Abstract
In this paper we suggest a model for how a significant part of the drag forces on two-dimensional objects can be derived using the circulation that is naturally maintained around the objects. We assume incompressible and inviscid potential flow and that the circulation is already generated. The resulting velocity field complements the one that is known to generate Prandtl’s induced drag in three dimensions. We demonstrate how fluid particles in a velocity field are attracted towards an object, and that this, due to conservation of momentum, results not only in lift, but also in drag forces. The magnitude of a disturbance velocity can be derived from the circulation of bound and shed vortices accompanying the object and parameters taken from the von Kármán vortex street description. Another part of the drag is generated by vortices that emerge behind blunt bodies when fluid particles do not follow the surface of the objects. We obtain a mathematical description of the resistance of several types of blunt bodies and rotating cylinders. The model involves no parameters that are derived from empirical data. Still, this inviscid approach corresponds well with experimental data in viscous flow and is close to a mathematical empirical description of rotating cylinders by W. G. Bickley.
Highlights
The model of perfect or ideal fluids is incapable of explaining many of the observed facts of fluid motion
It was the work by Lanchester [1] and Prandtl [2] that showed that a part of the drag of a finite wing in ideal fluids could be explained using the model of a circulation generated by the airfoil
Based on a random walk source model where particles have no viscosity, we observe that a particle front moving towards a profile in a simulated unsteady flow, will be separated at the profile into two fronts
Summary
The model of perfect or ideal fluids is incapable of explaining many of the observed facts of fluid motion. A model for unsteady potential flow in ideal fluids, called the ‘Random Walk Source Model’ is presented in [8] (see appendix for a brief description) As seen, this model generates the shape of a particle front emerging from a line source, creeping towards and past a wing section. When the particles cannot follow the surface of an object, the pressure loss behind the object is derived from the circulation which is naturally generated behind such objects (in viscous fluids) Both approaches intend to improve the understanding of drag of profiles and blunt bodies as a result of the circulation in ideal fluids. The results are shown to align well with experimental data
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