A SEMI-ANALYTICAL METHOD FOR A FLOW OF NON-VISCOUS FLUID AROUND AN AIRFOIL WITH A SHARP TRAILING EDGE

2021 ◽  
pp. 4-10
Author(s):  
Alexey A. Bondarchuk ◽  
Mezhlum A. Sumbatyan
Keyword(s):  
Viscous Fluid ◽  
Analytical Method ◽  
Velocity Vector ◽  
Point Vortex ◽  
Two Dimensional ◽  
Double Layer Potential ◽  
Boundary Contour ◽  
Trailing Edge ◽  
Layer Potential ◽  
Two Dimensional Flow

In the present work we propose a method to study a two-dimensional flow of non-viscous fluid around an airfoil with a sharp trailing edge, by the double-layer potential theory. The circulation of velocity vector is modeled by the potential of a point vortex whose center is located inside the boundary contour. The magnitude of the circulation is defined on the basis of the Joukowski-Chaplygin postulate. There are presented some results for a Joukowski rudde, as well as for the airfoil in the form of a pair of interacting circles. It is performed a comparison of the circulation with its theoretical value.

The slow transverse motion of a flat plate through a non-diffusive stratified fluid

1971 ◽  
Vol 47 (1) ◽  
pp. 171-181 ◽  
Author(s):  
G. S. Janowitz
Keyword(s):  
Viscous Fluid ◽  
Shear Layer ◽  
Flat Plate ◽  
Kinematic Viscosity ◽  
Vertical Plate ◽  
The Body ◽  
Vertical Shear ◽  
Transverse Motion ◽  
Two Dimensional ◽  
Two Dimensional Flow

We consider the two-dimensional flow produced by the slow horizontal motion of a vertical plate of height 2b through a vertically stratified (ρ = ρ0(1 - βz)) non-diffusive viscous fluid. Our results are valid when U2 [Lt ] Ub/ν [Lt ] 1, where U is the speed of the plate and ν the kinematic viscosity of the fluid. Upstream of the body we find a blocking column of length 10−2b4/(Uν/βg. This column is composed of cells of closed streamlines. The convergence of these cells near the tips of the plate leads to alternate jets. The plate itself is embedded in a vertical shear layer of thickness (Uν/βg)1/3. In the upstream portion of this layer the vertical velocities are of order U and in the downstream portion of order Ub/(Uν/βg)1/3 ([Gt ] U). The flow is uniform and undisturbed downstream of this layer.

On the roll-up of a trailing vortex sheet in the very near field

2003 ◽  
Vol 217 (5) ◽  
pp. 263-269 ◽  
Author(s):  
A L Heyes ◽  
S J Hubbard ◽  
A J Marquis ◽  
D A Smith
Keyword(s):  
Vortex Core ◽  
Near Field ◽  
Angle Of Attack ◽  
Point Vortex ◽  
Vortex Sheet ◽  
Measured Data ◽  
Tip Vortex ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Naca 0012

This paper addresses a discrepancy found between the rate of roll-up of a trailing vortex sheet calculated from point vortex simulations and that from measured data. Measurements of the wake behind a rectangular planform NACA 0012 section wing at 7.5° angle of attack show that some 50 per cent of the circulation in the wake is already present in the vortex core or “rolled-up region” at the trailing edge of the wing, and that there is no increase in the circulation contained within this region within one chord length downstream of the trailing edge. This conflicts with two-dimensional point vortex simulations of sheet roll-up which predict no initial core at the trailing edge and a constantly increasing value of circulation in the vortex in the downstream direction. A modification to include the effect of the tip vortex in the simulation is proposed and is shown to represent the behaviour of the vortex sheet in the very near field accurately.

scholarly journals Random representation of Blasius’ formula through stochastic complex integrals

2019 ◽  
Vol 11 (01) ◽  
pp. 1950004
Author(s):  
Kouji Yamamuro
Keyword(s):  
Viscous Fluid ◽  
Perfect Fluid ◽  
Complex Plane ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow

Two-dimensional flow is considered in the complex plane. We discuss Blasius’ formula in a perfect fluid through stochastic complex integrals. This formula is also investigated in a viscous fluid. We mention the theorems corresponding to Green’s formulae last.

scholarly journals On the late-time behaviour of a bounded, inviscid two-dimensional flow

2015 ◽  
Vol 783 ◽  
pp. 1-22 ◽  
Author(s):  
David G. Dritschel ◽  
Wanming Qi ◽  
J. B. Marston
Keyword(s):  
Large Scale ◽  
Point Vortex ◽  
Small Scale ◽  
Late Time ◽  
Two Dimensional ◽  
Time Behaviour ◽  
Vorticity Field ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Initial Vorticity

Using complementary numerical approaches at high resolution, we study the late-time behaviour of an inviscid incompressible two-dimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a small set of intermediate-wavenumber spherical harmonics, we find that, contrary to the predictions of equilibrium statistical mechanics, the flow does not evolve into a large-scale steady state. Instead, significant unsteadiness persists, characterised by a population of persistent small-scale vortices interacting with a large-scale oscillating quadrupolar vorticity field. Moreover, the vorticity develops a stepped, staircase distribution, consisting of nearly homogeneous regions separated by sharp gradients. The persistence of unsteadiness is explained by a simple point-vortex model characterising the interactions between the four main vortices which emerge.

Two-Dimensional Flow Losses of a Turbine Cascade With Boundary Layer Injection

1972 ◽  
Author(s):  
W. Tabakoff ◽  
R. Earley
Keyword(s):  
Boundary Layer ◽  
Analytical Method ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Flow Losses ◽  
Two Dimensional Flow ◽  
Incompressible Boundary ◽  
New Formulation ◽  
Mixing Losses

A method for determining the performance of a two-dimensional turbine cascade with boundary layer injection is developed using existing incompressible boundary layer approximate solutions with a new formulation for the injection. The overall cascade loss includes friction and wake mixing losses. The results of the analysis are compared with experimentally obtained data as a check of the validity of the new analytical method.

scholarly journals Self propulsion due to oscillations on the surface of a cylinder at low Reynolds number

1971 ◽  
Vol 5 (2) ◽  
pp. 255-264 ◽  
Author(s):  
J.R. Blake
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Low Reynolds Number ◽  
Infinite Cylinder ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Low Reynolds ◽  
Micro Organisms

The two-dimensional flow around an infinite cylinder at low Reynolds number has interested fluid dynamicists for many years. In this paper it is shown that an infinite cylinder can propel itself through a viscous fluid (for example micro-organisms) if it has certain undulations on its surface.

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