An-Kang Gao

The dynamics of laterally unconstrained flexible filaments in an inclined uniform flow is investigated numerically, inspired by the self-propelled behaviour of droplets and filaments in a crosswind. It is found that in addition to conventional downwind drifting, the filament can also undergo counterintuitive upwind motion, arising from a supercritical pitchfork bifurcation. Depending on the Reynolds number, bending stiffness and inflow inclination angle, the filament exhibits multiple wake and motion states, including static, quasi-static, vibrational and translational modes. In the reference frame translating laterally with the incoming flow, the upwind and downwind drifting states induced by different initial perturbations form a pair of dynamically equivalent, symmetry-related branches. Force decomposition shows that both the streamwise drag and lateral thrust predominantly originate from the normal force, and the corresponding scaling relations are identified. Stability analysis further reveals that the hydrodynamic forces near the equilibrium states behave as restoring forces. The resulting stable equilibria can be characterised by a generalised hydrodynamic potential, whose potential wells correspond to the stable states of the system. These findings provide insight into the dynamics of flexible structures in uniform flow.

This paper reviews field-based diagnostic theories of unsteady aerodynamic forces, ranging from formulations for total force and moment to recent developments in the diagnosis of local stress distributions. We first revisit the vorticity-moment theory (Wu, AIAA J, vol. 19, 1981, 432–441) as a starting point for field-based force analysis, with emphasis on far-field decay requirements and subsequent extensions to finite domains and compressible flows. We then consider the vortex-force theory and force-element theory, which provide more physically interpretable connections between the flow field and aerodynamic loads. Subsequently, we discuss decompositions of the pressure field based on its governing equation and boundary conditions. Finally, we examine the transition from total force and moment analysis to the diagnosis of local surface loading through weighted-integral methods. Overall, unsteady aerodynamic force theories have evolved from asking how the total load can be calculated from the surrounding flow field to asking how individual flow structures and physical processes determine the distribution of stress over the body surface.

In the velocity-correction scheme (VCS) for incompressible fluid–rigid-body interaction, numerical instability often arises from the explicit treatment of the Neumann pressure boundary condition on the body surface, where the wall acceleration at the new time step is approximated from velocity fields at previous time steps through a finite-difference method. To address this issue, we propose a stabilized VCS based on a decomposition of the pressure field into velocity-induced and acceleration-induced components, referred to as the pressure-decomposed velocity-correction scheme (PD-VCS). In the proposed method, only the velocity-induced pressure needs to be calculated from the pressure Poisson equation. The acceleration-induced component is implicitly included in the rigid-body equations of motion. This treatment eliminates the dependence of the numerical pressure boundary condition on the rigid-body acceleration and augments the effective inertia of the body, without introducing additional free parameters or coupling iterations. Numerical results demonstrate that the proposed method is stable and accurate over a wide range of density ratios, including the zero-mass limit of the rigid body.

Partial-slip boundaries have been demonstrated to be effective at drag reduction of underwater vehicles. However, in practical applications, covering the entire body surface with slip materials is cost-inefficient. To address this issue, a deep learning-based approach is developed to optimize the spatial distribution of slip boundaries on the SUBOFF bare-hull model under prescribed engineering constraints. First, a convolutional neural network surrogate model is trained to predict drag efficiently, enabling rapid evaluation of different slip-boundary configurations. The optimal distribution is then determined through systematic exploration of the parameter space. Numerical simulations of the optimized configurations reveal two key findings: (1) slip boundaries significantly influence the skin-friction drag, whereas their effect on pressure drag remains negligible and (2) a well-designed distributed partial-slip boundary can effectively regulate the development of near-wall turbulence, leading to enhanced the overall drag reduction performance. This study provides a promising framework for the intelligent design of drag-reducing surfaces for underwater vehicles.

Schematic diagram of unilateral constraint models and their hydrodynamic characteristics differences with bilateral constraints.

Whilst surface-stress integration remains the standard approach for fluid force evaluation, control-volume integral methods provide deeper physical insights through functional relationships between the flow field and the resultant force. In this work, by introducing a second-order tensor weight function into the Navier–Stokes equations, we develop a novel weighted-integral framework that offers greater flexibility and enhanced capability for fluid force diagnostics in incompressible flows. Firstly, in addition to the total force and moment, the weighted integral methods establish, for the first time, rigorous quantitative connections between the surface-stress distribution and the flow field, providing potential advantages for flexible body analyses. Secondly, the weighted integral methods offer alternative perspectives on force mechanisms, through vorticity dynamics or pressure view, when the weight function is set as divergence-free or curl-free, respectively. Thirdly, the derivative moment transformation (DMT)-based integral methods (Wu et al., J. Fluid Mech. vol. 576, 2007, 265–286) are generalised to weighted formulations, by which the interconnections among the three DMT methods are clarified. In the canonical problem of uniform flow past a circular cylinder, weighted integral methods demonstrate advantages in yielding new force expressions, improving numerical accuracy over original DMT methods, and enhancing surface-stress analysis. Finally, a force expression is derived that relies solely on velocity and acceleration at discrete points, without spatial derivatives, offering significant value for experimental force estimation. This weighted integral framework holds significant promise for flow diagnostics in fundamentals and applications.