Vortex force map for incompressible multi-body flows with application to wing–flap configurations

Abstract

The vortex force map method for incompressible viscous flows with multiple bodies is derived in this work. The method breaks the fluid force into inertial, vortex-pressure, viscous-pressure and skin-friction components, and it could be used to analyse the fluid dynamic forces on individual bodies in a multi-body assembly. For the first time, we provide a graphical representation of the vortex-pressure force – the vortex force map – for individual bodies in a multi-body assembly. We have shown that the vortex force map in a multi-body set-up differs from single-bodied counterparts from modifications to their hypothetical potential through a nonlinear cross-coupling, and that the inertial and viscous-pressure contributions contain influences from other bodies explicitly. We then demonstrate the multi-body vortex force decomposition method with a wing–flap starting flow problem using computational fluid dynamics data, identifying the positive and negative force-generating critical regions or directions. It is found that the dominant force is the vortex-pressure force, and the force variation against time is closely related to the evolution of the vortex structures. Furthermore, we showed that the existence of another body significantly alters the force contribution roles of vortices in the flow.

Vortex force map method to estimate unsteady forces from snapshot flowfield measurements

“…Li and Wu (2016) extended the VFM method to a high angle of attack problem. Further, the VFM method is extended to general aerofoils (Li and Wu, 2018), three-dimensional wings (Li et al, 2020b), viscous flows (Li et al, 2021), and multiple bodies (Wang et al, 2022). In addition, Li et al (2020a) developed a vortex moment map method to estimate the aerodynamic moment acting on a body.…”

“…This result represents a significant advancement towards the development of a nonintrusive PIV-based force measurement technique using the VFM method. For future work, the application of the vortex moment method (Li et al, 2020a) and the threedimensional VFM method (Li et al, 2020b) for single and multiple bodies (Wang et al, 2022) on PIV data will be further explored, with three-dimensional flowfields obtained from tomographic PIV and shake-the-box particle tracking. The VFM method for flexible bodies will be developed and applied to PIV data.…”

Vorticity forces of coherent structures on the NACA0012 aerofoil

“…This theory states that any real fluid element with non-zero vorticity can be considered a source of the hydrodynamic force, and has been applied to understand forces exerted on various objects in low-Reynolds-number flows (), such as flow passing multiple bluff bodies (Chang, Yang & Chu 2008; Wang et al. 2022), hovering flights (Hsieh, Chang & Chu 2009; Hsieh et al. 2010), impulsively started finite plates (Lee et al.…”

“…Chang (1992) further related the force on the moving, accelerating or oscillating body to different aspects of the flow field. This theory states that any real fluid element with non-zero vorticity can be considered a source of the hydrodynamic force, and has been applied to understand forces exerted on various objects in low-Reynolds-number flows (Re ∼ O(10-100)), such as flow passing multiple bluff bodies (Chang, Yang & Chu 2008;Wang et al 2022), hovering flights (Hsieh, Chang & Chu 2009;Hsieh et al 2010), impulsively started finite plates (Lee et al 2012), and the heaving aerofoil (Martín-Alcántara, Fernandez-Feria & Sanmiguel-Rojas 2015; Moriche, Flores & García-Villalba 2017). As the Reynolds number increases to a level where turbulence becomes a significant factor (Re ∼ O(10 4 )), we become curious about how the irregularities of turbulence impact the forces acting on an object.…”