and bending deformations of the hose are incorporated into the analysis. Additionally, internal damping forces are included via a damping coefficient.

Through a classical benchmark problem from ANCF studies, the validity of the developed dynamic model presented in this work has been rigorously verified. The simulation results demonstrate that under three distinct scenarios-fixed, extended, and shortened element lengths-the proposed dynamic model consistently achieves precise simulation of temporal morphological evolution in flexible hoses. The constant-length element cases are widely adopted as benchmark configurations in existing research, and the proposed model achieves accuracy comparable to previously reported results.

This study offers an effective methodology for creating a precise dynamic model of hose deployment and retrieval during aerial refueling. It provides a high-fidelity model for hose dynamics analysis and whiplash prevention. The model enables dynamic simulation of refueling hoses with arbitrary non-zero lengths. In practical aerial refueling operations, the refueling hose is subjected to various forces including aerodynamic forces, hydraulic forces from the fluid medium, and collision forces generated during docking. Building on the established dynamic model presented in this study, future research can extend the current work by incorporating these multi-physics interactions to conduct comprehensive dynamic simulations and analytical investigations of different phases within the aerial refueling process.