arXiv subjects

A. C. DeVoria

Publications and source records attributed to A. C. DeVoria.

3 recordsLinked to original sources

arXiv2020

A theoretical model for the separated flow around an accelerating flat plate using time-dependent self similarity

We present a model appropriate to the initial motion (2-3 chords of travel) of a flat-plate airfoil accelerating in an inviscid fluid. The separated flow structures are represented as vortex sheets in the conventional manner and similarity expansions locally applicable to the leading and trailing edges of the plate are developed. The topological character of vortex sheets is maintained rather than resorting to point vortex discretizations. Beyond this, there are two theoretical novelties to our approach as compared to previous studies. First, an expansion is applied to the attached outer flow rather than the vortex sheet circulations and positions. This allows the asymmetric effect of the sweeping component of the free-stream flow parallel to the plate to be built-in to the same governing equation as the singular-order flow. Second, we develop a time-dependent self similarity procedure that allows the modeling of more complex evolution of the flow structures. This is accomplished through an implicit time variation of the similarity variables. As a collective result, the predicted vortex dynamics and forces on the plate compare favorably to Navier-Stokes simulations. Lastly, the model is utilized to provide some new intuition about the separated flow at the leading edge.

physics.flu-dyn↗

arXiv2020

The force on a body moving in an inviscid fluid

This paper presents some novel contributions to the theory of inviscid flow regarding the forces exerted on a body moving through such a fluid in two dimensions. It is argued that acceleration of the body corresponds to vorticity generation that is independent of the instantaneous velocity of the body and thus the boundary condition on the normal velocity. The strength of the vortex sheet representing the body retains a degree of freedom that represents the net effect of the tangential boundary condition associated with the viscous flow governed by the higher-order Navier-Stokes equations. This degree of freedom is the circulation of the vorticity generated by the acceleration of the body. Equivalently, it is the net circulation around a contour enclosing the body and any shed vorticity. In accordance with Kelvin's circulation theorem, a non-zero value of the circulation around this system is necessarily communicated to infinity. This contrasts with the usual acceptance of the theorem as requiring this circulation to be zero at all times; a condition that is incapable of capturing the effect of newly generated vorticity on the body surface when it accelerates. Additionally, the usual boundary condition of continuity of normal velocity is relaxed to allow for fluid entrainment into surfaces of discontinuity that represent the mass contained within the viscous layers of the physical problem. The generalized force calculation is presented in detail. The importance of the vorticity generation due to body acceleration is demonstrated on some modeled problems relevant to biological propulsion.

physics.flu-dyn↗

arXiv2018

The vortex-entrainment sheet in an inviscid fluid: theory and separation at a sharp edge

In this paper a model for viscous boundary and shear layers in three-dimensions is introduced and termed a vortex-entrainment sheet. The vorticity in the layer is accounted for by a conventional vortex sheet. The mass and momentum in the layer are represented by a two dimensional surface having its own internal tangential flow. Namely, the sheet has a mass density per-unit-area making it dynamically distinct from the surrounding outer fluid. The mechanism of entrainment is represented by a discontinuity in the normal component of velocity across the sheet. The sheet mass is able to support a pressure jump, which in turn may cause additional entrainment. This feature was confirmed when the model was used to represent the Falkner-Skan boundary layers. The velocity field induced by the vortex-entrianment sheet is given by a generalized Birkhoff-Rott equation with a complex sheet strength. The model was also applied to the case of separation at a sharp edge. There is no requirement for an explicit Kutta condition in the form of a singularity removal as this condition is inherently satisfied through an appropriate balance of normal momentum with the pressure jump across the sheet. A pressure jump at the edge results in the generation of new vorticity. The shedding angle is dictated by the normal impulse of the intrinsic flow inside the bound sheets as they merge to form the free sheet. When there is zero entrainment everywhere the model reduces to the conventional vortex sheet with no mass. Consequently, the pressure jump must be zero and the shedding angle must be tangential so that the sheet simply convects off the wedge face. Lastly, the vortex-entrainment sheet model was demonstrated on two shedding example problems.

physics.flu-dyn↗